{"id":68292,"date":"2026-01-30T00:34:25","date_gmt":"2026-01-29T16:34:25","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/68292.html"},"modified":"2026-01-30T00:34:25","modified_gmt":"2026-01-29T16:34:25","slug":"pn-%e7%bb%93-%e5%9f%ba%e7%a1%80%e7%89%b9%e6%80%a7%e3%80%81%e7%94%b5%e5%ae%b9%e6%95%88%e5%ba%94%e3%80%81%e5%87%bb%e7%a9%bf%e6%9c%ba%e5%88%b6%e4%b8%8e%e8%80%97%e5%b0%bd%e5%b1%82%e7%89%b9%e6%80%a7","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/68292.html","title":{"rendered":"PN \u7ed3 | \u57fa\u7840\u7279\u6027\u3001\u7535\u5bb9\u6548\u5e94\u3001\u51fb\u7a7f\u673a\u5236\u4e0e\u8017\u5c3d\u5c42\u7279\u6027"},"content":{"rendered":"

\u6ce8：\u672c\u6587\u4e3a \u201cPN \u7ed3\u201d \u76f8\u5173\u5408\u8f91\u3002 \u56fe\u7247\u6e05\u6670\u5ea6\u53d7\u5f15\u6587\u539f\u56fe\u6240\u9650\u3002 \u7565\u4f5c\u91cd\u6392，\u672a\u6574\u7406\u53bb\u91cd\u3002 \u5982\u6709\u5185\u5bb9\u5f02\u5e38，\u8bf7\u770b\u539f\u6587\u3002<\/p>\n

\n

PN \u7ed3\u7684\u7535\u5bb9\u6548\u5e94<\/h2>\n

Ethan Jiang \u539f\u521b 2020-02-12 11:56:17<\/p>\n

\u672c\u6587\u5bf9 PN \u7ed3\u7684\u5355\u5411\u5bfc\u7535\u7279\u6027\u7684\u9891\u7387\u4f9d\u8d56\u6027\u8fdb\u884c\u89e3\u6790，\u8bf4\u660e\u8be5\u7279\u6027\u5e76\u975e\u5728\u6240\u6709\u5de5\u51b5\u4e0b\u6210\u7acb，\u5f53\u4fe1\u53f7\u9891\u7387\u8fbe\u5230\u7279\u5b9a\u503c\u65f6，PN \u7ed3\u5c06\u5931\u53bb\u5355\u5411\u5bfc\u7535\u7279\u6027\u3002\u540c\u65f6\u6df1\u5165\u5206\u6790 PN \u7ed3\u5728\u6b63\u5411\u504f\u7f6e\u3001\u53cd\u5411\u504f\u7f6e\u4e24\u79cd\u7535\u538b\u6761\u4ef6\u4e0b\u7684\u5de5\u4f5c\u539f\u7406，\u9610\u8ff0\u4e0d\u540c\u504f\u7f6e\u4e0b\u7684\u7535\u6d41\u5f62\u6210\u8fc7\u7a0b，\u5e76\u63a2\u7a76\u7535\u5bb9\u6548\u5e94\u5bf9 PN \u7ed3\u5bfc\u7535\u6027\u7684\u5f71\u54cd\u89c4\u5f8b\u3002<\/p>\n

PN \u7ed3\u5355\u5411\u5bfc\u7535\u6027\u7684\u5de5\u51b5\u9650\u5b9a<\/h3>\n

PN \u7ed3\u5e76\u975e\u5728\u4efb\u4f55\u60c5\u51b5\u4e0b\u5747\u5177\u5907\u5355\u5411\u5bfc\u7535\u6027，\u7b54\u6848\u4e3a：\u5426 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0<\/p>\n

\u52bf\u5792\u7535\u5bb9\u968f\u53cd\u5411\u504f\u7f6e\u7535\u538b\u7684\u589e\u52a0\u800c\u51cf\u5c0f，\u968f\u6b63\u5411\u504f\u7f6e\u7535\u538b\u7684\u589e\u52a0\u800c\u589e\u5927\u3002<\/p>\n

PN \u7ed3\u7684\u53cd\u5411\u7279\u6027<\/h3>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0<\/p>\n

\u70ed\u5e73\u8861\u72b6\u6001\u4e0b，N \u533a\u7684\u5c11\u5b50\u7a7a\u7a74\u3001P \u533a\u7684\u5c11\u5b50\u81ea\u7531\u7535\u5b50\u7684\u6d53\u5ea6\u5206\u5e03\u5982\u4e0b\u56fe\u6240\u793a： \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0<\/p>\n

\u5f53 P \u533a\u63a5\u8d1f\u6781\u3001N \u533a\u63a5\u6b63\u6781\u65f6，PN \u7ed3\u5904\u4e8e\u53cd\u5411\u504f\u7f6e\u72b6\u6001\u3002\u5916\u7535\u573a\u4e0e PN \u7ed3\u5185\u5efa\u7535\u573a\u540c\u5411，\u5bf9\u8f7d\u6d41\u5b50\u5f62\u6210\u53cd\u5411\u62bd\u53d6\u4f5c\u7528，\u8017\u5c3d\u533a\u5bbd\u5ea6\u589e\u5927，N \u533a\u4e0e P \u533a\u95f4\u7684\u7535\u52bf\u5dee\u5f62\u6210\u7684\u80fd\u5792\u9ad8\u5ea6\u63d0\u5347\u3002\u6b64\u65f6\u8f7d\u6d41\u5b50\u7684\u8f93\u8fd0\u4ee5\u5c11\u5b50\u7684\u6f02\u79fb\u8fd0\u52a8\u4e3a\u4e3b，\u6f02\u79fb\u8fd0\u52a8\u7684\u5f3a\u5ea6\u5927\u4e8e\u6269\u6563\u8fd0\u52a8，\u5f62\u6210\u7684\u53cd\u5411\u7535\u6d41\u6570\u503c\u6781\u5c0f；\u591a\u5b50\u56e0\u80fd\u5792\u963b\u6321\u65e0\u6cd5\u8fdb\u5165\u8017\u5c3d\u533a，PN \u7ed3\u5448\u73b0\u9ad8\u7535\u963b\u7279\u6027\u3002\u8017\u5c3d\u533a\u5185\u5f3a\u7535\u573a\u7684\u4f5c\u7528\u4f7f\u8f7d\u6d41\u5b50\u65e0\u6cd5\u505c\u7559，\u4e14\u8017\u5c3d\u533a\u8fb9\u754c\u5904\u7684\u5c11\u5b50\u6d53\u5ea6\u4f4e\u4e8e\u70ed\u5e73\u8861\u72b6\u6001\u4e0b\u7684\u5e73\u5747\u6d53\u5ea6\u3002 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0<\/p>\n

PN \u7ed3\u7684\u7535\u5bb9\u6548\u5e94\u53ef\u7b49\u6548\u4e3a\u5728\u4e8c\u6781\u7ba1\u4e24\u7aef\u5e76\u8054\u4e00\u4e2a\u7535\u5bb9，\u8be5\u7535\u5bb9\u7684\u5bb9\u503c\u4e3a\u7ed3\u7535\u5bb9，\u7ed3\u7535\u5bb9\u4e3a\u52bf\u5792\u7535\u5bb9\u4e0e\u6269\u6563\u7535\u5bb9\u7684\u4ee3\u6570\u548c\u3002\u5f53\u8f93\u5165\u4fe1\u53f7\u7684\u9891\u7387\u5347\u9ad8\u81f3\u7279\u5b9a\u503c\u65f6，\u7ed3\u7535\u5bb9\u7684\u5bb9\u6297\u964d\u4f4e\u81f3\u53ef\u5ffd\u7565\u7684\u7a0b\u5ea6，\u52a8\u6001\u4fe1\u53f7\u5c06\u5168\u90e8\u65bd\u52a0\u4e8e PN \u7ed3\u7684\u7b49\u6548\u7535\u963b\u4e0a，\u7ed3\u7535\u5bb9\u4e24\u7aef\u65e0\u538b\u964d，\u6b64\u65f6 PN \u7ed3\u7684\u5355\u5411\u5bfc\u7535\u7279\u6027\u6d88\u5931，\u7b49\u6548\u4e3a\u7ed3\u7535\u5bb9\u88ab\u77ed\u8def\u3002<\/p>\n

PN \u7ed3\u5b58\u5728\u4e00\u6781\u9650\u9891\u7387，\u5f53\u5916\u52a0\u7535\u538b\u7684\u9891\u7387\u8d85\u8fc7\u8be5\u6781\u9650\u9891\u7387\u65f6，PN \u7ed3\u5c06\u4e27\u5931\u5355\u5411\u5bfc\u7535\u7279\u6027\u3002 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0<\/p>\n

\u5f53 P \u533a（\u9633\u6781）\u63a5\u6b63\u6781\u3001N \u533a（\u9634\u6781）\u63a5\u8d1f\u6781\u65f6，PN \u7ed3\u5904\u4e8e\u6b63\u5411\u504f\u7f6e\u72b6\u6001\u3002\u5916\u7535\u573a\u4e0e\u5185\u5efa\u7535\u573a\u53cd\u5411，\u80fd\u5792\u9ad8\u5ea6\u964d\u4f4e，\u8f7d\u6d41\u5b50\u7684\u8f93\u8fd0\u4ee5\u591a\u5b50\u7684\u6269\u6563\u8fd0\u52a8\u4e3a\u4e3b，\u6269\u6563\u8fd0\u52a8\u7684\u5f3a\u5ea6\u5927\u4e8e\u6f02\u79fb\u8fd0\u52a8，\u5f62\u6210\u7684\u6b63\u5411\u7535\u6d41\u6570\u503c\u8f83\u5927\u3002 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0<\/p>\n

\u504f\u7f6e\u72b6\u6001\u5bf9\u6bd4<\/h4>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0<\/p>\n

\u52bf\u5792\u7535\u5bb9\u4e0e PN \u7ed3\u504f\u7f6e\u7535\u538b\u7684\u53d8\u5316\u89c4\u5f8b<\/h3>\n

\u52bf\u5792\u7535\u5bb9\u7684\u7269\u7406\u6839\u6e90\u5728\u4e8e PN \u7ed3\u8017\u5c3d\u5c42（\u5373\u7a7a\u95f4\u7535\u8377\u533a）\u4e2d\u7535\u8377\u6570\u91cf\u968f\u5916\u52a0\u7535\u538b\u53d8\u5316\u800c\u4ea7\u751f\u7684\u7535\u5bb9\u6548\u5e94\u3002\u5176\u5bb9\u503c <\/p>\n

C<\/p>\n

b<\/p>\n

C_b<\/p>\n

<\/span><\/span>C<\/span><\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e0e\u8017\u5c3d\u5c42\u5bbd\u5ea6 <\/p>\n

W<\/p>\n

W<\/p>\n

<\/span><\/span>W<\/span><\/span><\/span><\/span><\/span> \u6210\u53cd\u6bd4，\u5373<\/p>\n

<\/p>\n

C<\/p>\n

b<\/p>\n

=<\/p>\n

\u03b5<\/p>\n

s<\/p>\n

A<\/p>\n

W<\/p>\n

\u221d<\/p>\n

1<\/p>\n

W<\/p>\n

,<\/p>\n

C_b = \\\\frac{\\\\varepsilon_s A}{W} \\\\propto \\\\frac{1}{W}, <\/p>\n

<\/span><\/span>C<\/span><\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>W<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u221d<\/span><\/span><\/span><\/span><\/span><\/span>W<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

\u5176\u4e2d <\/p>\n

\u03b5<\/p>\n

s<\/p>\n

\\\\varepsilon_s<\/p>\n

<\/span><\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u534a\u5bfc\u4f53\u4ecb\u7535\u5e38\u6570，<\/p>\n

A<\/p>\n

A<\/p>\n

<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7ed3\u9762\u79ef\u3002\u56e0\u6b64，\u52bf\u5792\u7535\u5bb9\u7684\u53d8\u5316\u7531\u8017\u5c3d\u5c42\u5bbd\u5ea6\u7684\u6539\u53d8\u51b3\u5b9a，\u4e8c\u8005\u5448\u53cd\u5411\u5173\u7cfb\u3002\u968f\u7740 PN \u7ed3\u504f\u7f6e\u7535\u538b\u7684\u8c03\u6574，\u52bf\u5792\u7535\u5bb9\u7684\u5177\u4f53\u53d8\u5316\u89c4\u5f8b\u5982\u4e0b：<\/p>\n

  • \u53cd\u5411\u504f\u7f6e\u65f6：\u5f53\u53cd\u5411\u504f\u7f6e\u7535\u538b\u589e\u5927，\u5916\u52a0\u7535\u573a\u65b9\u5411\u4e0e\u5185\u5efa\u7535\u573a\u4e00\u81f4，\u589e\u5f3a\u4e86\u5bf9\u7a7a\u95f4\u7535\u8377\u533a\u8f7d\u6d41\u5b50\u7684\u62bd\u53d6\u4f5c\u7528，\u5bfc\u81f4\u8017\u5c3d\u5c42\u5bbd\u5ea6 \n

    W<\/p>\n

    W<\/p>\n

    <\/span><\/span>W<\/span><\/span><\/span><\/span><\/span> \u589e\u5927，\u52bf\u5792\u7535\u5bb9 <\/p>\n

    C<\/p>\n

    b<\/p>\n

    C_b<\/p>\n

    <\/span><\/span>C<\/span><\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u51cf\u5c0f；\u53cd\u4e4b，\u5f53\u53cd\u5411\u504f\u7f6e\u7535\u538b\u51cf\u5c0f\u65f6，\u8017\u5c3d\u5c42\u53d8\u7a84，<\/p>\n

    C<\/p>\n

    b<\/p>\n

    C_b<\/p>\n

    <\/span><\/span>C<\/span><\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u589e\u5927\u3002<\/li>\n

  • \u6b63\u5411\u504f\u7f6e\u65f6：\u5f53\u6b63\u5411\u504f\u7f6e\u7535\u538b\u589e\u5927，\u5916\u52a0\u7535\u573a\u65b9\u5411\u4e0e\u5185\u5efa\u7535\u573a\u76f8\u53cd，\u524a\u5f31\u4e86\u5185\u5efa\u7535\u573a\u5bf9\u591a\u6570\u8f7d\u6d41\u5b50\u7684\u963b\u6321\u4f5c\u7528，\u4f7f\u8017\u5c3d\u5c42\u5bbd\u5ea6 \n

    W<\/p>\n

    W<\/p>\n

    <\/span><\/span>W<\/span><\/span><\/span><\/span><\/span> \u51cf\u5c0f，\u52bf\u5792\u7535\u5bb9 <\/p>\n

    C<\/p>\n

    b<\/p>\n

    C_b<\/p>\n

    <\/span><\/span>C<\/span><\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u589e\u5927；\u53cd\u4e4b，\u5f53\u6b63\u5411\u504f\u7f6e\u7535\u538b\u51cf\u5c0f\u65f6，\u8017\u5c3d\u5c42\u5c55\u5bbd，<\/p>\n

    C<\/p>\n

    b<\/p>\n

    C_b<\/p>\n

    <\/span><\/span>C<\/span><\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u51cf\u5c0f\u3002<\/li>\n

    \u52bf\u5792\u7535\u5bb9\u7684\u5b9a\u91cf\u8868\u8fbe\u5f0f\u4e3a：<\/p>\n

    <\/p>\n

    C<\/p>\n

    b<\/p>\n

    =<\/p>\n

    C<\/p>\n

    b<\/p>\n

    0<\/p>\n

    (<\/p>\n

    1<\/p>\n

    \u2212<\/p>\n

    V<\/p>\n

    V<\/p>\n

    b<\/p>\n

    i<\/p>\n

    )<\/p>\n

    m<\/p>\n

    ,<\/p>\n

    C_b = \\\\frac{C_{b0}}{\\\\left(1 – \\\\frac{V}{V_{bi}}\\\\right)^m}, <\/p>\n

    <\/span><\/span>C<\/span><\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>V<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>C<\/span><\/span>b<\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u5176\u4e2d\u5404\u53c2\u6570\u5b9a\u4e49\u5982\u4e0b：<\/p>\n

      \n
    • \n

      C<\/p>\n

      b<\/p>\n

      0<\/p>\n

      C_{b0}<\/p>\n

      <\/span><\/span>C<\/span><\/span>b<\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>：PN \u7ed3\u5728\u96f6\u504f\u7f6e（<\/p>\n

      V<\/p>\n

      =<\/p>\n

      0<\/p>\n

      V = 0<\/p>\n

      <\/span><\/span>V<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>）\u65f6\u7684\u52bf\u5792\u7535\u5bb9；<\/li>\n

    • \n

      V<\/p>\n

      V<\/p>\n

      <\/span><\/span>V<\/span><\/span><\/span><\/span><\/span>：\u5916\u52a0\u504f\u7f6e\u7535\u538b（\u6ce8\u610f：\u6b64\u5904 <\/p>\n

      V<\/p>\n

      V<\/p>\n

      <\/span><\/span>V<\/span><\/span><\/span><\/span><\/span> \u4e3a\u4ee3\u6570\u91cf，\u53cd\u5411\u504f\u7f6e\u65f6 <\/p>\n

      V<\/p>\n

      <<\/p>\n

      0<\/p>\n

      V < 0<\/p>\n

      <\/span><\/span>V<\/span><\/span><<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>，\u6b63\u5411\u504f\u7f6e\u65f6 <\/p>\n

      V<\/p>\n

      ><\/p>\n

      0<\/p>\n

      V > 0<\/p>\n

      <\/span><\/span>V<\/span><\/span>><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>）；<\/li>\n

    • \n

      V<\/p>\n

      b<\/p>\n

      i<\/p>\n

      V_{bi}<\/p>\n

      <\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>：PN \u7ed3\u7684\u5185\u5efa\u7535\u52bf（\u7845\u57fa PN \u7ed3\u7ea6\u4e3a 0.6\u20130.8 V，\u4e0e\u63ba\u6742\u6d53\u5ea6\u548c\u6e29\u5ea6\u76f8\u5173）；<\/li>\n

    • \n

      m<\/p>\n

      m<\/p>\n

      <\/span><\/span>m<\/span><\/span><\/span><\/span><\/span>：\u68af\u5ea6\u7cfb\u6570，\u53d6\u51b3\u4e8e\u63ba\u6742\u5206\u5e03\u2014\u2014\u7a81\u53d8\u7ed3 <\/p>\n

      m<\/p>\n

      \u2248<\/p>\n

      1<\/p>\n

      2<\/p>\n

      m \\\\approx \\\\tfrac{1}{2}<\/p>\n

      <\/span><\/span>m<\/span><\/span>\u2248<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u7ebf\u6027\u7f13\u53d8\u7ed3 <\/p>\n

      m<\/p>\n

      \u2248<\/p>\n

      1<\/p>\n

      3<\/p>\n

      m \\\\approx \\\\tfrac{1}{3}<\/p>\n

      <\/span><\/span>m<\/span><\/span>\u2248<\/span><\/span><\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u8d85\u7a81\u53d8\u7ed3 <\/p>\n

      m<\/p>\n

      ><\/p>\n

      1<\/p>\n

      2<\/p>\n

      m > \\\\tfrac{1}{2}<\/p>\n

      <\/span><\/span>m<\/span><\/span>><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<\/ul>\n

      \u5bf9\u4e8e\u53cd\u5411\u504f\u7f6e（<\/p>\n

      V<\/p>\n

      <<\/p>\n

      0<\/p>\n

      V < 0<\/p>\n

      <\/span><\/span>V<\/span><\/span><<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>），\u4ee4 <\/p>\n

      \u2223<\/p>\n

      V<\/p>\n

      R<\/p>\n

      \u2223<\/p>\n

      =<\/p>\n

      \u2212<\/p>\n

      V<\/p>\n

      |V_R| = -V<\/p>\n

      <\/span><\/span>\u2223<\/span>V<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>V<\/span><\/span><\/span><\/span><\/span>，\u5219\u4e0a\u5f0f\u53ef\u6539\u5199\u4e3a：<\/p>\n

      <\/p>\n

      C<\/p>\n

      b<\/p>\n

      =<\/p>\n

      C<\/p>\n

      b<\/p>\n

      0<\/p>\n

      (<\/p>\n

      1<\/p>\n

      +<\/p>\n

      \u2223<\/p>\n

      V<\/p>\n

      R<\/p>\n

      \u2223<\/p>\n

      V<\/p>\n

      b<\/p>\n

      i<\/p>\n

      )<\/p>\n

      m<\/p>\n

      .<\/p>\n

      C_b = \\\\frac{C_{b0}}{\\\\left(1 + \\\\frac{|V_R|}{V_{bi}}\\\\right)^m}. <\/p>\n

      <\/span><\/span>C<\/span><\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>1<\/span><\/span>+<\/span><\/span><\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>V<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>C<\/span><\/span>b<\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u53ef\u89c1，\u968f\u7740\u53cd\u5411\u504f\u538b <\/p>\n

      \u2223<\/p>\n

      V<\/p>\n

      R<\/p>\n

      \u2223<\/p>\n

      |V_R|<\/p>\n

      <\/span><\/span>\u2223<\/span>V<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span><\/span><\/span><\/span> \u589e\u5927，\u5206\u6bcd\u589e\u5927，<\/p>\n

      C<\/p>\n

      b<\/p>\n

      C_b<\/p>\n

      <\/span><\/span>C<\/span><\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5355\u8c03\u51cf\u5c0f\u3002\u8fd9\u4e00\u5b9a\u91cf\u7ed3\u679c\u4e0e\u524d\u8ff0\u5b9a\u6027\u5206\u6790\u5b8c\u5168\u4e00\u81f4，\u4e5f\u7b26\u5408 PN \u7ed3\u52bf\u5792\u7535\u5bb9\u7684 C\u2013V \u7279\u6027\u66f2\u7ebf\u3002<\/p>\n

      \u9002\u7528\u8303\u56f4\u4e0e\u6781\u9650<\/h4>\n

      \u9700\u8981\u7279\u522b\u6307\u51fa，\u4e0a\u8ff0\u516c\u5f0f\u4e3b\u8981\u9002\u7528\u4e8e\u53cd\u5411\u504f\u7f6e\u53ca\u5f31\u6b63\u5411\u504f\u7f6e（<\/p>\n

      V<\/p>\n

      \u2272<\/p>\n

      0.7<\/p>\n

      V<\/p>\n

      b<\/p>\n

      i<\/p>\n

      V \\\\lesssim 0.7V_{bi}<\/p>\n

      <\/span><\/span>V<\/span><\/span>\u2272<\/span><\/span><\/span><\/span>0.7<\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>）\u7684\u60c5\u51b5\u3002\u5728\u5f3a\u6b63\u5411\u504f\u7f6e\u4e0b（<\/p>\n

      V<\/p>\n

      \u2192<\/p>\n

      V<\/p>\n

      b<\/p>\n

      i<\/p>\n

      V \\\\to V_{bi}<\/p>\n

      <\/span><\/span>V<\/span><\/span>\u2192<\/span><\/span><\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>）：<\/p>\n

        \n
      • \u8017\u5c3d\u5c42\u8fd1\u4f3c\u5931\u6548，\u516c\u5f0f\u5206\u6bcd\u8d8b\u8fd1\u4e8e\u96f6，\u9884\u6d4b \n

        C<\/p>\n

        b<\/p>\n

        \u2192<\/p>\n

        \u221e<\/p>\n

        C_b \\\\to \\\\infty<\/p>\n

        <\/span><\/span>C<\/span><\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2192<\/span><\/span><\/span><\/span>\u221e<\/span><\/span><\/span><\/span><\/span>，\u4e0e\u7269\u7406\u5b9e\u9645\u4e0d\u7b26；<\/li>\n

      • \u6b64\u65f6\u6269\u6563\u7535\u5bb9 \n

        C<\/p>\n

        d<\/p>\n

        C_d<\/p>\n

        <\/span><\/span>C<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>（\u7531\u5c11\u5b50\u7535\u8377\u5b58\u50a8\u6548\u5e94\u4ea7\u751f）\u5f00\u59cb\u5360\u7edd\u5bf9\u4e3b\u5bfc，\u5176\u503c\u901a\u5e38\u6bd4\u52bf\u5792\u7535\u5bb9\u5927 <\/p>\n

        10<\/p>\n

        2<\/p>\n

        \u223c<\/p>\n

        10<\/p>\n

        3<\/p>\n

        10^2 \\\\sim 10^3<\/p>\n

        <\/span><\/span>1<\/span>0<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u223c<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u500d，\u4e14\u968f\u6b63\u5411\u7535\u6d41\u8fd1\u4f3c\u6307\u6570\u589e\u957f；<\/li>\n

      • \u56e0\u6b64，\u5728\u6b63\u504f\u5bfc\u901a\u72b6\u6001\u4e0b，\u603b\u7ed3\u7535\u5bb9 \n

        C<\/p>\n

        j<\/p>\n

        =<\/p>\n

        C<\/p>\n

        b<\/p>\n

        +<\/p>\n

        C<\/p>\n

        d<\/p>\n

        \u2248<\/p>\n

        C<\/p>\n

        d<\/p>\n

        C_j = C_b + C_d \\\\approx C_d<\/p>\n

        <\/span><\/span>C<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>C<\/span><\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>C<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u52bf\u5792\u7535\u5bb9\u7684\u538b\u63a7\u7279\u6027\u4e0d\u518d\u5177\u6709\u5b9e\u9645\u610f\u4e49\u3002<\/li>\n<\/ul>\n

        \u5de5\u7a0b\u5e94\u7528\u4e2d\u7684**\u53d8\u5bb9\u4e8c\u6781\u7ba1（Varactor）**\u6b63\u662f\u5229\u7528\u53cd\u5411\u504f\u7f6e\u4e0b\u52bf\u5792\u7535\u5bb9\u7684\u538b\u63a7\u7279\u6027\u5b9e\u73b0\u8c03\u8c10\u529f\u80fd，\u6b64\u65f6\u5668\u4ef6\u59cb\u7ec8\u5de5\u4f5c\u5728\u53cd\u504f\u533a\u4ee5\u907f\u514d\u6269\u6563\u7535\u5bb9\u7684\u5e72\u6270\u3002<\/p>\n

        \u5e38\u89c1\u9519\u8bef\u8fa8\u6790<\/h4>\n

        \u9700\u7279\u522b\u6307\u51fa：\u52bf\u5792\u7535\u5bb9\u968f\u53cd\u5411\u7535\u538b\u7684\u589e\u5927\u800c\u51cf\u5c0f \u662f\u552f\u4e00\u6b63\u786e\u7684\u7ed3\u8bba\u3002\u5e38\u89c1\u7684\u9519\u8bef\u8ba4\u77e5\u4e3b\u8981\u6709\u4e24\u7c7b： （1）\u6df7\u6dc6\u52bf\u5792\u7535\u5bb9\u4e0e\u6269\u6563\u7535\u5bb9\u7684\u7535\u538b\u4f9d\u8d56\u7279\u6027\u2014\u2014\u6269\u6563\u7535\u5bb9\u5728\u6b63\u5411\u504f\u7f6e\u4e0b\u5360\u4e3b\u5bfc\u4e14\u968f\u6b63\u5411\u7535\u538b\u589e\u5927\u800c\u663e\u8457\u589e\u5927，\u4f46\u8be5\u7279\u6027\u4e0d\u9002\u7528\u4e8e\u52bf\u5792\u7535\u5bb9； （2）\u5ffd\u89c6\u516c\u5f0f\u4e2d\u7535\u538b <\/p>\n

        V<\/p>\n

        V<\/p>\n

        <\/span><\/span>V<\/span><\/span><\/span><\/span><\/span> \u7684\u7b26\u53f7\u7ea6\u5b9a，\u8bef\u5c06\u53cd\u5411\u7535\u538b\u4ee3\u5165\u6b63\u503c，\u5bfc\u81f4\u5bf9\u516c\u5f0f\u7684\u9519\u8bef\u89e3\u8bfb\u3002<\/p>\n

        \u7269\u7406\u672c\u8d28\u603b\u7ed3<\/h4>\n

        \u672c\u8d28\u4e0a，\u52bf\u5792\u7535\u5bb9\u7684\u53d8\u5316\u6e90\u4e8e\u8017\u5c3d\u5c42\u4e2d\u7a7a\u95f4\u7535\u8377\u91cf\u968f\u7535\u538b\u7684\u8c03\u6574\u3002\u6b64\u884c\u4e3a\u53ef\u7c7b\u6bd4\u4e8e\u5e73\u884c\u677f\u7535\u5bb9\u5668：\u7535\u5bb9\u4e0e\u6781\u677f\u95f4\u8ddd\u6210\u53cd\u6bd4，\u800c\u8017\u5c3d\u5c42\u5bbd\u5ea6 <\/p>\n

        W<\/p>\n

        W<\/p>\n

        <\/span><\/span>W<\/span><\/span><\/span><\/span><\/span> \u6b63\u597d\u7b49\u6548\u4e8e"\u6781\u677f\u95f4\u8ddd"\u3002\u56e0\u6b64，<\/p>\n

        W<\/p>\n

        W<\/p>\n

        <\/span><\/span>W<\/span><\/span><\/span><\/span><\/span> \u589e\u5927 \u2192 <\/p>\n

        C<\/p>\n

        b<\/p>\n

        C_b<\/p>\n

        <\/span><\/span>C<\/span><\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u51cf\u5c0f；<\/p>\n

        W<\/p>\n

        W<\/p>\n

        <\/span><\/span>W<\/span><\/span><\/span><\/span><\/span> \u51cf\u5c0f \u2192 <\/p>\n

        C<\/p>\n

        b<\/p>\n

        C_b<\/p>\n

        <\/span><\/span>C<\/span><\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u589e\u5927，\u8fd9\u4e00\u89c4\u5f8b\u662f\u52bf\u5792\u7535\u5bb9\u7684\u56fa\u6709\u7279\u6027\u3002<\/p>\n

        \n

        \u534a\u5bfc\u4f53\u5668\u4ef6\u7269\u7406：PN \u7ed3\u51fb\u7a7f\u673a\u5236\u4e0e\u7ed3\u7535\u5bb9\u7279\u6027<\/h2>\n

        GuiStar_\u674e\u4ec0\u4e48\u6069 \u539f\u521b，\u4fee\u8ba2\u4e8e 2023-03-01 19:35:22<\/p>\n

        1. PN \u7ed3\u7684\u51fb\u7a7f\u4e0e\u7535\u5bb9\u6548\u5e94<\/h2>\n

        \u9884\u5907\u77e5\u8bc6：\u4e8c\u6781\u7ba1\u4f0f\u5b89\u7279\u6027<\/h3>\n

        PN \u7ed3\u7684\u7535\u6d41-\u7535\u538b\u7279\u6027\u9075\u5faa\u8096\u514b\u5229\u65b9\u7a0b，\u5176\u5178\u578b\u7684\u4f0f\u5b89\u7279\u6027\u66f2\u7ebf\u5982\u56fe 1 \u6240\u793a，\u8be5\u66f2\u7ebf\u76f4\u89c2\u53cd\u6620\u4e86 PN \u7ed3\u5728\u4e0d\u540c\u5916\u52a0\u7535\u538b\u4e0b\u7684\u5bfc\u7535\u7279\u6027，\u662f\u5206\u6790\u51fb\u7a7f\u673a\u5236\u4e0e\u7535\u5bb9\u6548\u5e94\u7684\u57fa\u7840\u3002<\/p>\n

        \"\u4e8c\u6781\u7ba1\u4f0f\u5b89\u7279\u6027\u66f2\u7ebf\"<\/p>\n

        2. \u63ba\u6742\u6d53\u5ea6\u5bf9\u8017\u5c3d\u5c42\u7279\u6027\u7684\u5f71\u54cd<\/h2>\n

        2.1 \u70ed\u529b\u5b66\u5e73\u8861\u539f\u7406<\/h3>\n

        \u4ece\u70ed\u529b\u5b66\u89d2\u5ea6\u5206\u6790，\u5b64\u7acb\u7cfb\u7edf\u603b\u662f\u671d\u7740\u71b5\u589e\u52a0\u7684\u65b9\u5411\u6f14\u5316，\u5373\u7cfb\u7edf\u4f1a\u81ea\u53d1\u5730\u4ece\u975e\u5e73\u8861\u6001\u5411\u5e73\u8861\u6001\u8fc7\u6e21，\u524a\u5f31\u5176\u5185\u90e8\u7684\u975e\u5747\u5300\u6027\u3002\u8fd9\u4e00\u71b5\u589e\u539f\u7406\u5728\u534a\u5bfc\u4f53\u7269\u7406\u4e2d\u7684\u5177\u4f53\u4f53\u73b0\u4e3a，\u8f7d\u6d41\u5b50\u5177\u6709\u4ece\u9ad8\u6d53\u5ea6\u533a\u57df\u5411\u4f4e\u6d53\u5ea6\u533a\u57df\u6269\u6563\u7684\u8d8b\u52bf，\u6700\u7ec8\u8d8b\u4e8e\u5747\u5300\u7684\u6d53\u5ea6\u5206\u5e03，\u4ee5\u524a\u5f31\u6d53\u5ea6\u7684\u5c40\u90e8\u4e0d\u5747\u5300\u6027\u3002<\/p>\n

        \u4ee5\u6e29\u5ea6\u5206\u5e03\u4e3a\u4f8b，\u70ed\u91cf\u603b\u662f\u4ece\u9ad8\u6e29\u533a\u57df\u6d41\u5411\u4f4e\u6e29\u533a\u57df，\u76f4\u81f3\u7cfb\u7edf\u8fbe\u5230\u70ed\u5e73\u8861\u72b6\u6001，\u524a\u5f31\u6e29\u5ea6\u7684\u5c40\u90e8\u4e0d\u5747\u5300\u6027；\u540c\u7406，\u8f7d\u6d41\u5b50\u6d53\u5ea6\u4e5f\u9075\u5faa\u8fd9\u4e00\u89c4\u5f8b，\u901a\u8fc7\u6269\u6563\u8fd0\u52a8\u524a\u5f31\u6d53\u5ea6\u7684\u5c40\u90e8\u5dee\u5f02，\u8fd9\u662f PN \u7ed3\u8017\u5c3d\u5c42\u5f62\u6210\u7684\u91cd\u8981\u70ed\u529b\u5b66\u57fa\u7840\u3002<\/p>\n

        2.2 \u63ba\u6742\u6d53\u5ea6\u4e0e\u8017\u5c3d\u5c42\u5bbd\u5ea6\u7684\u5173\u7cfb<\/h3>\n

        \u8bbe <\/p>\n

        N<\/p>\n

        A<\/p>\n

        N_A<\/p>\n

        <\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u53d7\u4e3b\u6742\u8d28\u6d53\u5ea6（P \u533a），<\/p>\n

        N<\/p>\n

        D<\/p>\n

        N_D<\/p>\n

        <\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u65bd\u4e3b\u6742\u8d28\u6d53\u5ea6（N \u533a）\u3002\u6839\u636e\u6cca\u677e\u65b9\u7a0b\u4e0e\u7535\u8377\u4e2d\u6027\u6761\u4ef6，\u8017\u5c3d\u5c42\u5bbd\u5ea6 <\/p>\n

        W<\/p>\n

        W<\/p>\n

        <\/span><\/span>W<\/span><\/span><\/span><\/span><\/span> \u6ee1\u8db3：<\/p>\n

        <\/p>\n

        W<\/p>\n

        =<\/p>\n

        x<\/p>\n

        p<\/p>\n

        +<\/p>\n

        x<\/p>\n

        n<\/p>\n

        =<\/p>\n

        2<\/p>\n

        \u03b5<\/p>\n

        s<\/p>\n

        (<\/p>\n

        V<\/p>\n

        b<\/p>\n

        i<\/p>\n

        \u2212<\/p>\n

        V<\/p>\n

        )<\/p>\n

        q<\/p>\n

        (<\/p>\n

        1<\/p>\n

        N<\/p>\n

        A<\/p>\n

        +<\/p>\n

        1<\/p>\n

        N<\/p>\n

        D<\/p>\n

        )<\/p>\n

        W = x_p + x_n = \\\\sqrt{\\\\frac{2\\\\varepsilon_s(V_{bi}-V)}{q}\\\\left(\\\\frac{1}{N_A}+\\\\frac{1}{N_D}\\\\right)}<\/p>\n

        <\/span><\/span>W<\/span><\/span>=<\/span><\/span><\/span><\/span>x<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>x<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>V<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span><\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

        <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

        \u5176\u4e2d <\/p>\n

        \u03b5<\/p>\n

        s<\/p>\n

        \\\\varepsilon_s<\/p>\n

        <\/span><\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u534a\u5bfc\u4f53\u4ecb\u7535\u5e38\u6570，<\/p>\n

        V<\/p>\n

        b<\/p>\n

        i<\/p>\n

        V_{bi}<\/p>\n

        <\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u5185\u5efa\u7535\u52bf，<\/p>\n

        V<\/p>\n

        V<\/p>\n

        <\/span><\/span>V<\/span><\/span><\/span><\/span><\/span> \u4e3a\u5916\u52a0\u7535\u538b，<\/p>\n

        q<\/p>\n

        q<\/p>\n

        <\/span><\/span>q<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7535\u5b50\u7535\u8377\u91cf；\u6ce8：\u5916\u52a0\u7535\u538b <\/p>\n

        V<\/p>\n

        V<\/p>\n

        <\/span><\/span>V<\/span><\/span><\/span><\/span><\/span> \u7b26\u53f7\u89c4\u5219\u4e3a\u6b63\u504f\u53d6\u6b63\u3001\u53cd\u504f\u53d6\u8d1f，\u53cd\u5411\u504f\u538b\u65f6 <\/p>\n

        V<\/p>\n

        b<\/p>\n

        i<\/p>\n

        \u2212<\/p>\n

        V<\/p>\n

        V_{bi}-V<\/p>\n

        <\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>V<\/span><\/span><\/span><\/span><\/span> \u589e\u5927，\u8017\u5c3d\u5c42\u5bbd\u5ea6\u53d8\u5bbd\u3002<\/p>\n

        \u7531\u4e0a\u5f0f\u53ca\u71b5\u589e\u539f\u7406\u7684\u6d53\u5ea6\u6269\u6563\u7279\u6027\u53ef\u77e5：<\/p>\n

      • \n

        \u8017\u5c3d\u5c42\u5bbd\u5ea6\u4e0e\u63ba\u6742\u6d53\u5ea6\u6210\u53cd\u6bd4：\u5f53 <\/p>\n

        N<\/p>\n

        A<\/p>\n

        N_A<\/p>\n

        <\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u6216 <\/p>\n

        N<\/p>\n

        D<\/p>\n

        N_D<\/p>\n

        <\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u589e\u5927\u65f6，<\/p>\n

        W<\/p>\n

        W<\/p>\n

        <\/span><\/span>W<\/span><\/span><\/span><\/span><\/span> \u51cf\u5c0f\u3002\u8fd9\u662f\u56e0\u4e3a\u9ad8\u63ba\u6742\u6d53\u5ea6\u4e0b，\u591a\u5b50\u6d53\u5ea6\u8f83\u9ad8，\u4e3a\u524a\u5f31\u6d53\u5ea6\u5c40\u90e8\u4e0d\u5747\u5300\u6027，\u66f4\u591a\u591a\u5b50\u901a\u8fc7\u6269\u6563\u8fd0\u52a8\u5728\u8017\u5c3d\u5c42\u5f62\u6210\u66f4\u9ad8\u6d53\u5ea6\u7684\u7a7a\u95f4\u7535\u8377，\u65e0\u9700\u8f83\u5bbd\u7684\u8017\u5c3d\u5c42\u5373\u53ef\u5b9e\u73b0\u7535\u8377\u5e73\u8861，\u4ece\u800c\u538b\u7f29\u4e86\u7a7a\u95f4\u7535\u8377\u533a\u7684\u8303\u56f4\u3002<\/p>\n<\/li>\n

      • \n

        \u7a7a\u95f4\u7535\u8377\u5bc6\u5ea6\u4e0e\u63ba\u6742\u6d53\u5ea6\u6210\u6b63\u6bd4：\u8017\u5c3d\u5c42\u5185\u7684\u7535\u79bb\u6742\u8d28\u6d53\u5ea6\u76f4\u63a5\u7b49\u4e8e\u63ba\u6742\u6d53\u5ea6，\u56e0\u6b64\u9ad8\u63ba\u6742\u5bfc\u81f4\u66f4\u9ad8\u7684\u7a7a\u95f4\u7535\u8377\u5bc6\u5ea6，\u6ee1\u8db3 <\/p>\n

        \u2223<\/p>\n

        Q<\/p>\n

        \u2223<\/p>\n

        =<\/p>\n

        q<\/p>\n

        N<\/p>\n

        A<\/p>\n

        x<\/p>\n

        p<\/p>\n

        =<\/p>\n

        q<\/p>\n

        N<\/p>\n

        D<\/p>\n

        x<\/p>\n

        n<\/p>\n

        |Q| = qN_A x_p = qN_D x_n<\/p>\n

        <\/span><\/span>\u2223<\/span>Q<\/span>\u2223<\/span><\/span>=<\/span><\/span><\/span><\/span>q<\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>q<\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002\u4ece\u6d53\u5ea6\u5747\u5300\u5316\u8d8b\u52bf\u6765\u770b，\u9ad8\u63ba\u6742\u6d53\u5ea6\u53ef\u901a\u8fc7\u63d0\u9ad8\u7a7a\u95f4\u7535\u8377\u5bc6\u5ea6\u6765\u524a\u5f31\u6d53\u5ea6\u5c40\u90e8\u6027，\u8fdb\u4e00\u6b65\u9a8c\u8bc1\u4e86\u8fd9\u4e00\u5173\u7cfb\u3002<\/p>\n<\/li>\n

        3. PN \u7ed3\u7684\u51fb\u7a7f\u673a\u5236<\/h2>\n

        3.1 \u96ea\u5d29\u51fb\u7a7f（Avalanche Breakdown）<\/h3>\n

        \u5f53\u53cd\u5411\u504f\u538b <\/p>\n

        V<\/p>\n

        R<\/p>\n

        V_R<\/p>\n

        <\/span><\/span>V<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u589e\u5927\u65f6，\u8017\u5c3d\u5c42\u5bbd\u5ea6\u589e\u52a0，\u5185\u90e8\u7535\u573a\u5f3a\u5ea6 <\/p>\n

        E<\/p>\n

        \\\\mathcal{E}<\/p>\n

        <\/span><\/span>E<\/span><\/span><\/span><\/span><\/span> \u589e\u5f3a\u3002\u5728\u6b64\u5f3a\u7535\u573a\u4f5c\u7528\u4e0b，\u6f02\u79fb\u901a\u8fc7\u8017\u5c3d\u5c42\u7684\u8f7d\u6d41\u5b50（\u4e3b\u8981\u4e3a\u5c11\u6570\u8f7d\u6d41\u5b50，\u5185\u5efa\u7535\u573a\u5bf9\u591a\u5b50\u8d77\u963b\u788d\u4f5c\u7528，\u5bf9\u5c11\u5b50\u8d77\u52a0\u901f\u4f5c\u7528）\u83b7\u5f97\u8db3\u591f\u52a8\u80fd，\u4e0e\u6676\u683c\u539f\u5b50\u53d1\u751f\u78b0\u649e\u7535\u79bb（impact ionization），\u4ea7\u751f\u7535\u5b50-\u7a7a\u7a74\u5bf9\u3002<\/p>\n

        \u65b0\u751f\u6210\u7684\u7535\u5b50-\u7a7a\u7a74\u5bf9\u5728\u7535\u573a\u52a0\u901f\u4e0b\u7ee7\u7eed\u53d1\u751f\u78b0\u649e\u7535\u79bb，\u5f15\u53d1\u94fe\u5f0f\u53cd\u5e94，\u5f62\u6210\u8f7d\u6d41\u5b50\u7684\u500d\u589e\u6548\u5e94（multiplication）\u3002\u5f53\u500d\u589e\u56e0\u5b50 <\/p>\n

        M<\/p>\n

        M<\/p>\n

        <\/span><\/span>M<\/span><\/span><\/span><\/span><\/span> \u8d8b\u4e8e\u65e0\u7a77\u65f6，\u53cd\u5411\u7535\u6d41\u6025\u5267\u589e\u5927，\u5b9a\u4e49\u6b64\u65f6\u53d1\u751f\u96ea\u5d29\u51fb\u7a7f\u3002<\/p>\n

        \u51fb\u7a7f\u7535\u538b <\/p>\n

        V<\/p>\n

        B<\/p>\n

        R<\/p>\n

        V_{BR}<\/p>\n

        <\/span><\/span>V<\/span><\/span>BR<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e0e\u63ba\u6742\u6d53\u5ea6\u7684\u7ecf\u9a8c\u5173\u7cfb\u4e3a：<\/p>\n

        <\/p>\n

        V<\/p>\n

        B<\/p>\n

        R<\/p>\n

        \u221d<\/p>\n

        1<\/p>\n

        N<\/p>\n

        0.75<\/p>\n

        V_{BR} \\\\propto \\\\frac{1}{N^{0.75}}<\/p>\n

        <\/span><\/span>V<\/span><\/span>BR<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u221d<\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span>0.75<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

        \u56e0\u6b64，\u96ea\u5d29\u51fb\u7a7f\u901a\u5e38\u53d1\u751f\u5728\u4f4e\u63ba\u6742\u6d53\u5ea6\u7684 PN \u7ed3\u4e2d，\u6b64\u65f6\u8017\u5c3d\u5c42\u8f83\u5bbd，\u8f7d\u6d41\u5b50\u6709\u8db3\u591f\u7684\u52a0\u901f\u8ddd\u79bb\u83b7\u5f97\u8db3\u591f\u80fd\u91cf\u4ee5\u5f15\u53d1\u78b0\u649e\u7535\u79bb，\u6ee1\u8db3\u94fe\u5f0f\u53cd\u5e94\u7684\u53d1\u751f\u6761\u4ef6\u3002<\/p>\n

        3.2 \u9f50\u7eb3\u51fb\u7a7f（Zener Breakdown）<\/h3>\n

        \u5f53\u63ba\u6742\u6d53\u5ea6\u8f83\u9ad8（\u901a\u5e38 <\/p>\n

        \u2265<\/p>\n

        10<\/p>\n

        17<\/p>\n

        \u2009<\/p>\n

        c<\/p>\n

        m<\/p>\n

        \u2212<\/p>\n

        3<\/p>\n

        \\\\ge10^{17} \\\\,\\\\mathrm{cm}^{-3}<\/p>\n

        <\/span><\/span>\u2265<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>17<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>cm<\/span><\/span><\/span>\u2212<\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u9ad8\u63ba\u6742\u65f6 <\/p>\n

        ><\/p>\n

        10<\/p>\n

        18<\/p>\n

        \u2009<\/p>\n

        c<\/p>\n

        m<\/p>\n

        \u2212<\/p>\n

        3<\/p>\n

        >10^{18} \\\\,\\\\mathrm{cm}^{-3}<\/p>\n

        <\/span><\/span>><\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>18<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>cm<\/span><\/span><\/span>\u2212<\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>）\u65f6，\u8017\u5c3d\u5c42\u5bbd\u5ea6\u5f88\u7a84（<\/p>\n

        <<\/p>\n

        10
        \n \u2009<\/p>\n

        n<\/p>\n

        m<\/p>\n

        <10 \\\\,\\\\mathrm{nm}<\/p>\n

        <\/span><\/span><<\/span><\/span><\/span><\/span>10<\/span><\/span>nm<\/span><\/span><\/span><\/span><\/span><\/span>），\u5373\u4f7f\u8f83\u5c0f\u7684\u53cd\u5411\u7535\u538b\u4e5f\u80fd\u5efa\u7acb\u6781\u5f3a\u7684\u7535\u573a（<\/p>\n

        ><\/p>\n

        10<\/p>\n

        6<\/p>\n

        \u2009<\/p>\n

        V<\/p>\n

        \/<\/p>\n

        c<\/p>\n

        m<\/p>\n

        >10^6 \\\\,\\\\mathrm{V\/cm}<\/p>\n

        <\/span><\/span>><\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>V\/cm<\/span><\/span><\/span><\/span><\/span><\/span>，\u5373 <\/p>\n

        ><\/p>\n

        10<\/p>\n

        8<\/p>\n

        \u2009<\/p>\n

        V<\/p>\n

        \/<\/p>\n

        m<\/p>\n

        >10^8 \\\\,\\\\mathrm{V\/m}<\/p>\n

        <\/span><\/span>><\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>8<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>V\/m<\/span><\/span><\/span><\/span><\/span><\/span>）\u3002<\/p>\n

        \u5728\u6b64\u5f3a\u573a\u4f5c\u7528\u4e0b，\u76f4\u63a5\u7834\u574f\u8017\u5c3d\u5c42\u4e2d\u4e2d\u6027\u539f\u5b50\u7684\u5171\u4ef7\u952e（\u573a\u81f4\u7535\u79bb），\u6216\u4f7f\u4ef7\u5e26\u7535\u5b50\u901a\u8fc7\u91cf\u5b50\u96a7\u7a7f\u6548\u5e94\u76f4\u63a5\u7a7f\u8d8a\u7981\u5e26\u8fdb\u5165\u5bfc\u5e26，\u4ea7\u751f\u5927\u91cf\u7535\u5b50-\u7a7a\u7a74\u5bf9，\u5bfc\u81f4\u53cd\u5411\u7535\u6d41\u6025\u5267\u589e\u5927，\u8be5\u673a\u5236\u79f0\u4e3a\u9f50\u7eb3\u51fb\u7a7f\u6216\u96a7\u7a7f\u51fb\u7a7f\u3002<\/p>\n

        \u9f50\u7eb3\u51fb\u7a7f\u7535\u538b\u4e0e\u63ba\u6742\u6d53\u5ea6\u7684\u5173\u7cfb\u8868\u73b0\u4e3a：\u968f\u63ba\u6742\u6d53\u5ea6\u589e\u52a0，\u51fb\u7a7f\u7535\u538b\u964d\u4f4e\u3002\u8fd9\u662f\u56e0\u4e3a\u63ba\u6742\u6d53\u5ea6\u8d8a\u9ad8，\u8017\u5c3d\u5c42\u8d8a\u7a84，\u6240\u9700\u53cd\u5411\u7535\u538b\u8d8a\u5c0f\u5373\u53ef\u5efa\u7acb\u8d77\u5f15\u53d1\u9f50\u7eb3\u51fb\u7a7f\u7684\u5f3a\u7535\u573a\u3002<\/p>\n

        3.3 \u4e24\u79cd\u51fb\u7a7f\u673a\u5236\u7684\u6bd4\u8f83<\/h3>\n

        \u4e24\u79cd\u51fb\u7a7f\u673a\u5236\u5747\u5c5e\u4e8e PN \u7ed3\u53cd\u5411\u51fb\u7a7f\u73b0\u8c61，\u5728\u5b9e\u9645\u5668\u4ef6\u4e2d\u53ef\u80fd\u540c\u65f6\u5b58\u5728，\u4ec5\u56e0\u63ba\u6742\u6d53\u5ea6\u4e0d\u540c\u800c\u8868\u73b0\u51fa\u4e0d\u540c\u7684\u4e3b\u5bfc\u673a\u5236\u3002\u4e8c\u8005\u7684\u5177\u4f53\u7279\u5f81\u5bf9\u6bd4\u5982\u4e0b\u8868\u6240\u793a：<\/p>\n\n\u7279\u5f81\u96ea\u5d29\u51fb\u7a7f\u9f50\u7eb3\u51fb\u7a7f<\/tr>\n\n\n\n\n\n\n
        \u7269\u7406\u673a\u5236<\/td>\n\u78b0\u649e\u7535\u79bb\u4e0e\u8f7d\u6d41\u5b50\u500d\u589e（\u94fe\u5f0f\u53cd\u5e94）<\/td>\n\u91cf\u5b50\u96a7\u7a7f\u6216\u5f3a\u573a\u81f4\u7535\u79bb（\u5171\u4ef7\u952e\u7834\u574f）<\/td>\n<\/tr>\n
        \u63ba\u6742\u6d53\u5ea6<\/td>\n\u4f4e（<\/p>\n

        <<\/p>\n

        10<\/p>\n

        17<\/p>\n

        \u2009<\/p>\n

        c<\/p>\n

        m<\/p>\n

        \u2212<\/p>\n

        3<\/p>\n

        <10^{17} \\\\,\\\\mathrm{cm}^{-3}<\/p>\n

        <\/span><\/span><<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>17<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>cm<\/span><\/span><\/span>\u2212<\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5178\u578b\u503c <\/p>\n

        <<\/p>\n

        10<\/p>\n

        16<\/p>\n

        \u2009<\/p>\n

        c<\/p>\n

        m<\/p>\n

        \u2212<\/p>\n

        3<\/p>\n

        <10^{16} \\\\,\\\\mathrm{cm}^{-3}<\/p>\n

        <\/span><\/span><<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>16<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>cm<\/span><\/span><\/span>\u2212<\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>）<\/td>\n

        		\u9ad8（<\/p>\n

        \u2265<\/p>\n

        10<\/p>\n

        17<\/p>\n

        \u2009<\/p>\n

        c<\/p>\n

        m<\/p>\n

        \u2212<\/p>\n

        3<\/p>\n

        \\\\ge10^{17} \\\\,\\\\mathrm{cm}^{-3}<\/p>\n

        <\/span><\/span>\u2265<\/span><\/span><\/span><\/span>1<\/span>0<\/span><\/span>17<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>cm<\/span><\/span><\/span>\u2212<\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>）<\/td>\n<\/tr>\n

        \u8017\u5c3d\u5c42\u5bbd\u5ea6<\/td>\n\u5bbd<\/td>\n\u7a84<\/td>\n<\/tr>\n
        \u6e29\u5ea6\u7cfb\u6570<\/td>\n\u6b63（\u6b63\u6e29\u5ea6\u7cfb\u6570）<\/td>\n\u8d1f（\u8d1f\u6e29\u5ea6\u7cfb\u6570）<\/td>\n<\/tr>\n
        \u51fb\u7a7f\u7535\u538b<\/td>\n\u9ad8（\u901a\u5e38 <\/p>\n

        ><\/p>\n

        6
        \n \u2009<\/p>\n

        V<\/p>\n

        >6 \\\\,\\\\mathrm{V}<\/p>\n

        <\/span><\/span>><\/span><\/span><\/span><\/span>6<\/span><\/span>V<\/span><\/span><\/span><\/span><\/span>）<\/td>\n

        		\u4f4e（\u901a\u5e38 <\/p>\n

        <<\/p>\n

        6
        \n \u2009<\/p>\n

        V<\/p>\n

        <6 \\\\,\\\\mathrm{V}<\/p>\n

        <\/span><\/span><<\/span><\/span><\/span><\/span>6<\/span><\/span>V<\/span><\/span><\/span><\/span><\/span>）<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        \u5bf9\u4e8e\u7845 PN \u7ed3，\u5f53\u51fb\u7a7f\u7535\u538b <\/p>\n

        V<\/p>\n

        B<\/p>\n

        R<\/p>\n

        <<\/p>\n

        4.5
        \n \u2009<\/p>\n

        V<\/p>\n

        V_{BR} < 4.5 \\\\,\\\\mathrm{V}<\/p>\n

        <\/span><\/span>V<\/span><\/span>BR<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><<\/span><\/span><\/span><\/span>4.5<\/span><\/span>V<\/span><\/span><\/span><\/span><\/span> \u65f6\u4ee5\u9f50\u7eb3\u51fb\u7a7f\u4e3a\u4e3b；\u5f53 <\/p>\n

        V<\/p>\n

        B<\/p>\n

        R<\/p>\n

        ><\/p>\n

        6.5
        \n \u2009<\/p>\n

        V<\/p>\n

        V_{BR} > 6.5 \\\\,\\\\mathrm{V}<\/p>\n

        <\/span><\/span>V<\/span><\/span>BR<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>><\/span><\/span><\/span><\/span>6.5<\/span><\/span>V<\/span><\/span><\/span><\/span><\/span> \u65f6\u4ee5\u96ea\u5d29\u51fb\u7a7f\u4e3a\u4e3b；\u4e2d\u95f4\u533a\u57df\u4e3a\u4e24\u79cd\u673a\u5236\u7684\u6df7\u5408\u533a\u3002<\/p>\n

        4. PN \u7ed3\u7684\u7535\u5bb9\u7279\u6027<\/h2>\n

        PN \u7ed3\u7684\u7535\u5bb9\u6548\u5e94\u7531\u52bf\u5792\u7535\u5bb9 <\/p>\n

        C<\/p>\n

        j<\/p>\n

        C_j<\/p>\n

        <\/span><\/span>C<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>（\u7ed3\u7535\u5bb9）\u548c\u6269\u6563\u7535\u5bb9 <\/p>\n

        C<\/p>\n

        d<\/p>\n

        C_d<\/p>\n

        <\/span><\/span>C<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e24\u90e8\u5206\u7ec4\u6210，\u4e8c\u8005\u6e90\u4e8e\u4e0d\u540c\u7684\u7269\u7406\u673a\u5236，\u5728\u4e0d\u540c\u504f\u7f6e\u6761\u4ef6\u4e0b\u8868\u73b0\u51fa\u4e0d\u540c\u7684\u4e3b\u5bfc\u4f5c\u7528，\u5171\u540c\u51b3\u5b9a PN \u7ed3\u7684\u9ad8\u9891\u7279\u6027\u3002<\/p>\n

        4.1 \u52bf\u5792\u7535\u5bb9（Barrier Capacitance）<\/h3>\n

        \u52bf\u5792\u7535\u5bb9\u6e90\u4e8e\u8017\u5c3d\u5c42\u5185\u7a7a\u95f4\u7535\u8377\u968f\u5916\u52a0\u7535\u538b\u7684\u53d8\u5316\u3002\u8017\u5c3d\u5c42\u4e2d\u4e3b\u8981\u4e3a\u4e0d\u53ef\u79fb\u52a8\u7684\u7535\u79bb\u6742\u8d28\u7535\u8377，\u5f53\u5916\u52a0\u7535\u538b\u53d8\u5316\u65f6，\u8017\u5c3d\u5c42\u5bbd\u5ea6\u968f\u4e4b\u6539\u53d8，\u7a7a\u95f4\u7535\u8377\u603b\u91cf\u4e5f\u76f8\u5e94\u53d8\u5316，\u8fd9\u4e00\u5145\u653e\u7535\u8fc7\u7a0b\u7b49\u6548\u4e3a\u7535\u5bb9\u6548\u5e94，\u6839\u636e\u5b9a\u4e49\u5176\u7535\u5bb9\u503c\u4e3a：<\/p>\n

        <\/p>\n

        C<\/p>\n

        j<\/p>\n

        =<\/p>\n

        \u2223<\/p>\n

        d<\/p>\n

        Q<\/p>\n

        d<\/p>\n

        V<\/p>\n

        \u2223<\/p>\n

        =<\/p>\n

        \u03b5<\/p>\n

        s<\/p>\n

        A<\/p>\n

        W<\/p>\n

        C_j = \\\\left|\\\\frac{dQ}{dV}\\\\right| = \\\\frac{\\\\varepsilon_s A}{W}<\/p>\n

        <\/span><\/span>C<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/p>\n

        <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>V<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>Q<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

        <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>W<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

        \u5176\u4e2d <\/p>\n

        A<\/p>\n

        A<\/p>\n

        <\/span><\/span>A<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7ed3\u9762\u79ef，<\/p>\n

        W<\/p>\n

        W<\/p>\n

        <\/span><\/span>W<\/span><\/span><\/span><\/span><\/span> \u4e3a\u8017\u5c3d\u5c42\u5bbd\u5ea6\u3002<\/p>\n

        \u5bf9\u4e8e\u7a81\u53d8\u7ed3，\u52bf\u5792\u7535\u5bb9\u4e0e\u504f\u538b\u7684\u5173\u7cfb\u4e3a：<\/p>\n

        <\/p>\n

        C<\/p>\n

        j<\/p>\n

        =<\/p>\n

        C<\/p>\n

        j<\/p>\n

        0<\/p>\n

        (<\/p>\n

        1<\/p>\n

        \u2212<\/p>\n

        V<\/p>\n

        V<\/p>\n

        b<\/p>\n

        i<\/p>\n

        )<\/p>\n

        m<\/p>\n

        C_j = \\\\frac{C_{j0}}{\\\\left(1-\\\\frac{V}{V_{bi}}\\\\right)^m}<\/p>\n

        <\/span><\/span>C<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>V<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>C<\/span><\/span>j<\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

        \u5176\u4e2d <\/p>\n

        C<\/p>\n

        j<\/p>\n

        0<\/p>\n

        C_{j0}<\/p>\n

        <\/span><\/span>C<\/span><\/span>j<\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u96f6\u504f\u538b\u65f6\u7684\u7ed3\u7535\u5bb9，<\/p>\n

        m<\/p>\n

        m<\/p>\n

        <\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u4e3a\u68af\u5ea6\u7cfb\u6570（\u7a81\u53d8\u7ed3 <\/p>\n

        m<\/p>\n

        =<\/p>\n

        1<\/p>\n

        \/<\/p>\n

        2<\/p>\n

        m=1\/2<\/p>\n

        <\/span><\/span>m<\/span><\/span>=<\/span><\/span><\/span><\/span>1\/2<\/span><\/span><\/span><\/span><\/span>，\u7ebf\u6027\u7f13\u53d8\u7ed3 <\/p>\n

        m<\/p>\n

        =<\/p>\n

        1<\/p>\n

        \/<\/p>\n

        3<\/p>\n

        m=1\/3<\/p>\n

        <\/span><\/span>m<\/span><\/span>=<\/span><\/span><\/span><\/span>1\/3<\/span><\/span><\/span><\/span><\/span>）\u3002<\/p>\n

        \u7279\u6027\u5206\u6790：<\/p>\n

          \n
        • \n

          \u53cd\u504f\u65f6，<\/p>\n

          W<\/p>\n

          W<\/p>\n

          <\/span><\/span>W<\/span><\/span><\/span><\/span><\/span> \u968f <\/p>\n

          \u2223<\/p>\n

          V<\/p>\n

          R<\/p>\n

          \u2223<\/p>\n

          |V_R|<\/p>\n

          <\/span><\/span>\u2223<\/span>V<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span><\/span><\/span><\/span> \u589e\u5927\u800c\u589e\u5bbd，\u7a7a\u95f4\u7535\u8377\u603b\u91cf\u53d8\u5316\u7387\u51cf\u5c0f，<\/p>\n

          C<\/p>\n

          j<\/p>\n

          C_j<\/p>\n

          <\/span><\/span>C<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u968f\u4e4b\u51cf\u5c0f；<\/p>\n<\/li>\n

        • \n

          \u6b63\u504f\u65f6，<\/p>\n

          W<\/p>\n

          W<\/p>\n

          <\/span><\/span>W<\/span><\/span><\/span><\/span><\/span> \u53d8\u7a84，<\/p>\n

          C<\/p>\n

          j<\/p>\n

          C_j<\/p>\n

          <\/span><\/span>C<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u589e\u5927，\u4f46\u6b64\u65f6\u6269\u6563\u7535\u5bb9\u5360\u4e3b\u5bfc\u5730\u4f4d，\u52bf\u5792\u7535\u5bb9\u53ef\u5ffd\u7565\u4e0d\u8ba1（\u4ec5\u4e2d\u9ad8\u7535\u6d41\u6b63\u504f\u6761\u4ef6\u4e0b\u9002\u7528）\u3002<\/p>\n<\/li>\n<\/ul>\n

          4.2 \u6269\u6563\u7535\u5bb9（Diffusion Capacitance）<\/h3>\n

          \u6269\u6563\u7535\u5bb9\u6e90\u4e8e\u6b63\u504f\u538b\u4e0b\u5c11\u5b50\u7684\u6ce8\u5165\u4e0e\u5b58\u50a8\u6548\u5e94\u3002PN \u7ed3\u6b63\u504f\u65f6，\u5185\u5efa\u7535\u573a\u88ab\u524a\u5f31，\u5927\u91cf\u5c11\u5b50\u8d8a\u8fc7\u52bf\u5792\u6ce8\u5165\u5bf9\u65b9\u533a\u57df，\u5728\u6269\u6563\u533a\u5f62\u6210\u4ece\u8017\u5c3d\u5c42\u4ea4\u754c\u9762\u6307\u5411\u8fdc\u79bb\u4ea4\u754c\u9762\u7684\u9012\u51cf\u6d53\u5ea6\u68af\u5ea6\u3002<\/p>\n

          \u8be5\u975e\u5e73\u8861\u5c11\u5b50\u6d53\u5ea6\u68af\u5ea6\u968f\u5916\u52a0\u6b63\u504f\u7535\u538b\u7684\u53d8\u5316\u800c\u53d8\u5316，\u7535\u538b\u589e\u5927\u65f6\u6d53\u5ea6\u68af\u5ea6\u589e\u5927，\u6269\u6563\u533a\u5b58\u50a8\u7684\u5c11\u5b50\u7535\u8377\u603b\u91cf\u4e5f\u76f8\u5e94\u589e\u52a0，\u8fd9\u4e00\u5145\u653e\u7535\u8fc7\u7a0b\u7b49\u6548\u4e3a\u7535\u5bb9\u6548\u5e94，\u5b9a\u4e49\u6269\u6563\u7535\u5bb9\u4e3a\u5c11\u5b50\u7535\u8377\u968f\u7535\u538b\u7684\u53d8\u5316\u7387：<\/p>\n

          <\/p>\n

          C<\/p>\n

          d<\/p>\n

          =<\/p>\n

          d<\/p>\n

          Q<\/p>\n

          p<\/p>\n

          d<\/p>\n

          V<\/p>\n

          =<\/p>\n

          \u03c4<\/p>\n

          I<\/p>\n

          \u03b7<\/p>\n

          V<\/p>\n

          T<\/p>\n

          C_d = \\\\frac{dQ_p}{dV} = \\\\frac{\\\\tau I}{\\\\eta V_T}<\/p>\n

          <\/span><\/span>C<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>V<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>Q<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u03b7<\/span>V<\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c4<\/span>I<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u5176\u4e2d <\/p>\n

          \u03c4<\/p>\n

          \\\\tau<\/p>\n

          <\/span><\/span>\u03c4<\/span><\/span><\/span><\/span><\/span> \u4e3a\u5c11\u5b50\u5bff\u547d，<\/p>\n

          I<\/p>\n

          I<\/p>\n

          <\/span><\/span>I<\/span><\/span><\/span><\/span><\/span> \u4e3a\u6b63\u5411\u7535\u6d41，<\/p>\n

          V<\/p>\n

          T<\/p>\n

          =<\/p>\n

          k<\/p>\n

          T<\/p>\n

          \/<\/p>\n

          q<\/p>\n

          V_T = kT\/q<\/p>\n

          <\/span><\/span>V<\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>k<\/span>T<\/span>\/<\/span>q<\/span><\/span><\/span><\/span><\/span> \u4e3a\u70ed\u7535\u538b，<\/p>\n

          \u03b7<\/p>\n

          \\\\eta<\/p>\n

          <\/span><\/span>\u03b7<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7406\u60f3\u56e0\u5b50（<\/p>\n

          1<\/p>\n

          \u223c<\/p>\n

          2<\/p>\n

          1 \\\\sim 2<\/p>\n

          <\/span><\/span>1<\/span><\/span>\u223c<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>）；\u8be5\u516c\u5f0f\u4ec5\u9002\u7528\u4e8e\u4f4e\u9891\u5c0f\u4fe1\u53f7\u6761\u4ef6\u3002<\/p>\n

          4.3 \u4e24\u79cd\u7535\u5bb9\u7684\u6bd4\u8f83<\/h3>\n

          \u52bf\u5792\u7535\u5bb9\u4e0e\u6269\u6563\u7535\u5bb9\u7684\u7269\u7406\u672c\u8d28\u3001\u7279\u6027\u5b58\u5728\u663e\u8457\u5dee\u5f02，\u5177\u4f53\u5bf9\u6bd4\u5982\u4e0b\u8868\u6240\u793a：<\/p>\n\n\u53c2\u6570\u52bf\u5792\u7535\u5bb9 <\/p>\n

          C<\/p>\n

          j<\/p>\n

          C_j<\/p>\n

          <\/span><\/span>C<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u6269\u6563\u7535\u5bb9 <\/p>\n

          C<\/p>\n

          d<\/p>\n

          C_d<\/p>\n

          <\/span><\/span>C<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/tr>\n

          \n\n\n\n\n\n
          \u504f\u7f6e\u6761\u4ef6<\/td>\n\u4e3b\u8981\u5b58\u5728\u4e8e\u53cd\u504f\u53ca\u96f6\u504f，\u6b63\u504f\u65f6\u53ef\u5ffd\u7565<\/td>\n\u4e3b\u8981\u5b58\u5728\u4e8e\u6b63\u504f，\u53cd\u504f\u65f6\u53ef\u5ffd\u7565<\/td>\n<\/tr>\n
          \u7269\u7406\u6765\u6e90<\/td>\n\u8017\u5c3d\u5c42\u5bbd\u5ea6\u8c03\u5236\u5bfc\u81f4\u7a7a\u95f4\u7535\u8377\u53d8\u5316<\/td>\n\u5c11\u5b50\u6ce8\u5165\u4e0e\u5b58\u50a8\u5bfc\u81f4\u5c11\u5b50\u7535\u8377\u53d8\u5316<\/td>\n<\/tr>\n
          \u6570\u503c\u8303\u56f4<\/td>\n\u901a\u5e38\u4e3a pF \u91cf\u7ea7<\/td>\n\u6b63\u504f\u65f6\u53ef\u81f3 nF \u91cf\u7ea7<\/td>\n<\/tr>\n
          \u9891\u7387\u7279\u6027<\/td>\n\u9ad8\u9891\u7279\u6027\u597d，\u53d7\u9891\u7387\u5f71\u54cd\u5c0f<\/td>\n\u53d7\u9650\u4e8e\u5c11\u5b50\u5bff\u547d，\u9ad8\u9891\u65f6\u5931\u6548<\/td>\n<\/tr>\n
          \u7535\u538b\u4f9d\u8d56\u6027<\/td>\n<\/p>\n

          C<\/p>\n

          j<\/p>\n

          \u221d<\/p>\n

          (<\/p>\n

          V<\/p>\n

          b<\/p>\n

          i<\/p>\n

          \u2212<\/p>\n

          V<\/p>\n

          )<\/p>\n

          \u2212<\/p>\n

          m<\/p>\n

          C_j \\\\propto (V_{bi}-V)^{-m}<\/p>\n

          <\/span><\/span>C<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u221d<\/span><\/span><\/span><\/span>(<\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>V<\/span>)<\/span><\/span>\u2212<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>（\u7a81\u53d8\u7ed3 <\/p>\n

          m<\/p>\n

          =<\/p>\n

          1<\/p>\n

          \/<\/p>\n

          2<\/p>\n

          m=1\/2<\/p>\n

          <\/span><\/span>m<\/span><\/span>=<\/span><\/span><\/span><\/span>1\/2<\/span><\/span><\/span><\/span><\/span>，\u7ebf\u6027\u7f13\u53d8\u7ed3 <\/p>\n

          m<\/p>\n

          =<\/p>\n

          1<\/p>\n

          \/<\/p>\n

          3<\/p>\n

          m=1\/3<\/p>\n

          <\/span><\/span>m<\/span><\/span>=<\/span><\/span><\/span><\/span>1\/3<\/span><\/span><\/span><\/span><\/span>）<\/td>\n

          		<\/p>\n

          C<\/p>\n

          d<\/p>\n

          \u221d<\/p>\n

          exp<\/p>\n

          \u2061<\/p>\n

          (<\/p>\n

          q<\/p>\n

          V<\/p>\n

          \/<\/p>\n

          \u03b7<\/p>\n

          k<\/p>\n

          T<\/p>\n

          )<\/p>\n

          C_d \\\\propto \\\\exp(qV\/\\\\eta kT)<\/p>\n

          <\/span><\/span>C<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u221d<\/span><\/span><\/span><\/span>exp<\/span>(<\/span>q<\/span>V<\/span>\/<\/span>\u03b7<\/span>k<\/span>T<\/span>)<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

          PN \u7ed3\u7684\u603b\u7535\u5bb9\u4e3a\u4e8c\u8005\u4e4b\u548c，\u5373 <\/p>\n

          C<\/p>\n

          t<\/p>\n

          o<\/p>\n

          t<\/p>\n

          a<\/p>\n

          l<\/p>\n

          =<\/p>\n

          C<\/p>\n

          j<\/p>\n

          +<\/p>\n

          C<\/p>\n

          d<\/p>\n

          C_{total} = C_j + C_d<\/p>\n

          <\/span><\/span>C<\/span><\/span>t<\/span>o<\/span>t<\/span>a<\/span>l<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>C<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5b9e\u9645\u5e94\u7528\u4e2d\u53ef\u6839\u636e\u5de5\u4f5c\u70b9\u9009\u62e9\u4e3b\u5bfc\u7535\u5bb9\u5206\u91cf：\u53cd\u504f\u6216\u4f4e\u9891\u5c0f\u4fe1\u53f7\u6b63\u504f\u6761\u4ef6\u4e0b，<\/p>\n

          C<\/p>\n

          j<\/p>\n

          C_j<\/p>\n

          <\/span><\/span>C<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5360\u4e3b\u5bfc；\u5927\u7535\u6d41\u6b63\u504f\u6761\u4ef6\u4e0b，<\/p>\n

          C<\/p>\n

          d<\/p>\n

          C_d<\/p>\n

          <\/span><\/span>C<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u663e\u8457\u589e\u5927\u5e76\u6210\u4e3a\u4e3b\u8981\u7535\u5bb9\u5206\u91cf\u3002<\/p>\n

          \n

          \u7535\u573a\u5f3a\u5ea6\u3001\u7535\u52bf\u4ee5\u53ca PN \u7ed3\u8017\u5c3d\u5c42\u5bbd\u5ea6<\/h2>\n

          \u732b\u7684\u9ea6\u514b\u65af\u97e6 \u539f\u521b 2023-05-10 21:51:50 \u4fee\u8ba2<\/p>\n

          1. \u5f15\u8a00<\/h3>\n

          \u672c\u6587\u7cfb\u7edf\u9610\u8ff0 PN \u7ed3\u8017\u5c3d\u5c42\u7684\u57fa\u672c\u7269\u7406\u7279\u6027，\u91cd\u70b9\u63a8\u5bfc\u8017\u5c3d\u5c42\u5185\u7535\u573a\u5f3a\u5ea6\u3001\u9759\u7535\u7535\u52bf\u7684\u5206\u5e03\u89c4\u5f8b，\u5e76\u5efa\u7acb\u8017\u5c3d\u5c42\u5bbd\u5ea6\u4e0e\u63ba\u6742\u6d53\u5ea6\u3001\u5185\u5efa\u7535\u52bf\u4e4b\u95f4\u7684\u5b9a\u91cf\u5173\u7cfb\u3002\u5206\u6790\u57fa\u4e8e\u7a81\u53d8\u7ed3\u8fd1\u4f3c（abrupt junction approximation），\u5373\u5047\u8bbe\u7a7a\u95f4\u7535\u8377\u533a\u8fb9\u754c\u5904\u6742\u8d28\u6d53\u5ea6\u53d1\u751f\u7406\u60f3\u7a81\u53d8，\u5982\u56fe 1 \u6240\u793a\u3002\u5750\u6807\u7cfb\u91c7\u7528\u4e00\u7ef4\u76f4\u89d2\u5750\u6807\u7cfb，\u51b6\u91d1\u7ed3\u754c\u9762\u4f4d\u4e8e <\/p>\n

          x<\/p>\n

          =<\/p>\n

          0<\/p>\n

          x = 0<\/p>\n

          <\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>，P \u533a\u8017\u5c3d\u5c42\u8fb9\u754c\u4f4d\u4e8e <\/p>\n

          x<\/p>\n

          =<\/p>\n

          \u2212<\/p>\n

          X<\/p>\n

          p<\/p>\n

          x = -X_p<\/p>\n

          <\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，N \u533a\u8017\u5c3d\u5c42\u8fb9\u754c\u4f4d\u4e8e <\/p>\n

          x<\/p>\n

          =<\/p>\n

          +<\/p>\n

          X<\/p>\n

          n<\/p>\n

          x = +X_n<\/p>\n

          <\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>+<\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

          \"img\"<\/p>\n

          \u56fe 1\u3000PN \u7ed3\u7a7a\u95f4\u7535\u8377\u533a\u7ed3\u6784\u4e0e\u5750\u6807\u7cfb\u793a\u610f\u56fe<\/p>\n

          2. \u6cca\u677e\u65b9\u7a0b\u4e0e\u7535\u8377\u5206\u5e03<\/h3>\n

          2.1 \u57fa\u672c\u63a7\u5236\u65b9\u7a0b<\/h4>\n

          \u534a\u5bfc\u4f53\u5185\u9759\u7535\u52bf <\/p>\n

          \u03d5<\/p>\n

          (<\/p>\n

          x<\/p>\n

          )<\/p>\n

          \\\\phi(x)<\/p>\n

          <\/span><\/span>\u03d5<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e0e\u7a7a\u95f4\u7535\u8377\u5bc6\u5ea6 <\/p>\n

          \u03c1<\/p>\n

          (<\/p>\n

          x<\/p>\n

          )<\/p>\n

          \\\\rho(x)<\/p>\n

          <\/span><\/span>\u03c1<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span><\/span> \u6ee1\u8db3\u4e00\u7ef4\u6cca\u677e\u65b9\u7a0b：<\/p>\n

          <\/p>\n

          d<\/p>\n

          2<\/p>\n

          \u03d5<\/p>\n

          (<\/p>\n

          x<\/p>\n

          )<\/p>\n

          d<\/p>\n

          x<\/p>\n

          2<\/p>\n

          =<\/p>\n

          d<\/p>\n

          d<\/p>\n

          x<\/p>\n

          (<\/p>\n

          d<\/p>\n

          \u03d5<\/p>\n

          (<\/p>\n

          x<\/p>\n

          )<\/p>\n

          d<\/p>\n

          x<\/p>\n

          )<\/p>\n

          \u23df<\/p>\n

          =<\/p>\n

          \u2212<\/p>\n

          E<\/p>\n

          (<\/p>\n

          x<\/p>\n

          )<\/p>\n

          =<\/p>\n

          d<\/p>\n

          d<\/p>\n

          x<\/p>\n

          [<\/p>\n

          \u2212<\/p>\n

          E<\/p>\n

          (<\/p>\n

          x<\/p>\n

          )<\/p>\n

          ]<\/p>\n

          =<\/p>\n

          \u2212<\/p>\n

          d<\/p>\n

          E<\/p>\n

          (<\/p>\n

          x<\/p>\n

          )<\/p>\n

          d<\/p>\n

          x<\/p>\n

          =<\/p>\n

          \u2212<\/p>\n

          \u03c1<\/p>\n

          (<\/p>\n

          x<\/p>\n

          )<\/p>\n

          \u03b5<\/p>\n

          s<\/p>\n

          \\\\frac{\\\\mathrm{d}^{2}\\\\phi(x)}{\\\\mathrm{d}x^{2}} = \\\\frac{\\\\mathrm{d}}{\\\\mathrm{d}x}\\\\underbrace{\\\\left(\\\\frac{\\\\mathrm{d}\\\\phi(x)}{\\\\mathrm{d}x}\\\\right)}_{=-E(x)} = \\\\frac{\\\\mathrm{d}}{\\\\mathrm{d}x}[-E(x)] = -\\\\frac{\\\\mathrm{d}E(x)}{\\\\mathrm{d}x} = -\\\\frac{\\\\rho(x)}{\\\\varepsilon_s} <\/p>\n

          <\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03d5<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span>\u2212<\/span>E<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          <\/span><\/p>\n

          <\/span><\/p>\n

          <\/span><\/span><\/span><\/span>(<\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>\u03d5<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span>\u2212<\/span>E<\/span>(<\/span>x<\/span>)]<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>d<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>E<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c1<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u5176\u4e2d，\u7535\u52bf\u7684\u4e8c\u9636\u5bfc\u6570\u7b49\u4e8e\u7535\u573a\u4e00\u9636\u5bfc\u6570\u7684\u8d1f\u503c，<\/p>\n

          E<\/p>\n

          (<\/p>\n

          x<\/p>\n

          )<\/p>\n

          E(x)<\/p>\n

          <\/span><\/span>E<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7535\u573a\u5f3a\u5ea6，<\/p>\n

          \u03b5<\/p>\n

          s<\/p>\n

          \\\\varepsilon_{s}<\/p>\n

          <\/span><\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u534a\u5bfc\u4f53\u6750\u6599\u7684\u4ecb\u7535\u5e38\u6570\u3002<\/p>\n

          2.2 \u8017\u5c3d\u533a\u7535\u8377\u5206\u5e03<\/h4>\n

          \u5728\u8017\u5c3d\u5c42\u8fd1\u4f3c（depletion approximation）\u4e0b，\u8017\u5c3d\u533a\u5185\u8f7d\u6d41\u5b50\u5b8c\u5168\u8017\u5c3d，\u7a7a\u95f4\u7535\u8377\u5bc6\u5ea6\u7b49\u4e8e\u7535\u79bb\u6742\u8d28\u7535\u8377\u5bc6\u5ea6\u3002\u56e0\u6b64，<\/p>\n

          \u03c1<\/p>\n

          (<\/p>\n

          x<\/p>\n

          )<\/p>\n

          \\\\rho(x)<\/p>\n

          <\/span><\/span>\u03c1<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span><\/span> \u53ef\u7528\u5206\u6bb5\u51fd\u6570\u8868\u793a\u4e3a：<\/p>\n

          <\/p>\n

          \u03c1<\/p>\n

          (<\/p>\n

          x<\/p>\n

          )<\/p>\n

          =<\/p>\n

          {<\/p>\n

          \u2212<\/p>\n

          q<\/p>\n

          N<\/p>\n

          A<\/p>\n

          ,<\/p>\n

          \u2212<\/p>\n

          X<\/p>\n

          p<\/p>\n

          <<\/p>\n

          x<\/p>\n

          <<\/p>\n

          0<\/p>\n

          +<\/p>\n

          q<\/p>\n

          N<\/p>\n

          D<\/p>\n

          ,<\/p>\n

          0<\/p>\n

          <<\/p>\n

          x<\/p>\n

          <<\/p>\n

          X<\/p>\n

          n<\/p>\n

          \\\\rho(x) = \\\\begin{cases} -qN_{A}, & -X_{p} < x < 0 \\\\\\\\ +qN_{D}, & 0 < x < X_{n} \\\\end{cases} <\/p>\n

          <\/span><\/span>\u03c1<\/span>(<\/span>x<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>{<\/span><\/span><\/span>\u2212<\/span>q<\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span><\/span><\/span>+<\/span>q<\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><<\/span><\/span>x<\/span><\/span><<\/span><\/span>0<\/span><\/span><\/span><\/span>0<\/span><\/span><<\/span><\/span>x<\/span><\/span><<\/span><\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u5f0f\u4e2d，<\/p>\n

          q<\/p>\n

          q<\/p>\n

          <\/span><\/span>q<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7535\u5b50\u7535\u8377\u91cf\u7684\u7edd\u5bf9\u503c（<\/p>\n

          q<\/p>\n

          ><\/p>\n

          0<\/p>\n

          q > 0<\/p>\n

          <\/span><\/span>q<\/span><\/span>><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>），<\/p>\n

          N<\/p>\n

          A<\/p>\n

          N_{A}<\/p>\n

          <\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u548c <\/p>\n

          N<\/p>\n

          D<\/p>\n

          N_{D}<\/p>\n

          <\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5206\u522b\u4e3a P \u4fa7\u53d7\u4e3b\u63ba\u6742\u6d53\u5ea6\u4e0e N \u4fa7\u65bd\u4e3b\u63ba\u6742\u6d53\u5ea6\u3002<\/p>\n

          3. \u7535\u573a\u5f3a\u5ea6\u5206\u5e03<\/h3>\n

          3.1 \u7535\u573a\u5f3a\u5ea6\u7684\u63a8\u5bfc<\/h4>\n

          \u5bf9\u6cca\u677e\u65b9\u7a0b\u79ef\u5206\u6c42\u89e3\u7535\u573a\u5f3a\u5ea6 <\/p>\n

          E<\/p>\n

          (<\/p>\n

          x<\/p>\n

          )<\/p>\n

          E(x)<\/p>\n

          <\/span><\/span>E<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002\u6839\u636e\u70ed\u5e73\u8861\u6761\u4ef6，\u7535\u4e2d\u6027\u533a（<\/p>\n

          x<\/p>\n

          <<\/p>\n

          \u2212<\/p>\n

          X<\/p>\n

          p<\/p>\n

          x < -X_{p}<\/p>\n

          <\/span><\/span>x<\/span><\/span><<\/span><\/span><\/span><\/span>\u2212<\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e0e <\/p>\n

          x<\/p>\n

          ><\/p>\n

          X<\/p>\n

          n<\/p>\n

          x > X_{n}<\/p>\n

          <\/span><\/span>x<\/span><\/span>><\/span><\/span><\/span><\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>）\u5185\u7535\u573a\u5f3a\u5ea6\u4e3a\u96f6\u3002\u5229\u7528\u8fb9\u754c\u6761\u4ef6 <\/p>\n

          E<\/p>\n

          (<\/p>\n

          \u2212<\/p>\n

          X<\/p>\n

          p<\/p>\n

          )<\/p>\n

          =<\/p>\n

          0<\/p>\n

          E(-X_{p}) = 0<\/p>\n

          <\/span><\/span>E<\/span>(<\/span>\u2212<\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u4e0e <\/p>\n

          E<\/p>\n

          (<\/p>\n

          X<\/p>\n

          n<\/p>\n

          )<\/p>\n

          =<\/p>\n

          0<\/p>\n

          E(X_{n}) = 0<\/p>\n

          <\/span><\/span>E<\/span>(<\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u786e\u5b9a\u79ef\u5206\u5e38\u6570，\u5e76\u4fdd\u8bc1\u51b6\u91d1\u7ed3\u5904（<\/p>\n

          x<\/p>\n

          =<\/p>\n

          0<\/p>\n

          x = 0<\/p>\n

          <\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>）\u7535\u573a\u5f3a\u5ea6\u8fde\u7eed，\u53ef\u5f97：<\/p>\n

          <\/p>\n

          E<\/p>\n

          (<\/p>\n

          x<\/p>\n

          )<\/p>\n

          =<\/p>\n

          {<\/p>\n

          \u2212<\/p>\n

          q<\/p>\n

          N<\/p>\n

          A<\/p>\n

          \u03b5<\/p>\n

          s<\/p>\n

          (<\/p>\n

          x<\/p>\n

          +<\/p>\n

          X<\/p>\n

          p<\/p>\n

          )<\/p>\n

          ,<\/p>\n

          \u2212<\/p>\n

          X<\/p>\n

          p<\/p>\n

          \u2264<\/p>\n

          x<\/p>\n

          \u2264<\/p>\n

          0<\/p>\n

          \u2212<\/p>\n

          q<\/p>\n

          N<\/p>\n

          D<\/p>\n

          \u03b5<\/p>\n

          s<\/p>\n

          (<\/p>\n

          X<\/p>\n

          n<\/p>\n

          \u2212<\/p>\n

          x<\/p>\n

          )<\/p>\n

          ,<\/p>\n

          0<\/p>\n

          \u2264<\/p>\n

          x<\/p>\n

          \u2264<\/p>\n

          X<\/p>\n

          n<\/p>\n

          E(x) = \\\\begin{cases} -\\\\dfrac{qN_{A}}{\\\\varepsilon_{s}}(x + X_{p}), & -X_{p} \\\\leq x \\\\leq 0 \\\\\\\\[16pt] -\\\\dfrac{qN_{D}}{\\\\varepsilon_{s}}(X_{n} – x), & 0 \\\\leq x \\\\leq X_{n} \\\\end{cases} <\/p>\n

          <\/span><\/span>E<\/span>(<\/span>x<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>\u23a9<\/span><\/span><\/span><\/span><\/p>\n

          <\/span><\/span><\/span>\u23a8<\/span><\/span><\/span><\/span><\/p>\n

          <\/span><\/span><\/span>\u23a7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>x<\/span><\/span>+<\/span><\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>,<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>x<\/span>)<\/span>,<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2264<\/span><\/span>x<\/span><\/span>\u2264<\/span><\/span>0<\/span><\/span><\/span><\/span>0<\/span><\/span>\u2264<\/span><\/span>x<\/span><\/span>\u2264<\/span><\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          3.2 \u7535\u8377\u4e2d\u6027\u6761\u4ef6<\/h4>\n

          \u7531 <\/p>\n

          E<\/p>\n

          (<\/p>\n

          0<\/p>\n

          \u2212<\/p>\n

          )<\/p>\n

          =<\/p>\n

          E<\/p>\n

          (<\/p>\n

          0<\/p>\n

          +<\/p>\n

          )<\/p>\n

          E(0^{-}) = E(0^{+})<\/p>\n

          <\/span><\/span>E<\/span>(<\/span>0<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>E<\/span>(<\/span>0<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u53ef\u5f97：<\/p>\n

          <\/p>\n

          N<\/p>\n

          A<\/p>\n

          X<\/p>\n

          p<\/p>\n

          =<\/p>\n

          N<\/p>\n

          D<\/p>\n

          X<\/p>\n

          n<\/p>\n

          N_{A}X_{p} = N_{D}X_{n} <\/p>\n

          <\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u8be5\u5f0f\u8868\u660e，P \u533a\u5355\u4f4d\u9762\u79ef\u5185\u53d7\u4e3b\u79bb\u5b50\u603b\u7535\u8377\u91cf\u4e0e N \u533a\u5355\u4f4d\u9762\u79ef\u5185\u65bd\u4e3b\u79bb\u5b50\u603b\u7535\u8377\u91cf\u76f8\u7b49，\u4fdd\u8bc1\u6574\u4e2a\u5668\u4ef6\u7684\u7a7a\u95f4\u7535\u4e2d\u6027\u3002\u51b6\u91d1\u7ed3\u754c\u9762\u5904\u7535\u573a\u5f3a\u5ea6\u8fbe\u5230\u6700\u5927\u503c<\/p>\n

          <\/p>\n

          E<\/p>\n

          max<\/p>\n

          \u2061<\/p>\n

          =<\/p>\n

          \u2212<\/p>\n

          q<\/p>\n

          N<\/p>\n

          A<\/p>\n

          X<\/p>\n

          p<\/p>\n

          \u03b5<\/p>\n

          s<\/p>\n

          =<\/p>\n

          \u2212<\/p>\n

          q<\/p>\n

          N<\/p>\n

          D<\/p>\n

          X<\/p>\n

          n<\/p>\n

          \u03b5<\/p>\n

          s<\/p>\n

          E_{\\\\max} = -\\\\dfrac{qN_{A}X_{p}}{\\\\varepsilon_{s}} = -\\\\dfrac{qN_{D}X_{n}}{\\\\varepsilon_{s}}<\/p>\n

          <\/span><\/span>E<\/span><\/span>m<\/span>a<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u7535\u573a\u5f3a\u5ea6\u5206\u5e03\u5448\u4e09\u89d2\u5f62，\u5982\u56fe 2 \u6240\u793a\u3002<\/p>\n

          \"img\"<\/p>\n

          \u56fe 2\u3000PN \u7ed3\u8017\u5c3d\u5c42\u7535\u573a\u5f3a\u5ea6\u5206\u5e03\u793a\u610f\u56fe<\/p>\n

          4. \u7535\u52bf\u5206\u5e03<\/h3>\n

          4.1 \u9759\u7535\u52bf\u7684\u79ef\u5206\u6c42\u89e3<\/h4>\n

          \u4ee5 P \u533a\u7535\u4e2d\u6027\u533a\u8fb9\u754c\u4e3a\u7535\u52bf\u53c2\u8003\u70b9，\u8bbe <\/p>\n

          \u03d5<\/p>\n

          (<\/p>\n

          \u2212<\/p>\n

          X<\/p>\n

          p<\/p>\n

          )<\/p>\n

          =<\/p>\n

          0<\/p>\n

          \\\\phi(-X_{p}) = 0<\/p>\n

          <\/span><\/span>\u03d5<\/span>(<\/span>\u2212<\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u3002\u5bf9\u7535\u573a\u5f3a\u5ea6 <\/p>\n

          E<\/p>\n

          (<\/p>\n

          x<\/p>\n

          )<\/p>\n

          E(x)<\/p>\n

          <\/span><\/span>E<\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span><\/span> \u8fdb\u884c\u5206\u6bb5\u79ef\u5206，\u5e76\u4fdd\u8bc1 <\/p>\n

          x<\/p>\n

          =<\/p>\n

          0<\/p>\n

          x = 0<\/p>\n

          <\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u5904\u7535\u52bf\u8fde\u7eed，\u53ef\u5f97\u8017\u5c3d\u5c42\u5185\u7535\u52bf\u5206\u5e03：<\/p>\n

          <\/p>\n

          \u03d5<\/p>\n

          (<\/p>\n

          x<\/p>\n

          )<\/p>\n

          =<\/p>\n

          {<\/p>\n

          q<\/p>\n

          N<\/p>\n

          A<\/p>\n

          2<\/p>\n

          \u03b5<\/p>\n

          s<\/p>\n

          (<\/p>\n

          x<\/p>\n

          +<\/p>\n

          X<\/p>\n

          p<\/p>\n

          )<\/p>\n

          2<\/p>\n

          ,<\/p>\n

          \u2212<\/p>\n

          X<\/p>\n

          p<\/p>\n

          \u2264<\/p>\n

          x<\/p>\n

          \u2264<\/p>\n

          0<\/p>\n

          q<\/p>\n

          N<\/p>\n

          D<\/p>\n

          2<\/p>\n

          \u03b5<\/p>\n

          s<\/p>\n

          (<\/p>\n

          X<\/p>\n

          n<\/p>\n

          x<\/p>\n

          \u2212<\/p>\n

          x<\/p>\n

          2<\/p>\n

          2<\/p>\n

          )<\/p>\n

          +<\/p>\n

          q<\/p>\n

          N<\/p>\n

          A<\/p>\n

          2<\/p>\n

          \u03b5<\/p>\n

          s<\/p>\n

          X<\/p>\n

          p<\/p>\n

          2<\/p>\n

          ,<\/p>\n

          0<\/p>\n

          \u2264<\/p>\n

          x<\/p>\n

          \u2264<\/p>\n

          X<\/p>\n

          n<\/p>\n

          \\\\phi(x) = \\\\begin{cases} \\\\dfrac{qN_{A}}{2\\\\varepsilon_{s}}(x + X_{p})^{2}, &-X_{p} \\\\leq x \\\\leq 0 \\\\\\\\[16pt] \\\\dfrac{qN_{D}}{2\\\\varepsilon_{s}}\\\\left(X_{n}x – \\\\dfrac{x^{2}}{2}\\\\right) + \\\\dfrac{qN_{A}}{2\\\\varepsilon_{s}}X_{p}^{2}, & 0 \\\\leq x \\\\leq X_{n} \\\\end{cases} <\/p>\n

          <\/span><\/span>\u03d5<\/span>(<\/span>x<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>\u23a9<\/span><\/span><\/span><\/span><\/p>\n

          <\/span><\/span><\/span>\u23a8<\/span><\/span><\/span><\/span><\/p>\n

          <\/span><\/span><\/span>\u23a7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>x<\/span><\/span>+<\/span><\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>2<\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2264<\/span><\/span>x<\/span><\/span>\u2264<\/span><\/span>0<\/span><\/span><\/span><\/span>0<\/span><\/span>\u2264<\/span><\/span>x<\/span><\/span>\u2264<\/span><\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u7535\u52bf\u5206\u5e03\u66f2\u7ebf\u5982\u56fe 3 \u6240\u793a，\u5448\u629b\u7269\u7ebf\u578b\u3002<\/p>\n

          \"img\"<\/p>\n

          \u56fe 3\u3000PN \u7ed3\u8017\u5c3d\u5c42\u7535\u52bf\u5206\u5e03\u793a\u610f\u56fe<\/p>\n

          \u5728 P \u578b\u534a\u5bfc\u4f53\u4e00\u4fa7，\u8017\u5c3d\u5c42\u8fb9\u754c（\u4e0e\u7535\u4e2d\u6027\u533a\u4ea4\u754c\u5904）\u7684\u7535\u52bf\u88ab\u5b9a\u4e49\u4e3a\u96f6\u7535\u4f4d\u3002 \u5373： <\/p>\n

          \u03d5<\/p>\n

          (<\/p>\n

          x<\/p>\n

          )<\/p>\n

          \u2223<\/p>\n

          x<\/p>\n

          =<\/p>\n

          \u2212<\/p>\n

          X<\/p>\n

          p<\/p>\n

          =<\/p>\n

          0<\/p>\n

          \\\\phi(x)\\\\bigg|_{x=-X_p} = 0<\/p>\n

          <\/span><\/span>\u03d5<\/span>(<\/span>x<\/span>)<\/span><\/span><\/p>\n

          <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span>=<\/span>\u2212<\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          5. \u5185\u5efa\u7535\u52bf\u4e0e\u8017\u5c3d\u5c42\u5bbd\u5ea6<\/h3>\n

          5.1 \u5185\u5efa\u7535\u52bf\u8868\u8fbe\u5f0f<\/h4>\n

          <\/p>\n

          x<\/p>\n

          =<\/p>\n

          X<\/p>\n

          n<\/p>\n

          x = X_{n}<\/p>\n

          <\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5904\u7684\u7535\u52bf\u7edd\u5bf9\u503c\u5373\u4e3a PN \u7ed3\u7684\u5185\u5efa\u7535\u52bf（built-in potential）<\/p>\n

          V<\/p>\n

          b<\/p>\n

          i<\/p>\n

          V_{bi}<\/p>\n

          <\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>：<\/p>\n

          <\/p>\n

          V<\/p>\n

          b<\/p>\n

          i<\/p>\n

          =<\/p>\n

          \u03d5<\/p>\n

          (<\/p>\n

          X<\/p>\n

          n<\/p>\n

          )<\/p>\n

          =<\/p>\n

          q<\/p>\n

          2<\/p>\n

          \u03b5<\/p>\n

          s<\/p>\n

          (<\/p>\n

          N<\/p>\n

          D<\/p>\n

          X<\/p>\n

          n<\/p>\n

          2<\/p>\n

          +<\/p>\n

          N<\/p>\n

          A<\/p>\n

          X<\/p>\n

          p<\/p>\n

          2<\/p>\n

          )<\/p>\n

          V_{bi} = \\\\phi(X_{n}) = \\\\dfrac{q}{2\\\\varepsilon_{s}}\\\\left(N_{D}X_{n}^{2} + N_{A}X_{p}^{2}\\\\right) <\/p>\n

          <\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u03d5<\/span>(<\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          5.2 \u8017\u5c3d\u5c42\u5bbd\u5ea6\u516c\u5f0f<\/h4>\n

          \u8054\u7acb\u7535\u8377\u4e2d\u6027\u6761\u4ef6 <\/p>\n

          N<\/p>\n

          A<\/p>\n

          X<\/p>\n

          p<\/p>\n

          =<\/p>\n

          N<\/p>\n

          D<\/p>\n

          X<\/p>\n

          n<\/p>\n

          N_{A}X_{p} = N_{D}X_{n}<\/p>\n

          <\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e0e\u5185\u5efa\u7535\u52bf\u8868\u8fbe\u5f0f，\u53ef\u89e3\u5f97 N \u4fa7\u4e0e P \u4fa7\u8017\u5c3d\u5c42\u5bbd\u5ea6\u5206\u522b\u4e3a：<\/p>\n

          <\/p>\n

          X<\/p>\n

          n<\/p>\n

          =<\/p>\n

          2<\/p>\n

          \u03b5<\/p>\n

          s<\/p>\n

          V<\/p>\n

          b<\/p>\n

          i<\/p>\n

          q<\/p>\n

          \u22c5<\/p>\n

          N<\/p>\n

          A<\/p>\n

          N<\/p>\n

          D<\/p>\n

          (<\/p>\n

          N<\/p>\n

          A<\/p>\n

          +<\/p>\n

          N<\/p>\n

          D<\/p>\n

          )<\/p>\n

          X<\/p>\n

          p<\/p>\n

          =<\/p>\n

          2<\/p>\n

          \u03b5<\/p>\n

          s<\/p>\n

          V<\/p>\n

          b<\/p>\n

          i<\/p>\n

          q<\/p>\n

          \u22c5<\/p>\n

          N<\/p>\n

          D<\/p>\n

          N<\/p>\n

          A<\/p>\n

          (<\/p>\n

          N<\/p>\n

          A<\/p>\n

          +<\/p>\n

          N<\/p>\n

          D<\/p>\n

          )<\/p>\n

          \\\\begin{aligned} X_{n} = \\\\sqrt{\\\\dfrac{2\\\\varepsilon_{s}V_{bi}}{q} \\\\cdot \\\\dfrac{N_{A}}{N_{D}(N_{A} + N_{D})}} \\\\\\\\ X_{p} = \\\\sqrt{\\\\dfrac{2\\\\varepsilon_{s}V_{bi}}{q} \\\\cdot \\\\dfrac{N_{D}}{N_{A}(N_{A} + N_{D})}} \\\\end{aligned}<\/p>\n

          <\/span><\/span><\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>q<\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>q<\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u8017\u5c3d\u5c42\u603b\u5bbd\u5ea6 <\/p>\n

          W<\/p>\n

          =<\/p>\n

          X<\/p>\n

          n<\/p>\n

          +<\/p>\n

          X<\/p>\n

          p<\/p>\n

          W = X_{n} + X_{p}<\/p>\n

          <\/span><\/span>W<\/span><\/span>=<\/span><\/span><\/span><\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u53ef\u7b80\u5316\u4e3a：<\/p>\n

          <\/p>\n

          W<\/p>\n

          =<\/p>\n

          2<\/p>\n

          \u03b5<\/p>\n

          s<\/p>\n

          V<\/p>\n

          b<\/p>\n

          i<\/p>\n

          q<\/p>\n

          (<\/p>\n

          1<\/p>\n

          N<\/p>\n

          A<\/p>\n

          +<\/p>\n

          1<\/p>\n

          N<\/p>\n

          D<\/p>\n

          )<\/p>\n

          =<\/p>\n

          2<\/p>\n

          \u03b5<\/p>\n

          s<\/p>\n

          V<\/p>\n

          b<\/p>\n

          i<\/p>\n

          q<\/p>\n

          \u22c5<\/p>\n

          N<\/p>\n

          A<\/p>\n

          +<\/p>\n

          N<\/p>\n

          D<\/p>\n

          N<\/p>\n

          A<\/p>\n

          N<\/p>\n

          D<\/p>\n

          W = \\\\sqrt{\\\\dfrac{2\\\\varepsilon_{s}V_{bi}}{q}\\\\left(\\\\dfrac{1}{N_{A}} + \\\\dfrac{1}{N_{D}}\\\\right)} = \\\\sqrt{\\\\dfrac{2\\\\varepsilon_{s}V_{bi}}{q} \\\\cdot \\\\dfrac{N_{A} + N_{D}}{N_{A}N_{D}}} <\/p>\n

          <\/span><\/span>W<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span><\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          6. \u5916\u52a0\u504f\u7f6e\u7535\u538b\u5bf9\u8017\u5c3d\u5c42\u7684\u5f71\u54cd<\/h3>\n

          6.1 \u504f\u7f6e\u6761\u4ef6\u4e0e\u8fb9\u754c\u8bbe\u5b9a<\/h4>\n

          \u5f53 PN \u7ed3\u65bd\u52a0\u5916\u90e8\u76f4\u6d41\u504f\u7f6e\u7535\u538b <\/p>\n

          V<\/p>\n

          V<\/p>\n

          <\/span><\/span>V<\/span><\/span><\/span><\/span><\/span> \u65f6，\u70ed\u5e73\u8861\u88ab\u6253\u7834\u3002\u4e3a\u7edf\u4e00\u5206\u6790，\u91c7\u7528\u5982\u4e0b\u7535\u538b\u6781\u6027\u7ea6\u5b9a：<\/p>\n

            \n
          • \u6b63\u5411\u504f\u7f6e（P \u533a\u63a5\u6b63\u3001N \u533a\u63a5\u8d1f）：\n

            V<\/p>\n

            ><\/p>\n

            0<\/p>\n

            V > 0<\/p>\n

            <\/span><\/span>V<\/span><\/span>><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/li>\n

          • \u53cd\u5411\u504f\u7f6e（P \u533a\u63a5\u8d1f\u3001N \u533a\u63a5\u6b63）：\n

            V<\/p>\n

            <<\/p>\n

            0<\/p>\n

            V < 0<\/p>\n

            <\/span><\/span>V<\/span><\/span><<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n

            \u6b64\u65f6，\u8017\u5c3d\u5c42\u4e24\u4fa7\u7684\u603b\u7535\u52bf\u5dee\u7531\u5e73\u8861\u6001\u7684\u5185\u5efa\u7535\u52bf <\/p>\n

            V<\/p>\n

            b<\/p>\n

            i<\/p>\n

            V_{\\\\mathrm{bi}}<\/p>\n

            <\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u53d8\u4e3a\u6709\u6548\u52bf\u5792\u9ad8\u5ea6 <\/p>\n

            (<\/p>\n

            V<\/p>\n

            b<\/p>\n

            i<\/p>\n

            \u2212<\/p>\n

            V<\/p>\n

            )<\/p>\n

            (V_{\\\\mathrm{bi}} – V)<\/p>\n

            <\/span><\/span>(<\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>V<\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

            \u9009\u53d6 P \u533a\u4e2d\u6027\u533a\u8fb9\u754c <\/p>\n

            x<\/p>\n

            =<\/p>\n

            \u2212<\/p>\n

            X<\/p>\n

            p<\/p>\n

            x = -X_p<\/p>\n

            <\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4f5c\u4e3a\u7535\u52bf\u53c2\u8003\u70b9，\u5373 <\/p>\n

            \u03d5<\/p>\n

            (<\/p>\n

            \u2212<\/p>\n

            X<\/p>\n

            p<\/p>\n

            )<\/p>\n

            =<\/p>\n

            0<\/p>\n

            \\\\phi(-X_p) = 0<\/p>\n

            <\/span><\/span>\u03d5<\/span>(<\/span>\u2212<\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u3002\u6839\u636e\u9759\u7535\u573a\u8fde\u7eed\u6027，\u51b6\u91d1\u7ed3\u754c\u9762 <\/p>\n

            x<\/p>\n

            =<\/p>\n

            0<\/p>\n

            x = 0<\/p>\n

            <\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u5904\u7535\u52bf\u8fde\u7eed： <\/p>\n

            \u03d5<\/p>\n

            (<\/p>\n

            0<\/p>\n

            \u2212<\/p>\n

            )<\/p>\n

            =<\/p>\n

            \u03d5<\/p>\n

            (<\/p>\n

            0<\/p>\n

            +<\/p>\n

            )<\/p>\n

            =<\/p>\n

            \u03d5<\/p>\n

            (<\/p>\n

            0<\/p>\n

            )<\/p>\n

            .<\/p>\n

            \\\\phi(0^-) = \\\\phi(0^+) = \\\\phi(0). <\/p>\n

            <\/span><\/span>\u03d5<\/span>(<\/span>0<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03d5<\/span>(<\/span>0<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03d5<\/span>(<\/span>0<\/span>)<\/span>.<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

            6.2 \u8017\u5c3d\u5c42\u5bbd\u5ea6\u7684\u8868\u8fbe\u5f0f<\/h4>\n

            \u5728\u8017\u5c3d\u5c42\u8fd1\u4f3c\u4e0b，\u7a7a\u95f4\u7535\u8377\u533a\u5185\u7535\u8377\u5bc6\u5ea6\u4e3a\u5e38\u6570：<\/p>\n

              \n
            • P \u533a：\n

              \u03c1<\/p>\n

              =<\/p>\n

              \u2212<\/p>\n

              q<\/p>\n

              N<\/p>\n

              A<\/p>\n

              \\\\rho = -q N_A<\/p>\n

              <\/span><\/span>\u03c1<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>q<\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n

            • N \u533a：\n

              \u03c1<\/p>\n

              =<\/p>\n

              +<\/p>\n

              q<\/p>\n

              N<\/p>\n

              D<\/p>\n

              \\\\rho = +q N_D<\/p>\n

              <\/span><\/span>\u03c1<\/span><\/span>=<\/span><\/span><\/span><\/span>+<\/span>q<\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n

              \u5176\u4e2d <\/p>\n

              N<\/p>\n

              A<\/p>\n

              N_A<\/p>\n

              <\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3001<\/p>\n

              N<\/p>\n

              D<\/p>\n

              N_D<\/p>\n

              <\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u53d7\u4e3b\u4e0e\u65bd\u4e3b\u63ba\u6742\u6d53\u5ea6（\u53d6\u6b63\u503c），<\/p>\n

              q<\/p>\n

              q<\/p>\n

              <\/span><\/span>q<\/span><\/span><\/span><\/span><\/span> \u4e3a\u57fa\u672c\u7535\u8377\u91cf\u3002\u6cca\u677e\u65b9\u7a0b\u5728\u5404\u533a\u9000\u5316\u4e3a\u5206\u6bb5\u7ebf\u6027\u7684\u4e8c\u9636\u5fae\u5206\u65b9\u7a0b\u3002\u7531\u4e8e\u65b9\u7a0b\u5177\u6709\u7ebf\u6027\u7279\u6027，\u975e\u5e73\u8861\u6001\u4e0b\u7684\u89e3\u53ef\u76f4\u63a5\u7531\u5e73\u8861\u6001\u5f62\u5f0f\u63a8\u5e7f，\u4ec5\u9700\u5c06 <\/p>\n

              V<\/p>\n

              b<\/p>\n

              i<\/p>\n

              V_{\\\\mathrm{bi}}<\/p>\n

              <\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u66ff\u6362\u4e3a <\/p>\n

              (<\/p>\n

              V<\/p>\n

              b<\/p>\n

              i<\/p>\n

              \u2212<\/p>\n

              V<\/p>\n

              )<\/p>\n

              (V_{\\\\mathrm{bi}} – V)<\/p>\n

              <\/span><\/span>(<\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>V<\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

              \u7531\u6b64\u5f97\u5230\u603b\u8017\u5c3d\u5c42\u5bbd\u5ea6： <\/p>\n

              W<\/p>\n

              (<\/p>\n

              V<\/p>\n

              )<\/p>\n

              =<\/p>\n

              2<\/p>\n

              \u03b5<\/p>\n

              s<\/p>\n

              (<\/p>\n

              V<\/p>\n

              b<\/p>\n

              i<\/p>\n

              \u2212<\/p>\n

              V<\/p>\n

              )<\/p>\n

              q<\/p>\n

              \u22c5<\/p>\n

              N<\/p>\n

              A<\/p>\n

              +<\/p>\n

              N<\/p>\n

              D<\/p>\n

              N<\/p>\n

              A<\/p>\n

              N<\/p>\n

              D<\/p>\n

              ,<\/p>\n

              W(V) = \\\\sqrt{ \\\\frac{2\\\\varepsilon_s (V_{\\\\mathrm{bi}} – V)}{q} \\\\cdot \\\\frac{N_A + N_D}{N_A N_D} }, <\/p>\n

              <\/span><\/span>W<\/span>(<\/span>V<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>V<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span><\/span><\/span><\/span><\/span> \u5176\u4e2d <\/p>\n

              \u03b5<\/p>\n

              s<\/p>\n

              \\\\varepsilon_s<\/p>\n

              <\/span><\/span>\u03b5<\/span><\/span>s<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u534a\u5bfc\u4f53\u4ecb\u7535\u5e38\u6570\u3002<\/p>\n

              \u5185\u5efa\u7535\u52bf <\/p>\n

              V<\/p>\n

              b<\/p>\n

              i<\/p>\n

              V_{\\\\mathrm{bi}}<\/p>\n

              <\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7531\u6750\u6599\u53c2\u6570\u51b3\u5b9a： <\/p>\n

              V<\/p>\n

              b<\/p>\n

              i<\/p>\n

              =<\/p>\n

              k<\/p>\n

              T<\/p>\n

              q<\/p>\n

              ln<\/p>\n

              \u2061<\/p>\n

              !<\/p>\n

              (<\/p>\n

              N<\/p>\n

              A<\/p>\n

              N<\/p>\n

              D<\/p>\n

              n<\/p>\n

              i<\/p>\n

              2<\/p>\n

              )<\/p>\n

              ,<\/p>\n

              V_{\\\\mathrm{bi}} = \\\\frac{kT}{q} \\\\ln!\\\\left( \\\\frac{N_A N_D}{n_i^2} \\\\right), <\/p>\n

              <\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>q<\/span><\/span><\/span><\/span><\/span><\/span><\/span>k<\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>ln<\/span>!<\/span><\/span>(<\/span><\/span><\/span><\/span>n<\/span><\/span>i<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>,<\/span><\/span><\/span><\/span><\/span><\/span> \u5176\u4e2d <\/p>\n

              k<\/p>\n

              k<\/p>\n

              <\/span><\/span>k<\/span><\/span><\/span><\/span><\/span> \u4e3a\u73bb\u5c14\u5179\u66fc\u5e38\u6570，<\/p>\n

              T<\/p>\n

              T<\/p>\n

              <\/span><\/span>T<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7edd\u5bf9\u6e29\u5ea6，<\/p>\n

              n<\/p>\n

              i<\/p>\n

              n_i<\/p>\n

              <\/span><\/span>n<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u672c\u5f81\u8f7d\u6d41\u5b50\u6d53\u5ea6\u3002<\/p>\n

              6.3 \u5206\u533a\u5bbd\u5ea6\u4e0e\u7269\u7406\u884c\u4e3a<\/h4>\n

              \u7531\u8017\u5c3d\u533a\u5185\u7535\u4e2d\u6027\u6761\u4ef6（P \u533a\u8d1f\u7535\u8377\u603b\u91cf\u7b49\u4e8e N \u533a\u6b63\u7535\u8377\u603b\u91cf）：<\/p>\n

              <\/p>\n

              q<\/p>\n

              N<\/p>\n

              A<\/p>\n

              X<\/p>\n

              p<\/p>\n

              =<\/p>\n

              q<\/p>\n

              N<\/p>\n

              D<\/p>\n

              X<\/p>\n

              n<\/p>\n

              ,<\/p>\n

              q N_A X_p = q N_D X_n, <\/p>\n

              <\/span><\/span>q<\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>q<\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              \u53ef\u5f97\u8017\u5c3d\u5c42\u5728 P \u533a\u548c N \u533a\u7684\u5206\u533a\u5bbd\u5ea6：<\/p>\n

              <\/p>\n

              X<\/p>\n

              p<\/p>\n

              (<\/p>\n

              V<\/p>\n

              )<\/p>\n

              =<\/p>\n

              N<\/p>\n

              D<\/p>\n

              N<\/p>\n

              A<\/p>\n

              +<\/p>\n

              N<\/p>\n

              D<\/p>\n

              ,<\/p>\n

              W<\/p>\n

              (<\/p>\n

              V<\/p>\n

              )<\/p>\n

              ,<\/p>\n

              X<\/p>\n

              n<\/p>\n

              (<\/p>\n

              V<\/p>\n

              )<\/p>\n

              =<\/p>\n

              N<\/p>\n

              A<\/p>\n

              N<\/p>\n

              A<\/p>\n

              +<\/p>\n

              N<\/p>\n

              D<\/p>\n

              ,<\/p>\n

              W<\/p>\n

              (<\/p>\n

              V<\/p>\n

              )<\/p>\n

              .<\/p>\n

              X_p(V) = \\\\frac{N_D}{N_A + N_D} , W(V), \\\\quad X_n(V) = \\\\frac{N_A}{N_A + N_D} , W(V). <\/p>\n

              <\/span><\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>V<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>W<\/span>(<\/span>V<\/span>)<\/span>,<\/span><\/span><\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>V<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>W<\/span>(<\/span>V<\/span>)<\/span>.<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              \u7269\u7406\u89c4\u5f8b\u603b\u7ed3：<\/h5>\n
                \n
              • \u6b63\u5411\u504f\u7f6e（\n

                V<\/p>\n

                ><\/p>\n

                0<\/p>\n

                V > 0<\/p>\n

                <\/span><\/span>V<\/span><\/span>><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>）： \u6709\u6548\u52bf\u5792\u964d\u4f4e（<\/p>\n

                V<\/p>\n

                b<\/p>\n

                i<\/p>\n

                \u2212<\/p>\n

                V<\/p>\n

                <<\/p>\n

                V<\/p>\n

                b<\/p>\n

                i<\/p>\n

                V_{\\\\mathrm{bi}} – V < V_{\\\\mathrm{bi}}<\/p>\n

                <\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>V<\/span><\/span><<\/span><\/span><\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>），\u8017\u5c3d\u5c42\u53d8\u7a84（<\/p>\n

                W<\/p>\n

                W<\/p>\n

                <\/span><\/span>W<\/span><\/span><\/span><\/span><\/span> \u51cf\u5c0f），\u591a\u6570\u8f7d\u6d41\u5b50\u6269\u6563\u589e\u5f3a，\u5f62\u6210\u663e\u8457\u7684\u6b63\u5411\u7535\u6d41\u3002<\/li>\n

              • \u53cd\u5411\u504f\u7f6e（\n

                V<\/p>\n

                <<\/p>\n

                0<\/p>\n

                V < 0<\/p>\n

                <\/span><\/span>V<\/span><\/span><<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>）： \u6709\u6548\u52bf\u5792\u5347\u9ad8（<\/p>\n

                V<\/p>\n

                b<\/p>\n

                i<\/p>\n

                \u2212<\/p>\n

                V<\/p>\n

                ><\/p>\n

                V<\/p>\n

                b<\/p>\n

                i<\/p>\n

                V_{\\\\mathrm{bi}} – V > V_{\\\\mathrm{bi}}<\/p>\n

                <\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>V<\/span><\/span>><\/span><\/span><\/span><\/span>V<\/span><\/span>bi<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>），\u8017\u5c3d\u5c42\u5c55\u5bbd（<\/p>\n

                W<\/p>\n

                W<\/p>\n

                <\/span><\/span>W<\/span><\/span><\/span><\/span><\/span> \u589e\u5927），\u5c11\u6570\u8f7d\u6d41\u5b50\u6f02\u79fb\u4e3b\u5bfc，\u4ea7\u751f\u51e0\u4e4e\u6052\u5b9a\u7684\u53cd\u5411\u9971\u548c\u7535\u6d41\u3002<\/li>\n

              • \u975e\u5bf9\u79f0\u6269\u5c55\u7279\u6027： \u8017\u5c3d\u5c42\u4e3b\u8981\u5411\u4f4e\u63ba\u6742\u4e00\u4fa7\u5ef6\u4f38\u3002\u82e5 \n

                N<\/p>\n

                A<\/p>\n

                \u226b<\/p>\n

                N<\/p>\n

                D<\/p>\n

                N_A \\\\gg N_D<\/p>\n

                <\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u226b<\/span><\/span><\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5219 <\/p>\n

                X<\/p>\n

                n<\/p>\n

                \u226b<\/p>\n

                X<\/p>\n

                p<\/p>\n

                X_n \\\\gg X_p<\/p>\n

                <\/span><\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u226b<\/span><\/span><\/span><\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u603b\u5bbd\u5ea6 <\/p>\n

                W<\/p>\n

                \u2248<\/p>\n

                X<\/p>\n

                n<\/p>\n

                W \\\\approx X_n<\/p>\n

                <\/span><\/span>W<\/span><\/span>\u2248<\/span><\/span><\/span><\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>；\u53cd\u4e4b\u82e5 <\/p>\n

                N<\/p>\n

                D<\/p>\n

                \u226b<\/p>\n

                N<\/p>\n

                A<\/p>\n

                N_D \\\\gg N_A<\/p>\n

                <\/span><\/span>N<\/span><\/span>D<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u226b<\/span><\/span><\/span><\/span>N<\/span><\/span>A<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，\u5219 <\/p>\n

                W<\/p>\n

                \u2248<\/p>\n

                X<\/p>\n

                p<\/p>\n

                W \\\\approx X_p<\/p>\n

                <\/span><\/span>W<\/span><\/span>\u2248<\/span><\/span><\/span><\/span>X<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<\/ul>\n

                \u9644\u5f55：\u79ef\u5206\u8fd0\u7b97\u57fa\u7840<\/h3>\n

                \u672c\u6587\u6240\u6d89\u53ca\u7684\u79ef\u5206\u8fd0\u7b97\u57fa\u4e8e\u4ee5\u4e0b\u57fa\u672c\u516c\u5f0f：img \u56fe 4\u3000\u79ef\u5206\u8fd0\u7b97\u57fa\u7840\u516c\u5f0f<\/p>\n

                \u4e00\u3001\u5e42\u51fd\u6570\u4e0e\u6307\u6570\u51fd\u6570<\/h4>\n\n\u5e8f\u53f7\u516c\u5f0f\u9002\u7528\u6761\u4ef6<\/tr>\n\n\n\n\n
                (1)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                x<\/p>\n

                a<\/p>\n

                \u2009<\/p>\n

                d<\/p>\n

                x<\/p>\n

                =<\/p>\n

                x<\/p>\n

                a<\/p>\n

                +<\/p>\n

                1<\/p>\n

                a<\/p>\n

                +<\/p>\n

                1<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int x^{a}\\\\,\\\\mathrm{d}x = \\\\frac{x^{a+1}}{a+1} + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span>x<\/span><\/span>a<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>+<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>a<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n

                		<\/p>\n

                a<\/p>\n

                \u2260<\/p>\n

                \u2212<\/p>\n

                1<\/p>\n

                a \\\\neq -1<\/p>\n

                <\/span><\/span>a<\/span><\/span><\/span>\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

                (2)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                1<\/p>\n

                x<\/p>\n

                \u2009<\/p>\n

                d<\/p>\n

                x<\/p>\n

                =<\/p>\n

                ln<\/p>\n

                \u2061<\/p>\n

                \u2223<\/p>\n

                x<\/p>\n

                \u2223<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\frac{1}{x}\\\\,\\\\mathrm{d}x = \\\\ln\\\\lvert x\\\\rvert + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>ln<\/span>\u2223<\/span>x<\/span>\u2223<\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n

                		<\/p>\n

                x<\/p>\n

                \u2260<\/p>\n

                0<\/p>\n

                x \\\\neq 0<\/p>\n

                <\/span><\/span>x<\/span><\/span><\/span>\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

                (3)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                a<\/p>\n

                x<\/p>\n

                \u2009<\/p>\n

                d<\/p>\n

                x<\/p>\n

                =<\/p>\n

                a<\/p>\n

                x<\/p>\n

                ln<\/p>\n

                \u2061<\/p>\n

                a<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int a^{x}\\\\,\\\\mathrm{d}x = \\\\frac{a^{x}}{\\\\ln a} + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span>a<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>ln<\/span><\/span>a<\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n

                		<\/p>\n

                a<\/p>\n

                ><\/p>\n

                0<\/p>\n

                ,
                \n \u2005\u200a<\/p>\n

                a<\/p>\n

                \u2260<\/p>\n

                1<\/p>\n

                a > 0,\\\\; a \\\\neq 1<\/p>\n

                <\/span><\/span>a<\/span><\/span>><\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span><\/span>a<\/span><\/span><\/span>\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                \u4e8c\u3001\u4e09\u89d2\u51fd\u6570<\/h4>\n\n\u5e8f\u53f7\u516c\u5f0f<\/tr>\n\n\n\n\n\n\n\n\n\n
                (4)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                sin<\/p>\n

                \u2061<\/p>\n

                x
                \n \u2009<\/p>\n

                d<\/p>\n

                x<\/p>\n

                =<\/p>\n

                \u2212<\/p>\n

                cos<\/p>\n

                \u2061<\/p>\n

                x<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\sin x\\\\,\\\\mathrm{d}x = -\\\\cos x + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span>sin<\/span><\/span>x<\/span><\/span>d<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span>cos<\/span><\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

                (5)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                cos<\/p>\n

                \u2061<\/p>\n

                x
                \n \u2009<\/p>\n

                d<\/p>\n

                x<\/p>\n

                =<\/p>\n

                sin<\/p>\n

                \u2061<\/p>\n

                x<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\cos x\\\\,\\\\mathrm{d}x = \\\\sin x + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span>cos<\/span><\/span>x<\/span><\/span>d<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>sin<\/span><\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

                (6)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                tan<\/p>\n

                \u2061<\/p>\n

                x
                \n \u2009<\/p>\n

                d<\/p>\n

                x<\/p>\n

                =<\/p>\n

                \u2212<\/p>\n

                ln<\/p>\n

                \u2061<\/p>\n

                \u2223<\/p>\n

                cos<\/p>\n

                \u2061<\/p>\n

                x<\/p>\n

                \u2223<\/p>\n

                +<\/p>\n

                C<\/p>\n

                =<\/p>\n

                ln<\/p>\n

                \u2061<\/p>\n

                \u2223<\/p>\n

                sec<\/p>\n

                \u2061<\/p>\n

                x<\/p>\n

                \u2223<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\tan x\\\\,\\\\mathrm{d}x = -\\\\ln\\\\lvert \\\\cos x\\\\rvert + C = \\\\ln\\\\lvert \\\\sec x\\\\rvert + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span>tan<\/span><\/span>x<\/span><\/span>d<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span>ln<\/span>\u2223<\/span>cos<\/span><\/span>x<\/span>\u2223<\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span>=<\/span><\/span><\/span><\/span>ln<\/span>\u2223<\/span>sec<\/span><\/span>x<\/span>\u2223<\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

                (7)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                cot<\/p>\n

                \u2061<\/p>\n

                x
                \n \u2009<\/p>\n

                d<\/p>\n

                x<\/p>\n

                =<\/p>\n

                ln<\/p>\n

                \u2061<\/p>\n

                \u2223<\/p>\n

                sin<\/p>\n

                \u2061<\/p>\n

                x<\/p>\n

                \u2223<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\cot x\\\\,\\\\mathrm{d}x = \\\\ln\\\\lvert \\\\sin x\\\\rvert + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span>cot<\/span><\/span>x<\/span><\/span>d<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>ln<\/span>\u2223<\/span>sin<\/span><\/span>x<\/span>\u2223<\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

                (8)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                sec<\/p>\n

                \u2061<\/p>\n

                x
                \n \u2009<\/p>\n

                d<\/p>\n

                x<\/p>\n

                =<\/p>\n

                ln<\/p>\n

                \u2061<\/p>\n

                \u2223<\/p>\n

                sec<\/p>\n

                \u2061<\/p>\n

                x<\/p>\n

                +<\/p>\n

                tan<\/p>\n

                \u2061<\/p>\n

                x<\/p>\n

                \u2223<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\sec x\\\\,\\\\mathrm{d}x = \\\\ln\\\\lvert \\\\sec x + \\\\tan x\\\\rvert + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span>sec<\/span><\/span>x<\/span><\/span>d<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>ln<\/span>\u2223<\/span>sec<\/span><\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span>tan<\/span><\/span>x<\/span>\u2223<\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

                (9)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                csc<\/p>\n

                \u2061<\/p>\n

                x
                \n \u2009<\/p>\n

                d<\/p>\n

                x<\/p>\n

                =<\/p>\n

                ln<\/p>\n

                \u2061<\/p>\n

                \u2223<\/p>\n

                csc<\/p>\n

                \u2061<\/p>\n

                x<\/p>\n

                \u2212<\/p>\n

                cot<\/p>\n

                \u2061<\/p>\n

                x<\/p>\n

                \u2223<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\csc x\\\\,\\\\mathrm{d}x = \\\\ln\\\\lvert \\\\csc x – \\\\cot x\\\\rvert + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span>csc<\/span><\/span>x<\/span><\/span>d<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>ln<\/span>\u2223<\/span>csc<\/span><\/span>x<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>cot<\/span><\/span>x<\/span>\u2223<\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

                (10)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                sec<\/p>\n

                \u2061<\/p>\n

                2<\/p>\n

                x
                \n \u2009<\/p>\n

                d<\/p>\n

                x<\/p>\n

                =<\/p>\n

                tan<\/p>\n

                \u2061<\/p>\n

                x<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\sec^{2} x\\\\,\\\\mathrm{d}x = \\\\tan x + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span>sec<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>d<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>tan<\/span><\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

                (11)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                csc<\/p>\n

                \u2061<\/p>\n

                2<\/p>\n

                x
                \n \u2009<\/p>\n

                d<\/p>\n

                x<\/p>\n

                =<\/p>\n

                \u2212<\/p>\n

                cot<\/p>\n

                \u2061<\/p>\n

                x<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\csc^{2} x\\\\,\\\\mathrm{d}x = -\\\\cot x + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span>csc<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>d<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span>cot<\/span><\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                \u4e09\u3001\u53cd\u4e09\u89d2\u51fd\u6570\u4e0e\u4ee3\u6570\u51fd\u6570<\/h4>\n\n\u5e8f\u53f7\u516c\u5f0f<\/tr>\n\n\n\n\n\n\n\n
                (12)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                d<\/p>\n

                x<\/p>\n

                1<\/p>\n

                +<\/p>\n

                x<\/p>\n

                2<\/p>\n

                =<\/p>\n

                arctan<\/p>\n

                \u2061<\/p>\n

                x<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\frac{\\\\mathrm{d}x}{1+x^{2}} = \\\\arctan x + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span><\/span><\/span>1<\/span><\/span>+<\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>arctan<\/span><\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

                (13)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                d<\/p>\n

                x<\/p>\n

                x<\/p>\n

                2<\/p>\n

                +<\/p>\n

                a<\/p>\n

                2<\/p>\n

                =<\/p>\n

                1<\/p>\n

                a<\/p>\n

                arctan<\/p>\n

                \u2061<\/p>\n

                x<\/p>\n

                a<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\frac{\\\\mathrm{d}x}{x^{2}+a^{2}} = \\\\frac{1}{a}\\\\arctan\\\\frac{x}{a} + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span><\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>arctan<\/span><\/span><\/span><\/span>a<\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

                (14)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                d<\/p>\n

                x<\/p>\n

                x<\/p>\n

                2<\/p>\n

                \u2212<\/p>\n

                a<\/p>\n

                2<\/p>\n

                =<\/p>\n

                1<\/p>\n

                2<\/p>\n

                a<\/p>\n

                ln<\/p>\n

                \u2061<\/p>\n

                \u2223<\/p>\n

                x<\/p>\n

                \u2212<\/p>\n

                a<\/p>\n

                x<\/p>\n

                +<\/p>\n

                a<\/p>\n

                \u2223<\/p>\n

                +<\/p>\n

                C<\/p>\n

                =<\/p>\n

                1<\/p>\n

                2<\/p>\n

                a<\/p>\n

                ln<\/p>\n

                \u2061<\/p>\n

                \u2223<\/p>\n

                a<\/p>\n

                \u2212<\/p>\n

                x<\/p>\n

                a<\/p>\n

                +<\/p>\n

                x<\/p>\n

                \u2223<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\frac{\\\\mathrm{d}x}{x^{2}-a^{2}} = \\\\frac{1}{2a}\\\\ln\\\\left\\\\lvert \\\\frac{x-a}{x+a} \\\\right\\\\rvert + C = \\\\frac{1}{2a}\\\\ln\\\\left\\\\lvert \\\\frac{a-x}{a+x} \\\\right\\\\rvert + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span><\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>a<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>ln<\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>+<\/span><\/span>a<\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>\u2212<\/span><\/span>a<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>a<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>ln<\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>+<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>\u2212<\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

                (15)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                d<\/p>\n

                x<\/p>\n

                a<\/p>\n

                2<\/p>\n

                \u2212<\/p>\n

                x<\/p>\n

                2<\/p>\n

                =<\/p>\n

                1<\/p>\n

                2<\/p>\n

                a<\/p>\n

                ln<\/p>\n

                \u2061<\/p>\n

                \u2223<\/p>\n

                a<\/p>\n

                +<\/p>\n

                x<\/p>\n

                a<\/p>\n

                \u2212<\/p>\n

                x<\/p>\n

                \u2223<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\frac{\\\\mathrm{d}x}{a^{2}-x^{2}} = \\\\frac{1}{2a}\\\\ln\\\\left\\\\lvert \\\\frac{a+x}{a-x} \\\\right\\\\rvert + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span><\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span>a<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>ln<\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>\u2212<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>+<\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

                (16)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                d<\/p>\n

                x<\/p>\n

                1<\/p>\n

                \u2212<\/p>\n

                x<\/p>\n

                2<\/p>\n

                =<\/p>\n

                arcsin<\/p>\n

                \u2061<\/p>\n

                x<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\frac{\\\\mathrm{d}x}{\\\\sqrt{1-x^{2}}} = \\\\arcsin x + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span><\/span><\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>arcsin<\/span><\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

                (17)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                d<\/p>\n

                x<\/p>\n

                a<\/p>\n

                2<\/p>\n

                \u2212<\/p>\n

                x<\/p>\n

                2<\/p>\n

                =<\/p>\n

                arcsin<\/p>\n

                \u2061<\/p>\n

                x<\/p>\n

                a<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\frac{\\\\mathrm{d}x}{\\\\sqrt{a^{2}-x^{2}}} = \\\\arcsin\\\\frac{x}{a} + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>arcsin<\/span><\/span><\/span><\/span>a<\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                \u56db\u3001\u542b\u6839\u5f0f\u7684\u79ef\u5206（\u53cc\u66f2\/\u5bf9\u6570\u5f62\u5f0f）<\/h4>\n\n\u5e8f\u53f7\u516c\u5f0f<\/tr>\n\n\n\n\n
                (18)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                d<\/p>\n

                x<\/p>\n

                x<\/p>\n

                2<\/p>\n

                \u00b1<\/p>\n

                a<\/p>\n

                2<\/p>\n

                =<\/p>\n

                ln<\/p>\n

                \u2061<\/p>\n

                \u2223<\/p>\n

                x<\/p>\n

                +<\/p>\n

                x<\/p>\n

                2<\/p>\n

                \u00b1<\/p>\n

                a<\/p>\n

                2<\/p>\n

                \u2223<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\frac{\\\\mathrm{d}x}{\\\\sqrt{x^{2}\\\\pm a^{2}}} = \\\\ln\\\\left\\\\lvert x+\\\\sqrt{x^{2}\\\\pm a^{2}}\\\\right\\\\rvert + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00b1<\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>ln<\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>+<\/span><\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00b1<\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

                (19)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                a<\/p>\n

                2<\/p>\n

                \u2212<\/p>\n

                x<\/p>\n

                2<\/p>\n

                \u2009<\/p>\n

                d<\/p>\n

                x<\/p>\n

                =<\/p>\n

                x<\/p>\n

                2<\/p>\n

                a<\/p>\n

                2<\/p>\n

                \u2212<\/p>\n

                x<\/p>\n

                2<\/p>\n

                +<\/p>\n

                a<\/p>\n

                2<\/p>\n

                2<\/p>\n

                arcsin<\/p>\n

                \u2061<\/p>\n

                x<\/p>\n

                a<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\sqrt{a^{2}-x^{2}}\\\\,\\\\mathrm{d}x = \\\\frac{x}{2}\\\\sqrt{a^{2}-x^{2}} + \\\\frac{a^{2}}{2}\\\\arcsin\\\\frac{x}{a} + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>arcsin<\/span><\/span><\/span><\/span>a<\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n

                (20)<\/td>\n<\/p>\n

                \u222b<\/p>\n

                x<\/p>\n

                2<\/p>\n

                \u00b1<\/p>\n

                a<\/p>\n

                2<\/p>\n

                \u2009<\/p>\n

                d<\/p>\n

                x<\/p>\n

                =<\/p>\n

                x<\/p>\n

                2<\/p>\n

                x<\/p>\n

                2<\/p>\n

                \u00b1<\/p>\n

                a<\/p>\n

                2<\/p>\n

                \u00b1<\/p>\n

                a<\/p>\n

                2<\/p>\n

                2<\/p>\n

                ln<\/p>\n

                \u2061<\/p>\n

                \u2223<\/p>\n

                x<\/p>\n

                +<\/p>\n

                x<\/p>\n

                2<\/p>\n

                \u00b1<\/p>\n

                a<\/p>\n

                2<\/p>\n

                \u2223<\/p>\n

                +<\/p>\n

                C<\/p>\n

                \\\\displaystyle \\\\int \\\\sqrt{x^{2}\\\\pm a^{2}}\\\\,\\\\mathrm{d}x = \\\\frac{x}{2}\\\\sqrt{x^{2}\\\\pm a^{2}} \\\\pm \\\\frac{a^{2}}{2}\\\\ln\\\\left\\\\lvert x+\\\\sqrt{x^{2}\\\\pm a^{2}}\\\\right\\\\rvert + C<\/p>\n

                <\/span><\/span>\u222b<\/span><\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00b1<\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00b1<\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00b1<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>ln<\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>+<\/span><\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u00b1<\/span><\/span>a<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                <\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                \n

                PN \u7ed3\u7684\u7535\u5bb9\u6548\u5e94\u2014\u2014\u52bf\u5792\u7535\u5bb9\u548c\u6269\u6563\u7535\u5bb9<\/h2>\n

                \u5c0f\u5c0f\u77f3\u7070 \u539f\u521b 2024-07-17 11:22:52<\/p>\n

                PN \u7ed3\u5728\u7279\u5b9a\u6761\u4ef6\u4e0b\u5448\u73b0\u7535\u5bb9\u6548\u5e94，\u6839\u636e\u7535\u5bb9\u6548\u5e94\u7684\u4ea7\u751f\u673a\u7406，\u53ef\u5c06 PN \u7ed3\u7684\u7ed3\u7535\u5bb9\u5206\u4e3a\u52bf\u5792\u7535\u5bb9\u4e0e\u6269\u6563\u7535\u5bb9\u4e24\u7c7b，\u7ed3\u7535\u5bb9\u4e3a\u4e24\u7c7b\u7535\u5bb9\u7684\u4ee3\u6570\u548c\u3002<\/p>\n

                1 \u52bf\u5792\u7535\u5bb9<\/h3>\n

                \u5f53 PN \u7ed3\u7684\u5916\u52a0\u53cd\u5411\u504f\u7f6e\u7535\u538b\u53d1\u751f\u53d8\u5316\u65f6，\u8017\u5c3d\u5c42\u7684\u5bbd\u5ea6\u5c06\u968f\u4e4b\u6539\u53d8，\u8017\u5c3d\u5c42\u5185\u7684\u7a7a\u95f4\u7535\u8377\u6570\u91cf\u968f\u5916\u52a0\u7535\u538b\u7684\u53d8\u5316\u800c\u589e\u51cf，\u8be5\u7269\u7406\u8fc7\u7a0b\u4e0e\u7535\u5bb9\u5668\u7684\u5145\u3001\u653e\u7535\u8fc7\u7a0b\u7b49\u6548，\u7531\u6b64\u4ea7\u751f\u7684\u7535\u5bb9\u6548\u5e94\u79f0\u4e3a\u52bf\u5792\u7535\u5bb9，\u8bb0\u4e3a <\/p>\n

                C<\/p>\n

                b<\/p>\n

                C_b<\/p>\n

                <\/span><\/span>C<\/span><\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

                \u52bf\u5792\u7535\u5bb9\u4e3a\u975e\u7ebf\u6027\u7535\u5bb9，\u5176\u5bb9\u503c\u4e0e PN \u7ed3\u7684\u7ed3\u9762\u79ef\u3001\u8017\u5c3d\u5c42\u5bbd\u5ea6\u3001\u534a\u5bfc\u4f53\u7684\u4ecb\u7535\u5e38\u6570\u53ca\u5916\u52a0\u504f\u7f6e\u7535\u538b\u76f8\u5173\u3002\u5bf9\u4e8e\u5236\u5907\u5b8c\u6210\u7684 PN \u7ed3，\u52bf\u5792\u7535\u5bb9\u4e0e\u5916\u52a0\u7535\u538b <\/p>\n

                u<\/p>\n

                u<\/p>\n

                <\/span><\/span>u<\/span><\/span><\/span><\/span><\/span> \u7684\u5173\u7cfb\u5177\u6709\u660e\u786e\u7684\u53d8\u5316\u89c4\u5f8b\u3002\u5229\u7528 PN \u7ed3\u53cd\u5411\u504f\u7f6e\u65f6\u52bf\u5792\u7535\u5bb9\u968f\u5916\u52a0\u7535\u538b\u53d8\u5316\u7684\u7279\u6027，\u53ef\u5236\u5907\u5404\u7c7b\u53d8\u5bb9\u4e8c\u6781\u7ba1\u3002 \"img\"<\/p>\n

                2 \u6269\u6563\u7535\u5bb9<\/h3>\n

                \u70ed\u5e73\u8861\u72b6\u6001\u4e0b，PN \u7ed3\u5185\u7684\u5c11\u5b50\u6d53\u5ea6\u4e3a\u70ed\u5e73\u8861\u5c11\u5b50\u6d53\u5ea6；\u5f53 PN \u7ed3\u65bd\u52a0\u6b63\u5411\u504f\u7f6e\u7535\u538b\u65f6，\u4ece P \u533a\u6269\u6563\u81f3 N \u533a\u7684\u7a7a\u7a74\u4e0e\u4ece N \u533a\u6269\u6563\u81f3 P \u533a\u7684\u81ea\u7531\u7535\u5b50\u4e3a\u975e\u5e73\u8861\u5c11\u5b50\u3002<\/p>\n

                \u5f53\u5916\u52a0\u6b63\u5411\u504f\u7f6e\u7535\u538b\u6052\u5b9a，\u8017\u5c3d\u5c42\u4ea4\u754c\u9762\u9644\u8fd1\u7684\u975e\u5e73\u8861\u5c11\u5b50\u6d53\u5ea6\u6700\u9ad8，\u968f\u8fdc\u79bb\u4ea4\u754c\u9762，\u975e\u5e73\u8861\u5c11\u5b50\u6d53\u5ea6\u9010\u6e10\u964d\u4f4e\u5e76\u8d8b\u4e8e 0，\u5f62\u6210\u6cbf\u5750\u6807\u65b9\u5411\u7684\u6d53\u5ea6\u68af\u5ea6，\u975e\u5e73\u8861\u5c11\u5b50\u7684\u6269\u6563\u8fd0\u52a8\u5f62\u6210\u6269\u6563\u7535\u6d41\u3002\u5f53\u5916\u52a0\u6b63\u5411\u504f\u7f6e\u7535\u538b\u589e\u5927\u65f6，\u975e\u5e73\u8861\u5c11\u5b50\u7684\u6d53\u5ea6\u4e0e\u6d53\u5ea6\u68af\u5ea6\u5747\u589e\u5927，\u5b8f\u89c2\u8868\u73b0\u4e3a\u6b63\u5411\u7535\u6d41（\u6269\u6563\u7535\u6d41）\u589e\u5927；\u5f53\u5916\u52a0\u6b63\u5411\u504f\u7f6e\u7535\u538b\u51cf\u5c0f\u65f6，\u4e0a\u8ff0\u7269\u7406\u8fc7\u7a0b\u53cd\u5411\u8fdb\u884c\u3002<\/p>\n

                \"img\"<\/p>\n

                \u4e0d\u540c\u6b63\u5411\u504f\u7f6e\u7535\u538b\u4e0b P \u533a\u5c11\u5b50\u7684\u6d53\u5ea6\u5206\u5e03\u66f2\u7ebf\u4e2d，\u66f2\u7ebf\u4e0e <\/p>\n

                n<\/p>\n

                p<\/p>\n

                =<\/p>\n

                n<\/p>\n

                p<\/p>\n

                0<\/p>\n

                n_p=n_{p0}<\/p>\n

                <\/span><\/span>n<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>n<\/span><\/span>p<\/span>0<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u6c34\u5e73\u7ebf\u95f4\u7684\u9762\u79ef\u4ee3\u8868\u6269\u6563\u533a\u57df\u5185\u975e\u5e73\u8861\u5c11\u5b50\u7684\u603b\u6570\u91cf\u3002\u5f53\u5916\u52a0\u7535\u538b\u589e\u5927\u65f6，\u975e\u5e73\u8861\u5c11\u5b50\u7684\u6570\u91cf\u589e\u591a；\u5f53\u5916\u52a0\u7535\u538b\u51cf\u5c0f\u65f6，\u975e\u5e73\u8861\u5c11\u5b50\u7684\u6570\u91cf\u51cf\u5c11\u3002\u6269\u6563\u533a\u57df\u5185\u975e\u5e73\u8861\u5c11\u5b50\u7684\u7535\u8377\u79ef\u7d2f\u4e0e\u91ca\u653e\u8fc7\u7a0b\u4e0e\u7535\u5bb9\u5668\u7684\u5145\u3001\u653e\u7535\u8fc7\u7a0b\u7b49\u6548，\u7531\u6b64\u4ea7\u751f\u7684\u7535\u5bb9\u6548\u5e94\u79f0\u4e3a\u6269\u6563\u7535\u5bb9，\u8bb0\u4e3a <\/p>\n

                C<\/p>\n

                d<\/p>\n

                C_d<\/p>\n

                <\/span><\/span>C<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

                \u6269\u6563\u7535\u5bb9\u540c\u6837\u4e3a\u975e\u7ebf\u6027\u7535\u5bb9，\u5176\u5bb9\u503c\u4e0e\u6d41\u8fc7 PN \u7ed3\u7684\u6b63\u5411\u7535\u6d41 <\/p>\n

                i<\/p>\n

                i<\/p>\n

                <\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>\u3001\u6e29\u5ea6\u7684\u7535\u538b\u5f53\u91cf <\/p>\n

                U<\/p>\n

                T<\/p>\n

                U_T<\/p>\n

                <\/span><\/span>U<\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u53ca\u975e\u5e73\u8861\u5c11\u5b50\u7684\u5bff\u547d <\/p>\n

                \u03c4<\/p>\n

                \\\\tau<\/p>\n

                <\/span><\/span>\u03c4<\/span><\/span><\/span><\/span><\/span> \u76f8\u5173\u3002\u6b63\u5411\u7535\u6d41 <\/p>\n

                i<\/p>\n

                i<\/p>\n

                <\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u8d8a\u5927\u3001\u975e\u5e73\u8861\u5c11\u5b50\u5bff\u547d <\/p>\n

                \u03c4<\/p>\n

                \\\\tau<\/p>\n

                <\/span><\/span>\u03c4<\/span><\/span><\/span><\/span><\/span> \u8d8a\u957f\u3001\u6e29\u5ea6\u7684\u7535\u538b\u5f53\u91cf <\/p>\n

                U<\/p>\n

                T<\/p>\n

                U_T<\/p>\n

                <\/span><\/span>U<\/span><\/span>T<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u8d8a\u5c0f，\u6269\u6563\u7535\u5bb9 <\/p>\n

                C<\/p>\n

                d<\/p>\n

                C_d<\/p>\n

                <\/span><\/span>C<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u7684\u5bb9\u503c\u8d8a\u5927\u3002<\/p>\n

                PN \u7ed3\u7684\u7ed3\u7535\u5bb9 <\/p>\n

                C<\/p>\n

                j<\/p>\n

                C_j<\/p>\n

                <\/span><\/span>C<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e3a\u52bf\u5792\u7535\u5bb9 <\/p>\n

                C<\/p>\n

                b<\/p>\n

                C_b<\/p>\n

                <\/span><\/span>C<\/span><\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e0e\u6269\u6563\u7535\u5bb9 <\/p>\n

                C<\/p>\n

                d<\/p>\n

                C_d<\/p>\n

                <\/span><\/span>C<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4e4b\u548c，\u5373： <\/p>\n

                C<\/p>\n

                j<\/p>\n

                =<\/p>\n

                C<\/p>\n

                b<\/p>\n

                +<\/p>\n

                C<\/p>\n

                d<\/p>\n

                C_j=C_b+C_d<\/p>\n

                <\/span><\/span>C<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>C<\/span><\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u52bf\u5792\u7535\u5bb9\u4e0e\u6269\u6563\u7535\u5bb9\u7684\u5bb9\u503c\u5747\u8f83\u5c0f，\u7ed3\u9762\u79ef\u8f83\u5c0f\u7684 PN \u7ed3\u7ed3\u7535\u5bb9\u7ea6\u4e3a <\/p>\n

                1<\/p>\n

                \u00a0pF<\/p>\n

                1\\\\ \\\\text{pF}<\/p>\n

                <\/span><\/span>1<\/span>\u00a0<\/span>pF<\/span><\/span><\/span><\/span><\/span><\/span>，\u7ed3\u9762\u79ef\u8f83\u5927\u7684 PN \u7ed3\u7ed3\u7535\u5bb9\u4e3a\u51e0\u5341\u81f3\u51e0\u767e\u76ae\u6cd5\u3002\u5bf9\u4e8e\u4f4e\u9891\u4fe1\u53f7，\u7ed3\u7535\u5bb9\u5448\u73b0\u7684\u5bb9\u6297\u8f83\u5927，\u5176\u7535\u5bb9\u6548\u5e94\u53ef\u5ffd\u7565；\u4ec5\u5f53\u4fe1\u53f7\u9891\u7387\u8f83\u9ad8\u65f6，\u7ed3\u7535\u5bb9\u7684\u7535\u5bb9\u6548\u5e94\u624d\u9700\u8003\u8651\u3002<\/p>\n

                \n

                via:<\/h2>\n
                  \n
                • PN \u7ed3\u7684\u7535\u5bb9\u6548\u5e94_pn \u7ed3\u7535\u5bb9-CSDN \u535a\u5ba2 https:\/\/blog.csdn.net\/ethanjiangsq\/article\/details\/104272426<\/li>\n
                • \u6a21\u7535\u57fa\u7840：\u4e00\u6587\u5f7b\u5e95\u641e\u61c2\u4e8c\u6781\u7ba1\u51fb\u7a7f\u548c\u7ed3\u7535\u5bb9-CSDN\u535a\u5ba2 https:\/\/blog.csdn.net\/hhhbdbfb\/article\/details\/129287655<\/li>\n
                • \u7535\u573a\u5f3a\u5ea6，\u7535\u52bf\u4ee5\u53ca PN \u7ed3\u8017\u5c3d\u5c42\u5bbd\u5ea6_pn \u7ed3\u8017\u5c3d\u533a\u5bbd\u5ea6\u8ba1\u7b97\u516c\u5f0f-CSDN \u535a\u5ba2 https:\/\/blog.csdn.net\/weixin_44268068\/article\/details\/130509763<\/li>\n
                • PN \u7ed3\u7684\u7535\u5bb9\u6548\u5e94\u2014\u2014\u52bf\u5792\u7535\u5bb9\u548c\u6269\u6563\u7535\u5bb9-CSDN \u535a\u5ba2 https:\/\/blog.csdn.net\/weixin_65575911\/article\/details\/140485773<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

                  \u6ce8：\u672c\u6587\u4e3a \u201cPN \u7ed3\u201d \u76f8\u5173\u5408\u8f91\u3002 \u56fe\u7247\u6e05\u6670\u5ea6\u53d7\u5f15\u6587\u539f\u56fe\u6240\u9650\u3002 \u7565\u4f5c\u91cd\u6392，\u672a\u6574\u7406\u53bb\u91cd\u3002 \u5982\u6709\u5185\u5bb9\u5f02\u5e38，\u8bf7\u770b\u539f\u6587\u3002 PN \u7ed3\u7684\u7535\u5bb9\u6548\u5e94
                  \nEthan Jiang \u539f\u521b 2020-02-12 11:56:17
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