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Band Diagram ｜ 能带图",[241,517,518],{},[247,519],{"alt":520,"src":521},"RY3sbUaWhoVIo3xLPqycfvYMnzh.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-06.png",[523,524,525],"ol",{},[526,527,528],"li",{},"Ef is constant at equilibrium and Ec,Ev are known relative to Ef",[295,530,531,610,1316],{},[241,532,533,534,609],{},"热平衡时费米能级 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必须是常数",[241,611,612,1315],{},[316,613,615,755],{"className":614},[319],[316,616,618],{"className":617},[323],[325,619,620],{"xmlns":327},[329,621,622,752],{},[332,623,624,627,631,634,637,639,647,691,694,697,699,701,703,705,707,714],{},[338,625,626],{},"n",[350,628,630],{"stretchy":629},"false","(",[338,632,633],{},"x",[350,635,636],{"stretchy":629},")",[350,638,352],{},[335,640,641,644],{},[338,642,643],{},"N",[338,645,646],{},"c",[648,649,650,653],"msup",{},[338,651,652],{},"e",[332,654,655,658],{},[350,656,657],{},"−",[659,660,661,683],"mfrac",{},[332,662,663,669,671,673,675,677],{},[335,664,665,667],{},[338,666,550],{},[338,668,646],{},[350,670,630],{"stretchy":629},[338,672,633],{},[350,674,636],{"stretchy":629},[350,676,657],{},[335,678,679,681],{},[338,680,550],{},[338,682,553],{},[332,684,685,688],{},[338,686,687],{},"k",[338,689,690],{},"T",[350,692,693],{"separator":373},",",[451,695],{"width":696},"1em",[338,698,241],{},[350,700,630],{"stretchy":629},[338,702,633],{},[350,704,636],{"stretchy":629},[350,706,352],{},[335,708,709,711],{},[338,710,643],{},[338,712,713],{},"v",[648,715,716,718],{},[338,717,652],{},[332,719,720,722],{},[350,721,657],{},[659,723,724,746],{},[332,725,726,732,734,740,742,744],{},[335,727,728,730],{},[338,729,550],{},[338,731,553],{},[350,733,657],{},[335,735,736,738],{},[338,737,550],{},[338,739,713],{},[350,741,630],{"stretchy":629},[338,743,633],{},[350,745,636],{"stretchy":629},[332,747,748,750],{},[338,749,687],{},[338,751,690],{},[365,753,754],{"encoding":367},"n(x) = N_c e^{-\\frac{E_c(x) - E_F}{kT}}, \\quad p(x) = N_v e^{-\\frac{E_F - E_v(x)}{kT}}",[316,756,758,788,1081],{"className":757,"ariaHidden":373},[372],[316,759,761,765,768,772,775,779,782,785],{"className":760},[377],[316,762],{"className":763,"style":764},[381],"height:1em;vertical-align:-0.25em;",[316,766,626],{"className":767},[386,390],[316,769,630],{"className":770},[771],"mopen",[316,773,633],{"className":774},[386,390],[316,776,636],{"className":777},[778],"mclose",[316,780],{"className":781,"style":452},[451],[316,783,352],{"className":784},[456],[316,786],{"className":787,"style":452},[451],[316,789,791,795,838,1048,1052,1056,1060,1063,1066,1069,1072,1075,1078],{"className":790},[377],[316,792],{"className":793,"style":794},[381],"height:1.3837em;vertical-align:-0.25em;",[316,796,798,802],{"className":797},[386],[316,799,643],{"className":800,"style":801},[386,390],"margin-right:0.109em;",[316,803,805],{"className":804},[394],[316,806,808,830],{"className":807},[398,399],[316,809,811,827],{"className":810},[403],[316,812,815],{"className":813,"style":814},[407],"height:0.1514em;",[316,816,818,821],{"style":817},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[316,819],{"className":820,"style":416},[415],[316,822,824],{"className":823},[420,421,422,423],[316,825,646],{"className":826},[386,390,423],[316,828,438],{"className":829},[437],[316,831,833],{"className":832},[403],[316,834,836],{"className":835,"style":445},[407],[316,837],{},[316,839,841,844],{"className":840},[386],[316,842,652],{"className":843},[386,390],[316,845,847],{"className":846},[394],[316,848,850],{"className":849},[398],[316,851,853],{"className":852},[403],[316,854,857],{"className":855,"style":856},[407],"height:1.1337em;",[316,858,860,864],{"style":859},"top:-3.363em;margin-right:0.05em;",[316,861],{"className":862,"style":863},[415],"height:3em;",[316,865,867],{"className":866},[420,421,422,423],[316,868,870,873],{"className":869},[386,423],[316,871,657],{"className":872},[386,423],[316,874,876,882,1045],{"className":875},[386,423],[316,877],{"className":878},[771,879,420,880,881],"nulldelimiter","reset-size3","size6",[316,883,885],{"className":884},[659],[316,886,888,1036],{"className":887},[398,399],[316,889,891,1033],{"className":890},[403],[316,892,895,915,926],{"className":893,"style":894},[407],"height:1.101em;",[316,896,898,901],{"style":897},"top:-2.656em;",[316,899],{"className":900,"style":863},[415],[316,902,905],{"className":903},[420,880,904,423],"size1",[316,906,908,912],{"className":907},[386,423],[316,909,687],{"className":910,"style":911},[386,390,423],"margin-right:0.0315em;",[316,913,690],{"className":914,"style":597},[386,390,423],[316,916,918,921],{"style":917},"top:-3.2255em;",[316,919],{"className":920,"style":863},[415],[316,922],{"className":923,"style":925},[924,423],"frac-line","border-bottom-width:0.049em;",[316,927,929,932],{"style":928},"top:-3.5653em;",[316,930],{"className":931,"style":863},[415],[316,933,935],{"className":934},[420,880,904,423],[316,936,938,979,982,985,988,992],{"className":937},[386,423],[316,939,941,944],{"className":940},[386,423],[316,942,550],{"className":943,"style":430},[386,390,423],[316,945,947],{"className":946},[394],[316,948,950,970],{"className":949},[398,399],[316,951,953,967],{"className":952},[403],[316,954,957],{"className":955,"style":956},[407],"height:0.2306em;",[316,958,960,964],{"style":959},"top:-2.3em;margin-left:-0.0576em;margin-right:0.1em;",[316,961],{"className":962,"style":963},[415],"height:2.5em;",[316,965,646],{"className":966},[386,390,423],[316,968,438],{"className":969},[437],[316,971,973],{"className":972},[403],[316,974,977],{"className":975,"style":976},[407],"height:0.2em;",[316,978],{},[316,980,630],{"className":981},[771,423],[316,983,633],{"className":984},[386,390,423],[316,986,636],{"className":987},[778,423],[316,989,657],{"className":990},[991,423],"mbin",[316,993,995,998],{"className":994},[386,423],[316,996,550],{"className":997,"style":430},[386,390,423],[316,999,1001],{"className":1000},[394],[316,1002,1004,1024],{"className":1003},[398,399],[316,1005,1007,1021],{"className":1006},[403],[316,1008,1011],{"className":1009,"style":1010},[407],"height:0.3448em;",[316,1012,1014,1018],{"style":1013},"top:-2.3448em;margin-left:-0.0576em;margin-right:0.1em;",[316,1015],{"className":1016,"style":1017},[415],"height:2.6833em;",[316,1019,553],{"className":1020,"style":597},[386,390,423],[316,1022,438],{"className":1023},[437],[316,1025,1027],{"className":1026},[403],[316,1028,1031],{"className":1029,"style":1030},[407],"height:0.3385em;",[316,1032],{},[316,1034,438],{"className":1035},[437],[316,1037,1039],{"className":1038},[403],[316,1040,1043],{"className":1041,"style":1042},[407],"height:0.344em;",[316,1044],{},[316,1046],{"className":1047},[778,879,420,880,881],[316,1049,693],{"className":1050},[1051],"mpunct",[316,1053],{"className":1054,"style":1055},[451],"margin-right:1em;",[316,1057],{"className":1058,"style":1059},[451],"margin-right:0.1667em;",[316,1061,241],{"className":1062},[386,390],[316,1064,630],{"className":1065},[771],[316,1067,633],{"className":1068},[386,390],[316,1070,636],{"className":1071},[778],[316,1073],{"className":1074,"style":452},[451],[316,1076,352],{"className":1077},[456],[316,1079],{"className":1080,"style":452},[451],[316,1082,1084,1088,1129],{"className":1083},[377],[316,1085],{"className":1086,"style":1087},[381],"height:1.2837em;vertical-align:-0.15em;",[316,1089,1091,1094],{"className":1090},[386],[316,1092,643],{"className":1093,"style":801},[386,390],[316,1095,1097],{"className":1096},[394],[316,1098,1100,1121],{"className":1099},[398,399],[316,1101,1103,1118],{"className":1102},[403],[316,1104,1106],{"className":1105,"style":814},[407],[316,1107,1108,1111],{"style":817},[316,1109],{"className":1110,"style":416},[415],[316,1112,1114],{"className":1113},[420,421,422,423],[316,1115,713],{"className":1116,"style":1117},[386,390,423],"margin-right:0.0359em;",[316,1119,438],{"className":1120},[437],[316,1122,1124],{"className":1123},[403],[316,1125,1127],{"className":1126,"style":445},[407],[316,1128],{},[316,1130,1132,1135],{"className":1131},[386],[316,1133,652],{"className":1134},[386,390],[316,1136,1138],{"className":1137},[394],[316,1139,1141],{"className":1140},[398],[316,1142,1144],{"className":1143},[403],[316,1145,1147],{"className":1146,"style":856},[407],[316,1148,1149,1152],{"style":859},[316,1150],{"className":1151,"style":863},[415],[316,1153,1155],{"className":1154},[420,421,422,423],[316,1156,1158,1161],{"className":1157},[386,423],[316,1159,657],{"className":1160},[386,423],[316,1162,1164,1167,1312],{"className":1163},[386,423],[316,1165],{"className":1166},[771,879,420,880,881],[316,1168,1170],{"className":1169},[659],[316,1171,1173,1304],{"className":1172},[398,399],[316,1174,1176,1301],{"className":1175},[403],[316,1177,1179,1196,1204],{"className":1178,"style":894},[407],[316,1180,1181,1184],{"style":897},[316,1182],{"className":1183,"style":863},[415],[316,1185,1187],{"className":1186},[420,880,904,423],[316,1188,1190,1193],{"className":1189},[386,423],[316,1191,687],{"className":1192,"style":911},[386,390,423],[316,1194,690],{"className":1195,"style":597},[386,390,423],[316,1197,1198,1201],{"style":917},[316,1199],{"className":1200,"style":863},[415],[316,1202],{"className":1203,"style":925},[924,423],[316,1205,1206,1209],{"style":928},[316,1207],{"className":1208,"style":863},[415],[316,1210,1212],{"className":1211},[420,880,904,423],[316,1213,1215,1252,1255,1292,1295,1298],{"className":1214},[386,423],[316,1216,1218,1221],{"className":1217},[386,423],[316,1219,550],{"className":1220,"style":430},[386,390,423],[316,1222,1224],{"className":1223},[394],[316,1225,1227,1244],{"className":1226},[398,399],[316,1228,1230,1241],{"className":1229},[403],[316,1231,1233],{"className":1232,"style":1010},[407],[316,1234,1235,1238],{"style":1013},[316,1236],{"className":1237,"style":1017},[415],[316,1239,553],{"className":1240,"style":597},[386,390,423],[316,1242,438],{"className":1243},[437],[316,1245,1247],{"className":1246},[403],[316,1248,1250],{"className":1249,"style":1030},[407],[316,1251],{},[316,1253,657],{"className":1254},[991,423],[316,1256,1258,1261],{"className":1257},[386,423],[316,1259,550],{"className":1260,"style":430},[386,390,423],[316,1262,1264],{"className":1263},[394],[316,1265,1267,1284],{"className":1266},[398,399],[316,1268,1270,1281],{"className":1269},[403],[316,1271,1273],{"className":1272,"style":956},[407],[316,1274,1275,1278],{"style":959},[316,1276],{"className":1277,"style":963},[415],[316,1279,713],{"className":1280,"style":1117},[386,390,423],[316,1282,438],{"className":1283},[437],[316,1285,1287],{"className":1286},[403],[316,1288,1290],{"className":1289,"style":976},[407],[316,1291],{},[316,1293,630],{"className":1294},[771,423],[316,1296,633],{"className":1297},[386,390,423],[316,1299,636],{"className":1300},[778,423],[316,1302,438],{"className":1303},[437],[316,1305,1307],{"className":1306},[403],[316,1308,1310],{"className":1309,"style":1042},[407],[316,1311],{},[316,1313],{"className":1314},[778,879,420,880,881],"，由玻尔兹曼近似就可以算出不同位置x的电子or空穴浓度",[241,1317,1318,1319,1322,1323,1322,1393,1322,1396,1465,1322,1468,1322,1538],{},"所以",[291,1320,1321],{},"哪边"," ",[316,1324,1326,1344],{"className":1325},[319],[316,1327,1329],{"className":1328},[323],[325,1330,1331],{"xmlns":327},[329,1332,1333,1341],{},[332,1334,1335],{},[335,1336,1337,1339],{},[338,1338,550],{},[338,1340,646],{},[365,1342,1343],{"encoding":367},"E_c",[316,1345,1347],{"className":1346,"ariaHidden":373},[372],[316,1348,1350,1353],{"className":1349},[377],[316,1351],{"className":1352,"style":566},[381],[316,1354,1356,1359],{"className":1355},[386],[316,1357,550],{"className":1358,"style":430},[386,390],[316,1360,1362],{"className":1361},[394],[316,1363,1365,1385],{"className":1364},[398,399],[316,1366,1368,1382],{"className":1367},[403],[316,1369,1371],{"className":1370,"style":814},[407],[316,1372,1373,1376],{"style":587},[316,1374],{"className":1375,"style":416},[415],[316,1377,1379],{"className":1378},[420,421,422,423],[316,1380,646],{"className":1381},[386,390,423],[316,1383,438],{"className":1384},[437],[316,1386,1388],{"className":1387},[403],[316,1389,1391],{"className":1390,"style":445},[407],[316,1392],{},[291,1394,1395],{},"更低（更靠近",[316,1397,1399,1416],{"className":1398},[319],[316,1400,1402],{"className":1401},[323],[325,1403,1404],{"xmlns":327},[329,1405,1406,1414],{},[332,1407,1408],{},[335,1409,1410,1412],{},[338,1411,550],{},[338,1413,553],{},[365,1415,556],{"encoding":367},[316,1417,1419],{"className":1418,"ariaHidden":373},[372],[316,1420,1422,1425],{"className":1421},[377],[316,1423],{"className":1424,"style":566},[381],[316,1426,1428,1431],{"className":1427},[386],[316,1429,550],{"className":1430,"style":430},[386,390],[316,1432,1434],{"className":1433},[394],[316,1435,1437,1457],{"className":1436},[398,399],[316,1438,1440,1454],{"className":1439},[403],[316,1441,1443],{"className":1442,"style":408},[407],[316,1444,1445,1448],{"style":587},[316,1446],{"className":1447,"style":416},[415],[316,1449,1451],{"className":1450},[420,421,422,423],[316,1452,553],{"className":1453,"style":597},[386,390,423],[316,1455,438],{"className":1456},[437],[316,1458,1460],{"className":1459},[403],[316,1461,1463],{"className":1462,"style":445},[407],[316,1464],{},[291,1466,1467],{},"）哪边就更 n 型；哪边",[316,1469,1471,1489],{"className":1470},[319],[316,1472,1474],{"className":1473},[323],[325,1475,1476],{"xmlns":327},[329,1477,1478,1486],{},[332,1479,1480],{},[335,1481,1482,1484],{},[338,1483,550],{},[338,1485,713],{},[365,1487,1488],{"encoding":367},"E_v",[316,1490,1492],{"className":1491,"ariaHidden":373},[372],[316,1493,1495,1498],{"className":1494},[377],[316,1496],{"className":1497,"style":566},[381],[316,1499,1501,1504],{"className":1500},[386],[316,1502,550],{"className":1503,"style":430},[386,390],[316,1505,1507],{"className":1506},[394],[316,1508,1510,1530],{"className":1509},[398,399],[316,1511,1513,1527],{"className":1512},[403],[316,1514,1516],{"className":1515,"style":814},[407],[316,1517,1518,1521],{"style":587},[316,1519],{"className":1520,"style":416},[415],[316,1522,1524],{"className":1523},[420,421,422,423],[316,1525,713],{"className":1526,"style":1117},[386,390,423],[316,1528,438],{"className":1529},[437],[316,1531,1533],{"className":1532},[403],[316,1534,1536],{"className":1535,"style":445},[407],[316,1537],{},[291,1539,1540],{},"更高哪边就更 p 型",[523,1542,1543,1546],{},[526,1544,1545],{},"Ec and Ev are smooth , the exact shape to be determined",[526,1547,1548,1549,1552],{},"A depletion lay exists at the PN junction where n≈0 and p≈0\nThe built-in potential is generated due to ",[291,1550,1551],{},"band bending",".",[241,1554,1555],{},[247,1556],{"alt":1557,"src":1558},"OWJCb5THpoSR0ex1Uq9c5vDUn0M.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-03.png",[1560,1561,1563,1569,1575,2105,2110],"alert",{"type":1562},"question",[241,1564,1565,1568],{},[291,1566,1567],{},"Question: Can"," the built-in potential be measured with a voltmeter?",[241,1570,1571,1574],{},[291,1572,1573],{},"不可以。","使用一个标准的电压表直接测量PN结的内建电势 (Vbi)，读数将为0伏特。",[523,1576,1577,1580,2099],{},[526,1578,1579],{},"产生新的接触电势\n当电压表的金属探针接触P型区和N型区时，会在“金属-P型”和“金属-N型”的界面上形成两个新的接触电势 (Contact Potentials)。",[526,1581,1582,1583],{},"热平衡抵消\n电压表、探针和PN结形成一个完整的闭合回路。在热平衡状态下（无电流流过），此回路中所有电势差的总和必须为零。",[1584,1585,1586,1929],"ul",{},[526,1587,1588],{},[316,1589,1591,1661],{"className":1590},[319],[316,1592,1594],{"className":1593},[323],[325,1595,1596],{"xmlns":327},[329,1597,1598,1658],{},[332,1599,1600,1609,1612,1626,1628,1640,1642,1654,1656],{},[335,1601,1602,1605],{},[338,1603,1604],{},"V",[1606,1607,1608],"mtext",{},"测量值",[350,1610,1611],{},"+",[335,1613,1614,1616],{},[338,1615,1604],{},[332,1617,1618,1621,1623],{},[1606,1619,1620],{},"金属",[350,1622,657],{},[338,1624,1625],{},"P",[350,1627,1611],{},[335,1629,1630,1632],{},[338,1631,1604],{},[332,1633,1634,1636,1638],{},[338,1635,1625],{},[350,1637,657],{},[338,1639,643],{},[350,1641,1611],{},[335,1643,1644,1646],{},[338,1645,1604],{},[332,1647,1648,1650,1652],{},[338,1649,643],{},[350,1651,657],{},[1606,1653,1620],{},[350,1655,352],{},[354,1657,363],{},[365,1659,1660],{"encoding":367},"V_{测量值}+V_{金属-P}+V_{P-N}+V_{N-金属}=0",[316,1662,1664,1725,1791,1855,1919],{"className":1663,"ariaHidden":373},[372],[316,1665,1667,1670,1716,1719,1722],{"className":1666},[377],[316,1668],{"className":1669,"style":566},[381],[316,1671,1673,1677],{"className":1672},[386],[316,1674,1604],{"className":1675,"style":1676},[386,390],"margin-right:0.2222em;",[316,1678,1680],{"className":1679},[394],[316,1681,1683,1708],{"className":1682},[398,399],[316,1684,1686,1705],{"className":1685},[403],[316,1687,1689],{"className":1688,"style":408},[407],[316,1690,1692,1695],{"style":1691},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[316,1693],{"className":1694,"style":416},[415],[316,1696,1698],{"className":1697},[420,421,422,423],[316,1699,1701],{"className":1700},[386,423],[316,1702,1608],{"className":1703},[386,1704,423],"cjk_fallback",[316,1706,438],{"className":1707},[437],[316,1709,1711],{"className":1710},[403],[316,1712,1714],{"className":1713,"style":445},[407],[316,1715],{},[316,1717],{"className":1718,"style":1676},[451],[316,1720,1611],{"className":1721},[991],[316,1723],{"className":1724,"style":1676},[451],[316,1726,1728,1732,1782,1785,1788],{"className":1727},[377],[316,1729],{"className":1730,"style":1731},[381],"height:0.8917em;vertical-align:-0.2083em;",[316,1733,1735,1738],{"className":1734},[386],[316,1736,1604],{"className":1737,"style":1676},[386,390],[316,1739,1741],{"className":1740},[394],[316,1742,1744,1773],{"className":1743},[398,399],[316,1745,1747,1770],{"className":1746},[403],[316,1748,1750],{"className":1749,"style":408},[407],[316,1751,1752,1755],{"style":1691},[316,1753],{"className":1754,"style":416},[415],[316,1756,1758],{"className":1757},[420,421,422,423],[316,1759,1761,1764,1767],{"className":1760},[386,423],[316,1762,1620],{"className":1763},[386,1704,423],[316,1765,657],{"className":1766},[991,423],[316,1768,1625],{"className":1769,"style":597},[386,390,423],[316,1771,438],{"className":1772},[437],[316,1774,1776],{"className":1775},[403],[316,1777,1780],{"className":1778,"style":1779},[407],"height:0.2083em;",[316,1781],{},[316,1783],{"className":1784,"style":1676},[451],[316,1786,1611],{"className":1787},[991],[316,1789],{"className":1790,"style":1676},[451],[316,1792,1794,1797,1846,1849,1852],{"className":1793},[377],[316,1795],{"className":1796,"style":1731},[381],[316,1798,1800,1803],{"className":1799},[386],[316,1801,1604],{"className":1802,"style":1676},[386,390],[316,1804,1806],{"className":1805},[394],[316,1807,1809,1838],{"className":1808},[398,399],[316,1810,1812,1835],{"className":1811},[403],[316,1813,1815],{"className":1814,"style":408},[407],[316,1816,1817,1820],{"style":1691},[316,1818],{"className":1819,"style":416},[415],[316,1821,1823],{"className":1822},[420,421,422,423],[316,1824,1826,1829,1832],{"className":1825},[386,423],[316,1827,1625],{"className":1828,"style":597},[386,390,423],[316,1830,657],{"className":1831},[991,423],[316,1833,643],{"className":1834,"style":801},[386,390,423],[316,1836,438],{"className":1837},[437],[316,1839,1841],{"className":1840},[403],[316,1842,1844],{"className":1843,"style":1779},[407],[316,1845],{},[316,1847],{"className":1848,"style":1676},[451],[316,1850,1611],{"className":1851},[991],[316,1853],{"className":1854,"style":1676},[451],[316,1856,1858,1861,1910,1913,1916],{"className":1857},[377],[316,1859],{"className":1860,"style":1731},[381],[316,1862,1864,1867],{"className":1863},[386],[316,1865,1604],{"className":1866,"style":1676},[386,390],[316,1868,1870],{"className":1869},[394],[316,1871,1873,1902],{"className":1872},[398,399],[316,1874,1876,1899],{"className":1875},[403],[316,1877,1879],{"className":1878,"style":408},[407],[316,1880,1881,1884],{"style":1691},[316,1882],{"className":1883,"style":416},[415],[316,1885,1887],{"className":1886},[420,421,422,423],[316,1888,1890,1893,1896],{"className":1889},[386,423],[316,1891,643],{"className":1892,"style":801},[386,390,423],[316,1894,657],{"className":1895},[991,423],[316,1897,1620],{"className":1898},[386,1704,423],[316,1900,438],{"className":1901},[437],[316,1903,1905],{"className":1904},[403],[316,1906,1908],{"className":1907,"style":1779},[407],[316,1909],{},[316,1911],{"className":1912,"style":452},[451],[316,1914,352],{"className":1915},[456],[316,1917],{"className":1918,"style":452},[451],[316,1920,1922,1926],{"className":1921},[377],[316,1923],{"className":1924,"style":1925},[381],"height:0.6444em;",[316,1927,363],{"className":1928},[386],[526,1930,1931,1932,2017,2018,2098],{},"其中 ",[316,1933,1935,1959],{"className":1934},[319],[316,1936,1938],{"className":1937},[323],[325,1939,1940],{"xmlns":327},[329,1941,1942,1956],{},[332,1943,1944],{},[335,1945,1946,1948],{},[338,1947,1604],{},[332,1949,1950,1952,1954],{},[338,1951,1625],{},[350,1953,657],{},[338,1955,643],{},[365,1957,1958],{"encoding":367},"V_{P-N}",[316,1960,1962],{"className":1961,"ariaHidden":373},[372],[316,1963,1965,1968],{"className":1964},[377],[316,1966],{"className":1967,"style":1731},[381],[316,1969,1971,1974],{"className":1970},[386],[316,1972,1604],{"className":1973,"style":1676},[386,390],[316,1975,1977],{"className":1976},[394],[316,1978,1980,2009],{"className":1979},[398,399],[316,1981,1983,2006],{"className":1982},[403],[316,1984,1986],{"className":1985,"style":408},[407],[316,1987,1988,1991],{"style":1691},[316,1989],{"className":1990,"style":416},[415],[316,1992,1994],{"className":1993},[420,421,422,423],[316,1995,1997,2000,2003],{"className":1996},[386,423],[316,1998,1625],{"className":1999,"style":597},[386,390,423],[316,2001,657],{"className":2002},[991,423],[316,2004,643],{"className":2005,"style":801},[386,390,423],[316,2007,438],{"className":2008},[437],[316,2010,2012],{"className":2011},[403],[316,2013,2015],{"className":2014,"style":1779},[407],[316,2016],{}," 就是内建电势 ",[316,2019,2021,2044],{"className":2020},[319],[316,2022,2024],{"className":2023},[323],[325,2025,2026],{"xmlns":327},[329,2027,2028,2041],{},[332,2029,2030],{},[335,2031,2032,2034],{},[338,2033,1604],{},[332,2035,2036,2039],{},[338,2037,2038],{},"b",[338,2040,348],{},[365,2042,2043],{"encoding":367},"V_{bi}",[316,2045,2047],{"className":2046,"ariaHidden":373},[372],[316,2048,2050,2053],{"className":2049},[377],[316,2051],{"className":2052,"style":566},[381],[316,2054,2056,2059],{"className":2055},[386],[316,2057,1604],{"className":2058,"style":1676},[386,390],[316,2060,2062],{"className":2061},[394],[316,2063,2065,2090],{"className":2064},[398,399],[316,2066,2068,2087],{"className":2067},[403],[316,2069,2072],{"className":2070,"style":2071},[407],"height:0.3361em;",[316,2073,2074,2077],{"style":1691},[316,2075],{"className":2076,"style":416},[415],[316,2078,2080],{"className":2079},[420,421,422,423],[316,2081,2083],{"className":2082},[386,423],[316,2084,2086],{"className":2085},[386,390,423],"bi",[316,2088,438],{"className":2089},[437],[316,2091,2093],{"className":2092},[403],[316,2094,2096],{"className":2095,"style":445},[407],[316,2097],{},"。",[526,2100,2101,2102,2098],{},"物理规律决定了新产生的两个接触电势（V金属-P 和 VN-金属）与内建电势 Vbi ",[291,2103,2104],{},"恰好完全相互抵消",[1584,2106,2107],{},[526,2108,2109],{},"费米能级解释\n电压表测量的是其两探针之间的费米能级 (EF) 之差。在热平衡状态下，整个闭合回路的费米能级处处相等（为一条平线）。因此，两探针间的费米能级之差为零，电压表读数即为零。",[241,2111,2112,2113,2116],{},"只能通过",[291,2114,2115],{},"间接方法","（如C-V电容-电压特性测量法）来推算得出。",[256,2118,2120],{"id":2119},"quantitative-analysis-定量分析","Quantitative Analysis ｜ 定量分析",[2122,2123,2125],"h5",{"id":2124},"depletion-approximation","Depletion Approximation",[1560,2127,2129,2134,2137],{"type":2128},"tip",[241,2130,2131],{},[291,2132,2133],{},"Depletion approximation | 耗尽区近似",[241,2135,2136],{},"a. 耗尽区内没有可移动的电子和空穴；b. 耗尽区外假设为中性，净电荷浓度为0；",[523,2138,2139,2330],{},[526,2140,2141,2144,2145,2148,2149,2152,2153,2244,2245,2329],{},[291,2142,2143],{},"Inside the Depletion Region:"," It assumes there are ",[291,2146,2147],{},"no"," mobile electrons or holes (n=0, p=0). The charge consists ",[291,2150,2151],{},"only"," of fixed donor (",[316,2154,2156,2178],{"className":2155},[319],[316,2157,2159],{"className":2158},[323],[325,2160,2161],{"xmlns":327},[329,2162,2163,2175],{},[332,2164,2165],{},[2166,2167,2168,2170,2173],"msubsup",{},[338,2169,643],{},[338,2171,2172],{},"D",[350,2174,1611],{},[365,2176,2177],{"encoding":367},"N_D^+",[316,2179,2181],{"className":2180,"ariaHidden":373},[372],[316,2182,2184,2188],{"className":2183},[377],[316,2185],{"className":2186,"style":2187},[381],"height:1.105em;vertical-align:-0.2935em;",[316,2189,2191,2194],{"className":2190},[386],[316,2192,643],{"className":2193,"style":801},[386,390],[316,2195,2197],{"className":2196},[394],[316,2198,2200,2235],{"className":2199},[398,399],[316,2201,2203,2232],{"className":2202},[403],[316,2204,2207,2220],{"className":2205,"style":2206},[407],"height:0.8115em;",[316,2208,2210,2213],{"style":2209},"top:-2.4065em;margin-left:-0.109em;margin-right:0.05em;",[316,2211],{"className":2212,"style":416},[415],[316,2214,2216],{"className":2215},[420,421,422,423],[316,2217,2172],{"className":2218,"style":2219},[386,390,423],"margin-right:0.0278em;",[316,2221,2223,2226],{"style":2222},"top:-3.1031em;margin-right:0.05em;",[316,2224],{"className":2225,"style":416},[415],[316,2227,2229],{"className":2228},[420,421,422,423],[316,2230,1611],{"className":2231},[991,423],[316,2233,438],{"className":2234},[437],[316,2236,2238],{"className":2237},[403],[316,2239,2242],{"className":2240,"style":2241},[407],"height:0.2935em;",[316,2243],{},") and acceptor (",[316,2246,2248,2269],{"className":2247},[319],[316,2249,2251],{"className":2250},[323],[325,2252,2253],{"xmlns":327},[329,2254,2255,2266],{},[332,2256,2257],{},[2166,2258,2259,2261,2264],{},[338,2260,643],{},[338,2262,2263],{},"A",[350,2265,657],{},[365,2267,2268],{"encoding":367},"N_A^-",[316,2270,2272],{"className":2271,"ariaHidden":373},[372],[316,2273,2275,2278],{"className":2274},[377],[316,2276],{"className":2277,"style":2187},[381],[316,2279,2281,2284],{"className":2280},[386],[316,2282,643],{"className":2283,"style":801},[386,390],[316,2285,2287],{"className":2286},[394],[316,2288,2290,2321],{"className":2289},[398,399],[316,2291,2293,2318],{"className":2292},[403],[316,2294,2296,2307],{"className":2295,"style":2206},[407],[316,2297,2298,2301],{"style":2209},[316,2299],{"className":2300,"style":416},[415],[316,2302,2304],{"className":2303},[420,421,422,423],[316,2305,2263],{"className":2306},[386,390,423],[316,2308,2309,2312],{"style":2222},[316,2310],{"className":2311,"style":416},[415],[316,2313,2315],{"className":2314},[420,421,422,423],[316,2316,657],{"className":2317},[991,423],[316,2319,438],{"className":2320},[437],[316,2322,2324],{"className":2323},[403],[316,2325,2327],{"className":2326,"style":2241},[407],[316,2328],{},") ions.",[526,2331,2332,2335,2336,2339,2340,2393],{},[291,2333,2334],{},"Outside the Depletion Region (Neutral Region):"," It assumes the region is ",[291,2337,2338],{},"perfectly neutral",", meaning the net charge density is zero (",[316,2341,2343,2362],{"className":2342},[319],[316,2344,2346],{"className":2345},[323],[325,2347,2348],{"xmlns":327},[329,2349,2350,2359],{},[332,2351,2352,2355,2357],{},[338,2353,2354],{},"ρ",[350,2356,352],{},[354,2358,363],{},[365,2360,2361],{"encoding":367},"\\rho=0",[316,2363,2365,2384],{"className":2364,"ariaHidden":373},[372],[316,2366,2368,2372,2375,2378,2381],{"className":2367},[377],[316,2369],{"className":2370,"style":2371},[381],"height:0.625em;vertical-align:-0.1944em;",[316,2373,2354],{"className":2374},[386,390],[316,2376],{"className":2377,"style":452},[451],[316,2379,352],{"className":2380},[456],[316,2382],{"className":2383,"style":452},[451],[316,2385,2387,2390],{"className":2386},[377],[316,2388],{"className":2389,"style":1925},[381],[316,2391,363],{"className":2392},[386],").",[2122,2395,2397,2398],{"id":2396},"built-in-potential-vbiv_bivbi","Built-in Potential ",[316,2399,2401,2422],{"className":2400},[319],[316,2402,2404],{"className":2403},[323],[325,2405,2406],{"xmlns":327},[329,2407,2408,2420],{},[332,2409,2410],{},[335,2411,2412,2414],{},[338,2413,1604],{},[332,2415,2416,2418],{},[338,2417,2038],{},[338,2419,348],{},[365,2421,2043],{"encoding":367},[316,2423,2425],{"className":2424,"ariaHidden":373},[372],[316,2426,2428,2431],{"className":2427},[377],[316,2429],{"className":2430,"style":566},[381],[316,2432,2434,2437],{"className":2433},[386],[316,2435,1604],{"className":2436,"style":1676},[386,390],[316,2438,2440],{"className":2439},[394],[316,2441,2443,2466],{"className":2442},[398,399],[316,2444,2446,2463],{"className":2445},[403],[316,2447,2449],{"className":2448,"style":2071},[407],[316,2450,2451,2454],{"style":1691},[316,2452],{"className":2453,"style":416},[415],[316,2455,2457],{"className":2456},[420,421,422,423],[316,2458,2460],{"className":2459},[386,423],[316,2461,2086],{"className":2462},[386,390,423],[316,2464,438],{"className":2465},[437],[316,2467,2469],{"className":2468},[403],[316,2470,2472],{"className":2471,"style":445},[407],[316,2473],{},[241,2475,2476],{},[291,2477,2478],{},"Non-degenerately doped | 非简并掺杂",[241,2480,2481,2482,2485,2486,2555,2556,2628,2629,2699,2700,2098],{},"指半导体中",[291,2483,2484],{},"中等或轻度","的掺杂水平，掺杂浓度不足以使费米能级 (",[316,2487,2489,2506],{"className":2488},[319],[316,2490,2492],{"className":2491},[323],[325,2493,2494],{"xmlns":327},[329,2495,2496,2504],{},[332,2497,2498],{},[335,2499,2500,2502],{},[338,2501,550],{},[338,2503,553],{},[365,2505,556],{"encoding":367},[316,2507,2509],{"className":2508,"ariaHidden":373},[372],[316,2510,2512,2515],{"className":2511},[377],[316,2513],{"className":2514,"style":566},[381],[316,2516,2518,2521],{"className":2517},[386],[316,2519,550],{"className":2520,"style":430},[386,390],[316,2522,2524],{"className":2523},[394],[316,2525,2527,2547],{"className":2526},[398,399],[316,2528,2530,2544],{"className":2529},[403],[316,2531,2533],{"className":2532,"style":408},[407],[316,2534,2535,2538],{"style":587},[316,2536],{"className":2537,"style":416},[415],[316,2539,2541],{"className":2540},[420,421,422,423],[316,2542,553],{"className":2543,"style":597},[386,390,423],[316,2545,438],{"className":2546},[437],[316,2548,2550],{"className":2549},[403],[316,2551,2553],{"className":2552,"style":445},[407],[316,2554],{},") 进入导带 (",[316,2557,2559,2578],{"className":2558},[319],[316,2560,2562],{"className":2561},[323],[325,2563,2564],{"xmlns":327},[329,2565,2566,2575],{},[332,2567,2568],{},[335,2569,2570,2572],{},[338,2571,550],{},[338,2573,2574],{},"C",[365,2576,2577],{"encoding":367},"E_C",[316,2579,2581],{"className":2580,"ariaHidden":373},[372],[316,2582,2584,2587],{"className":2583},[377],[316,2585],{"className":2586,"style":566},[381],[316,2588,2590,2593],{"className":2589},[386],[316,2591,550],{"className":2592,"style":430},[386,390],[316,2594,2596],{"className":2595},[394],[316,2597,2599,2620],{"className":2598},[398,399],[316,2600,2602,2617],{"className":2601},[403],[316,2603,2605],{"className":2604,"style":408},[407],[316,2606,2607,2610],{"style":587},[316,2608],{"className":2609,"style":416},[415],[316,2611,2613],{"className":2612},[420,421,422,423],[316,2614,2574],{"className":2615,"style":2616},[386,390,423],"margin-right:0.0715em;",[316,2618,438],{"className":2619},[437],[316,2621,2623],{"className":2622},[403],[316,2624,2626],{"className":2625,"style":445},[407],[316,2627],{},") 或价带 (",[316,2630,2632,2650],{"className":2631},[319],[316,2633,2635],{"className":2634},[323],[325,2636,2637],{"xmlns":327},[329,2638,2639,2647],{},[332,2640,2641],{},[335,2642,2643,2645],{},[338,2644,550],{},[338,2646,1604],{},[365,2648,2649],{"encoding":367},"E_V",[316,2651,2653],{"className":2652,"ariaHidden":373},[372],[316,2654,2656,2659],{"className":2655},[377],[316,2657],{"className":2658,"style":566},[381],[316,2660,2662,2665],{"className":2661},[386],[316,2663,550],{"className":2664,"style":430},[386,390],[316,2666,2668],{"className":2667},[394],[316,2669,2671,2691],{"className":2670},[398,399],[316,2672,2674,2688],{"className":2673},[403],[316,2675,2677],{"className":2676,"style":408},[407],[316,2678,2679,2682],{"style":587},[316,2680],{"className":2681,"style":416},[415],[316,2683,2685],{"className":2684},[420,421,422,423],[316,2686,1604],{"className":2687,"style":1676},[386,390,423],[316,2689,438],{"className":2690},[437],[316,2692,2694],{"className":2693},[403],[316,2695,2697],{"className":2696,"style":445},[407],[316,2698],{},")。费米能级",[291,2701,2702],{},"始终位于禁带之内",[241,2704,2705,2706,2709,2710,2779,2780,2849,2850,2919],{},"Refers to a ",[291,2707,2708],{},"moderate or light"," doping level in semiconductors, where the doping concentration is not sufficient to shift the Fermi level (",[316,2711,2713,2730],{"className":2712},[319],[316,2714,2716],{"className":2715},[323],[325,2717,2718],{"xmlns":327},[329,2719,2720,2728],{},[332,2721,2722],{},[335,2723,2724,2726],{},[338,2725,550],{},[338,2727,553],{},[365,2729,556],{"encoding":367},[316,2731,2733],{"className":2732,"ariaHidden":373},[372],[316,2734,2736,2739],{"className":2735},[377],[316,2737],{"className":2738,"style":566},[381],[316,2740,2742,2745],{"className":2741},[386],[316,2743,550],{"className":2744,"style":430},[386,390],[316,2746,2748],{"className":2747},[394],[316,2749,2751,2771],{"className":2750},[398,399],[316,2752,2754,2768],{"className":2753},[403],[316,2755,2757],{"className":2756,"style":408},[407],[316,2758,2759,2762],{"style":587},[316,2760],{"className":2761,"style":416},[415],[316,2763,2765],{"className":2764},[420,421,422,423],[316,2766,553],{"className":2767,"style":597},[386,390,423],[316,2769,438],{"className":2770},[437],[316,2772,2774],{"className":2773},[403],[316,2775,2777],{"className":2776,"style":445},[407],[316,2778],{},") into the conduction band (",[316,2781,2783,2800],{"className":2782},[319],[316,2784,2786],{"className":2785},[323],[325,2787,2788],{"xmlns":327},[329,2789,2790,2798],{},[332,2791,2792],{},[335,2793,2794,2796],{},[338,2795,550],{},[338,2797,2574],{},[365,2799,2577],{"encoding":367},[316,2801,2803],{"className":2802,"ariaHidden":373},[372],[316,2804,2806,2809],{"className":2805},[377],[316,2807],{"className":2808,"style":566},[381],[316,2810,2812,2815],{"className":2811},[386],[316,2813,550],{"className":2814,"style":430},[386,390],[316,2816,2818],{"className":2817},[394],[316,2819,2821,2841],{"className":2820},[398,399],[316,2822,2824,2838],{"className":2823},[403],[316,2825,2827],{"className":2826,"style":408},[407],[316,2828,2829,2832],{"style":587},[316,2830],{"className":2831,"style":416},[415],[316,2833,2835],{"className":2834},[420,421,422,423],[316,2836,2574],{"className":2837,"style":2616},[386,390,423],[316,2839,438],{"className":2840},[437],[316,2842,2844],{"className":2843},[403],[316,2845,2847],{"className":2846,"style":445},[407],[316,2848],{},") or the valence band (",[316,2851,2853,2870],{"className":2852},[319],[316,2854,2856],{"className":2855},[323],[325,2857,2858],{"xmlns":327},[329,2859,2860,2868],{},[332,2861,2862],{},[335,2863,2864,2866],{},[338,2865,550],{},[338,2867,1604],{},[365,2869,2649],{"encoding":367},[316,2871,2873],{"className":2872,"ariaHidden":373},[372],[316,2874,2876,2879],{"className":2875},[377],[316,2877],{"className":2878,"style":566},[381],[316,2880,2882,2885],{"className":2881},[386],[316,2883,550],{"className":2884,"style":430},[386,390],[316,2886,2888],{"className":2887},[394],[316,2889,2891,2911],{"className":2890},[398,399],[316,2892,2894,2908],{"className":2893},[403],[316,2895,2897],{"className":2896,"style":408},[407],[316,2898,2899,2902],{"style":587},[316,2900],{"className":2901,"style":416},[415],[316,2903,2905],{"className":2904},[420,421,422,423],[316,2906,1604],{"className":2907,"style":1676},[386,390,423],[316,2909,438],{"className":2910},[437],[316,2912,2914],{"className":2913},[403],[316,2915,2917],{"className":2916,"style":445},[407],[316,2918],{},"). The Fermi level remains within the band gap at all times.",[241,2921,2922],{},[247,2923],{"alt":2924,"src":2925},"FisAbXuX0ooF3vxFjIhcYm3Znmd.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-13.png",[241,2927,2928,2929,3005],{},"Then we can get the value of ",[316,2930,2932,2953],{"className":2931},[319],[316,2933,2935],{"className":2934},[323],[325,2936,2937],{"xmlns":327},[329,2938,2939,2951],{},[332,2940,2941],{},[335,2942,2943,2945],{},[338,2944,1604],{},[332,2946,2947,2949],{},[338,2948,2038],{},[338,2950,348],{},[365,2952,2043],{"encoding":367},[316,2954,2956],{"className":2955,"ariaHidden":373},[372],[316,2957,2959,2962],{"className":2958},[377],[316,2960],{"className":2961,"style":566},[381],[316,2963,2965,2968],{"className":2964},[386],[316,2966,1604],{"className":2967,"style":1676},[386,390],[316,2969,2971],{"className":2970},[394],[316,2972,2974,2997],{"className":2973},[398,399],[316,2975,2977,2994],{"className":2976},[403],[316,2978,2980],{"className":2979,"style":2071},[407],[316,2981,2982,2985],{"style":1691},[316,2983],{"className":2984,"style":416},[415],[316,2986,2988],{"className":2987},[420,421,422,423],[316,2989,2991],{"className":2990},[386,423],[316,2992,2086],{"className":2993},[386,390,423],[316,2995,438],{"className":2996},[437],[316,2998,3000],{"className":2999},[403],[316,3001,3003],{"className":3002,"style":445},[407],[316,3004],{},[291,3006,3007],{},"(前提是非简并材料 non-degenerately doped):",[316,3009,3012],{"className":3010},[3011],"katex-display",[316,3013,3015,3087],{"className":3014},[319],[316,3016,3018],{"className":3017},[323],[325,3019,3021],{"xmlns":327,"display":3020},"block",[329,3022,3023,3084],{},[332,3024,3025,3035,3037,3047,3050,3053],{},[335,3026,3027,3029],{},[338,3028,1604],{},[332,3030,3031,3033],{},[338,3032,2038],{},[338,3034,348],{},[350,3036,352],{},[659,3038,3039,3045],{},[332,3040,3041,3043],{},[338,3042,687],{},[338,3044,690],{},[338,3046,652],{},[338,3048,3049],{},"ln",[350,3051,3052],{},"⁡",[332,3054,3055,3057,3082],{},[350,3056,630],{"fence":373},[659,3058,3059,3073],{},[332,3060,3061,3067],{},[335,3062,3063,3065],{},[338,3064,643],{},[338,3066,2263],{},[335,3068,3069,3071],{},[338,3070,643],{},[338,3072,2172],{},[2166,3074,3075,3077,3079],{},[338,3076,626],{},[338,3078,348],{},[354,3080,3081],{},"2",[350,3083,636],{"fence":373},[365,3085,3086],{"encoding":367},"V_{bi} = \\frac{kT}{e}\\ln\\left(\\frac{N_A N_D}{n_i^2}\\right)",[316,3088,3090,3148],{"className":3089,"ariaHidden":373},[372],[316,3091,3093,3096,3139,3142,3145],{"className":3092},[377],[316,3094],{"className":3095,"style":566},[381],[316,3097,3099,3102],{"className":3098},[386],[316,3100,1604],{"className":3101,"style":1676},[386,390],[316,3103,3105],{"className":3104},[394],[316,3106,3108,3131],{"className":3107},[398,399],[316,3109,3111,3128],{"className":3110},[403],[316,3112,3114],{"className":3113,"style":2071},[407],[316,3115,3116,3119],{"style":1691},[316,3117],{"className":3118,"style":416},[415],[316,3120,3122],{"className":3121},[420,421,422,423],[316,3123,3125],{"className":3124},[386,423],[316,3126,2086],{"className":3127},[386,390,423],[316,3129,438],{"className":3130},[437],[316,3132,3134],{"className":3133},[403],[316,3135,3137],{"className":3136,"style":445},[407],[316,3138],{},[316,3140],{"className":3141,"style":452},[451],[316,3143,352],{"className":3144},[456],[316,3146],{"className":3147,"style":452},[451],[316,3149,3151,3155,3226,3229,3233,3236],{"className":3150},[377],[316,3152],{"className":3153,"style":3154},[381],"height:2.4129em;vertical-align:-0.9629em;",[316,3156,3158,3161,3223],{"className":3157},[386],[316,3159],{"className":3160},[771,879],[316,3162,3164],{"className":3163},[659],[316,3165,3167,3214],{"className":3166},[398,399],[316,3168,3170,3211],{"className":3169},[403],[316,3171,3174,3186,3196],{"className":3172,"style":3173},[407],"height:1.3714em;",[316,3175,3177,3180],{"style":3176},"top:-2.314em;",[316,3178],{"className":3179,"style":863},[415],[316,3181,3183],{"className":3182},[386],[316,3184,652],{"className":3185},[386,390],[316,3187,3189,3192],{"style":3188},"top:-3.23em;",[316,3190],{"className":3191,"style":863},[415],[316,3193],{"className":3194,"style":3195},[924],"border-bottom-width:0.04em;",[316,3197,3199,3202],{"style":3198},"top:-3.677em;",[316,3200],{"className":3201,"style":863},[415],[316,3203,3205,3208],{"className":3204},[386],[316,3206,687],{"className":3207,"style":911},[386,390],[316,3209,690],{"className":3210,"style":597},[386,390],[316,3212,438],{"className":3213},[437],[316,3215,3217],{"className":3216},[403],[316,3218,3221],{"className":3219,"style":3220},[407],"height:0.686em;",[316,3222],{},[316,3224],{"className":3225},[778,879],[316,3227],{"className":3228,"style":1059},[451],[316,3230,3049],{"className":3231},[3232],"mop",[316,3234],{"className":3235,"style":1059},[451],[316,3237,3240,3249,3442],{"className":3238},[3239],"minner",[316,3241,3245],{"className":3242,"style":3244},[771,3243],"delimcenter","top:0em;",[316,3246,630],{"className":3247},[3248,422],"delimsizing",[316,3250,3252,3255,3439],{"className":3251},[386],[316,3253],{"className":3254},[771,879],[316,3256,3258],{"className":3257},[659],[316,3259,3261,3430],{"className":3260},[398,399],[316,3262,3264,3427],{"className":3263},[403],[316,3265,3268,3331,3339],{"className":3266,"style":3267},[407],"height:1.3603em;",[316,3269,3270,3273],{"style":3176},[316,3271],{"className":3272,"style":863},[415],[316,3274,3276],{"className":3275},[386],[316,3277,3279,3282],{"className":3278},[386],[316,3280,626],{"className":3281},[386,390],[316,3283,3285],{"className":3284},[394],[316,3286,3288,3322],{"className":3287},[398,399],[316,3289,3291,3319],{"className":3290},[403],[316,3292,3295,3307],{"className":3293,"style":3294},[407],"height:0.7959em;",[316,3296,3298,3301],{"style":3297},"top:-2.4231em;margin-left:0em;margin-right:0.05em;",[316,3299],{"className":3300,"style":416},[415],[316,3302,3304],{"className":3303},[420,421,422,423],[316,3305,348],{"className":3306},[386,390,423],[316,3308,3310,3313],{"style":3309},"top:-3.0448em;margin-right:0.05em;",[316,3311],{"className":3312,"style":416},[415],[316,3314,3316],{"className":3315},[420,421,422,423],[316,3317,3081],{"className":3318},[386,423],[316,3320,438],{"className":3321},[437],[316,3323,3325],{"className":3324},[403],[316,3326,3329],{"className":3327,"style":3328},[407],"height:0.2769em;",[316,3330],{},[316,3332,3333,3336],{"style":3188},[316,3334],{"className":3335,"style":863},[415],[316,3337],{"className":3338,"style":3195},[924],[316,3340,3341,3344],{"style":3198},[316,3342],{"className":3343,"style":863},[415],[316,3345,3347,3387],{"className":3346},[386],[316,3348,3350,3353],{"className":3349},[386],[316,3351,643],{"className":3352,"style":801},[386,390],[316,3354,3356],{"className":3355},[394],[316,3357,3359,3379],{"className":3358},[398,399],[316,3360,3362,3376],{"className":3361},[403],[316,3363,3365],{"className":3364,"style":408},[407],[316,3366,3367,3370],{"style":817},[316,3368],{"className":3369,"style":416},[415],[316,3371,3373],{"className":3372},[420,421,422,423],[316,3374,2263],{"className":3375},[386,390,423],[316,3377,438],{"className":3378},[437],[316,3380,3382],{"className":3381},[403],[316,3383,3385],{"className":3384,"style":445},[407],[316,3386],{},[316,3388,3390,3393],{"className":3389},[386],[316,3391,643],{"className":3392,"style":801},[386,390],[316,3394,3396],{"className":3395},[394],[316,3397,3399,3419],{"className":3398},[398,399],[316,3400,3402,3416],{"className":3401},[403],[316,3403,3405],{"className":3404,"style":408},[407],[316,3406,3407,3410],{"style":817},[316,3408],{"className":3409,"style":416},[415],[316,3411,3413],{"className":3412},[420,421,422,423],[316,3414,2172],{"className":3415,"style":2219},[386,390,423],[316,3417,438],{"className":3418},[437],[316,3420,3422],{"className":3421},[403],[316,3423,3425],{"className":3424,"style":445},[407],[316,3426],{},[316,3428,438],{"className":3429},[437],[316,3431,3433],{"className":3432},[403],[316,3434,3437],{"className":3435,"style":3436},[407],"height:0.9629em;",[316,3438],{},[316,3440],{"className":3441},[778,879],[316,3443,3445],{"className":3444,"style":3244},[778,3243],[316,3446,636],{"className":3447},[3248,422],[2122,3449,3451,3527],{"id":3450},"vbiv_bivbi-for-abrupt-pn-junctions",[316,3452,3454,3475],{"className":3453},[319],[316,3455,3457],{"className":3456},[323],[325,3458,3459],{"xmlns":327},[329,3460,3461,3473],{},[332,3462,3463],{},[335,3464,3465,3467],{},[338,3466,1604],{},[332,3468,3469,3471],{},[338,3470,2038],{},[338,3472,348],{},[365,3474,2043],{"encoding":367},[316,3476,3478],{"className":3477,"ariaHidden":373},[372],[316,3479,3481,3484],{"className":3480},[377],[316,3482],{"className":3483,"style":566},[381],[316,3485,3487,3490],{"className":3486},[386],[316,3488,1604],{"className":3489,"style":1676},[386,390],[316,3491,3493],{"className":3492},[394],[316,3494,3496,3519],{"className":3495},[398,399],[316,3497,3499,3516],{"className":3498},[403],[316,3500,3502],{"className":3501,"style":2071},[407],[316,3503,3504,3507],{"style":1691},[316,3505],{"className":3506,"style":416},[415],[316,3508,3510],{"className":3509},[420,421,422,423],[316,3511,3513],{"className":3512},[386,423],[316,3514,2086],{"className":3515},[386,390,423],[316,3517,438],{"className":3518},[437],[316,3520,3522],{"className":3521},[403],[316,3523,3525],{"className":3524,"style":445},[407],[316,3526],{}," for Abrupt PN Junctions",[241,3529,3530,1322,3536,1322,3612,1322,3617,3693],{},[3531,3532,3533],"mark",{},[291,3534,3535],{},"The heavy doping side pretty much determine the",[316,3537,3539,3560],{"className":3538},[319],[316,3540,3542],{"className":3541},[323],[325,3543,3544],{"xmlns":327},[329,3545,3546,3558],{},[332,3547,3548],{},[335,3549,3550,3552],{},[338,3551,1604],{},[332,3553,3554,3556],{},[338,3555,2038],{},[338,3557,348],{},[365,3559,2043],{"encoding":367},[316,3561,3563],{"className":3562,"ariaHidden":373},[372],[316,3564,3566,3569],{"className":3565},[377],[316,3567],{"className":3568,"style":566},[381],[316,3570,3572,3575],{"className":3571},[386],[316,3573,1604],{"className":3574,"style":1676},[386,390],[316,3576,3578],{"className":3577},[394],[316,3579,3581,3604],{"className":3580},[398,399],[316,3582,3584,3601],{"className":3583},[403],[316,3585,3587],{"className":3586,"style":2071},[407],[316,3588,3589,3592],{"style":1691},[316,3590],{"className":3591,"style":416},[415],[316,3593,3595],{"className":3594},[420,421,422,423],[316,3596,3598],{"className":3597},[386,423],[316,3599,2086],{"className":3600},[386,390,423],[316,3602,438],{"className":3603},[437],[316,3605,3607],{"className":3606},[403],[316,3608,3610],{"className":3609,"style":445},[407],[316,3611],{},[3531,3613,3614],{},[291,3615,3616],{},"| 重掺杂这一边决定了",[316,3618,3620,3641],{"className":3619},[319],[316,3621,3623],{"className":3622},[323],[325,3624,3625],{"xmlns":327},[329,3626,3627,3639],{},[332,3628,3629],{},[335,3630,3631,3633],{},[338,3632,1604],{},[332,3634,3635,3637],{},[338,3636,2038],{},[338,3638,348],{},[365,3640,2043],{"encoding":367},[316,3642,3644],{"className":3643,"ariaHidden":373},[372],[316,3645,3647,3650],{"className":3646},[377],[316,3648],{"className":3649,"style":566},[381],[316,3651,3653,3656],{"className":3652},[386],[316,3654,1604],{"className":3655,"style":1676},[386,390],[316,3657,3659],{"className":3658},[394],[316,3660,3662,3685],{"className":3661},[398,399],[316,3663,3665,3682],{"className":3664},[403],[316,3666,3668],{"className":3667,"style":2071},[407],[316,3669,3670,3673],{"style":1691},[316,3671],{"className":3672,"style":416},[415],[316,3674,3676],{"className":3675},[420,421,422,423],[316,3677,3679],{"className":3678},[386,423],[316,3680,2086],{"className":3681},[386,390,423],[316,3683,438],{"className":3684},[437],[316,3686,3688],{"className":3687},[403],[316,3689,3691],{"className":3690,"style":445},[407],[316,3692],{},[3531,3694,3695],{},[291,3696,3697],{},"和电场的大小",[241,3699,3700],{},[247,3701],{"alt":3702,"src":3703},"LdKlbEtk4oVJdVxVhwDci1plnhe.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-02.png",[2122,3705,3707],{"id":3706},"calculation-of-ex-vx","Calculation of E(x) V(x)",[241,3709,3710],{},[247,3711],{"alt":3712,"src":3713},"AlAmbzqq5oqIuPxLnHOczG0dnCe.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-17.png",[241,3715,3716],{},[291,3717,3718],{},"The electric field is continuous at x= 0",[241,3720,3721],{},"电场是连续不光滑函数，电势是连续且光滑的函数",[241,3723,3724,3725,3839],{},"对电场进行积分可以得到(此处令 ",[316,3726,3728,3758],{"className":3727},[319],[316,3729,3731],{"className":3730},[323],[325,3732,3733],{"xmlns":327},[329,3734,3735,3755],{},[332,3736,3737,3739,3741,3743,3749,3751,3753],{},[338,3738,1604],{},[350,3740,630],{"stretchy":629},[350,3742,657],{},[335,3744,3745,3747],{},[338,3746,633],{},[338,3748,241],{},[350,3750,636],{"stretchy":629},[350,3752,352],{},[354,3754,363],{},[365,3756,3757],{"encoding":367},"V(-x_p) = 0",[316,3759,3761,3830],{"className":3760,"ariaHidden":373},[372],[316,3762,3764,3768,3771,3774,3777,3818,3821,3824,3827],{"className":3763},[377],[316,3765],{"className":3766,"style":3767},[381],"height:1.0361em;vertical-align:-0.2861em;",[316,3769,1604],{"className":3770,"style":1676},[386,390],[316,3772,630],{"className":3773},[771],[316,3775,657],{"className":3776},[386],[316,3778,3780,3783],{"className":3779},[386],[316,3781,633],{"className":3782},[386,390],[316,3784,3786],{"className":3785},[394],[316,3787,3789,3809],{"className":3788},[398,399],[316,3790,3792,3806],{"className":3791},[403],[316,3793,3795],{"className":3794,"style":814},[407],[316,3796,3797,3800],{"style":411},[316,3798],{"className":3799,"style":416},[415],[316,3801,3803],{"className":3802},[420,421,422,423],[316,3804,241],{"className":3805},[386,390,423],[316,3807,438],{"className":3808},[437],[316,3810,3812],{"className":3811},[403],[316,3813,3816],{"className":3814,"style":3815},[407],"height:0.2861em;",[316,3817],{},[316,3819,636],{"className":3820},[778],[316,3822],{"className":3823,"style":452},[451],[316,3825,352],{"className":3826},[456],[316,3828],{"className":3829,"style":452},[451],[316,3831,3833,3836],{"className":3832},[377],[316,3834],{"className":3835,"style":1925},[381],[316,3837,363],{"className":3838},[386]," 作为0电势参考点)",[523,3841,3842],{},[526,3843,3844],{},"On the P side:",[316,3846,3848],{"className":3847},[3011],[316,3849,3851,3954],{"className":3850},[319],[316,3852,3854],{"className":3853},[323],[325,3855,3856],{"xmlns":327,"display":3020},[329,3857,3858,3951],{},[332,3859,3860,3862,3864,3866,3868,3870,3872,3874,3876,3893,3895,3897,3899,3901,3904,3906,3908,3933,3935,3941,3943,3945],{},[338,3861,1604],{},[350,3863,630],{"stretchy":629},[338,3865,633],{},[350,3867,636],{"stretchy":629},[350,3869,657],{},[354,3871,363],{},[350,3873,352],{},[350,3875,657],{},[2166,3877,3878,3881,3891],{},[350,3879,3880],{},"∫",[332,3882,3883,3885],{},[350,3884,657],{},[335,3886,3887,3889],{},[338,3888,633],{},[338,3890,241],{},[354,3892,363],{},[338,3894,550],{},[350,3896,630],{"stretchy":629},[338,3898,633],{},[350,3900,636],{"stretchy":629},[338,3902,3903],{},"d",[338,3905,633],{},[350,3907,352],{},[659,3909,3910,3921],{},[332,3911,3912,3915],{},[338,3913,3914],{},"q",[335,3916,3917,3919],{},[338,3918,643],{},[338,3920,2263],{},[332,3922,3923,3925],{},[354,3924,3081],{},[335,3926,3927,3930],{},[338,3928,3929],{},"ε",[338,3931,3932],{},"s",[350,3934,630],{"stretchy":629},[335,3936,3937,3939],{},[338,3938,633],{},[338,3940,241],{},[350,3942,1611],{},[338,3944,633],{},[648,3946,3947,3949],{},[350,3948,636],{"stretchy":629},[354,3950,3081],{},[365,3952,3953],{"encoding":367},"V(x) - 0 = -\\int_{-x_p}^{0} E(x)dx = \\frac{qN_A}{2\\varepsilon_s}(x_p + x)^2",[316,3955,3957,3984,4002,4152,4354],{"className":3956,"ariaHidden":373},[372],[316,3958,3960,3963,3966,3969,3972,3975,3978,3981],{"className":3959},[377],[316,3961],{"className":3962,"style":764},[381],[316,3964,1604],{"className":3965,"style":1676},[386,390],[316,3967,630],{"className":3968},[771],[316,3970,633],{"className":3971},[386,390],[316,3973,636],{"className":3974},[778],[316,3976],{"className":3977,"style":1676},[451],[316,3979,657],{"className":3980},[991],[316,3982],{"className":3983,"style":1676},[451],[316,3985,3987,3990,3993,3996,3999],{"className":3986},[377],[316,3988],{"className":3989,"style":1925},[381],[316,3991,363],{"className":3992},[386],[316,3994],{"className":3995,"style":452},[451],[316,3997,352],{"className":3998},[456],[316,4000],{"className":4001,"style":452},[451],[316,4003,4005,4009,4012,4015,4122,4125,4128,4131,4134,4137,4140,4143,4146,4149],{"className":4004},[377],[316,4006],{"className":4007,"style":4008},[381],"height:2.6733em;vertical-align:-1.1093em;",[316,4010,657],{"className":4011},[386],[316,4013],{"className":4014,"style":1059},[451],[316,4016,4018,4024],{"className":4017},[3232],[316,4019,3880],{"className":4020,"style":4023},[3232,4021,4022],"op-symbol","large-op","margin-right:0.4445em;position:relative;top:-0.0011em;",[316,4025,4027],{"className":4026},[394],[316,4028,4030,4113],{"className":4029},[398,399],[316,4031,4033,4110],{"className":4032},[403],[316,4034,4037,4095],{"className":4035,"style":4036},[407],"height:1.564em;",[316,4038,4040,4043],{"style":4039},"top:-1.7881em;margin-left:-0.4445em;margin-right:0.05em;",[316,4041],{"className":4042,"style":416},[415],[316,4044,4046],{"className":4045},[420,421,422,423],[316,4047,4049,4052],{"className":4048},[386,423],[316,4050,657],{"className":4051},[386,423],[316,4053,4055,4058],{"className":4054},[386,423],[316,4056,633],{"className":4057},[386,390,423],[316,4059,4061],{"className":4060},[394],[316,4062,4064,4086],{"className":4063},[398,399],[316,4065,4067,4083],{"className":4066},[403],[316,4068,4071],{"className":4069,"style":4070},[407],"height:0.1645em;",[316,4072,4074,4077],{"style":4073},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[316,4075],{"className":4076,"style":963},[415],[316,4078,4080],{"className":4079},[420,880,904,423],[316,4081,241],{"className":4082},[386,390,423],[316,4084,438],{"className":4085},[437],[316,4087,4089],{"className":4088},[403],[316,4090,4093],{"className":4091,"style":4092},[407],"height:0.2819em;",[316,4094],{},[316,4096,4098,4101],{"style":4097},"top:-3.8129em;margin-right:0.05em;",[316,4099],{"className":4100,"style":416},[415],[316,4102,4104],{"className":4103},[420,421,422,423],[316,4105,4107],{"className":4106},[386,423],[316,4108,363],{"className":4109},[386,423],[316,4111,438],{"className":4112},[437],[316,4114,4116],{"className":4115},[403],[316,4117,4120],{"className":4118,"style":4119},[407],"height:1.1093em;",[316,4121],{},[316,4123],{"className":4124,"style":1059},[451],[316,4126,550],{"className":4127,"style":430},[386,390],[316,4129,630],{"className":4130},[771],[316,4132,633],{"className":4133},[386,390],[316,4135,636],{"className":4136},[778],[316,4138,3903],{"className":4139},[386,390],[316,4141,633],{"className":4142},[386,390],[316,4144],{"className":4145,"style":452},[451],[316,4147,352],{"className":4148},[456],[316,4150],{"className":4151,"style":452},[451],[316,4153,4155,4159,4302,4305,4345,4348,4351],{"className":4154},[377],[316,4156],{"className":4157,"style":4158},[381],"height:2.1963em;vertical-align:-0.836em;",[316,4160,4162,4165,4299],{"className":4161},[386],[316,4163],{"className":4164},[771,879],[316,4166,4168],{"className":4167},[659],[316,4169,4171,4290],{"className":4170},[398,399],[316,4172,4174,4287],{"className":4173},[403],[316,4175,4177,4228,4236],{"className":4176,"style":3267},[407],[316,4178,4179,4182],{"style":3176},[316,4180],{"className":4181,"style":863},[415],[316,4183,4185,4188],{"className":4184},[386],[316,4186,3081],{"className":4187},[386],[316,4189,4191,4194],{"className":4190},[386],[316,4192,3929],{"className":4193},[386,390],[316,4195,4197],{"className":4196},[394],[316,4198,4200,4220],{"className":4199},[398,399],[316,4201,4203,4217],{"className":4202},[403],[316,4204,4206],{"className":4205,"style":814},[407],[316,4207,4208,4211],{"style":411},[316,4209],{"className":4210,"style":416},[415],[316,4212,4214],{"className":4213},[420,421,422,423],[316,4215,3932],{"className":4216},[386,390,423],[316,4218,438],{"className":4219},[437],[316,4221,4223],{"className":4222},[403],[316,4224,4226],{"className":4225,"style":445},[407],[316,4227],{},[316,4229,4230,4233],{"style":3188},[316,4231],{"className":4232,"style":863},[415],[316,4234],{"className":4235,"style":3195},[924],[316,4237,4238,4241],{"style":3198},[316,4239],{"className":4240,"style":863},[415],[316,4242,4244,4247],{"className":4243},[386],[316,4245,3914],{"className":4246,"style":1117},[386,390],[316,4248,4250,4253],{"className":4249},[386],[316,4251,643],{"className":4252,"style":801},[386,390],[316,4254,4256],{"className":4255},[394],[316,4257,4259,4279],{"className":4258},[398,399],[316,4260,4262,4276],{"className":4261},[403],[316,4263,4265],{"className":4264,"style":408},[407],[316,4266,4267,4270],{"style":817},[316,4268],{"className":4269,"style":416},[415],[316,4271,4273],{"className":4272},[420,421,422,423],[316,4274,2263],{"className":4275},[386,390,423],[316,4277,438],{"className":4278},[437],[316,4280,4282],{"className":4281},[403],[316,4283,4285],{"className":4284,"style":445},[407],[316,4286],{},[316,4288,438],{"className":4289},[437],[316,4291,4293],{"className":4292},[403],[316,4294,4297],{"className":4295,"style":4296},[407],"height:0.836em;",[316,4298],{},[316,4300],{"className":4301},[778,879],[316,4303,630],{"className":4304},[771],[316,4306,4308,4311],{"className":4307},[386],[316,4309,633],{"className":4310},[386,390],[316,4312,4314],{"className":4313},[394],[316,4315,4317,4337],{"className":4316},[398,399],[316,4318,4320,4334],{"className":4319},[403],[316,4321,4323],{"className":4322,"style":814},[407],[316,4324,4325,4328],{"style":411},[316,4326],{"className":4327,"style":416},[415],[316,4329,4331],{"className":4330},[420,421,422,423],[316,4332,241],{"className":4333},[386,390,423],[316,4335,438],{"className":4336},[437],[316,4338,4340],{"className":4339},[403],[316,4341,4343],{"className":4342,"style":3815},[407],[316,4344],{},[316,4346],{"className":4347,"style":1676},[451],[316,4349,1611],{"className":4350},[991],[316,4352],{"className":4353,"style":1676},[451],[316,4355,4357,4361,4364],{"className":4356},[377],[316,4358],{"className":4359,"style":4360},[381],"height:1.1141em;vertical-align:-0.25em;",[316,4362,633],{"className":4363},[386,390],[316,4365,4367,4370],{"className":4366},[778],[316,4368,636],{"className":4369},[778],[316,4371,4373],{"className":4372},[394],[316,4374,4376],{"className":4375},[398],[316,4377,4379],{"className":4378},[403],[316,4380,4383],{"className":4381,"style":4382},[407],"height:0.8641em;",[316,4384,4386,4389],{"style":4385},"top:-3.113em;margin-right:0.05em;",[316,4387],{"className":4388,"style":416},[415],[316,4390,4392],{"className":4391},[420,421,422,423],[316,4393,3081],{"className":4394},[386,423],[523,4396,4397],{},[526,4398,4399],{},"On the N side :",[316,4401,4403],{"className":4402},[3011],[316,4404,4406,4531],{"className":4405},[319],[316,4407,4409],{"className":4408},[323],[325,4410,4411],{"xmlns":327,"display":3020},[329,4412,4413,4528],{},[332,4414,4415,4425,4427,4429,4431,4433,4435,4437,4439,4451,4453,4455,4457,4459,4461,4463,4466,4468,4470,4472,4474,4476,4486,4488,4510,4512,4518,4520,4522],{},[335,4416,4417,4419],{},[338,4418,1604],{},[332,4420,4421,4423],{},[338,4422,2038],{},[338,4424,348],{},[350,4426,657],{},[338,4428,1604],{},[350,4430,630],{"stretchy":629},[338,4432,633],{},[350,4434,636],{"stretchy":629},[350,4436,352],{},[350,4438,657],{},[2166,4440,4441,4443,4449],{},[350,4442,3880],{},[335,4444,4445,4447],{},[338,4446,633],{},[338,4448,626],{},[354,4450,363],{},[338,4452,550],{},[350,4454,630],{"stretchy":629},[338,4456,633],{},[350,4458,636],{"stretchy":629},[338,4460,3903],{},[338,4462,633],{},[451,4464],{"linebreak":4465},"newline",[338,4467,1604],{},[350,4469,630],{"stretchy":629},[338,4471,633],{},[350,4473,636],{"stretchy":629},[350,4475,352],{},[335,4477,4478,4480],{},[338,4479,1604],{},[332,4481,4482,4484],{},[338,4483,2038],{},[338,4485,348],{},[350,4487,657],{},[659,4489,4490,4500],{},[332,4491,4492,4494],{},[338,4493,3914],{},[335,4495,4496,4498],{},[338,4497,643],{},[338,4499,2172],{},[332,4501,4502,4504],{},[354,4503,3081],{},[335,4505,4506,4508],{},[338,4507,3929],{},[338,4509,3932],{},[350,4511,630],{"stretchy":629},[335,4513,4514,4516],{},[338,4515,633],{},[338,4517,626],{},[350,4519,657],{},[338,4521,633],{},[648,4523,4524,4526],{},[350,4525,636],{"stretchy":629},[354,4527,3081],{},[365,4529,4530],{"encoding":367},"V_{bi} - V(x) = -\\int_{x_n}^{0}E(x)dx \\\\ V(x) =V_{bi} - \\frac{qN_D}{2\\varepsilon_s}(x_n - x)^2",[316,4532,4534,4592,4619,4749,4752,4779,4837,5037],{"className":4533,"ariaHidden":373},[372],[316,4535,4537,4540,4583,4586,4589],{"className":4536},[377],[316,4538],{"className":4539,"style":566},[381],[316,4541,4543,4546],{"className":4542},[386],[316,4544,1604],{"className":4545,"style":1676},[386,390],[316,4547,4549],{"className":4548},[394],[316,4550,4552,4575],{"className":4551},[398,399],[316,4553,4555,4572],{"className":4554},[403],[316,4556,4558],{"className":4557,"style":2071},[407],[316,4559,4560,4563],{"style":1691},[316,4561],{"className":4562,"style":416},[415],[316,4564,4566],{"className":4565},[420,421,422,423],[316,4567,4569],{"className":4568},[386,423],[316,4570,2086],{"className":4571},[386,390,423],[316,4573,438],{"className":4574},[437],[316,4576,4578],{"className":4577},[403],[316,4579,4581],{"className":4580,"style":445},[407],[316,4582],{},[316,4584],{"className":4585,"style":1676},[451],[316,4587,657],{"className":4588},[991],[316,4590],{"className":4591,"style":1676},[451],[316,4593,4595,4598,4601,4604,4607,4610,4613,4616],{"className":4594},[377],[316,4596],{"className":4597,"style":764},[381],[316,4599,1604],{"className":4600,"style":1676},[386,390],[316,4602,630],{"className":4603},[771],[316,4605,633],{"className":4606},[386,390],[316,4608,636],{"className":4609},[778],[316,4611],{"className":4612,"style":452},[451],[316,4614,352],{"className":4615},[456],[316,4617],{"className":4618,"style":452},[451],[316,4620,4622,4626,4629,4632,4728,4731,4734,4737,4740,4743,4746],{"className":4621},[377],[316,4623],{"className":4624,"style":4625},[381],"height:2.5761em;vertical-align:-1.012em;",[316,4627,657],{"className":4628},[386],[316,4630],{"className":4631,"style":1059},[451],[316,4633,4635,4638],{"className":4634},[3232],[316,4636,3880],{"className":4637,"style":4023},[3232,4021,4022],[316,4639,4641],{"className":4640},[394],[316,4642,4644,4719],{"className":4643},[398,399],[316,4645,4647,4716],{"className":4646},[403],[316,4648,4650,4702],{"className":4649,"style":4036},[407],[316,4651,4652,4655],{"style":4039},[316,4653],{"className":4654,"style":416},[415],[316,4656,4658],{"className":4657},[420,421,422,423],[316,4659,4661],{"className":4660},[386,423],[316,4662,4664,4667],{"className":4663},[386,423],[316,4665,633],{"className":4666},[386,390,423],[316,4668,4670],{"className":4669},[394],[316,4671,4673,4693],{"className":4672},[398,399],[316,4674,4676,4690],{"className":4675},[403],[316,4677,4679],{"className":4678,"style":4070},[407],[316,4680,4681,4684],{"style":4073},[316,4682],{"className":4683,"style":963},[415],[316,4685,4687],{"className":4686},[420,880,904,423],[316,4688,626],{"className":4689},[386,390,423],[316,4691,438],{"className":4692},[437],[316,4694,4696],{"className":4695},[403],[316,4697,4700],{"className":4698,"style":4699},[407],"height:0.143em;",[316,4701],{},[316,4703,4704,4707],{"style":4097},[316,4705],{"className":4706,"style":416},[415],[316,4708,4710],{"className":4709},[420,421,422,423],[316,4711,4713],{"className":4712},[386,423],[316,4714,363],{"className":4715},[386,423],[316,4717,438],{"className":4718},[437],[316,4720,4722],{"className":4721},[403],[316,4723,4726],{"className":4724,"style":4725},[407],"height:1.012em;",[316,4727],{},[316,4729],{"className":4730,"style":1059},[451],[316,4732,550],{"className":4733,"style":430},[386,390],[316,4735,630],{"className":4736},[771],[316,4738,633],{"className":4739},[386,390],[316,4741,636],{"className":4742},[778],[316,4744,3903],{"className":4745},[386,390],[316,4747,633],{"className":4748},[386,390],[316,4750],{"className":4751},[451,4465],[316,4753,4755,4758,4761,4764,4767,4770,4773,4776],{"className":4754},[377],[316,4756],{"className":4757,"style":764},[381],[316,4759,1604],{"className":4760,"style":1676},[386,390],[316,4762,630],{"className":4763},[771],[316,4765,633],{"className":4766},[386,390],[316,4768,636],{"className":4769},[778],[316,4771],{"className":4772,"style":452},[451],[316,4774,352],{"className":4775},[456],[316,4777],{"className":4778,"style":452},[451],[316,4780,4782,4785,4828,4831,4834],{"className":4781},[377],[316,4783],{"className":4784,"style":566},[381],[316,4786,4788,4791],{"className":4787},[386],[316,4789,1604],{"className":4790,"style":1676},[386,390],[316,4792,4794],{"className":4793},[394],[316,4795,4797,4820],{"className":4796},[398,399],[316,4798,4800,4817],{"className":4799},[403],[316,4801,4803],{"className":4802,"style":2071},[407],[316,4804,4805,4808],{"style":1691},[316,4806],{"className":4807,"style":416},[415],[316,4809,4811],{"className":4810},[420,421,422,423],[316,4812,4814],{"className":4813},[386,423],[316,4815,2086],{"className":4816},[386,390,423],[316,4818,438],{"className":4819},[437],[316,4821,4823],{"className":4822},[403],[316,4824,4826],{"className":4825,"style":445},[407],[316,4827],{},[316,4829],{"className":4830,"style":1676},[451],[316,4832,657],{"className":4833},[991],[316,4835],{"className":4836,"style":1676},[451],[316,4838,4840,4843,4985,4988,5028,5031,5034],{"className":4839},[377],[316,4841],{"className":4842,"style":4158},[381],[316,4844,4846,4849,4982],{"className":4845},[386],[316,4847],{"className":4848},[771,879],[316,4850,4852],{"className":4851},[659],[316,4853,4855,4974],{"className":4854},[398,399],[316,4856,4858,4971],{"className":4857},[403],[316,4859,4861,4912,4920],{"className":4860,"style":3267},[407],[316,4862,4863,4866],{"style":3176},[316,4864],{"className":4865,"style":863},[415],[316,4867,4869,4872],{"className":4868},[386],[316,4870,3081],{"className":4871},[386],[316,4873,4875,4878],{"className":4874},[386],[316,4876,3929],{"className":4877},[386,390],[316,4879,4881],{"className":4880},[394],[316,4882,4884,4904],{"className":4883},[398,399],[316,4885,4887,4901],{"className":4886},[403],[316,4888,4890],{"className":4889,"style":814},[407],[316,4891,4892,4895],{"style":411},[316,4893],{"className":4894,"style":416},[415],[316,4896,4898],{"className":4897},[420,421,422,423],[316,4899,3932],{"className":4900},[386,390,423],[316,4902,438],{"className":4903},[437],[316,4905,4907],{"className":4906},[403],[316,4908,4910],{"className":4909,"style":445},[407],[316,4911],{},[316,4913,4914,4917],{"style":3188},[316,4915],{"className":4916,"style":863},[415],[316,4918],{"className":4919,"style":3195},[924],[316,4921,4922,4925],{"style":3198},[316,4923],{"className":4924,"style":863},[415],[316,4926,4928,4931],{"className":4927},[386],[316,4929,3914],{"className":4930,"style":1117},[386,390],[316,4932,4934,4937],{"className":4933},[386],[316,4935,643],{"className":4936,"style":801},[386,390],[316,4938,4940],{"className":4939},[394],[316,4941,4943,4963],{"className":4942},[398,399],[316,4944,4946,4960],{"className":4945},[403],[316,4947,4949],{"className":4948,"style":408},[407],[316,4950,4951,4954],{"style":817},[316,4952],{"className":4953,"style":416},[415],[316,4955,4957],{"className":4956},[420,421,422,423],[316,4958,2172],{"className":4959,"style":2219},[386,390,423],[316,4961,438],{"className":4962},[437],[316,4964,4966],{"className":4965},[403],[316,4967,4969],{"className":4968,"style":445},[407],[316,4970],{},[316,4972,438],{"className":4973},[437],[316,4975,4977],{"className":4976},[403],[316,4978,4980],{"className":4979,"style":4296},[407],[316,4981],{},[316,4983],{"className":4984},[778,879],[316,4986,630],{"className":4987},[771],[316,4989,4991,4994],{"className":4990},[386],[316,4992,633],{"className":4993},[386,390],[316,4995,4997],{"className":4996},[394],[316,4998,5000,5020],{"className":4999},[398,399],[316,5001,5003,5017],{"className":5002},[403],[316,5004,5006],{"className":5005,"style":814},[407],[316,5007,5008,5011],{"style":411},[316,5009],{"className":5010,"style":416},[415],[316,5012,5014],{"className":5013},[420,421,422,423],[316,5015,626],{"className":5016},[386,390,423],[316,5018,438],{"className":5019},[437],[316,5021,5023],{"className":5022},[403],[316,5024,5026],{"className":5025,"style":445},[407],[316,5027],{},[316,5029],{"className":5030,"style":1676},[451],[316,5032,657],{"className":5033},[991],[316,5035],{"className":5036,"style":1676},[451],[316,5038,5040,5043,5046],{"className":5039},[377],[316,5041],{"className":5042,"style":4360},[381],[316,5044,633],{"className":5045},[386,390],[316,5047,5049,5052],{"className":5048},[778],[316,5050,636],{"className":5051},[778],[316,5053,5055],{"className":5054},[394],[316,5056,5058],{"className":5057},[398],[316,5059,5061],{"className":5060},[403],[316,5062,5064],{"className":5063,"style":4382},[407],[316,5065,5066,5069],{"style":4385},[316,5067],{"className":5068,"style":416},[415],[316,5070,5072],{"className":5071},[420,421,422,423],[316,5073,3081],{"className":5074},[386,423],[241,5076,5077,5078,5500,5501],{},"也可以得到",[316,5079,5081,5149],{"className":5080},[319],[316,5082,5084],{"className":5083},[323],[325,5085,5086],{"xmlns":327},[329,5087,5088,5146],{},[332,5089,5090,5100,5102,5124,5126,5134,5136,5144],{},[335,5091,5092,5094],{},[338,5093,1604],{},[332,5095,5096,5098],{},[338,5097,2038],{},[338,5099,348],{},[350,5101,352],{},[659,5103,5104,5114],{},[332,5105,5106,5108],{},[338,5107,3914],{},[335,5109,5110,5112],{},[338,5111,643],{},[338,5113,2263],{},[332,5115,5116,5118],{},[354,5117,3081],{},[335,5119,5120,5122],{},[338,5121,3929],{},[338,5123,3932],{},[350,5125,630],{"stretchy":629},[2166,5127,5128,5130,5132],{},[338,5129,633],{},[338,5131,241],{},[354,5133,3081],{},[350,5135,1611],{},[2166,5137,5138,5140,5142],{},[338,5139,633],{},[338,5141,626],{},[354,5143,3081],{},[350,5145,636],{"stretchy":629},[365,5147,5148],{"encoding":367},"V_{bi} =\\frac{qN_A}{2\\varepsilon_s}(x_p^2 + x_n^2)",[316,5150,5152,5210,5438],{"className":5151,"ariaHidden":373},[372],[316,5153,5155,5158,5201,5204,5207],{"className":5154},[377],[316,5156],{"className":5157,"style":566},[381],[316,5159,5161,5164],{"className":5160},[386],[316,5162,1604],{"className":5163,"style":1676},[386,390],[316,5165,5167],{"className":5166},[394],[316,5168,5170,5193],{"className":5169},[398,399],[316,5171,5173,5190],{"className":5172},[403],[316,5174,5176],{"className":5175,"style":2071},[407],[316,5177,5178,5181],{"style":1691},[316,5179],{"className":5180,"style":416},[415],[316,5182,5184],{"className":5183},[420,421,422,423],[316,5185,5187],{"className":5186},[386,423],[316,5188,2086],{"className":5189},[386,390,423],[316,5191,438],{"className":5192},[437],[316,5194,5196],{"className":5195},[403],[316,5197,5199],{"className":5198,"style":445},[407],[316,5200],{},[316,5202],{"className":5203,"style":452},[451],[316,5205,352],{"className":5206},[456],[316,5208],{"className":5209,"style":452},[451],[316,5211,5213,5217,5371,5374,5429,5432,5435],{"className":5212},[377],[316,5214],{"className":5215,"style":5216},[381],"height:1.3695em;vertical-align:-0.4451em;",[316,5218,5220,5223,5368],{"className":5219},[386],[316,5221],{"className":5222},[771,879],[316,5224,5226],{"className":5225},[659],[316,5227,5229,5359],{"className":5228},[398,399],[316,5230,5232,5356],{"className":5231},[403],[316,5233,5236,5291,5299],{"className":5234,"style":5235},[407],"height:0.9244em;",[316,5237,5239,5242],{"style":5238},"top:-2.655em;",[316,5240],{"className":5241,"style":863},[415],[316,5243,5245],{"className":5244},[420,421,422,423],[316,5246,5248,5251],{"className":5247},[386,423],[316,5249,3081],{"className":5250},[386,423],[316,5252,5254,5257],{"className":5253},[386,423],[316,5255,3929],{"className":5256},[386,390,423],[316,5258,5260],{"className":5259},[394],[316,5261,5263,5283],{"className":5262},[398,399],[316,5264,5266,5280],{"className":5265},[403],[316,5267,5269],{"className":5268,"style":4070},[407],[316,5270,5271,5274],{"style":4073},[316,5272],{"className":5273,"style":963},[415],[316,5275,5277],{"className":5276},[420,880,904,423],[316,5278,3932],{"className":5279},[386,390,423],[316,5281,438],{"className":5282},[437],[316,5284,5286],{"className":5285},[403],[316,5287,5289],{"className":5288,"style":4699},[407],[316,5290],{},[316,5292,5293,5296],{"style":3188},[316,5294],{"className":5295,"style":863},[415],[316,5297],{"className":5298,"style":3195},[924],[316,5300,5302,5305],{"style":5301},"top:-3.4461em;",[316,5303],{"className":5304,"style":863},[415],[316,5306,5308],{"className":5307},[420,421,422,423],[316,5309,5311,5314],{"className":5310},[386,423],[316,5312,3914],{"className":5313,"style":1117},[386,390,423],[316,5315,5317,5320],{"className":5316},[386,423],[316,5318,643],{"className":5319,"style":801},[386,390,423],[316,5321,5323],{"className":5322},[394],[316,5324,5326,5347],{"className":5325},[398,399],[316,5327,5329,5344],{"className":5328},[403],[316,5330,5332],{"className":5331,"style":1010},[407],[316,5333,5335,5338],{"style":5334},"top:-2.3567em;margin-left:-0.109em;margin-right:0.0714em;",[316,5336],{"className":5337,"style":963},[415],[316,5339,5341],{"className":5340},[420,880,904,423],[316,5342,2263],{"className":5343},[386,390,423],[316,5345,438],{"className":5346},[437],[316,5348,5350],{"className":5349},[403],[316,5351,5354],{"className":5352,"style":5353},[407],"height:0.1433em;",[316,5355],{},[316,5357,438],{"className":5358},[437],[316,5360,5362],{"className":5361},[403],[316,5363,5366],{"className":5364,"style":5365},[407],"height:0.4451em;",[316,5367],{},[316,5369],{"className":5370},[778,879],[316,5372,630],{"className":5373},[771],[316,5375,5377,5380],{"className":5376},[386],[316,5378,633],{"className":5379},[386,390],[316,5381,5383],{"className":5382},[394],[316,5384,5386,5420],{"className":5385},[398,399],[316,5387,5389,5417],{"className":5388},[403],[316,5390,5393,5405],{"className":5391,"style":5392},[407],"height:0.8141em;",[316,5394,5396,5399],{"style":5395},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[316,5397],{"className":5398,"style":416},[415],[316,5400,5402],{"className":5401},[420,421,422,423],[316,5403,241],{"className":5404},[386,390,423],[316,5406,5408,5411],{"style":5407},"top:-3.063em;margin-right:0.05em;",[316,5409],{"className":5410,"style":416},[415],[316,5412,5414],{"className":5413},[420,421,422,423],[316,5415,3081],{"className":5416},[386,423],[316,5418,438],{"className":5419},[437],[316,5421,5423],{"className":5422},[403],[316,5424,5427],{"className":5425,"style":5426},[407],"height:0.3831em;",[316,5428],{},[316,5430],{"className":5431,"style":1676},[451],[316,5433,1611],{"className":5434},[991],[316,5436],{"className":5437,"style":1676},[451],[316,5439,5441,5445,5497],{"className":5440},[377],[316,5442],{"className":5443,"style":5444},[381],"height:1.0641em;vertical-align:-0.25em;",[316,5446,5448,5451],{"className":5447},[386],[316,5449,633],{"className":5450},[386,390],[316,5452,5454],{"className":5453},[394],[316,5455,5457,5488],{"className":5456},[398,399],[316,5458,5460,5485],{"className":5459},[403],[316,5461,5463,5474],{"className":5462,"style":5392},[407],[316,5464,5465,5468],{"style":5395},[316,5466],{"className":5467,"style":416},[415],[316,5469,5471],{"className":5470},[420,421,422,423],[316,5472,626],{"className":5473},[386,390,423],[316,5475,5476,5479],{"style":5407},[316,5477],{"className":5478,"style":416},[415],[316,5480,5482],{"className":5481},[420,421,422,423],[316,5483,3081],{"className":5484},[386,423],[316,5486,438],{"className":5487},[437],[316,5489,5491],{"className":5490},[403],[316,5492,5495],{"className":5493,"style":5494},[407],"height:0.247em;",[316,5496],{},[316,5498,636],{"className":5499},[778],"同时有",[316,5502,5504,5535],{"className":5503},[319],[316,5505,5507],{"className":5506},[323],[325,5508,5509],{"xmlns":327},[329,5510,5511,5532],{},[332,5512,5513,5516,5518,5524,5526],{},[338,5514,5515],{},"W",[350,5517,352],{},[335,5519,5520,5522],{},[338,5521,633],{},[338,5523,626],{},[350,5525,1611],{},[335,5527,5528,5530],{},[338,5529,633],{},[338,5531,241],{},[365,5533,5534],{"encoding":367},"W = x_n + x_p",[316,5536,5538,5557,5613],{"className":5537,"ariaHidden":373},[372],[316,5539,5541,5545,5548,5551,5554],{"className":5540},[377],[316,5542],{"className":5543,"style":5544},[381],"height:0.6833em;",[316,5546,5515],{"className":5547,"style":597},[386,390],[316,5549],{"className":5550,"style":452},[451],[316,5552,352],{"className":5553},[456],[316,5555],{"className":5556,"style":452},[451],[316,5558,5560,5564,5604,5607,5610],{"className":5559},[377],[316,5561],{"className":5562,"style":5563},[381],"height:0.7333em;vertical-align:-0.15em;",[316,5565,5567,5570],{"className":5566},[386],[316,5568,633],{"className":5569},[386,390],[316,5571,5573],{"className":5572},[394],[316,5574,5576,5596],{"className":5575},[398,399],[316,5577,5579,5593],{"className":5578},[403],[316,5580,5582],{"className":5581,"style":814},[407],[316,5583,5584,5587],{"style":411},[316,5585],{"className":5586,"style":416},[415],[316,5588,5590],{"className":5589},[420,421,422,423],[316,5591,626],{"className":5592},[386,390,423],[316,5594,438],{"className":5595},[437],[316,5597,5599],{"className":5598},[403],[316,5600,5602],{"className":5601,"style":445},[407],[316,5603],{},[316,5605],{"className":5606,"style":1676},[451],[316,5608,1611],{"className":5609},[991],[316,5611],{"className":5612,"style":1676},[451],[316,5614,5616,5620],{"className":5615},[377],[316,5617],{"className":5618,"style":5619},[381],"height:0.7167em;vertical-align:-0.2861em;",[316,5621,5623,5626],{"className":5622},[386],[316,5624,633],{"className":5625},[386,390],[316,5627,5629],{"className":5628},[394],[316,5630,5632,5652],{"className":5631},[398,399],[316,5633,5635,5649],{"className":5634},[403],[316,5636,5638],{"className":5637,"style":814},[407],[316,5639,5640,5643],{"style":411},[316,5641],{"className":5642,"style":416},[415],[316,5644,5646],{"className":5645},[420,421,422,423],[316,5647,241],{"className":5648},[386,390,423],[316,5650,438],{"className":5651},[437],[316,5653,5655],{"className":5654},[403],[316,5656,5658],{"className":5657,"style":3815},[407],[316,5659],{},[241,5661,5662],{},"得到如下一系列公式",[316,5664,5666],{"className":5665},[3011],[316,5667,5669,5743],{"className":5668},[319],[316,5670,5672],{"className":5671},[323],[325,5673,5674],{"xmlns":327,"display":3020},[329,5675,5676,5740],{},[332,5677,5678,5680,5682],{},[338,5679,5515],{},[350,5681,352],{},[5683,5684,5685],"msqrt",{},[332,5686,5687,5711],{},[659,5688,5689,5709],{},[332,5690,5691,5693,5699],{},[354,5692,3081],{},[335,5694,5695,5697],{},[338,5696,3929],{},[338,5698,3932],{},[335,5700,5701,5703],{},[338,5702,1604],{},[332,5704,5705,5707],{},[338,5706,2038],{},[338,5708,348],{},[338,5710,3914],{},[332,5712,5713,5715,5726,5728,5738],{},[350,5714,630],{"fence":373},[659,5716,5717,5720],{},[354,5718,5719],{},"1",[335,5721,5722,5724],{},[338,5723,643],{},[338,5725,2263],{},[350,5727,1611],{},[659,5729,5730,5732],{},[354,5731,5719],{},[335,5733,5734,5736],{},[338,5735,643],{},[338,5737,2172],{},[350,5739,636],{"fence":373},[365,5741,5742],{"encoding":367},"W = \\sqrt{\\frac{2\\varepsilon_sV_{bi}}{q}\\left(\\frac{1}{N_A} + \\frac{1}{N_D} \\right)}",[316,5744,5746,5764],{"className":5745,"ariaHidden":373},[372],[316,5747,5749,5752,5755,5758,5761],{"className":5748},[377],[316,5750],{"className":5751,"style":5544},[381],[316,5753,5515],{"className":5754,"style":597},[386,390],[316,5756],{"className":5757,"style":452},[451],[316,5759,352],{"className":5760},[456],[316,5762],{"className":5763,"style":452},[451],[316,5765,5767,5771],{"className":5766},[377],[316,5768],{"className":5769,"style":5770},[381],"height:3.04em;vertical-align:-1.1561em;",[316,5772,5775],{"className":5773},[386,5774],"sqrt",[316,5776,5778,6196],{"className":5777},[398,399],[316,5779,5781,6193],{"className":5780},[403],[316,5782,5785,6170],{"className":5783,"style":5784},[407],"height:1.8839em;",[316,5786,5790,5794],{"className":5787,"style":5789},[5788],"svg-align","top:-5em;",[316,5791],{"className":5792,"style":5793},[415],"height:5em;",[316,5795,5798,5944,5947],{"className":5796,"style":5797},[386],"padding-left:1em;",[316,5799,5801,5804,5941],{"className":5800},[386],[316,5802],{"className":5803},[771,879],[316,5805,5807],{"className":5806},[659],[316,5808,5810,5932],{"className":5809},[398,399],[316,5811,5813,5929],{"className":5812},[403],[316,5814,5816,5827,5835],{"className":5815,"style":3267},[407],[316,5817,5818,5821],{"style":3176},[316,5819],{"className":5820,"style":863},[415],[316,5822,5824],{"className":5823},[386],[316,5825,3914],{"className":5826,"style":1117},[386,390],[316,5828,5829,5832],{"style":3188},[316,5830],{"className":5831,"style":863},[415],[316,5833],{"className":5834,"style":3195},[924],[316,5836,5837,5840],{"style":3198},[316,5838],{"className":5839,"style":863},[415],[316,5841,5843,5846,5886],{"className":5842},[386],[316,5844,3081],{"className":5845},[386],[316,5847,5849,5852],{"className":5848},[386],[316,5850,3929],{"className":5851},[386,390],[316,5853,5855],{"className":5854},[394],[316,5856,5858,5878],{"className":5857},[398,399],[316,5859,5861,5875],{"className":5860},[403],[316,5862,5864],{"className":5863,"style":814},[407],[316,5865,5866,5869],{"style":411},[316,5867],{"className":5868,"style":416},[415],[316,5870,5872],{"className":5871},[420,421,422,423],[316,5873,3932],{"className":5874},[386,390,423],[316,5876,438],{"className":5877},[437],[316,5879,5881],{"className":5880},[403],[316,5882,5884],{"className":5883,"style":445},[407],[316,5885],{},[316,5887,5889,5892],{"className":5888},[386],[316,5890,1604],{"className":5891,"style":1676},[386,390],[316,5893,5895],{"className":5894},[394],[316,5896,5898,5921],{"className":5897},[398,399],[316,5899,5901,5918],{"className":5900},[403],[316,5902,5904],{"className":5903,"style":2071},[407],[316,5905,5906,5909],{"style":1691},[316,5907],{"className":5908,"style":416},[415],[316,5910,5912],{"className":5911},[420,421,422,423],[316,5913,5915],{"className":5914},[386,423],[316,5916,2086],{"className":5917},[386,390,423],[316,5919,438],{"className":5920},[437],[316,5922,5924],{"className":5923},[403],[316,5925,5927],{"className":5926,"style":445},[407],[316,5928],{},[316,5930,438],{"className":5931},[437],[316,5933,5935],{"className":5934},[403],[316,5936,5939],{"className":5937,"style":5938},[407],"height:0.8804em;",[316,5940],{},[316,5942],{"className":5943},[778,879],[316,5945],{"className":5946,"style":1059},[451],[316,5948,5950,5956,6056,6059,6062,6065,6164],{"className":5949},[3239],[316,5951,5953],{"className":5952,"style":3244},[771,3243],[316,5954,630],{"className":5955},[3248,422],[316,5957,5959,5962,6053],{"className":5958},[386],[316,5960],{"className":5961},[771,879],[316,5963,5965],{"className":5964},[659],[316,5966,5968,6045],{"className":5967},[398,399],[316,5969,5971,6042],{"className":5970},[403],[316,5972,5975,6023,6031],{"className":5973,"style":5974},[407],"height:1.3214em;",[316,5976,5977,5980],{"style":3176},[316,5978],{"className":5979,"style":863},[415],[316,5981,5983],{"className":5982},[386],[316,5984,5986,5989],{"className":5985},[386],[316,5987,643],{"className":5988,"style":801},[386,390],[316,5990,5992],{"className":5991},[394],[316,5993,5995,6015],{"className":5994},[398,399],[316,5996,5998,6012],{"className":5997},[403],[316,5999,6001],{"className":6000,"style":408},[407],[316,6002,6003,6006],{"style":817},[316,6004],{"className":6005,"style":416},[415],[316,6007,6009],{"className":6008},[420,421,422,423],[316,6010,2263],{"className":6011},[386,390,423],[316,6013,438],{"className":6014},[437],[316,6016,6018],{"className":6017},[403],[316,6019,6021],{"className":6020,"style":445},[407],[316,6022],{},[316,6024,6025,6028],{"style":3188},[316,6026],{"className":6027,"style":863},[415],[316,6029],{"className":6030,"style":3195},[924],[316,6032,6033,6036],{"style":3198},[316,6034],{"className":6035,"style":863},[415],[316,6037,6039],{"className":6038},[386],[316,6040,5719],{"className":6041},[386],[316,6043,438],{"className":6044},[437],[316,6046,6048],{"className":6047},[403],[316,6049,6051],{"className":6050,"style":4296},[407],[316,6052],{},[316,6054],{"className":6055},[778,879],[316,6057],{"className":6058,"style":1676},[451],[316,6060,1611],{"className":6061},[991],[316,6063],{"className":6064,"style":1676},[451],[316,6066,6068,6071,6161],{"className":6067},[386],[316,6069],{"className":6070},[771,879],[316,6072,6074],{"className":6073},[659],[316,6075,6077,6153],{"className":6076},[398,399],[316,6078,6080,6150],{"className":6079},[403],[316,6081,6083,6131,6139],{"className":6082,"style":5974},[407],[316,6084,6085,6088],{"style":3176},[316,6086],{"className":6087,"style":863},[415],[316,6089,6091],{"className":6090},[386],[316,6092,6094,6097],{"className":6093},[386],[316,6095,643],{"className":6096,"style":801},[386,390],[316,6098,6100],{"className":6099},[394],[316,6101,6103,6123],{"className":6102},[398,399],[316,6104,6106,6120],{"className":6105},[403],[316,6107,6109],{"className":6108,"style":408},[407],[316,6110,6111,6114],{"style":817},[316,6112],{"className":6113,"style":416},[415],[316,6115,6117],{"className":6116},[420,421,422,423],[316,6118,2172],{"className":6119,"style":2219},[386,390,423],[316,6121,438],{"className":6122},[437],[316,6124,6126],{"className":6125},[403],[316,6127,6129],{"className":6128,"style":445},[407],[316,6130],{},[316,6132,6133,6136],{"style":3188},[316,6134],{"className":6135,"style":863},[415],[316,6137],{"className":6138,"style":3195},[924],[316,6140,6141,6144],{"style":3198},[316,6142],{"className":6143,"style":863},[415],[316,6145,6147],{"className":6146},[386],[316,6148,5719],{"className":6149},[386],[316,6151,438],{"className":6152},[437],[316,6154,6156],{"className":6155},[403],[316,6157,6159],{"className":6158,"style":4296},[407],[316,6160],{},[316,6162],{"className":6163},[778,879],[316,6165,6167],{"className":6166,"style":3244},[778,3243],[316,6168,636],{"className":6169},[3248,422],[316,6171,6173,6176],{"style":6172},"top:-3.8439em;",[316,6174],{"className":6175,"style":5793},[415],[316,6177,6181],{"className":6178,"style":6180},[6179],"hide-tail","min-width:1.02em;height:3.08em;",[6182,6183,6189],"svg",{"xmlns":6184,"width":6185,"height":6186,"viewBox":6187,"preserveAspectRatio":6188},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","3.08em","0 0 400000 3240","xMinYMin slice",[6190,6191],"path",{"d":6192},"M473,2793\nc339.3,-1799.3,509.3,-2700,510,-2702 l0 -0\nc3.3,-7.3,9.3,-11,18,-11 H400000v40H1017.7\ns-90.5,478,-276.2,1466c-185.7,988,-279.5,1483,-281.5,1485c-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2c0,-1.3,-5.3,-32,-16,-92c-50.7,-293.3,-119.7,-693.3,-207,-1200\nc0,-1.3,-5.3,8.7,-16,30c-10.7,21.3,-21.3,42.7,-32,64s-16,33,-16,33s-26,-26,-26,-26\ns76,-153,76,-153s77,-151,77,-151c0.7,0.7,35.7,202,105,604c67.3,400.7,102,602.7,104,\n606zM1001 80h400000v40H1017.7z",[316,6194,438],{"className":6195},[437],[316,6197,6199],{"className":6198},[403],[316,6200,6203],{"className":6201,"style":6202},[407],"height:1.1561em;",[316,6204],{},[241,6206,6207],{},[247,6208],{"alt":6209,"src":6210},"H1DUbVMEsosHNrxYaZncDIvfndh.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-19.png",[295,6212,6213,6218,6223,6238,6241],{},[241,6214,6215],{},[291,6216,6217],{},"Question: 如果想要制造一个耐高压的器件（high voltage device），应该如何设计？",[241,6219,6220],{},[291,6221,6222],{},"Answer:",[241,6224,6225,6226,6229,6230,6233,6234,6237],{},"To design a high-voltage ",[291,6227,6228],{},"abrupt PN junction,"," the key is to have ",[291,6231,6232],{},"one side heavily doped"," (e.g., P+) and the other side ",[291,6235,6236],{},"very lightly doped"," (e.g., an N- drift region).",[241,6239,6240],{},"This way, under reverse bias, the depletion layer (W) extends almost entirely into this lightly doped side.",[241,6242,6243],{},"A very low doping concentration (N_) allows the depletion region to become very wide, supporting a large voltage (V_) before the internal electric field reaches the critical breakdown field (E_).",[295,6245,6246,6249,6252],{},[241,6247,6248],{},"要设计一个耐高压的突变PN结器件，关键是使其一侧重掺杂（例如P+），而另一侧极轻掺杂（例如N-漂移区），而不是使用“本征掺杂”。",[241,6250,6251],{},"这样，在反向偏压下，耗尽层（W）会几乎完全延伸到这个轻掺杂区。",[241,6253,6254],{},"极低的掺杂浓度 (N_) 会使耗尽层变得非常宽，从而在内部电场达到临界击穿场强（E_）之前，器件可以承受非常高的电压（V_）。",[241,6256,6257],{},[247,6258],{"alt":6259,"src":6260},"RnIAbcIvToWfXwxo6rLcNKB5nie.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-08.png",[295,6262,6263],{},[241,6264,6265,6266,6670],{},"不过我觉得除非题目条件没给，不然最好不要用",[316,6267,6269,6335],{"className":6268},[319],[316,6270,6272],{"className":6271},[323],[325,6273,6274],{"xmlns":327},[329,6275,6276,6332],{},[332,6277,6278,6288,6290,6300,6303,6305],{},[335,6279,6280,6282],{},[338,6281,1604],{},[332,6283,6284,6286],{},[338,6285,2038],{},[338,6287,348],{},[350,6289,352],{},[659,6291,6292,6298],{},[332,6293,6294,6296],{},[338,6295,687],{},[338,6297,690],{},[338,6299,3914],{},[338,6301,6302],{},"l",[338,6304,626],{},[332,6306,6307,6309,6330],{},[350,6308,630],{"fence":373},[659,6310,6311,6324],{},[648,6312,6313,6315],{},[338,6314,643],{},[648,6316,6317,6319],{},[332,6318],{},[350,6320,6323],{"mathvariant":6321,"lspace":6322,"rspace":6322},"normal","0em","′",[335,6325,6326,6328],{},[338,6327,626],{},[338,6329,348],{},[350,6331,636],{"fence":373},[365,6333,6334],{"encoding":367},"V_{bi} = \\frac{kT}{q}ln\\left( \\frac{N^{'}}{n_i}\\right)",[316,6336,6338,6396],{"className":6337,"ariaHidden":373},[372],[316,6339,6341,6344,6387,6390,6393],{"className":6340},[377],[316,6342],{"className":6343,"style":566},[381],[316,6345,6347,6350],{"className":6346},[386],[316,6348,1604],{"className":6349,"style":1676},[386,390],[316,6351,6353],{"className":6352},[394],[316,6354,6356,6379],{"className":6355},[398,399],[316,6357,6359,6376],{"className":6358},[403],[316,6360,6362],{"className":6361,"style":2071},[407],[316,6363,6364,6367],{"style":1691},[316,6365],{"className":6366,"style":416},[415],[316,6368,6370],{"className":6369},[420,421,422,423],[316,6371,6373],{"className":6372},[386,423],[316,6374,2086],{"className":6375},[386,390,423],[316,6377,438],{"className":6378},[437],[316,6380,6382],{"className":6381},[403],[316,6383,6385],{"className":6384,"style":445},[407],[316,6386],{},[316,6388],{"className":6389,"style":452},[451],[316,6391,352],{"className":6392},[456],[316,6394],{"className":6395,"style":452},[451],[316,6397,6399,6403,6477,6481,6484,6487],{"className":6398},[377],[316,6400],{"className":6401,"style":6402},[381],"height:1.8255em;vertical-align:-0.65em;",[316,6404,6406,6409,6474],{"className":6405},[386],[316,6407],{"className":6408},[771,879],[316,6410,6412],{"className":6411},[659],[316,6413,6415,6465],{"className":6414},[398,399],[316,6416,6418,6462],{"className":6417},[403],[316,6419,6422,6436,6444],{"className":6420,"style":6421},[407],"height:0.8801em;",[316,6423,6424,6427],{"style":5238},[316,6425],{"className":6426,"style":863},[415],[316,6428,6430],{"className":6429},[420,421,422,423],[316,6431,6433],{"className":6432},[386,423],[316,6434,3914],{"className":6435,"style":1117},[386,390,423],[316,6437,6438,6441],{"style":3188},[316,6439],{"className":6440,"style":863},[415],[316,6442],{"className":6443,"style":3195},[924],[316,6445,6447,6450],{"style":6446},"top:-3.394em;",[316,6448],{"className":6449,"style":863},[415],[316,6451,6453],{"className":6452},[420,421,422,423],[316,6454,6456,6459],{"className":6455},[386,423],[316,6457,687],{"className":6458,"style":911},[386,390,423],[316,6460,690],{"className":6461,"style":597},[386,390,423],[316,6463,438],{"className":6464},[437],[316,6466,6468],{"className":6467},[403],[316,6469,6472],{"className":6470,"style":6471},[407],"height:0.4811em;",[316,6473],{},[316,6475],{"className":6476},[778,879],[316,6478,6302],{"className":6479,"style":6480},[386,390],"margin-right:0.0197em;",[316,6482,626],{"className":6483},[386,390],[316,6485],{"className":6486,"style":1059},[451],[316,6488,6490,6497,6664],{"className":6489},[3239],[316,6491,6493],{"className":6492,"style":3244},[771,3243],[316,6494,630],{"className":6495},[3248,6496],"size2",[316,6498,6500,6503,6661],{"className":6499},[386],[316,6501],{"className":6502},[771,879],[316,6504,6506],{"className":6505},[659],[316,6507,6509,6653],{"className":6508},[398,399],[316,6510,6512,6650],{"className":6511},[403],[316,6513,6516,6568,6576],{"className":6514,"style":6515},[407],"height:1.1755em;",[316,6517,6518,6521],{"style":5238},[316,6519],{"className":6520,"style":863},[415],[316,6522,6524],{"className":6523},[420,421,422,423],[316,6525,6527],{"className":6526},[386,423],[316,6528,6530,6533],{"className":6529},[386,423],[316,6531,626],{"className":6532},[386,390,423],[316,6534,6536],{"className":6535},[394],[316,6537,6539,6560],{"className":6538},[398,399],[316,6540,6542,6557],{"className":6541},[403],[316,6543,6546],{"className":6544,"style":6545},[407],"height:0.3281em;",[316,6547,6548,6551],{"style":4073},[316,6549],{"className":6550,"style":963},[415],[316,6552,6554],{"className":6553},[420,880,904,423],[316,6555,348],{"className":6556},[386,390,423],[316,6558,438],{"className":6559},[437],[316,6561,6563],{"className":6562},[403],[316,6564,6566],{"className":6565,"style":4699},[407],[316,6567],{},[316,6569,6570,6573],{"style":3188},[316,6571],{"className":6572,"style":863},[415],[316,6574],{"className":6575,"style":3195},[924],[316,6577,6578,6581],{"style":6446},[316,6579],{"className":6580,"style":863},[415],[316,6582,6584],{"className":6583},[420,421,422,423],[316,6585,6587],{"className":6586},[386,423],[316,6588,6590,6593],{"className":6589},[386,423],[316,6591,643],{"className":6592,"style":801},[386,390,423],[316,6594,6596],{"className":6595},[394],[316,6597,6599],{"className":6598},[398],[316,6600,6602],{"className":6601},[403],[316,6603,6606],{"className":6604,"style":6605},[407],"height:1.1164em;",[316,6607,6609,6613],{"style":6608},"top:-3.1164em;margin-right:0.0714em;",[316,6610],{"className":6611,"style":6612},[415],"height:2.6854em;",[316,6614,6616],{"className":6615},[420,880,904,423],[316,6617,6619],{"className":6618},[386,423],[316,6620,6622,6624],{"className":6621},[386,423],[316,6623],{},[316,6625,6627],{"className":6626},[394],[316,6628,6630],{"className":6629},[398],[316,6631,6633],{"className":6632},[403],[316,6634,6637],{"className":6635,"style":6636},[407],"height:0.9596em;",[316,6638,6640,6644],{"style":6639},"top:-2.9596em;margin-right:0.1em;",[316,6641],{"className":6642,"style":6643},[415],"height:2.5556em;",[316,6645,6647],{"className":6646},[386,423],[316,6648,6323],{"className":6649},[386,423],[316,6651,438],{"className":6652},[437],[316,6654,6656],{"className":6655},[403],[316,6657,6659],{"className":6658,"style":5365},[407],[316,6660],{},[316,6662],{"className":6663},[778,879],[316,6665,6667],{"className":6666,"style":3244},[778,3243],[316,6668,636],{"className":6669},[3248,6496],", 因为近似感觉不太合理",[241,6672,6673,1322,6676,1322,6752,6755,6760,6763],{},[3531,6674,6675],{},"对于",[316,6677,6679,6700],{"className":6678},[319],[316,6680,6682],{"className":6681},[323],[325,6683,6684],{"xmlns":327},[329,6685,6686,6698],{},[332,6687,6688],{},[335,6689,6690,6692],{},[338,6691,1604],{},[332,6693,6694,6696],{},[338,6695,2038],{},[338,6697,348],{},[365,6699,2043],{"encoding":367},[316,6701,6703],{"className":6702,"ariaHidden":373},[372],[316,6704,6706,6709],{"className":6705},[377],[316,6707],{"className":6708,"style":566},[381],[316,6710,6712,6715],{"className":6711},[386],[316,6713,1604],{"className":6714,"style":1676},[386,390],[316,6716,6718],{"className":6717},[394],[316,6719,6721,6744],{"className":6720},[398,399],[316,6722,6724,6741],{"className":6723},[403],[316,6725,6727],{"className":6726,"style":2071},[407],[316,6728,6729,6732],{"style":1691},[316,6730],{"className":6731,"style":416},[415],[316,6733,6735],{"className":6734},[420,421,422,423],[316,6736,6738],{"className":6737},[386,423],[316,6739,2086],{"className":6740},[386,390,423],[316,6742,438],{"className":6743},[437],[316,6745,6747],{"className":6746},[403],[316,6748,6750],{"className":6749,"style":445},[407],[316,6751],{},[3531,6753,6754],{},"而言，对于它影响的主要因素是",[3531,6756,6757],{},[291,6758,6759],{},"高掺杂杂质浓度",[3531,6761,6762],{},"；而对于耗尽区宽度 W而言，它的主导因素是",[3531,6764,6765],{},[291,6766,6767],{},"低掺杂杂质浓度",[2122,6769,6771],{"id":6770},"examples-例题","Examples ｜ 例题",[241,6773,6774],{},[247,6775],{"alt":6776,"src":6777},"Da9VbeJZfoZ1nAxiVkSctEsNnQf.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-20.png",[2122,6779,6781],{"id":6780},"net-doping-concentration","Net doping Concentration",[241,6783,6784,6785,6788],{},"通常，集成电路（IC）器件中的P-N结是通过",[291,6786,6787],{},"补偿掺杂（counter-doping）","形成的",[241,6790,6791],{},[247,6792],{"alt":6793,"src":6794},"GrTUbzleHoQEw1xiNSacdcSinqU.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-01.png",[2122,6796,6798],{"id":6797},"reverse-biased-pn-junction","Reverse -Biased PN Junction",[295,6800,6801,6807,6813],{},[241,6802,6803,6806],{},[291,6804,6805],{},"Question:","为什么光电传感器（photo detector）一般工作在反向偏置状态?",[241,6808,6809],{},[247,6810],{"alt":6811,"src":6812},"FLJkbwYM6oGXIWxeGghc8dA6nsg.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-09.png",[523,6814,6815,6825,6836,6846],{},[526,6816,6817,6818,6821,6822,2098],{},"反向偏置使",[291,6819,6820],{},"耗尽层更宽","，这增大了有效的光吸收区域，从而能",[291,6823,6824],{},"产生并收集更多的光生载流子",[526,6826,6827,6828,6831,6832,6835],{},"器件本身的反向偏置电流（即",[291,6829,6830],{},"暗电流","）非常小，因此，由光生电子-空穴对引起的",[291,6833,6834],{},"额外电流变化会非常显著","，易于检测。",[526,6837,6838,6839,6842,6843,1552],{},"Reverse bias creates a ",[291,6840,6841],{},"wider depletion layer",", which increases the effective light absorption region, thus ",[291,6844,6845],{},"generating and collecting more photogenerated carriers",[526,6847,6848,6849,6852,6853,6856,6857,6860],{},"The device's own reverse bias current (i.e., ",[291,6850,6851],{},"dark current",") is very small, so the ",[291,6854,6855],{},"additional current change"," caused by photogenerated electron-hole pairs becomes ",[291,6858,6859],{},"very significant"," and easy to detect.",[241,6862,6863],{},[247,6864],{"alt":6865,"src":6866},"UKtTbhAUmoeTVNx3JTfcpEK7n7b.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-12.png",[241,6868,6869,6870,6873],{},"随着反向偏置电压增加，耗尽区宽度",[291,6871,6872],{},"增加(widen)","-> 这就导致了电容效应",[256,6875,6877],{"id":6876},"capacitance-voltage-characteristics-电容电压特性","Capacitance -Voltage Characteristics | 电容电压特性",[2122,6879,6881],{"id":6880},"depletion-capacitance-耗尽电容","Depletion Capacitance ｜ 耗尽电容",[241,6883,6884,6885,6888,6891],{},"反偏PN结（Reverse-biased Junction）的电容主要是由",[291,6886,6887],{},"耗尽",[291,6889,6890],{},"电容","主导的",[241,6893,6894],{},[247,6895],{"alt":6896,"src":6897},"Fo7nb3PB3ovlKHx5amccKwoFnvc.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-11.png",[2122,6899,6900],{"id":6900},"利用图像测量参数",[241,6902,6903],{},[247,6904],{"alt":6905,"src":6906},"RSPTbpCyXoXqHJxmXvwcOHOJndo.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-10.png",[295,6908,6909,6981,7087],{},[241,6910,6911,1322,6914],{},[291,6912,6913],{},"Light doping concentration approximately  less than",[316,6915,6917,6937],{"className":6916},[319],[316,6918,6920],{"className":6919},[323],[325,6921,6922],{"xmlns":327},[329,6923,6924,6934],{},[332,6925,6926],{},[648,6927,6928,6931],{},[354,6929,6930],{},"10",[354,6932,6933],{},"16",[365,6935,6936],{"encoding":367},"10^{16}",[316,6938,6940],{"className":6939,"ariaHidden":373},[372],[316,6941,6943,6946,6949],{"className":6942},[377],[316,6944],{"className":6945,"style":5392},[381],[316,6947,5719],{"className":6948},[386],[316,6950,6952,6955],{"className":6951},[386],[316,6953,363],{"className":6954},[386],[316,6956,6958],{"className":6957},[394],[316,6959,6961],{"className":6960},[398],[316,6962,6964],{"className":6963},[403],[316,6965,6967],{"className":6966,"style":5392},[407],[316,6968,6969,6972],{"style":5407},[316,6970],{"className":6971,"style":416},[415],[316,6973,6975],{"className":6974},[420,421,422,423],[316,6976,6978],{"className":6977},[386,423],[316,6979,6933],{"className":6980},[386,423],[241,6982,6983,1322,6986],{},[291,6984,6985],{},"Heavy doping concentration approximately  larger than",[316,6987,6989,7024],{"className":6988},[319],[316,6990,6992],{"className":6991},[323],[325,6993,6994],{"xmlns":327},[329,6995,6996,7021],{},[332,6997,6998],{},[648,6999,7000,7002],{},[354,7001,6930],{},[332,7003,7004,7007,7010,7013,7016,7018],{},[354,7005,7006],{},"17",[1606,7008,7009],{}," ",[338,7011,7012],{},"o",[338,7014,7015],{},"r",[1606,7017,7009],{},[354,7019,7020],{},"18",[365,7022,7023],{"encoding":367},"10^{17 \\space or  \\space 18}",[316,7025,7027],{"className":7026,"ariaHidden":373},[372],[316,7028,7030,7033,7036],{"className":7029},[377],[316,7031],{"className":7032,"style":5392},[381],[316,7034,5719],{"className":7035},[386],[316,7037,7039,7042],{"className":7038},[386],[316,7040,363],{"className":7041},[386],[316,7043,7045],{"className":7044},[394],[316,7046,7048],{"className":7047},[398],[316,7049,7051],{"className":7050},[403],[316,7052,7054],{"className":7053,"style":5392},[407],[316,7055,7056,7059],{"style":5407},[316,7057],{"className":7058,"style":416},[415],[316,7060,7062],{"className":7061},[420,421,422,423],[316,7063,7065,7068,7074,7078,7084],{"className":7064},[386,423],[316,7066,7006],{"className":7067},[386,423],[316,7069,7071],{"className":7070},[451,423],[316,7072,7009],{"className":7073},[423],[316,7075,7077],{"className":7076,"style":2219},[386,390,423],"or",[316,7079,7081],{"className":7080},[451,423],[316,7082,7009],{"className":7083},[423],[316,7085,7020],{"className":7086},[386,423],[241,7088,7089],{},[247,7090],{"alt":7091,"src":7092},"A5DA94BB-9657-4BA1-ADC0-AB74C6D52AD1.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-16.png",[2122,7094,7096],{"id":7095},"example-例题","Example ｜ 例题",[241,7098,7099],{},[247,7100],{"alt":7101,"src":7102},"C4esbmMmtotKIoxdwRPc6hatnAc.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-07.png",[295,7104,7105,7109,7114],{},[241,7106,7107],{},[291,7108,6222],{},[241,7110,7111],{},[291,7112,7113],{},"Chinese Version",[523,7115,7116,7119,7125,7128],{},[526,7117,7118],{},"测量 N_l (轻掺杂): 非常准确。N_l 是根据 1\u002FC^2 曲线的斜率 (Slope) 算出的。C-V法对轻掺杂一侧的浓度非常敏感，这是业界用于测量 N_l 的标准方法。",[526,7120,7121,7122],{},"测量 N_h (重掺杂): 非常不准确。N_h 是根据截距 (V_) 反推的。由于 V_ 与 N_h 呈对数 (\\ln) 关系（V_ \\propto \\ln(N_h)），V_ 对 N_h 的巨大变化并不敏感。反之，测量 V_ 时的微小误差，在通过指数 (e^x) 运算反推 N_h 时会被指数级放大，导致结果严重失准。\n",[291,7123,7124],{},"English Version",[526,7126,7127],{},"Determining N_l (lighter doping): Very Accurate.N_l is calculated from the slope of the 1\u002FC^2 plot. The C-V method is very sensitive to the lighter doping concentration and is the standard way to measure it.",[526,7129,7130],{},"Determining N_h (heavier doping): Very Inaccurate. N_h is extracted from the intercept (V_). Because V_ has only a logarithmic (\\ln) dependence on N_h (V_ \\propto \\ln(N_h)), V_ is very insensitive to large changes in N_h. Conversely, small measurement errors in V_ are exponentially (e^x) amplified when solving for N_h, leading to highly inaccurate results.",[236,7132,7134],{"id":7133},"pn-junction-break-down","PN Junction Break Down",[241,7136,7137,7138,7141],{},"当给PN结施加的反向电压（V为负）大到一定程度，超过一个阈值 V_B（击穿电压）时，反向电流会",[291,7139,7140],{},"突然急剧增大","。这种现象就是“击穿”。",[241,7143,7144],{},[247,7145],{"alt":7146,"src":7147},"UxW3bPtZPoPMLaxAiG6czo0En2e.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-24.png",[241,7149,7150],{},[291,7151,7152],{},"Zener Diode is designed to operate in the breakdown mode",[295,7154,7155],{},[241,7156,7157,7158,7161,7162,7165,7166,7169],{},"PN结的",[291,7159,7160],{},"击穿特性本身是可逆的","（如果控制电流），但它导致的",[291,7163,7164],{},"发热","往往是",[291,7167,7168],{},"不可逆的破坏","。普通二极管应避免击穿；而齐纳二极管则巧妙地利用了“击穿时电压恒定”这一特性，通过特殊设计（并配合限流电阻R）使其能安全地工作在击穿区，实现了稳压功能",[523,7171,7172,7181],{},[526,7173,7174,7177,7178,2098],{},[291,7175,7176],{},"好处 (Good Thing):"," 击穿时，二极管两端的电压几乎恒定不变（钳位在 V_B）——",[291,7179,7180],{},"Zener Diode",[526,7182,7183,7186,7187,7190,7191,7194],{},[291,7184,7185],{},"坏处 (Bad Thing):"," 击穿时的大电流会",[291,7188,7189],{},"产生大量的热","（焦耳热），如果这个电流不加限制，高温会",[291,7192,7193],{},"不可逆地 (irreversible)"," 烧毁器件",[256,7196,7198],{"id":7197},"breakdown-voltage","Breakdown Voltage",[241,7200,7201,7202,1322,7205,7291,7292,7295],{},"当反向电压 V_R 增大，使",[291,7203,7204],{},"峰值电场",[316,7206,7208,7236],{"className":7207},[319],[316,7209,7211],{"className":7210},[323],[325,7212,7213],{"xmlns":327},[329,7214,7215,7233],{},[332,7216,7217],{},[335,7218,7219,7222],{},[338,7220,550],{"mathvariant":7221},"bold",[332,7223,7224,7226,7228,7231],{},[338,7225,241],{"mathvariant":7221},[338,7227,652],{"mathvariant":7221},[338,7229,7230],{"mathvariant":7221},"a",[338,7232,687],{"mathvariant":7221},[365,7234,7235],{"encoding":367},"\\mathbf{E_{peak}}",[316,7237,7239],{"className":7238,"ariaHidden":373},[372],[316,7240,7242,7246],{"className":7241},[377],[316,7243],{"className":7244,"style":7245},[381],"height:0.9722em;vertical-align:-0.2861em;",[316,7247,7249,7253],{"className":7248},[386],[316,7250,550],{"className":7251},[386,7252],"mathbf",[316,7254,7256],{"className":7255},[394],[316,7257,7259,7283],{"className":7258},[398,399],[316,7260,7262,7280],{"className":7261},[403],[316,7263,7265],{"className":7264,"style":2071},[407],[316,7266,7267,7270],{"style":411},[316,7268],{"className":7269,"style":416},[415],[316,7271,7273],{"className":7272},[420,421,422,423],[316,7274,7276],{"className":7275},[386,423],[316,7277,7279],{"className":7278},[386,7252,423],"peak",[316,7281,438],{"className":7282},[437],[316,7284,7286],{"className":7285},[403],[316,7287,7289],{"className":7288,"style":3815},[407],[316,7290],{}," 达到了材料所能承受的",[291,7293,7294],{},"临界电场 E_"," 时，击穿发生",[7297,7298,7300],"table",{"style":7299},"width: 100%; border: 0; border-collapse: collapse; border-spacing: 0;",[7301,7302,7303],"tbody",{},[7304,7305,7307,7308,7307,7324],"tr",{"style":7306},"border: none;","\n  ",[7309,7310,7312,7318,7307],"td",{"style":7311},"width: 37.9%; text-align: center; border: none; padding: 0.3em; margin: 0;",[241,7313,7314],{},[247,7315],{"alt":7316,"src":7317},"P9HybAHduo4CZMxrY3pckFICncg.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-05.png",[241,7319,7320],{},[247,7321],{"alt":7322,"src":7323},"XTOAbGsNKoDMklxWeXJc1lEUnXc.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-14.png",[7309,7325,7327,7307],{"style":7326},"width: 62.1%; text-align: center; border: none; padding: 0.3em; margin: 0;",[241,7328,7329],{},[247,7330],{"alt":7331,"src":7332},"XnL4bdeKuoM339x9kc7c4mYEn4c.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-15.png",[241,7334,7335,7425,7426,7671],{},[316,7336,7338,7365],{"className":7337},[319],[316,7339,7341],{"className":7340},[323],[325,7342,7343],{"xmlns":327},[329,7344,7345,7362],{},[332,7346,7347],{},[335,7348,7349,7351],{},[338,7350,550],{},[332,7352,7353,7355,7357,7359],{},[338,7354,646],{},[338,7356,7015],{},[338,7358,348],{},[338,7360,7361],{},"t",[365,7363,7364],{"encoding":367},"E_{crit}",[316,7366,7368],{"className":7367,"ariaHidden":373},[372],[316,7369,7371,7374],{"className":7370},[377],[316,7372],{"className":7373,"style":566},[381],[316,7375,7377,7380],{"className":7376},[386],[316,7378,550],{"className":7379,"style":430},[386,390],[316,7381,7383],{"className":7382},[394],[316,7384,7386,7417],{"className":7385},[398,399],[316,7387,7389,7414],{"className":7388},[403],[316,7390,7393],{"className":7391,"style":7392},[407],"height:0.3117em;",[316,7394,7395,7398],{"style":587},[316,7396],{"className":7397,"style":416},[415],[316,7399,7401],{"className":7400},[420,421,422,423],[316,7402,7404,7408,7411],{"className":7403},[386,423],[316,7405,7407],{"className":7406,"style":2219},[386,390,423],"cr",[316,7409,348],{"className":7410},[386,390,423],[316,7412,7361],{"className":7413},[386,390,423],[316,7415,438],{"className":7416},[437],[316,7418,7420],{"className":7419},[403],[316,7421,7423],{"className":7422,"style":445},[407],[316,7424],{},"是一个材料参数（如",[316,7427,7429,7489],{"className":7428},[319],[316,7430,7432],{"className":7431},[323],[325,7433,7434],{"xmlns":327},[329,7435,7436,7486],{},[332,7437,7438,7460,7463,7466,7469,7476,7478,7481,7483],{},[335,7439,7440,7442],{},[338,7441,550],{},[332,7443,7444,7446,7448,7450],{},[338,7445,646],{},[338,7447,7015],{},[338,7449,348],{},[335,7451,7452,7454],{},[338,7453,7361],{},[332,7455,7456,7458],{},[338,7457,345],{},[338,7459,348],{},[350,7461,7462],{},"≈",[354,7464,7465],{},"3",[350,7467,7468],{},"×",[648,7470,7471,7473],{},[354,7472,6930],{},[354,7474,7475],{},"5",[338,7477,1604],{},[338,7479,7480],{"mathvariant":6321},"\u002F",[338,7482,646],{},[338,7484,7485],{},"m",[365,7487,7488],{"encoding":367},"E_{crit_{Si}} \\approx 3 \\times 10^5 V\u002Fcm",[316,7490,7492,7602,7621],{"className":7491,"ariaHidden":373},[372],[316,7493,7495,7499,7593,7596,7599],{"className":7494},[377],[316,7496],{"className":7497,"style":7498},[381],"height:0.9336em;vertical-align:-0.2503em;",[316,7500,7502,7505],{"className":7501},[386],[316,7503,550],{"className":7504,"style":430},[386,390],[316,7506,7508],{"className":7507},[394],[316,7509,7511,7584],{"className":7510},[398,399],[316,7512,7514,7581],{"className":7513},[403],[316,7515,7517],{"className":7516,"style":7392},[407],[316,7518,7519,7522],{"style":587},[316,7520],{"className":7521,"style":416},[415],[316,7523,7525],{"className":7524},[420,421,422,423],[316,7526,7528,7531,7534],{"className":7527},[386,423],[316,7529,7407],{"className":7530,"style":2219},[386,390,423],[316,7532,348],{"className":7533},[386,390,423],[316,7535,7537,7540],{"className":7536},[386,423],[316,7538,7361],{"className":7539},[386,390,423],[316,7541,7543],{"className":7542},[394],[316,7544,7546,7573],{"className":7545},[398,399],[316,7547,7549,7570],{"className":7548},[403],[316,7550,7552],{"className":7551,"style":1010},[407],[316,7553,7555,7558],{"style":7554},"top:-2.3567em;margin-left:0em;margin-right:0.0714em;",[316,7556],{"className":7557,"style":963},[415],[316,7559,7561],{"className":7560},[420,880,904,423],[316,7562,7564,7567],{"className":7563},[386,423],[316,7565,345],{"className":7566,"style":430},[386,390,423],[316,7568,348],{"className":7569},[386,390,423],[316,7571,438],{"className":7572},[437],[316,7574,7576],{"className":7575},[403],[316,7577,7579],{"className":7578,"style":5353},[407],[316,7580],{},[316,7582,438],{"className":7583},[437],[316,7585,7587],{"className":7586},[403],[316,7588,7591],{"className":7589,"style":7590},[407],"height:0.2503em;",[316,7592],{},[316,7594],{"className":7595,"style":452},[451],[316,7597,7462],{"className":7598},[456],[316,7600],{"className":7601,"style":452},[451],[316,7603,7605,7609,7612,7615,7618],{"className":7604},[377],[316,7606],{"className":7607,"style":7608},[381],"height:0.7278em;vertical-align:-0.0833em;",[316,7610,7465],{"className":7611},[386],[316,7613],{"className":7614,"style":1676},[451],[316,7616,7468],{"className":7617},[991],[316,7619],{"className":7620,"style":1676},[451],[316,7622,7624,7627,7630,7659,7662,7665,7668],{"className":7623},[377],[316,7625],{"className":7626,"style":5444},[381],[316,7628,5719],{"className":7629},[386],[316,7631,7633,7636],{"className":7632},[386],[316,7634,363],{"className":7635},[386],[316,7637,7639],{"className":7638},[394],[316,7640,7642],{"className":7641},[398],[316,7643,7645],{"className":7644},[403],[316,7646,7648],{"className":7647,"style":5392},[407],[316,7649,7650,7653],{"style":5407},[316,7651],{"className":7652,"style":416},[415],[316,7654,7656],{"className":7655},[420,421,422,423],[316,7657,7475],{"className":7658},[386,423],[316,7660,1604],{"className":7661,"style":1676},[386,390],[316,7663,7480],{"className":7664},[386],[316,7666,646],{"className":7667},[386,390],[316,7669,7485],{"className":7670},[386,390],"）。",[241,7673,7674,7675],{},"这里给出了一个重要的公式——击穿电压",[316,7676,7678,7824],{"className":7677},[319],[316,7679,7681],{"className":7680},[323],[325,7682,7683],{"xmlns":327},[329,7684,7685,7821],{},[332,7686,7687,7698,7700,7745,7747,7757,7759,7809,7811],{},[335,7688,7689,7691],{},[338,7690,1604],{},[332,7692,7693,7696],{},[338,7694,7695],{},"B",[338,7697,2172],{},[350,7699,352],{},[659,7701,7702,7726],{},[332,7703,7704,7710],{},[335,7705,7706,7708],{},[338,7707,3929],{},[338,7709,3932],{},[2166,7711,7712,7714,7724],{},[338,7713,550],{},[332,7715,7716,7718,7720,7722],{},[338,7717,646],{},[338,7719,7015],{},[338,7721,348],{},[338,7723,7361],{},[354,7725,3081],{},[332,7727,7728,7730,7732],{},[354,7729,3081],{},[338,7731,3914],{},[335,7733,7734,7736],{},[338,7735,643],{},[332,7737,7738,7740,7743],{},[338,7739,652],{},[338,7741,7742],{},"f",[338,7744,7742],{},[350,7746,657],{},[335,7748,7749,7751],{},[338,7750,1604],{},[332,7752,7753,7755],{},[338,7754,2038],{},[338,7756,348],{},[350,7758,7462],{},[659,7760,7761,7785],{},[332,7762,7763,7769],{},[335,7764,7765,7767],{},[338,7766,3929],{},[338,7768,3932],{},[2166,7770,7771,7773,7783],{},[338,7772,550],{},[332,7774,7775,7777,7779,7781],{},[338,7776,646],{},[338,7778,7015],{},[338,7780,348],{},[338,7782,7361],{},[354,7784,3081],{},[332,7786,7787,7789,7791],{},[354,7788,3081],{},[338,7790,3914],{},[335,7792,7793,7795],{},[338,7794,643],{},[332,7796,7797,7799,7801,7804,7807],{},[338,7798,6302],{},[338,7800,348],{},[338,7802,7803],{},"g",[338,7805,7806],{},"h",[338,7808,7361],{},[350,7810,657],{},[335,7812,7813,7815],{},[338,7814,1604],{},[332,7816,7817,7819],{},[338,7818,2038],{},[338,7820,348],{},[365,7822,7823],{"encoding":367},"V_{BD} = \\frac{\\varepsilon_s E_{crit}^2}{2qN_{eff}} - V_{bi} \\approx  \\frac{\\varepsilon_s E_{crit}^2}{2qN_{light}} - V_{bi}",[316,7825,7827,7889,8132,8190,8428],{"className":7826,"ariaHidden":373},[372],[316,7828,7830,7833,7880,7883,7886],{"className":7829},[377],[316,7831],{"className":7832,"style":566},[381],[316,7834,7836,7839],{"className":7835},[386],[316,7837,1604],{"className":7838,"style":1676},[386,390],[316,7840,7842],{"className":7841},[394],[316,7843,7845,7872],{"className":7844},[398,399],[316,7846,7848,7869],{"className":7847},[403],[316,7849,7851],{"className":7850,"style":408},[407],[316,7852,7853,7856],{"style":1691},[316,7854],{"className":7855,"style":416},[415],[316,7857,7859],{"className":7858},[420,421,422,423],[316,7860,7862,7866],{"className":7861},[386,423],[316,7863,7695],{"className":7864,"style":7865},[386,390,423],"margin-right:0.0502em;",[316,7867,2172],{"className":7868,"style":2219},[386,390,423],[316,7870,438],{"className":7871},[437],[316,7873,7875],{"className":7874},[403],[316,7876,7878],{"className":7877,"style":445},[407],[316,7879],{},[316,7881],{"className":7882,"style":452},[451],[316,7884,352],{"className":7885},[456],[316,7887],{"className":7888,"style":452},[451],[316,7890,7892,7896,8123,8126,8129],{"className":7891},[377],[316,7893],{"className":7894,"style":7895},[381],"height:1.6822em;vertical-align:-0.5481em;",[316,7897,7899,7902,8120],{"className":7898},[386],[316,7900],{"className":7901},[771,879],[316,7903,7905],{"className":7904},[659],[316,7906,7908,8111],{"className":7907},[398,399],[316,7909,7911,8108],{"className":7910},[403],[316,7912,7915,7984,7992],{"className":7913,"style":7914},[407],"height:1.1341em;",[316,7916,7917,7920],{"style":5238},[316,7918],{"className":7919,"style":863},[415],[316,7921,7923],{"className":7922},[420,421,422,423],[316,7924,7926,7929,7932],{"className":7925},[386,423],[316,7927,3081],{"className":7928},[386,423],[316,7930,3914],{"className":7931,"style":1117},[386,390,423],[316,7933,7935,7938],{"className":7934},[386,423],[316,7936,643],{"className":7937,"style":801},[386,390,423],[316,7939,7941],{"className":7940},[394],[316,7942,7944,7975],{"className":7943},[398,399],[316,7945,7947,7972],{"className":7946},[403],[316,7948,7950],{"className":7949,"style":1010},[407],[316,7951,7953,7956],{"style":7952},"top:-2.3488em;margin-left:-0.109em;margin-right:0.0714em;",[316,7954],{"className":7955,"style":963},[415],[316,7957,7959],{"className":7958},[420,880,904,423],[316,7960,7962,7965,7969],{"className":7961},[386,423],[316,7963,652],{"className":7964},[386,390,423],[316,7966,7742],{"className":7967,"style":7968},[386,390,423],"margin-right:0.1076em;",[316,7970,7742],{"className":7971,"style":7968},[386,390,423],[316,7973,438],{"className":7974},[437],[316,7976,7978],{"className":7977},[403],[316,7979,7982],{"className":7980,"style":7981},[407],"height:0.2901em;",[316,7983],{},[316,7985,7986,7989],{"style":3188},[316,7987],{"className":7988,"style":863},[415],[316,7990],{"className":7991,"style":3195},[924],[316,7993,7995,7998],{"style":7994},"top:-3.5102em;",[316,7996],{"className":7997,"style":863},[415],[316,7999,8001],{"className":8000},[420,421,422,423],[316,8002,8004,8044],{"className":8003},[386,423],[316,8005,8007,8010],{"className":8006},[386,423],[316,8008,3929],{"className":8009},[386,390,423],[316,8011,8013],{"className":8012},[394],[316,8014,8016,8036],{"className":8015},[398,399],[316,8017,8019,8033],{"className":8018},[403],[316,8020,8022],{"className":8021,"style":4070},[407],[316,8023,8024,8027],{"style":4073},[316,8025],{"className":8026,"style":963},[415],[316,8028,8030],{"className":8029},[420,880,904,423],[316,8031,3932],{"className":8032},[386,390,423],[316,8034,438],{"className":8035},[437],[316,8037,8039],{"className":8038},[403],[316,8040,8042],{"className":8041,"style":4699},[407],[316,8043],{},[316,8045,8047,8050],{"className":8046},[386,423],[316,8048,550],{"className":8049,"style":430},[386,390,423],[316,8051,8053],{"className":8052},[394],[316,8054,8056,8099],{"className":8055},[398,399],[316,8057,8059,8096],{"className":8058},[403],[316,8060,8063,8084],{"className":8061,"style":8062},[407],"height:0.8913em;",[316,8064,8066,8069],{"style":8065},"top:-2.214em;margin-left:-0.0576em;margin-right:0.0714em;",[316,8067],{"className":8068,"style":963},[415],[316,8070,8072],{"className":8071},[420,880,904,423],[316,8073,8075,8078,8081],{"className":8074},[386,423],[316,8076,7407],{"className":8077,"style":2219},[386,390,423],[316,8079,348],{"className":8080},[386,390,423],[316,8082,7361],{"className":8083},[386,390,423],[316,8085,8087,8090],{"style":8086},"top:-2.931em;margin-right:0.0714em;",[316,8088],{"className":8089,"style":963},[415],[316,8091,8093],{"className":8092},[420,880,904,423],[316,8094,3081],{"className":8095},[386,423],[316,8097,438],{"className":8098},[437],[316,8100,8102],{"className":8101},[403],[316,8103,8106],{"className":8104,"style":8105},[407],"height:0.286em;",[316,8107],{},[316,8109,438],{"className":8110},[437],[316,8112,8114],{"className":8113},[403],[316,8115,8118],{"className":8116,"style":8117},[407],"height:0.5481em;",[316,8119],{},[316,8121],{"className":8122},[778,879],[316,8124],{"className":8125,"style":1676},[451],[316,8127,657],{"className":8128},[991],[316,8130],{"className":8131,"style":1676},[451],[316,8133,8135,8138,8181,8184,8187],{"className":8134},[377],[316,8136],{"className":8137,"style":566},[381],[316,8139,8141,8144],{"className":8140},[386],[316,8142,1604],{"className":8143,"style":1676},[386,390],[316,8145,8147],{"className":8146},[394],[316,8148,8150,8173],{"className":8149},[398,399],[316,8151,8153,8170],{"className":8152},[403],[316,8154,8156],{"className":8155,"style":2071},[407],[316,8157,8158,8161],{"style":1691},[316,8159],{"className":8160,"style":416},[415],[316,8162,8164],{"className":8163},[420,421,422,423],[316,8165,8167],{"className":8166},[386,423],[316,8168,2086],{"className":8169},[386,390,423],[316,8171,438],{"className":8172},[437],[316,8174,8176],{"className":8175},[403],[316,8177,8179],{"className":8178,"style":445},[407],[316,8180],{},[316,8182],{"className":8183,"style":452},[451],[316,8185,7462],{"className":8186},[456],[316,8188],{"className":8189,"style":452},[451],[316,8191,8193,8196,8419,8422,8425],{"className":8192},[377],[316,8194],{"className":8195,"style":7895},[381],[316,8197,8199,8202,8416],{"className":8198},[386],[316,8200],{"className":8201},[771,879],[316,8203,8205],{"className":8204},[659],[316,8206,8208,8408],{"className":8207},[398,399],[316,8209,8211,8405],{"className":8210},[403],[316,8212,8214,8286,8294],{"className":8213,"style":7914},[407],[316,8215,8216,8219],{"style":5238},[316,8217],{"className":8218,"style":863},[415],[316,8220,8222],{"className":8221},[420,421,422,423],[316,8223,8225,8228,8231],{"className":8224},[386,423],[316,8226,3081],{"className":8227},[386,423],[316,8229,3914],{"className":8230,"style":1117},[386,390,423],[316,8232,8234,8237],{"className":8233},[386,423],[316,8235,643],{"className":8236,"style":801},[386,390,423],[316,8238,8240],{"className":8239},[394],[316,8241,8243,8278],{"className":8242},[398,399],[316,8244,8246,8275],{"className":8245},[403],[316,8247,8249],{"className":8248,"style":1010},[407],[316,8250,8251,8254],{"style":7952},[316,8252],{"className":8253,"style":963},[415],[316,8255,8257],{"className":8256},[420,880,904,423],[316,8258,8260,8263,8266,8269,8272],{"className":8259},[386,423],[316,8261,6302],{"className":8262,"style":6480},[386,390,423],[316,8264,348],{"className":8265},[386,390,423],[316,8267,7803],{"className":8268,"style":1117},[386,390,423],[316,8270,7806],{"className":8271},[386,390,423],[316,8273,7361],{"className":8274},[386,390,423],[316,8276,438],{"className":8277},[437],[316,8279,8281],{"className":8280},[403],[316,8282,8284],{"className":8283,"style":7981},[407],[316,8285],{},[316,8287,8288,8291],{"style":3188},[316,8289],{"className":8290,"style":863},[415],[316,8292],{"className":8293,"style":3195},[924],[316,8295,8296,8299],{"style":7994},[316,8297],{"className":8298,"style":863},[415],[316,8300,8302],{"className":8301},[420,421,422,423],[316,8303,8305,8345],{"className":8304},[386,423],[316,8306,8308,8311],{"className":8307},[386,423],[316,8309,3929],{"className":8310},[386,390,423],[316,8312,8314],{"className":8313},[394],[316,8315,8317,8337],{"className":8316},[398,399],[316,8318,8320,8334],{"className":8319},[403],[316,8321,8323],{"className":8322,"style":4070},[407],[316,8324,8325,8328],{"style":4073},[316,8326],{"className":8327,"style":963},[415],[316,8329,8331],{"className":8330},[420,880,904,423],[316,8332,3932],{"className":8333},[386,390,423],[316,8335,438],{"className":8336},[437],[316,8338,8340],{"className":8339},[403],[316,8341,8343],{"className":8342,"style":4699},[407],[316,8344],{},[316,8346,8348,8351],{"className":8347},[386,423],[316,8349,550],{"className":8350,"style":430},[386,390,423],[316,8352,8354],{"className":8353},[394],[316,8355,8357,8397],{"className":8356},[398,399],[316,8358,8360,8394],{"className":8359},[403],[316,8361,8363,8383],{"className":8362,"style":8062},[407],[316,8364,8365,8368],{"style":8065},[316,8366],{"className":8367,"style":963},[415],[316,8369,8371],{"className":8370},[420,880,904,423],[316,8372,8374,8377,8380],{"className":8373},[386,423],[316,8375,7407],{"className":8376,"style":2219},[386,390,423],[316,8378,348],{"className":8379},[386,390,423],[316,8381,7361],{"className":8382},[386,390,423],[316,8384,8385,8388],{"style":8086},[316,8386],{"className":8387,"style":963},[415],[316,8389,8391],{"className":8390},[420,880,904,423],[316,8392,3081],{"className":8393},[386,423],[316,8395,438],{"className":8396},[437],[316,8398,8400],{"className":8399},[403],[316,8401,8403],{"className":8402,"style":8105},[407],[316,8404],{},[316,8406,438],{"className":8407},[437],[316,8409,8411],{"className":8410},[403],[316,8412,8414],{"className":8413,"style":8117},[407],[316,8415],{},[316,8417],{"className":8418},[778,879],[316,8420],{"className":8421,"style":1676},[451],[316,8423,657],{"className":8424},[991],[316,8426],{"className":8427,"style":1676},[451],[316,8429,8431,8434],{"className":8430},[377],[316,8432],{"className":8433,"style":566},[381],[316,8435,8437,8440],{"className":8436},[386],[316,8438,1604],{"className":8439,"style":1676},[386,390],[316,8441,8443],{"className":8442},[394],[316,8444,8446,8469],{"className":8445},[398,399],[316,8447,8449,8466],{"className":8448},[403],[316,8450,8452],{"className":8451,"style":2071},[407],[316,8453,8454,8457],{"style":1691},[316,8455],{"className":8456,"style":416},[415],[316,8458,8460],{"className":8459},[420,421,422,423],[316,8461,8463],{"className":8462},[386,423],[316,8464,2086],{"className":8465},[386,390,423],[316,8467,438],{"className":8468},[437],[316,8470,8472],{"className":8471},[403],[316,8473,8475],{"className":8474,"style":445},[407],[316,8476],{},[295,8478,8479,8562],{},[241,8480,8481,1322,8484,8558,8561],{},[291,8482,8483],{},"如何提高击穿电压",[316,8485,8487,8505],{"className":8486},[319],[316,8488,8490],{"className":8489},[323],[325,8491,8492],{"xmlns":327},[329,8493,8494,8502],{},[332,8495,8496],{},[335,8497,8498,8500],{},[338,8499,1604],{"mathvariant":7221},[338,8501,7695],{"mathvariant":7221},[365,8503,8504],{"encoding":367},"\\mathbf{V_B}",[316,8506,8508],{"className":8507,"ariaHidden":373},[372],[316,8509,8511,8515],{"className":8510},[377],[316,8512],{"className":8513,"style":8514},[381],"height:0.8361em;vertical-align:-0.15em;",[316,8516,8518,8522],{"className":8517},[386],[316,8519,1604],{"className":8520,"style":8521},[386,7252],"margin-right:0.016em;",[316,8523,8525],{"className":8524},[394],[316,8526,8528,8550],{"className":8527},[398,399],[316,8529,8531,8547],{"className":8530},[403],[316,8532,8535],{"className":8533,"style":8534},[407],"height:0.3303em;",[316,8536,8538,8541],{"style":8537},"top:-2.55em;margin-left:-0.016em;margin-right:0.05em;",[316,8539],{"className":8540,"style":416},[415],[316,8542,8544],{"className":8543},[420,421,422,423],[316,8545,7695],{"className":8546},[386,7252,423],[316,8548,438],{"className":8549},[437],[316,8551,8553],{"className":8552},[403],[316,8554,8556],{"className":8555,"style":445},[407],[316,8557],{},[291,8559,8560],{},"？"," （耐高压器件的设计）",[523,8563,8564,8832],{},[526,8565,8566,8569,8653,8656],{},[291,8567,8568],{},"降低掺杂浓度 (",[316,8570,8572,8600],{"className":8571},[319],[316,8573,8575],{"className":8574},[323],[325,8576,8577],{"xmlns":327},[329,8578,8579,8597],{},[332,8580,8581],{},[335,8582,8583,8585],{},[338,8584,643],{"mathvariant":7221},[332,8586,8587,8589,8591,8593,8595],{},[338,8588,6302],{"mathvariant":7221},[338,8590,348],{"mathvariant":7221},[338,8592,7803],{"mathvariant":7221},[338,8594,7806],{"mathvariant":7221},[338,8596,7361],{"mathvariant":7221},[365,8598,8599],{"encoding":367},"\\mathbf{N_{light}}",[316,8601,8603],{"className":8602,"ariaHidden":373},[372],[316,8604,8606,8609],{"className":8605},[377],[316,8607],{"className":8608,"style":7245},[381],[316,8610,8612,8615],{"className":8611},[386],[316,8613,643],{"className":8614},[386,7252],[316,8616,8618],{"className":8617},[394],[316,8619,8621,8645],{"className":8620},[398,399],[316,8622,8624,8642],{"className":8623},[403],[316,8625,8627],{"className":8626,"style":2071},[407],[316,8628,8629,8632],{"style":411},[316,8630],{"className":8631,"style":416},[415],[316,8633,8635],{"className":8634},[420,421,422,423],[316,8636,8638],{"className":8637},[386,423],[316,8639,8641],{"className":8640},[386,7252,423],"light",[316,8643,438],{"className":8644},[437],[316,8646,8648],{"className":8647},[403],[316,8649,8651],{"className":8650,"style":3815},[407],[316,8652],{},[291,8654,8655],{},")：",[1584,8657,8658,8829],{},[526,8659,8660,8661,8828],{},"从公式 ",[316,8662,8664,8705],{"className":8663},[319],[316,8665,8667],{"className":8666},[323],[325,8668,8669],{"xmlns":327},[329,8670,8671,8702],{},[332,8672,8673,8679,8682,8684,8686],{},[335,8674,8675,8677],{},[338,8676,1604],{},[338,8678,7695],{},[350,8680,8681],{},"∝",[354,8683,5719],{},[338,8685,7480],{"mathvariant":6321},[335,8687,8688,8690],{},[338,8689,643],{},[332,8691,8692,8694,8696,8698,8700],{},[338,8693,6302],{},[338,8695,348],{},[338,8697,7803],{},[338,8699,7806],{},[338,8701,7361],{},[365,8703,8704],{"encoding":367},"V_B \\propto 1\u002FN_{light}",[316,8706,8708,8763],{"className":8707,"ariaHidden":373},[372],[316,8709,8711,8714,8754,8757,8760],{"className":8710},[377],[316,8712],{"className":8713,"style":566},[381],[316,8715,8717,8720],{"className":8716},[386],[316,8718,1604],{"className":8719,"style":1676},[386,390],[316,8721,8723],{"className":8722},[394],[316,8724,8726,8746],{"className":8725},[398,399],[316,8727,8729,8743],{"className":8728},[403],[316,8730,8732],{"className":8731,"style":408},[407],[316,8733,8734,8737],{"style":1691},[316,8735],{"className":8736,"style":416},[415],[316,8738,8740],{"className":8739},[420,421,422,423],[316,8741,7695],{"className":8742,"style":7865},[386,390,423],[316,8744,438],{"className":8745},[437],[316,8747,8749],{"className":8748},[403],[316,8750,8752],{"className":8751,"style":445},[407],[316,8753],{},[316,8755],{"className":8756,"style":452},[451],[316,8758,8681],{"className":8759},[456],[316,8761],{"className":8762,"style":452},[451],[316,8764,8766,8769,8773],{"className":8765},[377],[316,8767],{"className":8768,"style":3767},[381],[316,8770,8772],{"className":8771},[386],"1\u002F",[316,8774,8776,8779],{"className":8775},[386],[316,8777,643],{"className":8778,"style":801},[386,390],[316,8780,8782],{"className":8781},[394],[316,8783,8785,8820],{"className":8784},[398,399],[316,8786,8788,8817],{"className":8787},[403],[316,8789,8791],{"className":8790,"style":2071},[407],[316,8792,8793,8796],{"style":817},[316,8794],{"className":8795,"style":416},[415],[316,8797,8799],{"className":8798},[420,421,422,423],[316,8800,8802,8805,8808,8811,8814],{"className":8801},[386,423],[316,8803,6302],{"className":8804,"style":6480},[386,390,423],[316,8806,348],{"className":8807},[386,390,423],[316,8809,7803],{"className":8810,"style":1117},[386,390,423],[316,8812,7806],{"className":8813},[386,390,423],[316,8815,7361],{"className":8816},[386,390,423],[316,8818,438],{"className":8819},[437],[316,8821,8823],{"className":8822},[403],[316,8824,8826],{"className":8825,"style":3815},[407],[316,8827],{}," 可知，掺杂越轻， V_B 越高。",[526,8830,8831],{},"这就是为什么高压器件需要一个宽的、极轻掺杂的“漂移区”。",[526,8833,8834,8837,8919,8921],{},[291,8835,8836],{},"提高临界电场 (",[316,8838,8840,8866],{"className":8839},[319],[316,8841,8843],{"className":8842},[323],[325,8844,8845],{"xmlns":327},[329,8846,8847,8863],{},[332,8848,8849],{},[335,8850,8851,8853],{},[338,8852,550],{"mathvariant":7221},[332,8854,8855,8857,8859,8861],{},[338,8856,646],{"mathvariant":7221},[338,8858,7015],{"mathvariant":7221},[338,8860,348],{"mathvariant":7221},[338,8862,7361],{"mathvariant":7221},[365,8864,8865],{"encoding":367},"\\mathbf{E_{crit}}",[316,8867,8869],{"className":8868,"ariaHidden":373},[372],[316,8870,8872,8875],{"className":8871},[377],[316,8873],{"className":8874,"style":8514},[381],[316,8876,8878,8881],{"className":8877},[386],[316,8879,550],{"className":8880},[386,7252],[316,8882,8884],{"className":8883},[394],[316,8885,8887,8911],{"className":8886},[398,399],[316,8888,8890,8908],{"className":8889},[403],[316,8891,8893],{"className":8892,"style":2071},[407],[316,8894,8895,8898],{"style":411},[316,8896],{"className":8897,"style":416},[415],[316,8899,8901],{"className":8900},[420,421,422,423],[316,8902,8904],{"className":8903},[386,423],[316,8905,8907],{"className":8906},[386,7252,423],"crit",[316,8909,438],{"className":8910},[437],[316,8912,8914],{"className":8913},[403],[316,8915,8917],{"className":8916,"style":445},[407],[316,8918],{},[291,8920,8655],{},[1584,8922,8923,9179],{},[526,8924,8660,8925,9091,9092,9178],{},[316,8926,8928,8964],{"className":8927},[319],[316,8929,8931],{"className":8930},[323],[325,8932,8933],{"xmlns":327},[329,8934,8935,8961],{},[332,8936,8937,8943,8945],{},[335,8938,8939,8941],{},[338,8940,1604],{},[338,8942,7695],{},[350,8944,8681],{},[2166,8946,8947,8949,8959],{},[338,8948,550],{},[332,8950,8951,8953,8955,8957],{},[338,8952,646],{},[338,8954,7015],{},[338,8956,348],{},[338,8958,7361],{},[354,8960,3081],{},[365,8962,8963],{"encoding":367},"V_B \\propto E_{crit}^2",[316,8965,8967,9022],{"className":8966,"ariaHidden":373},[372],[316,8968,8970,8973,9013,9016,9019],{"className":8969},[377],[316,8971],{"className":8972,"style":566},[381],[316,8974,8976,8979],{"className":8975},[386],[316,8977,1604],{"className":8978,"style":1676},[386,390],[316,8980,8982],{"className":8981},[394],[316,8983,8985,9005],{"className":8984},[398,399],[316,8986,8988,9002],{"className":8987},[403],[316,8989,8991],{"className":8990,"style":408},[407],[316,8992,8993,8996],{"style":1691},[316,8994],{"className":8995,"style":416},[415],[316,8997,8999],{"className":8998},[420,421,422,423],[316,9000,7695],{"className":9001,"style":7865},[386,390,423],[316,9003,438],{"className":9004},[437],[316,9006,9008],{"className":9007},[403],[316,9009,9011],{"className":9010,"style":445},[407],[316,9012],{},[316,9014],{"className":9015,"style":452},[451],[316,9017,8681],{"className":9018},[456],[316,9020],{"className":9021,"style":452},[451],[316,9023,9025,9029],{"className":9024},[377],[316,9026],{"className":9027,"style":9028},[381],"height:1.0728em;vertical-align:-0.2587em;",[316,9030,9032,9035],{"className":9031},[386],[316,9033,550],{"className":9034,"style":430},[386,390],[316,9036,9038],{"className":9037},[394],[316,9039,9041,9082],{"className":9040},[398,399],[316,9042,9044,9079],{"className":9043},[403],[316,9045,9047,9068],{"className":9046,"style":5392},[407],[316,9048,9050,9053],{"style":9049},"top:-2.4413em;margin-left:-0.0576em;margin-right:0.05em;",[316,9051],{"className":9052,"style":416},[415],[316,9054,9056],{"className":9055},[420,421,422,423],[316,9057,9059,9062,9065],{"className":9058},[386,423],[316,9060,7407],{"className":9061,"style":2219},[386,390,423],[316,9063,348],{"className":9064},[386,390,423],[316,9066,7361],{"className":9067},[386,390,423],[316,9069,9070,9073],{"style":5407},[316,9071],{"className":9072,"style":416},[415],[316,9074,9076],{"className":9075},[420,421,422,423],[316,9077,3081],{"className":9078},[386,423],[316,9080,438],{"className":9081},[437],[316,9083,9085],{"className":9084},[403],[316,9086,9089],{"className":9087,"style":9088},[407],"height:0.2587em;",[316,9090],{}," 可知，",[316,9093,9095,9120],{"className":9094},[319],[316,9096,9098],{"className":9097},[323],[325,9099,9100],{"xmlns":327},[329,9101,9102,9118],{},[332,9103,9104],{},[335,9105,9106,9108],{},[338,9107,550],{},[332,9109,9110,9112,9114,9116],{},[338,9111,646],{},[338,9113,7015],{},[338,9115,348],{},[338,9117,7361],{},[365,9119,7364],{"encoding":367},[316,9121,9123],{"className":9122,"ariaHidden":373},[372],[316,9124,9126,9129],{"className":9125},[377],[316,9127],{"className":9128,"style":566},[381],[316,9130,9132,9135],{"className":9131},[386],[316,9133,550],{"className":9134,"style":430},[386,390],[316,9136,9138],{"className":9137},[394],[316,9139,9141,9170],{"className":9140},[398,399],[316,9142,9144,9167],{"className":9143},[403],[316,9145,9147],{"className":9146,"style":7392},[407],[316,9148,9149,9152],{"style":587},[316,9150],{"className":9151,"style":416},[415],[316,9153,9155],{"className":9154},[420,421,422,423],[316,9156,9158,9161,9164],{"className":9157},[386,423],[316,9159,7407],{"className":9160,"style":2219},[386,390,423],[316,9162,348],{"className":9163},[386,390,423],[316,9165,7361],{"className":9166},[386,390,423],[316,9168,438],{"className":9169},[437],[316,9171,9173],{"className":9172},[403],[316,9174,9176],{"className":9175,"style":445},[407],[316,9177],{}," 影响巨大。",[526,9180,9181,9182,9185,9186,9272],{},"使用",[291,9183,9184],{},"宽禁带半导体","（如 SiC, GaN），它们的 ",[316,9187,9189,9214],{"className":9188},[319],[316,9190,9192],{"className":9191},[323],[325,9193,9194],{"xmlns":327},[329,9195,9196,9212],{},[332,9197,9198],{},[335,9199,9200,9202],{},[338,9201,550],{},[332,9203,9204,9206,9208,9210],{},[338,9205,646],{},[338,9207,7015],{},[338,9209,348],{},[338,9211,7361],{},[365,9213,7364],{"encoding":367},[316,9215,9217],{"className":9216,"ariaHidden":373},[372],[316,9218,9220,9223],{"className":9219},[377],[316,9221],{"className":9222,"style":566},[381],[316,9224,9226,9229],{"className":9225},[386],[316,9227,550],{"className":9228,"style":430},[386,390],[316,9230,9232],{"className":9231},[394],[316,9233,9235,9264],{"className":9234},[398,399],[316,9236,9238,9261],{"className":9237},[403],[316,9239,9241],{"className":9240,"style":7392},[407],[316,9242,9243,9246],{"style":587},[316,9244],{"className":9245,"style":416},[415],[316,9247,9249],{"className":9248},[420,421,422,423],[316,9250,9252,9255,9258],{"className":9251},[386,423],[316,9253,7407],{"className":9254,"style":2219},[386,390,423],[316,9256,348],{"className":9257},[386,390,423],[316,9259,7361],{"className":9260},[386,390,423],[316,9262,438],{"className":9263},[437],[316,9265,9267],{"className":9266},[403],[316,9268,9270],{"className":9269,"style":445},[407],[316,9271],{}," 远高于Si，因此是制作高压器件的理想材料。",[1560,9274,9275,9280,9613,9616],{"type":1562},[241,9276,9277],{},[291,9278,9279],{},"为什么宽禁带半导体击穿场强大？",[241,9281,9282,9283,9286,9287,9290,9291,9371,9372,1322,9375,9446,9447,9371],{},"高压器件的击穿主要是",[291,9284,9285],{},"雪崩击穿","。这个过程依赖于",[291,9288,9289],{},"碰撞电离 (Impact Ionization)","，碰撞电离所需要的最小动能（即“门槛能量” ",[316,9292,9294,9316],{"className":9293},[319],[316,9295,9297],{"className":9296},[323],[325,9298,9299],{"xmlns":327},[329,9300,9301,9313],{},[332,9302,9303],{},[335,9304,9305,9307],{},[338,9306,550],{},[332,9308,9309,9311],{},[338,9310,7361],{},[338,9312,7806],{},[365,9314,9315],{"encoding":367},"E_{th}",[316,9317,9319],{"className":9318,"ariaHidden":373},[372],[316,9320,9322,9325],{"className":9321},[377],[316,9323],{"className":9324,"style":566},[381],[316,9326,9328,9331],{"className":9327},[386],[316,9329,550],{"className":9330,"style":430},[386,390],[316,9332,9334],{"className":9333},[394],[316,9335,9337,9363],{"className":9336},[398,399],[316,9338,9340,9360],{"className":9339},[403],[316,9341,9343],{"className":9342,"style":2071},[407],[316,9344,9345,9348],{"style":587},[316,9346],{"className":9347,"style":416},[415],[316,9349,9351],{"className":9350},[420,421,422,423],[316,9352,9354,9357],{"className":9353},[386,423],[316,9355,7361],{"className":9356},[386,390,423],[316,9358,7806],{"className":9359},[386,390,423],[316,9361,438],{"className":9362},[437],[316,9364,9366],{"className":9365},[403],[316,9367,9369],{"className":9368,"style":445},[407],[316,9370],{},"）",[291,9373,9374],{},"正比于禁带宽度",[316,9376,9378,9396],{"className":9377},[319],[316,9379,9381],{"className":9380},[323],[325,9382,9383],{"xmlns":327},[329,9384,9385,9393],{},[332,9386,9387],{},[335,9388,9389,9391],{},[338,9390,550],{},[338,9392,7803],{},[365,9394,9395],{"encoding":367},"E_g",[316,9397,9399],{"className":9398,"ariaHidden":373},[372],[316,9400,9402,9406],{"className":9401},[377],[316,9403],{"className":9404,"style":9405},[381],"height:0.9694em;vertical-align:-0.2861em;",[316,9407,9409,9412],{"className":9408},[386],[316,9410,550],{"className":9411,"style":430},[386,390],[316,9413,9415],{"className":9414},[394],[316,9416,9418,9438],{"className":9417},[398,399],[316,9419,9421,9435],{"className":9420},[403],[316,9422,9424],{"className":9423,"style":814},[407],[316,9425,9426,9429],{"style":587},[316,9427],{"className":9428,"style":416},[415],[316,9430,9432],{"className":9431},[420,421,422,423],[316,9433,7803],{"className":9434,"style":1117},[386,390,423],[316,9436,438],{"className":9437},[437],[316,9439,9441],{"className":9440},[403],[316,9442,9444],{"className":9443,"style":3815},[407],[316,9445],{},"。（一个近似值是 ",[316,9448,9450,9485],{"className":9449},[319],[316,9451,9453],{"className":9452},[323],[325,9454,9455],{"xmlns":327},[329,9456,9457,9482],{},[332,9458,9459,9469,9471,9474,9476],{},[335,9460,9461,9463],{},[338,9462,550],{},[332,9464,9465,9467],{},[338,9466,7361],{},[338,9468,7806],{},[350,9470,7462],{},[354,9472,9473],{},"1.5",[350,9475,7468],{},[335,9477,9478,9480],{},[338,9479,550],{},[338,9481,7803],{},[365,9483,9484],{"encoding":367},"E_{th} \\approx 1.5 \\times E_g",[316,9486,9488,9549,9567],{"className":9487,"ariaHidden":373},[372],[316,9489,9491,9494,9540,9543,9546],{"className":9490},[377],[316,9492],{"className":9493,"style":566},[381],[316,9495,9497,9500],{"className":9496},[386],[316,9498,550],{"className":9499,"style":430},[386,390],[316,9501,9503],{"className":9502},[394],[316,9504,9506,9532],{"className":9505},[398,399],[316,9507,9509,9529],{"className":9508},[403],[316,9510,9512],{"className":9511,"style":2071},[407],[316,9513,9514,9517],{"style":587},[316,9515],{"className":9516,"style":416},[415],[316,9518,9520],{"className":9519},[420,421,422,423],[316,9521,9523,9526],{"className":9522},[386,423],[316,9524,7361],{"className":9525},[386,390,423],[316,9527,7806],{"className":9528},[386,390,423],[316,9530,438],{"className":9531},[437],[316,9533,9535],{"className":9534},[403],[316,9536,9538],{"className":9537,"style":445},[407],[316,9539],{},[316,9541],{"className":9542,"style":452},[451],[316,9544,7462],{"className":9545},[456],[316,9547],{"className":9548,"style":452},[451],[316,9550,9552,9555,9558,9561,9564],{"className":9551},[377],[316,9553],{"className":9554,"style":7608},[381],[316,9556,9473],{"className":9557},[386],[316,9559],{"className":9560,"style":1676},[451],[316,9562,7468],{"className":9563},[991],[316,9565],{"className":9566,"style":1676},[451],[316,9568,9570,9573],{"className":9569},[377],[316,9571],{"className":9572,"style":9405},[381],[316,9574,9576,9579],{"className":9575},[386],[316,9577,550],{"className":9578,"style":430},[386,390],[316,9580,9582],{"className":9581},[394],[316,9583,9585,9605],{"className":9584},[398,399],[316,9586,9588,9602],{"className":9587},[403],[316,9589,9591],{"className":9590,"style":814},[407],[316,9592,9593,9596],{"style":587},[316,9594],{"className":9595,"style":416},[415],[316,9597,9599],{"className":9598},[420,421,422,423],[316,9600,7803],{"className":9601,"style":1117},[386,390,423],[316,9603,438],{"className":9604},[437],[316,9606,9608],{"className":9607},[403],[316,9609,9611],{"className":9610,"style":3815},[407],[316,9612],{},[241,9614,9615],{},"因此，逻辑链是：",[241,9617,9618,9621,1322,9690,1322,9693,9724,1322,9727,9755,9758,9759,9787,9790,9876],{},[291,9619,9620],{},"宽禁带 (",[316,9622,9624,9641],{"className":9623},[319],[316,9625,9627],{"className":9626},[323],[325,9628,9629],{"xmlns":327},[329,9630,9631,9639],{},[332,9632,9633],{},[335,9634,9635,9637],{},[338,9636,550],{},[338,9638,7803],{},[365,9640,9395],{"encoding":367},[316,9642,9644],{"className":9643,"ariaHidden":373},[372],[316,9645,9647,9650],{"className":9646},[377],[316,9648],{"className":9649,"style":9405},[381],[316,9651,9653,9656],{"className":9652},[386],[316,9654,550],{"className":9655,"style":430},[386,390],[316,9657,9659],{"className":9658},[394],[316,9660,9662,9682],{"className":9661},[398,399],[316,9663,9665,9679],{"className":9664},[403],[316,9666,9668],{"className":9667,"style":814},[407],[316,9669,9670,9673],{"style":587},[316,9671],{"className":9672,"style":416},[415],[316,9674,9676],{"className":9675},[420,421,422,423],[316,9677,7803],{"className":9678,"style":1117},[386,390,423],[316,9680,438],{"className":9681},[437],[316,9683,9685],{"className":9684},[403],[316,9686,9688],{"className":9687,"style":3815},[407],[316,9689],{},[291,9691,9692],{},"大)",[316,9694,9696,9711],{"className":9695},[319],[316,9697,9699],{"className":9698},[323],[325,9700,9701],{"xmlns":327},[329,9702,9703,9708],{},[332,9704,9705],{},[350,9706,9707],{},"⇒",[365,9709,9710],{"encoding":367},"\\Rightarrow",[316,9712,9714],{"className":9713,"ariaHidden":373},[372],[316,9715,9717,9721],{"className":9716},[377],[316,9718],{"className":9719,"style":9720},[381],"height:0.3669em;",[316,9722,9707],{"className":9723},[456],[291,9725,9726],{},"碰撞电离的能量高",[316,9728,9730,9743],{"className":9729},[319],[316,9731,9733],{"className":9732},[323],[325,9734,9735],{"xmlns":327},[329,9736,9737,9741],{},[332,9738,9739],{},[350,9740,9707],{},[365,9742,9710],{"encoding":367},[316,9744,9746],{"className":9745,"ariaHidden":373},[372],[316,9747,9749,9752],{"className":9748},[377],[316,9750],{"className":9751,"style":9720},[381],[316,9753,9707],{"className":9754},[456],[291,9756,9757],{},"载流子需要被更强的电场加速，才能获得这份能量","  ",[316,9760,9762,9775],{"className":9761},[319],[316,9763,9765],{"className":9764},[323],[325,9766,9767],{"xmlns":327},[329,9768,9769,9773],{},[332,9770,9771],{},[350,9772,9707],{},[365,9774,9710],{"encoding":367},[316,9776,9778],{"className":9777,"ariaHidden":373},[372],[316,9779,9781,9784],{"className":9780},[377],[316,9782],{"className":9783,"style":9720},[381],[316,9785,9707],{"className":9786},[456],[291,9788,9789],{},"能够触发雪崩的“临界电场” (",[316,9791,9793,9818],{"className":9792},[319],[316,9794,9796],{"className":9795},[323],[325,9797,9798],{"xmlns":327},[329,9799,9800,9816],{},[332,9801,9802],{},[335,9803,9804,9806],{},[338,9805,550],{},[332,9807,9808,9810,9812,9814],{},[338,9809,646],{},[338,9811,7015],{},[338,9813,348],{},[338,9815,7361],{},[365,9817,7364],{"encoding":367},[316,9819,9821],{"className":9820,"ariaHidden":373},[372],[316,9822,9824,9827],{"className":9823},[377],[316,9825],{"className":9826,"style":566},[381],[316,9828,9830,9833],{"className":9829},[386],[316,9831,550],{"className":9832,"style":430},[386,390],[316,9834,9836],{"className":9835},[394],[316,9837,9839,9868],{"className":9838},[398,399],[316,9840,9842,9865],{"className":9841},[403],[316,9843,9845],{"className":9844,"style":7392},[407],[316,9846,9847,9850],{"style":587},[316,9848],{"className":9849,"style":416},[415],[316,9851,9853],{"className":9852},[420,421,422,423],[316,9854,9856,9859,9862],{"className":9855},[386,423],[316,9857,7407],{"className":9858,"style":2219},[386,390,423],[316,9860,348],{"className":9861},[386,390,423],[316,9863,7361],{"className":9864},[386,390,423],[316,9866,438],{"className":9867},[437],[316,9869,9871],{"className":9870},[403],[316,9872,9874],{"className":9873,"style":445},[407],[316,9875],{},[291,9877,9878],{},") 非常强。",[256,9880,9882],{"id":9881},"tunneling-breakdown","Tunneling Breakdown",[241,9884,9885],{},[247,9886],{"alt":9887,"src":9888},"MuJHblb8ZoOItvx9fDfc1ISrnzc.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-18.png",[523,9890,9891,9905,10044,10054],{},[526,9892,9893,9896],{},[291,9894,9895],{},"发生条件：",[1584,9897,9898],{},[526,9899,9900,9901,9904],{},"在",[291,9902,9903],{},"两边都重掺杂 (N_A, N_D 都很高)"," 的PN结中占主导。",[526,9906,9907,1322,9910,9913],{},[291,9908,9909],{},"物理过程：",[291,9911,9912],{},"量子隧道效应 (Quantum Tunneling)",[1584,9914,9915,10037],{},[526,9916,9917,9918,1322,9946,9949,9950,10036],{},"两边都重掺杂 ",[316,9919,9921,9934],{"className":9920},[319],[316,9922,9924],{"className":9923},[323],[325,9925,9926],{"xmlns":327},[329,9927,9928,9932],{},[332,9929,9930],{},[350,9931,9707],{},[365,9933,9710],{"encoding":367},[316,9935,9937],{"className":9936,"ariaHidden":373},[372],[316,9938,9940,9943],{"className":9939},[377],[316,9941],{"className":9942,"style":9720},[381],[316,9944,9707],{"className":9945},[456],[291,9947,9948],{},"耗尽区宽度非常窄","（",[316,9951,9953,9977],{"className":9952},[319],[316,9954,9956],{"className":9955},[323],[325,9957,9958],{"xmlns":327},[329,9959,9960,9974],{},[332,9961,9962],{},[335,9963,9964,9966],{},[338,9965,5515],{},[332,9967,9968,9970,9972],{},[338,9969,3903],{},[338,9971,652],{},[338,9973,241],{},[365,9975,9976],{"encoding":367},"W_{dep}",[316,9978,9980],{"className":9979,"ariaHidden":373},[372],[316,9981,9983,9986],{"className":9982},[377],[316,9984],{"className":9985,"style":9405},[381],[316,9987,9989,9992],{"className":9988},[386],[316,9990,5515],{"className":9991,"style":597},[386,390],[316,9993,9995],{"className":9994},[394],[316,9996,9998,10028],{"className":9997},[398,399],[316,9999,10001,10025],{"className":10000},[403],[316,10002,10004],{"className":10003,"style":2071},[407],[316,10005,10007,10010],{"style":10006},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[316,10008],{"className":10009,"style":416},[415],[316,10011,10013],{"className":10012},[420,421,422,423],[316,10014,10016,10019,10022],{"className":10015},[386,423],[316,10017,3903],{"className":10018},[386,390,423],[316,10020,652],{"className":10021},[386,390,423],[316,10023,241],{"className":10024},[386,390,423],[316,10026,438],{"className":10027},[437],[316,10029,10031],{"className":10030},[403],[316,10032,10034],{"className":10033,"style":3815},[407],[316,10035],{}," 极窄）",[526,10038,10039,10040,10043],{},"势垒虽然高，但非常薄，P区的电子（在价带）可以直接",[291,10041,10042],{},"“隧穿”","通过这个薄势垒，到达N区的导带，形成大电流。",[526,10045,10046,10049],{},[291,10047,10048],{},"特性：",[1584,10050,10051],{},[526,10052,10053],{},"通常发生在较低的电压下（例如 V_B \u003C 5\\text{V}）。",[526,10055,10056,9758,10059,10062],{},[291,10057,10058],{},"应用：",[291,10060,10061],{},"Zener Diode | 齐纳二极管",[1584,10063,10064,10074,10086,10116],{},[526,10065,10066,10069,10070,10073],{},[291,10067,10068],{},"设计："," 专门",[291,10071,10072],{},"被设计用来安全工作在击穿模式","的二极管。（通常 V_B \u003C 5\\text{V} 是齐纳击穿为主， V_B > 6\\text{V} 是雪崩击穿为主）。",[526,10075,10076,1322,10079,10082,10083,2098],{},[291,10077,10078],{},"功能：",[291,10080,10081],{},"稳压 (Voltage Regulator)"," 或 ",[291,10084,10085],{},"电压钳位 (Clamping)",[526,10087,10088,10091],{},[291,10089,10090],{},"电路：",[523,10092,10093,10099,10105],{},[526,10094,10095,10096,2098],{},"齐纳二极管",[291,10097,10098],{},"反向偏置",[526,10100,10101,10102,2098],{},"与被保护的负载（如 IC）",[291,10103,10104],{},"并联",[526,10106,10107,10108,10111,10112,10115],{},"必须",[291,10109,10110],{},"串联","一个",[291,10113,10114],{},"限流电阻 (R)","，以防止过热烧毁。",[526,10117,10118,10121,10122,10192,10193,10262],{},[291,10119,10120],{},"工作原理："," 当输入电压(A-B)超过",[316,10123,10125,10143],{"className":10124},[319],[316,10126,10128],{"className":10127},[323],[325,10129,10130],{"xmlns":327},[329,10131,10132,10140],{},[332,10133,10134],{},[335,10135,10136,10138],{},[338,10137,1604],{},[338,10139,7695],{},[365,10141,10142],{"encoding":367},"V_B",[316,10144,10146],{"className":10145,"ariaHidden":373},[372],[316,10147,10149,10152],{"className":10148},[377],[316,10150],{"className":10151,"style":566},[381],[316,10153,10155,10158],{"className":10154},[386],[316,10156,1604],{"className":10157,"style":1676},[386,390],[316,10159,10161],{"className":10160},[394],[316,10162,10164,10184],{"className":10163},[398,399],[316,10165,10167,10181],{"className":10166},[403],[316,10168,10170],{"className":10169,"style":408},[407],[316,10171,10172,10175],{"style":1691},[316,10173],{"className":10174,"style":416},[415],[316,10176,10178],{"className":10177},[420,421,422,423],[316,10179,7695],{"className":10180,"style":7865},[386,390,423],[316,10182,438],{"className":10183},[437],[316,10185,10187],{"className":10186},[403],[316,10188,10190],{"className":10189,"style":445},[407],[316,10191],{},"（例如3.7V）时，二极管击穿，将C-D两点的电压“钳位”在 ",[316,10194,10196,10213],{"className":10195},[319],[316,10197,10199],{"className":10198},[323],[325,10200,10201],{"xmlns":327},[329,10202,10203,10211],{},[332,10204,10205],{},[335,10206,10207,10209],{},[338,10208,1604],{},[338,10210,7695],{},[365,10212,10142],{"encoding":367},[316,10214,10216],{"className":10215,"ariaHidden":373},[372],[316,10217,10219,10222],{"className":10218},[377],[316,10220],{"className":10221,"style":566},[381],[316,10223,10225,10228],{"className":10224},[386],[316,10226,1604],{"className":10227,"style":1676},[386,390],[316,10229,10231],{"className":10230},[394],[316,10232,10234,10254],{"className":10233},[398,399],[316,10235,10237,10251],{"className":10236},[403],[316,10238,10240],{"className":10239,"style":408},[407],[316,10241,10242,10245],{"style":1691},[316,10243],{"className":10244,"style":416},[415],[316,10246,10248],{"className":10247},[420,421,422,423],[316,10249,7695],{"className":10250,"style":7865},[386,390,423],[316,10252,438],{"className":10253},[437],[316,10255,10257],{"className":10256},[403],[316,10258,10260],{"className":10259,"style":445},[407],[316,10261],{}," (3.7V)，从而保护IC。",[256,10264,10266],{"id":10265},"avalanche-breakdown-雪崩击穿","Avalanche Breakdown  | 雪崩击穿",[241,10268,10269],{},[247,10270],{"alt":10271,"src":10272},"PixPin_2025-11-12_20-35-39.png","\u002Fimg\u002FMicroelectronicDevices\u002FLecture5-04.png",[523,10274,10275,10291,10510],{},[526,10276,10277,10280],{},[291,10278,10279],{},"发生条件  |  Condition：",[1584,10281,10282,10288],{},[526,10283,9900,10284,10287],{},[291,10285,10286],{},"轻掺杂","（或中等掺杂）的PN结中占主导。",[526,10289,10290],{},"此时 V_B 较高，耗尽层较宽。",[526,10292,10293,1322,10295,10297],{},[291,10294,9909],{},[291,10296,9289],{},[1584,10298,10299,10405],{},[526,10300,10301,10302,10330,10331,10334,10335,10338,10341,10369,10370,10372,10400,10401,10404],{},"耗尽区电场强，电子被加速获得很高能量\n",[316,10303,10305,10318],{"className":10304},[319],[316,10306,10308],{"className":10307},[323],[325,10309,10310],{"xmlns":327},[329,10311,10312,10316],{},[332,10313,10314],{},[350,10315,9707],{},[365,10317,9710],{"encoding":367},[316,10319,10321],{"className":10320,"ariaHidden":373},[372],[316,10322,10324,10327],{"className":10323},[377],[316,10325],{"className":10326,"style":9720},[381],[316,10328,9707],{"className":10329},[456],"高能电子",[291,10332,10333],{},"撞击","晶格，将价带电子“撞”出，产生一个新的",[291,10336,10337],{},"电子-空穴对",[10339,10340],"br",{},[316,10342,10344,10357],{"className":10343},[319],[316,10345,10347],{"className":10346},[323],[325,10348,10349],{"xmlns":327},[329,10350,10351,10355],{},[332,10352,10353],{},[350,10354,9707],{},[365,10356,9710],{"encoding":367},[316,10358,10360],{"className":10359,"ariaHidden":373},[372],[316,10361,10363,10366],{"className":10362},[377],[316,10364],{"className":10365,"style":9720},[381],[316,10367,9707],{"className":10368},[456],"新产生的载流子也被加速，再去撞击，产生更多的载流子",[10339,10371],{},[316,10373,10375,10388],{"className":10374},[319],[316,10376,10378],{"className":10377},[323],[325,10379,10380],{"xmlns":327},[329,10381,10382,10386],{},[332,10383,10384],{},[350,10385,9707],{},[365,10387,9710],{"encoding":367},[316,10389,10391],{"className":10390,"ariaHidden":373},[372],[316,10392,10394,10397],{"className":10393},[377],[316,10395],{"className":10396,"style":9720},[381],[316,10398,9707],{"className":10399},[456],"  这个过程像雪崩一样，是一个",[291,10402,10403],{},"正反馈 (Positive Feedback)","，导致载流子数量和电流剧增。",[526,10406,10407,10408,10436,10437,10440,10441,1552,10444,10446,10474,10475,10477,10505,10506,10509],{},"In the strong electric field of the depletion region, electrons are accelerated and gain high kinetic energy.\n",[316,10409,10411,10424],{"className":10410},[319],[316,10412,10414],{"className":10413},[323],[325,10415,10416],{"xmlns":327},[329,10417,10418,10422],{},[332,10419,10420],{},[350,10421,9707],{},[365,10423,9710],{"encoding":367},[316,10425,10427],{"className":10426,"ariaHidden":373},[372],[316,10428,10430,10433],{"className":10429},[377],[316,10431],{"className":10432,"style":9720},[381],[316,10434,9707],{"className":10435},[456]," These energetic electrons ",[291,10438,10439],{},"impact"," the crystal lattice, \"knocking out\" a valence electron and ",[291,10442,10443],{},"generating a new electron-hole pair",[10339,10445],{},[316,10447,10449,10462],{"className":10448},[319],[316,10450,10452],{"className":10451},[323],[325,10453,10454],{"xmlns":327},[329,10455,10456,10460],{},[332,10457,10458],{},[350,10459,9707],{},[365,10461,9710],{"encoding":367},[316,10463,10465],{"className":10464,"ariaHidden":373},[372],[316,10466,10468,10471],{"className":10467},[377],[316,10469],{"className":10470,"style":9720},[381],[316,10472,9707],{"className":10473},[456]," The newly generated carriers are also accelerated, impacting the lattice again to generate even more carriers.",[10339,10476],{},[316,10478,10480,10493],{"className":10479},[319],[316,10481,10483],{"className":10482},[323],[325,10484,10485],{"xmlns":327},[329,10486,10487,10491],{},[332,10488,10489],{},[350,10490,9707],{},[365,10492,9710],{"encoding":367},[316,10494,10496],{"className":10495,"ariaHidden":373},[372],[316,10497,10499,10502],{"className":10498},[377],[316,10500],{"className":10501,"style":9720},[381],[316,10503,9707],{"className":10504},[456],"This process, like an avalanche, is a ",[291,10507,10508],{},"positive feedback"," loop, leading to a dramatic, exponential increase in carrier concentration and current.",[526,10511,10512,10514],{},[291,10513,10058],{},[1584,10515,10516,10519],{},[526,10517,10518],{},"雪崩光电探测器 (APD, Avalanche Photodetector) 利用此效应来放大微弱的光信号。",[526,10520,10521,10522,10525,10526,10529],{},"雪崩过程本身",[291,10523,10524],{},"不会","损坏器件，是",[291,10527,10528],{},"过热","导致损坏。",{"title":10531,"searchDepth":10532,"depth":10532,"links":10533},"",4,[10534],{"id":233,"depth":10535,"text":234,"children":10536},2,[10537,10539,10543,10565],{"id":238,"depth":10538,"text":239},3,{"id":253,"depth":10538,"text":254,"children":10540},[10541,10542],{"id":258,"depth":10532,"text":259},{"id":271,"depth":10532,"text":272},{"id":281,"depth":10538,"text":282,"children":10544},[10545,10546,10547,10548,10560],{"id":285,"depth":10532,"text":286},{"id":302,"depth":10532,"text":303},{"id":514,"depth":10532,"text":515},{"id":2119,"depth":10532,"text":2120,"children":10549},[10550,10552,10554,10556,10557,10558,10559],{"id":2124,"depth":10551,"text":2125},5,{"id":2396,"depth":10551,"text":10553},"Built-in Potential VbiV_{bi}Vbi​",{"id":3450,"depth":10551,"text":10555},"VbiV_{bi}Vbi​ for Abrupt PN Junctions",{"id":3706,"depth":10551,"text":3707},{"id":6770,"depth":10551,"text":6771},{"id":6780,"depth":10551,"text":6781},{"id":6797,"depth":10551,"text":6798},{"id":6876,"depth":10532,"text":6877,"children":10561},[10562,10563,10564],{"id":6880,"depth":10551,"text":6881},{"id":6900,"depth":10551,"text":6900},{"id":7095,"depth":10551,"text":7096},{"id":7133,"depth":10538,"text":7134,"children":10566},[10567,10568,10569],{"id":7197,"depth":10532,"text":7198},{"id":9881,"depth":10532,"text":9882},{"id":10265,"depth":10532,"text":10266},[189],"PN 结的制备与理想模型、电荷密度与泊松方程、耗尽近似、内建电势、电容电压特性、反向偏置与击穿（隧穿击穿、雪崩击穿）","md",null,{"slots":10575},{},{"text":10577,"minutes":10578,"time":10579,"words":10580},"14 min read",13.52,811200,2704,{"title":141,"description":10571},{"loc":140,"images":10583},[10584,10585,10586,10587,10588,10589,10590,10591,10592,10593,10594,10595,10596,10597,10598,10599,10600,10601,10602,10603,10604,10605,10606,10607,10608],{"loc":250},{"loc":268},{"loc":278},{"loc":309},{"loc":521},{"loc":1558},{"loc":2925},{"loc":3703},{"loc":3713},{"loc":6210},{"loc":6260},{"loc":6777},{"loc":6794},{"loc":6812},{"loc":6866},{"loc":6897},{"loc":6906},{"loc":7092},{"loc":7102},{"loc":7147},{"loc":7317},{"loc":7323},{"loc":7332},{"loc":9888},{"loc":10272},[176,10610],"课程笔记","tech","gqeqDYeHiO7QlVNAWtHrrOm2bXEckWqN-jdI49yVu5A",[10614,10615],{"title":136,"path":135,"stem":134,"date":137,"type":10611,"children":-1},{"title":146,"path":145,"stem":144,"date":147,"type":10611,"children":-1},1789011906683]