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less easily deflected.",[279,280],"hr",{},[231,282,283],{},"About Phonon Scattering and Charge-Charge Scattering",[231,285,286,245,289,292,293,296,297,300],{},[242,287,288],{},"Phonon scattering",[242,290,291],{},"collision"," (碰撞) of mobile charge carriers with the ",[242,294,295],{},"vibrating crystal lattice","(振动的晶格), or equivalently ",[242,298,299],{},"with phonons",", the quantized particles that carry lattice-vibration energy (声子是晶格振动能量的量子).",[255,302,303,573,583,600],{},[258,304,305,308,309,312,313,316,317,320,321,324,325,561,562,565,566,568,569,572],{},[242,306,307],{},"Temperature",": As temperature increases, ",[242,310,311],{},"lattice vibrations"," become stronger and the ",[242,314,315],{},"phonon density"," rises, leading to more frequent carrier–phonon collisions. This ",[242,318,319],{},"increases"," phonon scattering and ",[242,322,323],{},"reduces"," mobility; roughly, the phonon-limited mobility scales as ",[326,327,330,406],"span",{"className":328},[329],"katex",[326,331,334],{"className":332},[333],"katex-mathml",[335,336,338],"math",{"xmlns":337},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[339,340,341,401],"semantics",{},[342,343,344,368,372],"mrow",{},[345,346,347,351],"msub",{},[348,349,350],"mi",{},"μ",[342,352,353,355,358,361,364,366],{},[348,354,231],{},[348,356,357],{},"h",[348,359,360],{},"o",[348,362,363],{},"n",[348,365,360],{},[348,367,363],{},[369,370,371],"mo",{},"∝",[373,374,375,378],"msup",{},[348,376,377],{},"T",[342,379,380,384,387,391,395,398],{},[369,381,383],{"stretchy":382},"false","(",[369,385,386],{},"−",[388,389,390],"mn",{},"3",[348,392,394],{"mathvariant":393},"normal","\u002F",[388,396,397],{},"2",[369,399,400],{"stretchy":382},")",[402,403,405],"annotation",{"encoding":404},"application\u002Fx-tex","μ_{phonon} ∝ T^{(-3\u002F2)}",[326,407,411,508],{"className":408,"ariaHidden":410},[409],"katex-html","true",[326,412,415,420,496,501,505],{"className":413},[414],"base",[326,416],{"className":417,"style":419},[418],"strut","height:0.7167em;vertical-align:-0.2861em;",[326,421,424,428],{"className":422},[423],"mord",[326,425,350],{"className":426},[423,427],"mathnormal",[326,429,432],{"className":430},[431],"msupsub",[326,433,437,487],{"className":434},[435,436],"vlist-t","vlist-t2",[326,438,441,482],{"className":439},[440],"vlist-r",[326,442,446],{"className":443,"style":445},[444],"vlist","height:0.3361em;",[326,447,449,454],{"style":448},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[326,450],{"className":451,"style":453},[452],"pstrut","height:2.7em;",[326,455,461],{"className":456},[457,458,459,460],"sizing","reset-size6","size3","mtight",[326,462,464,467,470,473,476,479],{"className":463},[423,460],[326,465,231],{"className":466},[423,427,460],[326,468,357],{"className":469},[423,427,460],[326,471,360],{"className":472},[423,427,460],[326,474,363],{"className":475},[423,427,460],[326,477,360],{"className":478},[423,427,460],[326,480,363],{"className":481},[423,427,460],[326,483,486],{"className":484},[485],"vlist-s","​",[326,488,490],{"className":489},[440],[326,491,494],{"className":492,"style":493},[444],"height:0.2861em;",[326,495],{},[326,497],{"className":498,"style":500},[499],"mspace","margin-right:0.2778em;",[326,502,371],{"className":503},[504],"mrel",[326,506],{"className":507,"style":500},[499],[326,509,511,515],{"className":510},[414],[326,512],{"className":513,"style":514},[418],"height:0.888em;",[326,516,518,522],{"className":517},[423],[326,519,377],{"className":520,"style":521},[423,427],"margin-right:0.1389em;",[326,523,525],{"className":524},[431],[326,526,528],{"className":527},[435],[326,529,531],{"className":530},[440],[326,532,534],{"className":533,"style":514},[444],[326,535,537,540],{"style":536},"top:-3.063em;margin-right:0.05em;",[326,538],{"className":539,"style":453},[452],[326,541,543],{"className":542},[457,458,459,460],[326,544,546,550,553,557],{"className":545},[423,460],[326,547,383],{"className":548},[549,460],"mopen",[326,551,386],{"className":552},[423,460],[326,554,556],{"className":555},[423,460],"3\u002F2",[326,558,400],{"className":559},[560,460],"mclose",", so higher T → lower μ.\n",[242,563,564],{},"Charge–charge scattering"," (载流子–载流子散射) is the ",[242,567,248],{}," (偏转) of a mobile charge carrier by the ",[242,570,571],{},"Coulomb force from other mobile carriers"," (electron–electron or electron–hole interactions).",[258,574,575,578,579,582],{},[242,576,577],{},"Carrier Concentration",": It is only significant at ",[242,580,581],{},"high carrier concentrations",", where many carriers are present and the probability of carrier–carrier Coulomb interactions becomes large, thus reducing mobility.",[258,584,585,587,588,591,592,595,596,599],{},[242,586,307],{},": With increasing temperature, carriers move faster, so their ",[242,589,590],{},"interaction time"," with any given charged neighbor is shorter and the ",[242,593,594],{},"Coulomb deflection angle"," becomes smaller. Therefore ",[242,597,598],{},"charge–charge scattering becomes weaker"," as temperature rises, and its impact on mobility decreases.",[258,601,602],{},"Net Current: In the absence of an electric field or concentration\u002Ftemperature gradients, carriers undergo only random thermal motion; the average current in any direction is zero. Directed current requires a driving force (electric field for drift, or concentration\u002Ftemperature gradients for diffusion), while scattering mainly limits how large this directed motion (mobility, diffusivity) can become.",[279,604],{},[235,606,608],{"id":607},"_2what-is-matthiessens-rule-in-carrier-mobility-calculationwhat-is-the-basic-ground-for-this-rulewhere-does-it-come-from","2.What is Matthiessen's Rule in carrier mobility calculation?What is the basic ground for this Rule(Where does it come from)?",[326,610,613],{"className":611},[612],"katex-display",[326,614,616,670],{"className":615},[329],[326,617,619],{"className":618},[333],[335,620,622],{"xmlns":337,"display":621},"block",[339,623,624,667],{},[342,625,626,629,631,639,642,644,646,653,656,658,660],{},[388,627,628],{},"1",[348,630,394],{"mathvariant":393},[345,632,633,635],{},[348,634,350],{},[636,637,638],"mtext",{},"total",[369,640,641],{},"=",[388,643,628],{},[348,645,394],{"mathvariant":393},[345,647,648,650],{},[348,649,350],{},[636,651,652],{},"phonon",[369,654,655],{},"+",[388,657,628],{},[348,659,394],{"mathvariant":393},[345,661,662,664],{},[348,663,350],{},[636,665,666],{},"impurity",[402,668,669],{"encoding":404},"1\u002F\\mu_{\\text{total}} = 1\u002F\\mu_{\\text{phonon}} + 1\u002F\\mu_{\\text{impurity}}",[326,671,673,741,808],{"className":672,"ariaHidden":410},[409],[326,674,676,680,684,732,735,738],{"className":675},[414],[326,677],{"className":678,"style":679},[418],"height:1em;vertical-align:-0.25em;",[326,681,683],{"className":682},[423],"1\u002F",[326,685,687,690],{"className":686},[423],[326,688,350],{"className":689},[423,427],[326,691,693],{"className":692},[431],[326,694,696,723],{"className":695},[435,436],[326,697,699,720],{"className":698},[440],[326,700,702],{"className":701,"style":445},[444],[326,703,704,707],{"style":448},[326,705],{"className":706,"style":453},[452],[326,708,710],{"className":709},[457,458,459,460],[326,711,713],{"className":712},[423,460],[326,714,717],{"className":715},[423,716,460],"text",[326,718,638],{"className":719},[423,460],[326,721,486],{"className":722},[485],[326,724,726],{"className":725},[440],[326,727,730],{"className":728,"style":729},[444],"height:0.15em;",[326,731],{},[326,733],{"className":734,"style":500},[499],[326,736,641],{"className":737},[504],[326,739],{"className":740,"style":500},[499],[326,742,744,748,751,797,801,805],{"className":743},[414],[326,745],{"className":746,"style":747},[418],"height:1.0361em;vertical-align:-0.2861em;",[326,749,683],{"className":750},[423],[326,752,754,757],{"className":753},[423],[326,755,350],{"className":756},[423,427],[326,758,760],{"className":759},[431],[326,761,763,789],{"className":762},[435,436],[326,764,766,786],{"className":765},[440],[326,767,769],{"className":768,"style":445},[444],[326,770,771,774],{"style":448},[326,772],{"className":773,"style":453},[452],[326,775,777],{"className":776},[457,458,459,460],[326,778,780],{"className":779},[423,460],[326,781,783],{"className":782},[423,716,460],[326,784,652],{"className":785},[423,460],[326,787,486],{"className":788},[485],[326,790,792],{"className":791},[440],[326,793,795],{"className":794,"style":493},[444],[326,796],{},[326,798],{"className":799,"style":800},[499],"margin-right:0.2222em;",[326,802,655],{"className":803},[804],"mbin",[326,806],{"className":807,"style":800},[499],[326,809,811,814,817],{"className":810},[414],[326,812],{"className":813,"style":747},[418],[326,815,683],{"className":816},[423],[326,818,820,823],{"className":819},[423],[326,821,350],{"className":822},[423,427],[326,824,826],{"className":825},[431],[326,827,829,856],{"className":828},[435,436],[326,830,832,853],{"className":831},[440],[326,833,836],{"className":834,"style":835},[444],"height:0.3175em;",[326,837,838,841],{"style":448},[326,839],{"className":840,"style":453},[452],[326,842,844],{"className":843},[457,458,459,460],[326,845,847],{"className":846},[423,460],[326,848,850],{"className":849},[423,716,460],[326,851,666],{"className":852},[423,460],[326,854,486],{"className":855},[485],[326,857,859],{"className":858},[440],[326,860,862],{"className":861,"style":493},[444],[326,863],{},[231,865,866,867,870,871],{},"The ",[242,868,869],{},"probability"," that a carrier will be scattered by mechanism i within a time period dt is ",[326,872,874,905],{"className":873},[329],[326,875,877],{"className":876},[333],[335,878,879],{"xmlns":337},[339,880,881,902],{},[342,882,883],{},[884,885,886,894],"mfrac",{},[342,887,888,891],{},[348,889,890],{},"d",[348,892,893],{},"t",[345,895,896,899],{},[348,897,898],{},"τ",[348,900,901],{},"i",[402,903,904],{"encoding":404},"\\frac{dt}{\\tau_i}",[326,906,908],{"className":907,"ariaHidden":410},[409],[326,909,911,915],{"className":910},[414],[326,912],{"className":913,"style":914},[418],"height:1.3252em;vertical-align:-0.4451em;",[326,916,918,922,1036],{"className":917},[423],[326,919],{"className":920},[549,921],"nulldelimiter",[326,923,925],{"className":924},[884],[326,926,928,1027],{"className":927},[435,436],[326,929,931,1024],{"className":930},[440],[326,932,935,995,1006],{"className":933,"style":934},[444],"height:0.8801em;",[326,936,938,942],{"style":937},"top:-2.655em;",[326,939],{"className":940,"style":941},[452],"height:3em;",[326,943,945],{"className":944},[457,458,459,460],[326,946,948],{"className":947},[423,460],[326,949,951,955],{"className":950},[423,460],[326,952,898],{"className":953,"style":954},[423,427,460],"margin-right:0.1132em;",[326,956,958],{"className":957},[431],[326,959,961,986],{"className":960},[435,436],[326,962,964,983],{"className":963},[440],[326,965,968],{"className":966,"style":967},[444],"height:0.3281em;",[326,969,971,975],{"style":970},"top:-2.357em;margin-left:-0.1132em;margin-right:0.0714em;",[326,972],{"className":973,"style":974},[452],"height:2.5em;",[326,976,980],{"className":977},[457,978,979,460],"reset-size3","size1",[326,981,901],{"className":982},[423,427,460],[326,984,486],{"className":985},[485],[326,987,989],{"className":988},[440],[326,990,993],{"className":991,"style":992},[444],"height:0.143em;",[326,994],{},[326,996,998,1001],{"style":997},"top:-3.23em;",[326,999],{"className":1000,"style":941},[452],[326,1002],{"className":1003,"style":1005},[1004],"frac-line","border-bottom-width:0.04em;",[326,1007,1009,1012],{"style":1008},"top:-3.394em;",[326,1010],{"className":1011,"style":941},[452],[326,1013,1015],{"className":1014},[457,458,459,460],[326,1016,1018,1021],{"className":1017},[423,460],[326,1019,890],{"className":1020},[423,427,460],[326,1022,893],{"className":1023},[423,427,460],[326,1025,486],{"className":1026},[485],[326,1028,1030],{"className":1029},[440],[326,1031,1034],{"className":1032,"style":1033},[444],"height:0.4451em;",[326,1035],{},[326,1037],{"className":1038},[560,921],[1040,1041,1042],"blockquote",{},[231,1043,1044,1045,1118,1119,1122,1123],{},"where ",[326,1046,1048,1066],{"className":1047},[329],[326,1049,1051],{"className":1050},[333],[335,1052,1053],{"xmlns":337},[339,1054,1055,1063],{},[342,1056,1057],{},[345,1058,1059,1061],{},[348,1060,898],{},[348,1062,901],{},[402,1064,1065],{"encoding":404},"\\tau_i",[326,1067,1069],{"className":1068,"ariaHidden":410},[409],[326,1070,1072,1076],{"className":1071},[414],[326,1073],{"className":1074,"style":1075},[418],"height:0.5806em;vertical-align:-0.15em;",[326,1077,1079,1082],{"className":1078},[423],[326,1080,898],{"className":1081,"style":954},[423,427],[326,1083,1085],{"className":1084},[431],[326,1086,1088,1110],{"className":1087},[435,436],[326,1089,1091,1107],{"className":1090},[440],[326,1092,1095],{"className":1093,"style":1094},[444],"height:0.3117em;",[326,1096,1098,1101],{"style":1097},"top:-2.55em;margin-left:-0.1132em;margin-right:0.05em;",[326,1099],{"className":1100,"style":453},[452],[326,1102,1104],{"className":1103},[457,458,459,460],[326,1105,901],{"className":1106},[423,427,460],[326,1108,486],{"className":1109},[485],[326,1111,1113],{"className":1112},[440],[326,1114,1116],{"className":1115,"style":729},[444],[326,1117],{}," is ",[242,1120,1121],{},"the mean time"," between scattering events due to mechanism ",[326,1124,1126,1139],{"className":1125},[329],[326,1127,1129],{"className":1128},[333],[335,1130,1131],{"xmlns":337},[339,1132,1133,1137],{},[342,1134,1135],{},[348,1136,901],{},[402,1138,901],{"encoding":404},[326,1140,1142],{"className":1141,"ariaHidden":410},[409],[326,1143,1145,1149],{"className":1144},[414],[326,1146],{"className":1147,"style":1148},[418],"height:0.6595em;",[326,1150,901],{"className":1151},[423,427],[231,1153,1154,1155,1359],{},"The probability that a carrier will be scattered within a time period dt is ",[326,1156,1158,1191],{"className":1157},[329],[326,1159,1161],{"className":1160},[333],[335,1162,1163],{"xmlns":337},[339,1164,1165,1188],{},[342,1166,1167,1174],{},[345,1168,1169,1172],{},[369,1170,1171],{},"∑",[348,1173,901],{},[884,1175,1176,1182],{},[342,1177,1178,1180],{},[348,1179,890],{},[348,1181,893],{},[345,1183,1184,1186],{},[348,1185,898],{},[348,1187,901],{},[402,1189,1190],{"encoding":404},"\\sum_i\\frac{dt}{\\tau_i}",[326,1192,1194],{"className":1193,"ariaHidden":410},[409],[326,1195,1197,1200,1247,1251],{"className":1196},[414],[326,1198],{"className":1199,"style":914},[418],[326,1201,1204,1210],{"className":1202},[1203],"mop",[326,1205,1171],{"className":1206,"style":1209},[1203,1207,1208],"op-symbol","small-op","position:relative;top:0em;",[326,1211,1213],{"className":1212},[431],[326,1214,1216,1238],{"className":1215},[435,436],[326,1217,1219,1235],{"className":1218},[440],[326,1220,1223],{"className":1221,"style":1222},[444],"height:0.162em;",[326,1224,1226,1229],{"style":1225},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[326,1227],{"className":1228,"style":453},[452],[326,1230,1232],{"className":1231},[457,458,459,460],[326,1233,901],{"className":1234},[423,427,460],[326,1236,486],{"className":1237},[485],[326,1239,1241],{"className":1240},[440],[326,1242,1245],{"className":1243,"style":1244},[444],"height:0.2997em;",[326,1246],{},[326,1248],{"className":1249,"style":1250},[499],"margin-right:0.1667em;",[326,1252,1254,1257,1356],{"className":1253},[423],[326,1255],{"className":1256},[549,921],[326,1258,1260],{"className":1259},[884],[326,1261,1263,1348],{"className":1262},[435,436],[326,1264,1266,1345],{"className":1265},[440],[326,1267,1269,1320,1328],{"className":1268,"style":934},[444],[326,1270,1271,1274],{"style":937},[326,1272],{"className":1273,"style":941},[452],[326,1275,1277],{"className":1276},[457,458,459,460],[326,1278,1280],{"className":1279},[423,460],[326,1281,1283,1286],{"className":1282},[423,460],[326,1284,898],{"className":1285,"style":954},[423,427,460],[326,1287,1289],{"className":1288},[431],[326,1290,1292,1312],{"className":1291},[435,436],[326,1293,1295,1309],{"className":1294},[440],[326,1296,1298],{"className":1297,"style":967},[444],[326,1299,1300,1303],{"style":970},[326,1301],{"className":1302,"style":974},[452],[326,1304,1306],{"className":1305},[457,978,979,460],[326,1307,901],{"className":1308},[423,427,460],[326,1310,486],{"className":1311},[485],[326,1313,1315],{"className":1314},[440],[326,1316,1318],{"className":1317,"style":992},[444],[326,1319],{},[326,1321,1322,1325],{"style":997},[326,1323],{"className":1324,"style":941},[452],[326,1326],{"className":1327,"style":1005},[1004],[326,1329,1330,1333],{"style":1008},[326,1331],{"className":1332,"style":941},[452],[326,1334,1336],{"className":1335},[457,458,459,460],[326,1337,1339,1342],{"className":1338},[423,460],[326,1340,890],{"className":1341},[423,427,460],[326,1343,893],{"className":1344},[423,427,460],[326,1346,486],{"className":1347},[485],[326,1349,1351],{"className":1350},[440],[326,1352,1354],{"className":1353,"style":1033},[444],[326,1355],{},[326,1357],{"className":1358},[560,921],"(assume that each mechanism i is independent to each other)",[231,1361,1362,1363],{},"So the total possibility of carrier scattering is ",[326,1364,1366,1412],{"className":1365},[329],[326,1367,1369],{"className":1368},[333],[335,1370,1371],{"xmlns":337},[339,1372,1373,1409],{},[342,1374,1375,1377,1379,1381,1387,1389,1395],{},[348,1376,890],{},[348,1378,893],{},[348,1380,394],{"mathvariant":393},[345,1382,1383,1385],{},[348,1384,898],{},[636,1386,638],{},[369,1388,641],{},[345,1390,1391,1393],{},[369,1392,1171],{},[348,1394,901],{},[884,1396,1397,1403],{},[342,1398,1399,1401],{},[348,1400,890],{},[348,1402,893],{},[345,1404,1405,1407],{},[348,1406,898],{},[348,1408,901],{},[402,1410,1411],{"encoding":404},"dt \u002F \\tau_{\\text{total}} = \\sum_i\\frac{dt}{\\tau_i}",[326,1413,1415,1485],{"className":1414,"ariaHidden":410},[409],[326,1416,1418,1421,1424,1427,1430,1476,1479,1482],{"className":1417},[414],[326,1419],{"className":1420,"style":679},[418],[326,1422,890],{"className":1423},[423,427],[326,1425,893],{"className":1426},[423,427],[326,1428,394],{"className":1429},[423],[326,1431,1433,1436],{"className":1432},[423],[326,1434,898],{"className":1435,"style":954},[423,427],[326,1437,1439],{"className":1438},[431],[326,1440,1442,1468],{"className":1441},[435,436],[326,1443,1445,1465],{"className":1444},[440],[326,1446,1448],{"className":1447,"style":445},[444],[326,1449,1450,1453],{"style":1097},[326,1451],{"className":1452,"style":453},[452],[326,1454,1456],{"className":1455},[457,458,459,460],[326,1457,1459],{"className":1458},[423,460],[326,1460,1462],{"className":1461},[423,716,460],[326,1463,638],{"className":1464},[423,460],[326,1466,486],{"className":1467},[485],[326,1469,1471],{"className":1470},[440],[326,1472,1474],{"className":1473,"style":729},[444],[326,1475],{},[326,1477],{"className":1478,"style":500},[499],[326,1480,641],{"className":1481},[504],[326,1483],{"className":1484,"style":500},[499],[326,1486,1488,1491,1531,1534],{"className":1487},[414],[326,1489],{"className":1490,"style":914},[418],[326,1492,1494,1497],{"className":1493},[1203],[326,1495,1171],{"className":1496,"style":1209},[1203,1207,1208],[326,1498,1500],{"className":1499},[431],[326,1501,1503,1523],{"className":1502},[435,436],[326,1504,1506,1520],{"className":1505},[440],[326,1507,1509],{"className":1508,"style":1222},[444],[326,1510,1511,1514],{"style":1225},[326,1512],{"className":1513,"style":453},[452],[326,1515,1517],{"className":1516},[457,458,459,460],[326,1518,901],{"className":1519},[423,427,460],[326,1521,486],{"className":1522},[485],[326,1524,1526],{"className":1525},[440],[326,1527,1529],{"className":1528,"style":1244},[444],[326,1530],{},[326,1532],{"className":1533,"style":1250},[499],[326,1535,1537,1540,1639],{"className":1536},[423],[326,1538],{"className":1539},[549,921],[326,1541,1543],{"className":1542},[884],[326,1544,1546,1631],{"className":1545},[435,436],[326,1547,1549,1628],{"className":1548},[440],[326,1550,1552,1603,1611],{"className":1551,"style":934},[444],[326,1553,1554,1557],{"style":937},[326,1555],{"className":1556,"style":941},[452],[326,1558,1560],{"className":1559},[457,458,459,460],[326,1561,1563],{"className":1562},[423,460],[326,1564,1566,1569],{"className":1565},[423,460],[326,1567,898],{"className":1568,"style":954},[423,427,460],[326,1570,1572],{"className":1571},[431],[326,1573,1575,1595],{"className":1574},[435,436],[326,1576,1578,1592],{"className":1577},[440],[326,1579,1581],{"className":1580,"style":967},[444],[326,1582,1583,1586],{"style":970},[326,1584],{"className":1585,"style":974},[452],[326,1587,1589],{"className":1588},[457,978,979,460],[326,1590,901],{"className":1591},[423,427,460],[326,1593,486],{"className":1594},[485],[326,1596,1598],{"className":1597},[440],[326,1599,1601],{"className":1600,"style":992},[444],[326,1602],{},[326,1604,1605,1608],{"style":997},[326,1606],{"className":1607,"style":941},[452],[326,1609],{"className":1610,"style":1005},[1004],[326,1612,1613,1616],{"style":1008},[326,1614],{"className":1615,"style":941},[452],[326,1617,1619],{"className":1618},[457,458,459,460],[326,1620,1622,1625],{"className":1621},[423,460],[326,1623,890],{"className":1624},[423,427,460],[326,1626,893],{"className":1627},[423,427,460],[326,1629,486],{"className":1630},[485],[326,1632,1634],{"className":1633},[440],[326,1635,1637],{"className":1636,"style":1033},[444],[326,1638],{},[326,1640],{"className":1641},[560,921],[231,1643,1644,1645],{},"Then we get ",[326,1646,1648,1694],{"className":1647},[329],[326,1649,1651],{"className":1650},[333],[335,1652,1653],{"xmlns":337},[339,1654,1655,1691],{},[342,1656,1657,1659,1661,1667,1669,1671,1673,1679,1681,1683,1685],{},[388,1658,628],{},[348,1660,394],{"mathvariant":393},[345,1662,1663,1665],{},[348,1664,898],{},[636,1666,638],{},[369,1668,641],{},[388,1670,628],{},[348,1672,394],{"mathvariant":393},[345,1674,1675,1677],{},[348,1676,898],{},[636,1678,652],{},[369,1680,655],{},[388,1682,628],{},[348,1684,394],{"mathvariant":393},[345,1686,1687,1689],{},[348,1688,898],{},[636,1690,666],{},[402,1692,1693],{"encoding":404},"1\u002F\\tau_{\\text{total}} = 1\u002F\\tau_{\\text{phonon}} + 1\u002F\\tau_{\\text{impurity}}",[326,1695,1697,1761,1825],{"className":1696,"ariaHidden":410},[409],[326,1698,1700,1703,1706,1752,1755,1758],{"className":1699},[414],[326,1701],{"className":1702,"style":679},[418],[326,1704,683],{"className":1705},[423],[326,1707,1709,1712],{"className":1708},[423],[326,1710,898],{"className":1711,"style":954},[423,427],[326,1713,1715],{"className":1714},[431],[326,1716,1718,1744],{"className":1717},[435,436],[326,1719,1721,1741],{"className":1720},[440],[326,1722,1724],{"className":1723,"style":445},[444],[326,1725,1726,1729],{"style":1097},[326,1727],{"className":1728,"style":453},[452],[326,1730,1732],{"className":1731},[457,458,459,460],[326,1733,1735],{"className":1734},[423,460],[326,1736,1738],{"className":1737},[423,716,460],[326,1739,638],{"className":1740},[423,460],[326,1742,486],{"className":1743},[485],[326,1745,1747],{"className":1746},[440],[326,1748,1750],{"className":1749,"style":729},[444],[326,1751],{},[326,1753],{"className":1754,"style":500},[499],[326,1756,641],{"className":1757},[504],[326,1759],{"className":1760,"style":500},[499],[326,1762,1764,1767,1770,1816,1819,1822],{"className":1763},[414],[326,1765],{"className":1766,"style":747},[418],[326,1768,683],{"className":1769},[423],[326,1771,1773,1776],{"className":1772},[423],[326,1774,898],{"className":1775,"style":954},[423,427],[326,1777,1779],{"className":1778},[431],[326,1780,1782,1808],{"className":1781},[435,436],[326,1783,1785,1805],{"className":1784},[440],[326,1786,1788],{"className":1787,"style":445},[444],[326,1789,1790,1793],{"style":1097},[326,1791],{"className":1792,"style":453},[452],[326,1794,1796],{"className":1795},[457,458,459,460],[326,1797,1799],{"className":1798},[423,460],[326,1800,1802],{"className":1801},[423,716,460],[326,1803,652],{"className":1804},[423,460],[326,1806,486],{"className":1807},[485],[326,1809,1811],{"className":1810},[440],[326,1812,1814],{"className":1813,"style":493},[444],[326,1815],{},[326,1817],{"className":1818,"style":800},[499],[326,1820,655],{"className":1821},[804],[326,1823],{"className":1824,"style":800},[499],[326,1826,1828,1831,1834],{"className":1827},[414],[326,1829],{"className":1830,"style":747},[418],[326,1832,683],{"className":1833},[423],[326,1835,1837,1840],{"className":1836},[423],[326,1838,898],{"className":1839,"style":954},[423,427],[326,1841,1843],{"className":1842},[431],[326,1844,1846,1872],{"className":1845},[435,436],[326,1847,1849,1869],{"className":1848},[440],[326,1850,1852],{"className":1851,"style":835},[444],[326,1853,1854,1857],{"style":1097},[326,1855],{"className":1856,"style":453},[452],[326,1858,1860],{"className":1859},[457,458,459,460],[326,1861,1863],{"className":1862},[423,460],[326,1864,1866],{"className":1865},[423,716,460],[326,1867,666],{"className":1868},[423,460],[326,1870,486],{"className":1871},[485],[326,1873,1875],{"className":1874},[440],[326,1876,1878],{"className":1877,"style":493},[444],[326,1879],{},[231,1881,1882,1883,2051,2052],{},"As ",[326,1884,1886,1919],{"className":1885},[329],[326,1887,1889],{"className":1888},[333],[335,1890,1891],{"xmlns":337},[339,1892,1893,1916],{},[342,1894,1895,1897,1899],{},[348,1896,350],{},[369,1898,641],{},[884,1900,1901,1908],{},[342,1902,1903,1906],{},[348,1904,1905],{},"q",[348,1907,893],{},[373,1909,1910,1913],{},[348,1911,1912],{},"m",[369,1914,1915],{},"∗",[402,1917,1918],{"encoding":404},"\\mu=\\frac{qt}{m^*}",[326,1920,1922,1941],{"className":1921,"ariaHidden":410},[409],[326,1923,1925,1929,1932,1935,1938],{"className":1924},[414],[326,1926],{"className":1927,"style":1928},[418],"height:0.625em;vertical-align:-0.1944em;",[326,1930,350],{"className":1931},[423,427],[326,1933],{"className":1934,"style":500},[499],[326,1936,641],{"className":1937},[504],[326,1939],{"className":1940,"style":500},[499],[326,1942,1944,1948],{"className":1943},[414],[326,1945],{"className":1946,"style":1947},[418],"height:1.2217em;vertical-align:-0.345em;",[326,1949,1951,1954,2048],{"className":1950},[423],[326,1952],{"className":1953},[549,921],[326,1955,1957],{"className":1956},[884],[326,1958,1960,2039],{"className":1959},[435,436],[326,1961,1963,2036],{"className":1962},[440],[326,1964,1967,2009,2017],{"className":1965,"style":1966},[444],"height:0.8767em;",[326,1968,1969,1972],{"style":937},[326,1970],{"className":1971,"style":941},[452],[326,1973,1975],{"className":1974},[457,458,459,460],[326,1976,1978],{"className":1977},[423,460],[326,1979,1981,1984],{"className":1980},[423,460],[326,1982,1912],{"className":1983},[423,427,460],[326,1985,1987],{"className":1986},[431],[326,1988,1990],{"className":1989},[435],[326,1991,1993],{"className":1992},[440],[326,1994,1997],{"className":1995,"style":1996},[444],"height:0.6183em;",[326,1998,2000,2003],{"style":1999},"top:-2.786em;margin-right:0.0714em;",[326,2001],{"className":2002,"style":974},[452],[326,2004,2006],{"className":2005},[457,978,979,460],[326,2007,1915],{"className":2008},[804,460],[326,2010,2011,2014],{"style":997},[326,2012],{"className":2013,"style":941},[452],[326,2015],{"className":2016,"style":1005},[1004],[326,2018,2020,2023],{"style":2019},"top:-3.4461em;",[326,2021],{"className":2022,"style":941},[452],[326,2024,2026],{"className":2025},[457,458,459,460],[326,2027,2029,2033],{"className":2028},[423,460],[326,2030,1905],{"className":2031,"style":2032},[423,427,460],"margin-right:0.0359em;",[326,2034,893],{"className":2035},[423,427,460],[326,2037,486],{"className":2038},[485],[326,2040,2042],{"className":2041},[440],[326,2043,2046],{"className":2044,"style":2045},[444],"height:0.345em;",[326,2047],{},[326,2049],{"className":2050},[560,921],", we could get ",[326,2053,2055,2100],{"className":2054},[329],[326,2056,2058],{"className":2057},[333],[335,2059,2060],{"xmlns":337},[339,2061,2062,2098],{},[342,2063,2064,2066,2068,2074,2076,2078,2080,2086,2088,2090,2092],{},[388,2065,628],{},[348,2067,394],{"mathvariant":393},[345,2069,2070,2072],{},[348,2071,350],{},[636,2073,638],{},[369,2075,641],{},[388,2077,628],{},[348,2079,394],{"mathvariant":393},[345,2081,2082,2084],{},[348,2083,350],{},[636,2085,652],{},[369,2087,655],{},[388,2089,628],{},[348,2091,394],{"mathvariant":393},[345,2093,2094,2096],{},[348,2095,350],{},[636,2097,666],{},[402,2099,669],{"encoding":404},[326,2101,2103,2167,2231],{"className":2102,"ariaHidden":410},[409],[326,2104,2106,2109,2112,2158,2161,2164],{"className":2105},[414],[326,2107],{"className":2108,"style":679},[418],[326,2110,683],{"className":2111},[423],[326,2113,2115,2118],{"className":2114},[423],[326,2116,350],{"className":2117},[423,427],[326,2119,2121],{"className":2120},[431],[326,2122,2124,2150],{"className":2123},[435,436],[326,2125,2127,2147],{"className":2126},[440],[326,2128,2130],{"className":2129,"style":445},[444],[326,2131,2132,2135],{"style":448},[326,2133],{"className":2134,"style":453},[452],[326,2136,2138],{"className":2137},[457,458,459,460],[326,2139,2141],{"className":2140},[423,460],[326,2142,2144],{"className":2143},[423,716,460],[326,2145,638],{"className":2146},[423,460],[326,2148,486],{"className":2149},[485],[326,2151,2153],{"className":2152},[440],[326,2154,2156],{"className":2155,"style":729},[444],[326,2157],{},[326,2159],{"className":2160,"style":500},[499],[326,2162,641],{"className":2163},[504],[326,2165],{"className":2166,"style":500},[499],[326,2168,2170,2173,2176,2222,2225,2228],{"className":2169},[414],[326,2171],{"className":2172,"style":747},[418],[326,2174,683],{"className":2175},[423],[326,2177,2179,2182],{"className":2178},[423],[326,2180,350],{"className":2181},[423,427],[326,2183,2185],{"className":2184},[431],[326,2186,2188,2214],{"className":2187},[435,436],[326,2189,2191,2211],{"className":2190},[440],[326,2192,2194],{"className":2193,"style":445},[444],[326,2195,2196,2199],{"style":448},[326,2197],{"className":2198,"style":453},[452],[326,2200,2202],{"className":2201},[457,458,459,460],[326,2203,2205],{"className":2204},[423,460],[326,2206,2208],{"className":2207},[423,716,460],[326,2209,652],{"className":2210},[423,460],[326,2212,486],{"className":2213},[485],[326,2215,2217],{"className":2216},[440],[326,2218,2220],{"className":2219,"style":493},[444],[326,2221],{},[326,2223],{"className":2224,"style":800},[499],[326,2226,655],{"className":2227},[804],[326,2229],{"className":2230,"style":800},[499],[326,2232,2234,2237,2240],{"className":2233},[414],[326,2235],{"className":2236,"style":747},[418],[326,2238,683],{"className":2239},[423],[326,2241,2243,2246],{"className":2242},[423],[326,2244,350],{"className":2245},[423,427],[326,2247,2249],{"className":2248},[431],[326,2250,2252,2278],{"className":2251},[435,436],[326,2253,2255,2275],{"className":2254},[440],[326,2256,2258],{"className":2257,"style":835},[444],[326,2259,2260,2263],{"style":448},[326,2261],{"className":2262,"style":453},[452],[326,2264,2266],{"className":2265},[457,458,459,460],[326,2267,2269],{"className":2268},[423,460],[326,2270,2272],{"className":2271},[423,716,460],[326,2273,666],{"className":2274},[423,460],[326,2276,486],{"className":2277},[485],[326,2279,2281],{"className":2280},[440],[326,2282,2284],{"className":2283,"style":493},[444],[326,2285],{},[279,2287],{},[235,2289,2291],{"id":2290},"_3what-is-the-effective-mass-of-electronin-a-semiconductorlist-two-factors-that-may-have-influence-on-its-value","3.What is the “effective mass of electron”in a semiconductor?List two factors that may have influence on its value.",[231,2293,866,2294,2297,2357,2359,2360,2363],{},[242,2295,2296],{},"effective mass (",[326,2298,2300,2318],{"className":2299},[329],[326,2301,2303],{"className":2302},[333],[335,2304,2305],{"xmlns":337},[339,2306,2307,2315],{},[342,2308,2309],{},[373,2310,2311,2313],{},[348,2312,1912],{},[369,2314,1915],{},[402,2316,2317],{"encoding":404},"m^*",[326,2319,2321],{"className":2320,"ariaHidden":410},[409],[326,2322,2324,2328],{"className":2323},[414],[326,2325],{"className":2326,"style":2327},[418],"height:0.6887em;",[326,2329,2331,2334],{"className":2330},[423],[326,2332,1912],{"className":2333},[423,427],[326,2335,2337],{"className":2336},[431],[326,2338,2340],{"className":2339},[435],[326,2341,2343],{"className":2342},[440],[326,2344,2346],{"className":2345,"style":2327},[444],[326,2347,2348,2351],{"style":536},[326,2349],{"className":2350,"style":453},[452],[326,2352,2354],{"className":2353},[457,458,459,460],[326,2355,1915],{"className":2356},[804,460],[242,2358,400],{}," is the mass parameter that makes an electron in a ",[242,2361,2362],{},"periodic crystal respond to forces","(在周期性晶格势场中对于外界力量的质量参数) (electric, magnetic) as if it were a free particle.",[231,2365,2366],{},"It is influenced by:",[2368,2369,2370,2383,2453],"ol",{},[258,2371,2372,2375,2378,2379,2382],{},[242,2373,2374],{},"The Material",[242,2376,2377],{},":"," Its value is determined by the material's unique electronic ",[242,2380,2381],{},"band structure",".",[258,2384,2385,2388,2390,2391,2394,2395,2382],{},[242,2386,2387],{},"Crystal Direction",[242,2389,2377],{}," Different crystal directions have ",[242,2392,2393],{},"different band curvature"," (能带弯曲)→ different ",[326,2396,2398,2415],{"className":2397},[329],[326,2399,2401],{"className":2400},[333],[335,2402,2403],{"xmlns":337},[339,2404,2405,2413],{},[342,2406,2407],{},[373,2408,2409,2411],{},[348,2410,1912],{},[369,2412,1915],{},[402,2414,2317],{"encoding":404},[326,2416,2418],{"className":2417,"ariaHidden":410},[409],[326,2419,2421,2424],{"className":2420},[414],[326,2422],{"className":2423,"style":2327},[418],[326,2425,2427,2430],{"className":2426},[423],[326,2428,1912],{"className":2429},[423,427],[326,2431,2433],{"className":2432},[431],[326,2434,2436],{"className":2435},[435],[326,2437,2439],{"className":2438},[440],[326,2440,2442],{"className":2441,"style":2327},[444],[326,2443,2444,2447],{"style":536},[326,2445],{"className":2446,"style":453},[452],[326,2448,2450],{"className":2449},[457,458,459,460],[326,2451,1915],{"className":2452},[804,460],[258,2454,2455,2458,2459,2462,2463,2644,2645,2382],{},[242,2456,2457],{},"Strain",": Changes lattice spacing\u002Fsymmetry(改变晶格间距\u002F对称性), ",[242,2460,2461],{},"reshaping band curvature"," (",[326,2464,2466,2502],{"className":2465},[329],[326,2467,2469],{"className":2468},[333],[335,2470,2471],{"xmlns":337},[339,2472,2473,2499],{},[342,2474,2475],{},[884,2476,2477,2488],{},[342,2478,2479,2485],{},[373,2480,2481,2483],{},[348,2482,890],{},[388,2484,397],{},[348,2486,2487],{},"E",[342,2489,2490,2492],{},[348,2491,890],{},[373,2493,2494,2497],{},[348,2495,2496],{},"k",[388,2498,397],{},[402,2500,2501],{"encoding":404},"\\frac{d^2E}{dk^2}",[326,2503,2505],{"className":2504,"ariaHidden":410},[409],[326,2506,2508,2512],{"className":2507},[414],[326,2509],{"className":2510,"style":2511},[418],"height:1.3629em;vertical-align:-0.345em;",[326,2513,2515,2518,2641],{"className":2514},[423],[326,2516],{"className":2517},[549,921],[326,2519,2521],{"className":2520},[884],[326,2522,2524,2633],{"className":2523},[435,436],[326,2525,2527,2630],{"className":2526},[440],[326,2528,2531,2576,2584],{"className":2529,"style":2530},[444],"height:1.0179em;",[326,2532,2533,2536],{"style":937},[326,2534],{"className":2535,"style":941},[452],[326,2537,2539],{"className":2538},[457,458,459,460],[326,2540,2542,2545],{"className":2541},[423,460],[326,2543,890],{"className":2544},[423,427,460],[326,2546,2548,2552],{"className":2547},[423,460],[326,2549,2496],{"className":2550,"style":2551},[423,427,460],"margin-right:0.0315em;",[326,2553,2555],{"className":2554},[431],[326,2556,2558],{"className":2557},[435],[326,2559,2561],{"className":2560},[440],[326,2562,2565],{"className":2563,"style":2564},[444],"height:0.7463em;",[326,2566,2567,2570],{"style":1999},[326,2568],{"className":2569,"style":974},[452],[326,2571,2573],{"className":2572},[457,978,979,460],[326,2574,397],{"className":2575},[423,460],[326,2577,2578,2581],{"style":997},[326,2579],{"className":2580,"style":941},[452],[326,2582],{"className":2583,"style":1005},[1004],[326,2585,2586,2589],{"style":1008},[326,2587],{"className":2588,"style":941},[452],[326,2590,2592],{"className":2591},[457,458,459,460],[326,2593,2595,2626],{"className":2594},[423,460],[326,2596,2598,2601],{"className":2597},[423,460],[326,2599,890],{"className":2600},[423,427,460],[326,2602,2604],{"className":2603},[431],[326,2605,2607],{"className":2606},[435],[326,2608,2610],{"className":2609},[440],[326,2611,2614],{"className":2612,"style":2613},[444],"height:0.8913em;",[326,2615,2617,2620],{"style":2616},"top:-2.931em;margin-right:0.0714em;",[326,2618],{"className":2619,"style":974},[452],[326,2621,2623],{"className":2622},[457,978,979,460],[326,2624,397],{"className":2625},[423,460],[326,2627,2487],{"className":2628,"style":2629},[423,427,460],"margin-right:0.0576em;",[326,2631,486],{"className":2632},[485],[326,2634,2636],{"className":2635},[440],[326,2637,2639],{"className":2638,"style":2045},[444],[326,2640],{},[326,2642],{"className":2643},[560,921],") → different ",[326,2646,2648,2665],{"className":2647},[329],[326,2649,2651],{"className":2650},[333],[335,2652,2653],{"xmlns":337},[339,2654,2655,2663],{},[342,2656,2657],{},[373,2658,2659,2661],{},[348,2660,1912],{},[369,2662,1915],{},[402,2664,2317],{"encoding":404},[326,2666,2668],{"className":2667,"ariaHidden":410},[409],[326,2669,2671,2674],{"className":2670},[414],[326,2672],{"className":2673,"style":2327},[418],[326,2675,2677,2680],{"className":2676},[423],[326,2678,1912],{"className":2679},[423,427],[326,2681,2683],{"className":2682},[431],[326,2684,2686],{"className":2685},[435],[326,2687,2689],{"className":2688},[440],[326,2690,2692],{"className":2691,"style":2327},[444],[326,2693,2694,2697],{"style":536},[326,2695],{"className":2696,"style":453},[452],[326,2698,2700],{"className":2699},[457,458,459,460],[326,2701,1915],{"className":2702},[804,460],[279,2704],{},[235,2706,2708],{"id":2707},"_4list-three-ways-to-increase-carrier-mobility-in-a-semiconductor-in-general-how-does-carrier-mobility-impact-an-electronic-devices-performance","4.List three ways to increase carrier mobility in a semiconductor. In general, how does carrier mobility impact an electronic device's performance?",[231,2710,2711],{},[242,2712,2713],{},"Three Ways to Increase Mobility:",[2368,2715,2716,2724,2730],{},[258,2717,2718,2721,2723],{},[242,2719,2720],{},"Decrease Dopant Concentration",[242,2722,2377],{}," Reduces impurity scattering.",[258,2725,2726,2729],{},[242,2727,2728],{},"Lower the lattice temperature"," to suppress(抑制) phonon scattering (phonon density↓, mobility↑).",[258,2731,2732,2735,2737,2738,2741,2742],{},[242,2733,2734],{},"Use Strain Engineering",[242,2736,2377],{}," Straining the crystal lattice (e.g. strained silicon) can ",[242,2739,2740],{},"alter the band structure"," to reduce effective mass, thereby improving mobility\n",[242,2743,2744],{},"Impact on Device Performance:",[231,2746,2747,2748,2462,2751,2805,2806,2809,2810,2813,2814,2889],{},"Higher carrier mobility directly results in ",[242,2749,2750],{},"higher current drive",[326,2752,2754,2773],{"className":2753},[329],[326,2755,2757],{"className":2756},[333],[335,2758,2759],{"xmlns":337},[339,2760,2761,2770],{},[342,2762,2763,2766,2768],{},[348,2764,2765],{},"I",[369,2767,371],{},[348,2769,350],{},[402,2771,2772],{"encoding":404},"I \\propto \\mu",[326,2774,2776,2796],{"className":2775,"ariaHidden":410},[409],[326,2777,2779,2783,2787,2790,2793],{"className":2778},[414],[326,2780],{"className":2781,"style":2782},[418],"height:0.6833em;",[326,2784,2765],{"className":2785,"style":2786},[423,427],"margin-right:0.0785em;",[326,2788],{"className":2789,"style":500},[499],[326,2791,371],{"className":2792},[504],[326,2794],{"className":2795,"style":500},[499],[326,2797,2799,2802],{"className":2798},[414],[326,2800],{"className":2801,"style":1928},[418],[326,2803,350],{"className":2804},[423,427],") and ",[242,2807,2808],{},"lower resistance",". This allows transistors to ",[242,2811,2812],{},"switch faster",", leading to higher operating frequencies (",[326,2815,2817,2836],{"className":2816},[329],[326,2818,2820],{"className":2819},[333],[335,2821,2822],{"xmlns":337},[339,2823,2824,2833],{},[342,2825,2826],{},[345,2827,2828,2831],{},[348,2829,2830],{},"f",[348,2832,377],{},[402,2834,2835],{"encoding":404},"f_T",[326,2837,2839],{"className":2838,"ariaHidden":410},[409],[326,2840,2842,2846],{"className":2841},[414],[326,2843],{"className":2844,"style":2845},[418],"height:0.8889em;vertical-align:-0.1944em;",[326,2847,2849,2853],{"className":2848},[423],[326,2850,2830],{"className":2851,"style":2852},[423,427],"margin-right:0.1076em;",[326,2854,2856],{"className":2855},[431],[326,2857,2859,2881],{"className":2858},[435,436],[326,2860,2862,2878],{"className":2861},[440],[326,2863,2866],{"className":2864,"style":2865},[444],"height:0.3283em;",[326,2867,2869,2872],{"style":2868},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[326,2870],{"className":2871,"style":453},[452],[326,2873,2875],{"className":2874},[457,458,459,460],[326,2876,377],{"className":2877,"style":521},[423,427,460],[326,2879,486],{"className":2880},[485],[326,2882,2884],{"className":2883},[440],[326,2885,2887],{"className":2886,"style":729},[444],[326,2888],{},") and improved overall device speed.",[279,2891],{},[235,2893,2895],{"id":2894},"_5what-is-the-concept-ofvelocity-saturationin-a-semiconductorhow-does-it-impact-an-electronic-devices-behavior","5.What is the concept of“velocity saturation”in a semiconductor?How does it impact an electronic device's behavior?",[231,2897,2898,2899,2902,2903,2906,2907,2910,2911,2914,2915],{},"When the ",[242,2900,2901],{},"kinetic energy","(动能) of a carrier exceeds a critical value(达到某个临界值), it ",[242,2904,2905],{},"generates an optical phonon","(光学声子) and ",[242,2908,2909],{},"loses the kinetic energy",". Therefore, the kinetic energy is capped at large E, and the ",[242,2912,2913],{},"velocity does not rise"," above a saturation velocity, ",[326,2916,2918,2945],{"className":2917},[329],[326,2919,2921],{"className":2920},[333],[335,2922,2923],{"xmlns":337},[339,2924,2925,2942],{},[342,2926,2927],{},[345,2928,2929,2932],{},[348,2930,2931],{},"v",[342,2933,2934,2937,2940],{},[348,2935,2936],{},"s",[348,2938,2939],{},"a",[348,2941,893],{},[402,2943,2944],{"encoding":404},"v_{sat}",[326,2946,2948],{"className":2947,"ariaHidden":410},[409],[326,2949,2951,2954],{"className":2950},[414],[326,2952],{"className":2953,"style":1075},[418],[326,2955,2957,2960],{"className":2956},[423],[326,2958,2931],{"className":2959,"style":2032},[423,427],[326,2961,2963],{"className":2962},[431],[326,2964,2966,2997],{"className":2965},[435,436],[326,2967,2969,2994],{"className":2968},[440],[326,2970,2973],{"className":2971,"style":2972},[444],"height:0.2806em;",[326,2974,2976,2979],{"style":2975},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[326,2977],{"className":2978,"style":453},[452],[326,2980,2982],{"className":2981},[457,458,459,460],[326,2983,2985,2988,2991],{"className":2984},[423,460],[326,2986,2936],{"className":2987},[423,427,460],[326,2989,2939],{"className":2990},[423,427,460],[326,2992,893],{"className":2993},[423,427,460],[326,2995,486],{"className":2996},[485],[326,2998,3000],{"className":2999},[440],[326,3001,3003],{"className":3002,"style":729},[444],[326,3004],{},[231,3006,3007,3008,3011,3012,3015,3016,2382],{},"In short-channel transistors, this effect is what causes the ",[242,3009,3010],{},"drain current to saturate",", limiting the ",[242,3013,3014],{},"maximum current"," and ",[242,3017,3018],{},"switching speed",[279,3020],{},[235,3022,3024],{"id":3023},"_6what-are-the-basic-driving-forces-for-two-types-of-carrier-movement-drift-and-diffusionrespectively","6.What are the basic driving forces for two types of carrier movement, drift and diffusion,respectively?",[255,3026,3027,3036],{},[258,3028,3029,3032,3033,2382],{},[242,3030,3031],{},"Drift","\ncharged particle motion under the influence of an ",[242,3034,3035],{},"electric field",[258,3037,3038,3041,3042,3045,3046,2382],{},[242,3039,3040],{},"Diffusion","\nparticle motion due to ",[242,3043,3044],{},"concentration gradient"," or ",[242,3047,3048],{},"temperature gradient",[279,3050],{},[235,3052,3054],{"id":3053},"_7regarding-carrier-movement-in-semiconductorwhat-is-the-difference-between-thermal-velocity-and-drift-velocity","7.Regarding carrier movement in semiconductor,what is the difference between thermal velocity and drift velocity?",[255,3056,3057,3077],{},[258,3058,3059,245,3062,3065,3066,3069,3070,245,3073,3076],{},[242,3060,3061],{},"Thermal velocity",[242,3063,3064],{},"random"," motion(随机) of carriers in all directions ",[242,3067,3068],{},"due to thermal energy",", while ",[242,3071,3072],{},"drift velocity",[242,3074,3075],{},"small average velocity"," (很小的平均漂移速度) superimposed(叠加) on this random motion when an electric field is applied.",[258,3078,3079,3081,3082,3392,3394,3395,3397,3398,3692],{},[242,3080,3061],{}," depends on temperature and effective mass ",[326,3083,3085,3132],{"className":3084},[329],[326,3086,3088],{"className":3087},[333],[335,3089,3090],{"xmlns":337},[339,3091,3092,3129],{},[342,3093,3094,3105,3107],{},[345,3095,3096,3099],{},[348,3097,3098],{},"V",[342,3100,3101,3103],{},[348,3102,893],{},[348,3104,357],{},[369,3106,641],{},[3108,3109,3110],"msqrt",{},[884,3111,3112,3120],{},[342,3113,3114,3116,3118],{},[388,3115,390],{},[348,3117,2496],{},[348,3119,377],{},[3121,3122,3123,3125,3127],"msubsup",{},[348,3124,1912],{},[348,3126,363],{},[369,3128,1915],{},[402,3130,3131],{"encoding":404},"V_{th} = \\sqrt{\\frac{3kT}{m^*_n}}",[326,3133,3135,3198],{"className":3134,"ariaHidden":410},[409],[326,3136,3138,3142,3189,3192,3195],{"className":3137},[414],[326,3139],{"className":3140,"style":3141},[418],"height:0.8333em;vertical-align:-0.15em;",[326,3143,3145,3148],{"className":3144},[423],[326,3146,3098],{"className":3147,"style":800},[423,427],[326,3149,3151],{"className":3150},[431],[326,3152,3154,3181],{"className":3153},[435,436],[326,3155,3157,3178],{"className":3156},[440],[326,3158,3160],{"className":3159,"style":445},[444],[326,3161,3163,3166],{"style":3162},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[326,3164],{"className":3165,"style":453},[452],[326,3167,3169],{"className":3168},[457,458,459,460],[326,3170,3172,3175],{"className":3171},[423,460],[326,3173,893],{"className":3174},[423,427,460],[326,3176,357],{"className":3177},[423,427,460],[326,3179,486],{"className":3180},[485],[326,3182,3184],{"className":3183},[440],[326,3185,3187],{"className":3186,"style":729},[444],[326,3188],{},[326,3190],{"className":3191,"style":500},[499],[326,3193,641],{"className":3194},[504],[326,3196],{"className":3197,"style":500},[499],[326,3199,3201,3205],{"className":3200},[414],[326,3202],{"className":3203,"style":3204},[418],"height:1.84em;vertical-align:-0.6875em;",[326,3206,3209],{"className":3207},[423,3208],"sqrt",[326,3210,3212,3383],{"className":3211},[435,436],[326,3213,3215,3380],{"className":3214},[440],[326,3216,3219,3357],{"className":3217,"style":3218},[444],"height:1.1525em;",[326,3220,3224,3228],{"className":3221,"style":3223},[3222],"svg-align","top:-3.8em;",[326,3225],{"className":3226,"style":3227},[452],"height:3.8em;",[326,3229,3232],{"className":3230,"style":3231},[423],"padding-left:1em;",[326,3233,3235,3238,3354],{"className":3234},[423],[326,3236],{"className":3237},[549,921],[326,3239,3241],{"className":3240},[884],[326,3242,3244,3345],{"className":3243},[435,436],[326,3245,3247,3342],{"className":3246},[440],[326,3248,3250,3314,3322],{"className":3249,"style":934},[444],[326,3251,3252,3255],{"style":937},[326,3253],{"className":3254,"style":941},[452],[326,3256,3258],{"className":3257},[457,458,459,460],[326,3259,3261],{"className":3260},[423,460],[326,3262,3264,3267],{"className":3263},[423,460],[326,3265,1912],{"className":3266},[423,427,460],[326,3268,3270],{"className":3269},[431],[326,3271,3273,3305],{"className":3272},[435,436],[326,3274,3276,3302],{"className":3275},[440],[326,3277,3279,3291],{"className":3278,"style":1996},[444],[326,3280,3282,3285],{"style":3281},"top:-2.214em;margin-left:0em;margin-right:0.0714em;",[326,3283],{"className":3284,"style":974},[452],[326,3286,3288],{"className":3287},[457,978,979,460],[326,3289,363],{"className":3290},[423,427,460],[326,3292,3293,3296],{"style":1999},[326,3294],{"className":3295,"style":974},[452],[326,3297,3299],{"className":3298},[457,978,979,460],[326,3300,1915],{"className":3301},[804,460],[326,3303,486],{"className":3304},[485],[326,3306,3308],{"className":3307},[440],[326,3309,3312],{"className":3310,"style":3311},[444],"height:0.286em;",[326,3313],{},[326,3315,3316,3319],{"style":997},[326,3317],{"className":3318,"style":941},[452],[326,3320],{"className":3321,"style":1005},[1004],[326,3323,3324,3327],{"style":1008},[326,3325],{"className":3326,"style":941},[452],[326,3328,3330],{"className":3329},[457,458,459,460],[326,3331,3333,3336,3339],{"className":3332},[423,460],[326,3334,390],{"className":3335},[423,460],[326,3337,2496],{"className":3338,"style":2551},[423,427,460],[326,3340,377],{"className":3341,"style":521},[423,427,460],[326,3343,486],{"className":3344},[485],[326,3346,3348],{"className":3347},[440],[326,3349,3352],{"className":3350,"style":3351},[444],"height:0.5452em;",[326,3353],{},[326,3355],{"className":3356},[560,921],[326,3358,3360,3363],{"style":3359},"top:-3.1125em;",[326,3361],{"className":3362,"style":3227},[452],[326,3364,3368],{"className":3365,"style":3367},[3366],"hide-tail","min-width:1.02em;height:1.88em;",[3369,3370,3376],"svg",{"xmlns":3371,"width":3372,"height":3373,"viewBox":3374,"preserveAspectRatio":3375},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.88em","0 0 400000 1944","xMinYMin slice",[3377,3378],"path",{"d":3379},"M983 90\nl0 -0\nc4,-6.7,10,-10,18,-10 H400000v40\nH1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7\ns-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744\nc-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30\nc26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722\nc56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5\nc53.7,-170.3,84.5,-266.8,92.5,-289.5z\nM1001 80h400000v40h-400000z",[326,3381,486],{"className":3382},[485],[326,3384,3386],{"className":3385},[440],[326,3387,3390],{"className":3388,"style":3389},[444],"height:0.6875em;",[326,3391],{},[242,3393,2382],{}," But ",[242,3396,3072],{}," depends on the electric field's value , meaning free time and effective mass ",[326,3399,3401,3454],{"className":3400},[329],[326,3402,3404],{"className":3403},[333],[335,3405,3406],{"xmlns":337},[339,3407,3408,3451],{},[342,3409,3410,3413,3419,3421,3423],{},[348,3411,3412],{"mathvariant":393},"∣",[345,3414,3415,3417],{},[348,3416,3098],{},[348,3418,890],{},[348,3420,3412],{"mathvariant":393},[369,3422,641],{},[884,3424,3425,3443],{},[342,3426,3427,3429,3431],{},[348,3428,1905],{},[348,3430,2487],{},[345,3432,3433,3435],{},[348,3434,898],{},[342,3436,3437,3439,3441],{},[348,3438,1912],{},[348,3440,901],{},[348,3442,363],{},[3121,3444,3445,3447,3449],{},[348,3446,1912],{},[348,3448,363],{},[369,3450,1915],{},[402,3452,3453],{"encoding":404},"|V_{d}| = \\frac{qE\\tau_{min}}{m^*_n}",[326,3455,3457,3521],{"className":3456,"ariaHidden":410},[409],[326,3458,3460,3463,3466,3509,3512,3515,3518],{"className":3459},[414],[326,3461],{"className":3462,"style":679},[418],[326,3464,3412],{"className":3465},[423],[326,3467,3469,3472],{"className":3468},[423],[326,3470,3098],{"className":3471,"style":800},[423,427],[326,3473,3475],{"className":3474},[431],[326,3476,3478,3501],{"className":3477},[435,436],[326,3479,3481,3498],{"className":3480},[440],[326,3482,3484],{"className":3483,"style":445},[444],[326,3485,3486,3489],{"style":3162},[326,3487],{"className":3488,"style":453},[452],[326,3490,3492],{"className":3491},[457,458,459,460],[326,3493,3495],{"className":3494},[423,460],[326,3496,890],{"className":3497},[423,427,460],[326,3499,486],{"className":3500},[485],[326,3502,3504],{"className":3503},[440],[326,3505,3507],{"className":3506,"style":729},[444],[326,3508],{},[326,3510,3412],{"className":3511},[423],[326,3513],{"className":3514,"style":500},[499],[326,3516,641],{"className":3517},[504],[326,3519],{"className":3520,"style":500},[499],[326,3522,3524,3528],{"className":3523},[414],[326,3525],{"className":3526,"style":3527},[418],"height:1.4696em;vertical-align:-0.5452em;",[326,3529,3531,3534,3689],{"className":3530},[423],[326,3532],{"className":3533},[549,921],[326,3535,3537],{"className":3536},[884],[326,3538,3540,3681],{"className":3539},[435,436],[326,3541,3543,3678],{"className":3542},[440],[326,3544,3547,3609,3617],{"className":3545,"style":3546},[444],"height:0.9244em;",[326,3548,3549,3552],{"style":937},[326,3550],{"className":3551,"style":941},[452],[326,3553,3555],{"className":3554},[457,458,459,460],[326,3556,3558],{"className":3557},[423,460],[326,3559,3561,3564],{"className":3560},[423,460],[326,3562,1912],{"className":3563},[423,427,460],[326,3565,3567],{"className":3566},[431],[326,3568,3570,3601],{"className":3569},[435,436],[326,3571,3573,3598],{"className":3572},[440],[326,3574,3576,3587],{"className":3575,"style":1996},[444],[326,3577,3578,3581],{"style":3281},[326,3579],{"className":3580,"style":974},[452],[326,3582,3584],{"className":3583},[457,978,979,460],[326,3585,363],{"className":3586},[423,427,460],[326,3588,3589,3592],{"style":1999},[326,3590],{"className":3591,"style":974},[452],[326,3593,3595],{"className":3594},[457,978,979,460],[326,3596,1915],{"className":3597},[804,460],[326,3599,486],{"className":3600},[485],[326,3602,3604],{"className":3603},[440],[326,3605,3607],{"className":3606,"style":3311},[444],[326,3608],{},[326,3610,3611,3614],{"style":997},[326,3612],{"className":3613,"style":941},[452],[326,3615],{"className":3616,"style":1005},[1004],[326,3618,3619,3622],{"style":2019},[326,3620],{"className":3621,"style":941},[452],[326,3623,3625],{"className":3624},[457,458,459,460],[326,3626,3628,3631,3634],{"className":3627},[423,460],[326,3629,1905],{"className":3630,"style":2032},[423,427,460],[326,3632,2487],{"className":3633,"style":2629},[423,427,460],[326,3635,3637,3640],{"className":3636},[423,460],[326,3638,898],{"className":3639,"style":954},[423,427,460],[326,3641,3643],{"className":3642},[431],[326,3644,3646,3670],{"className":3645},[435,436],[326,3647,3649,3667],{"className":3648},[440],[326,3650,3652],{"className":3651,"style":967},[444],[326,3653,3654,3657],{"style":970},[326,3655],{"className":3656,"style":974},[452],[326,3658,3660],{"className":3659},[457,978,979,460],[326,3661,3663],{"className":3662},[423,460],[326,3664,3666],{"className":3665},[423,427,460],"min",[326,3668,486],{"className":3669},[485],[326,3671,3673],{"className":3672},[440],[326,3674,3676],{"className":3675,"style":992},[444],[326,3677],{},[326,3679,486],{"className":3680},[485],[326,3682,3684],{"className":3683},[440],[326,3685,3687],{"className":3686,"style":3351},[444],[326,3688],{},[326,3690],{"className":3691},[560,921],[242,3693,2382],{},[279,3695],{},[235,3697,3699],{"id":3698},"_8what-is-the-carrier-generation-process-in-semiconductorslist-three-possible-mechanisms-for-this-process","8.What is the carrier generation process in semiconductors?List three possible mechanisms for this process.",[231,3701,3702,3705,3706,3709],{},[242,3703,3704],{},"Carrier generation"," is the process that ",[242,3707,3708],{},"creates electron–hole pairs"," in a semiconductor by exciting electrons from the valence band to the conduction band (possibly via defect levels可能经过缺陷能级).",[231,3711,3712],{},"Three possible mechanisms",[255,3714,3715],{},[258,3716,3717,3720,3723,3724,3814,3815,3885,3886,3957,3958],{},[242,3718,3719],{},"Band-to-Band Generation（带-带产生）",[242,3721,3722],{},"Thermal energy or photons with energy"," ",[326,3725,3727,3749],{"className":3726},[329],[326,3728,3730],{"className":3729},[333],[335,3731,3732],{"xmlns":337},[339,3733,3734,3746],{},[342,3735,3736,3739],{},[369,3737,3738],{},"≥",[345,3740,3741,3743],{},[348,3742,2487],{},[348,3744,3745],{},"g",[402,3747,3748],{"encoding":404},"\\ge E_g",[326,3750,3752,3765],{"className":3751,"ariaHidden":410},[409],[326,3753,3755,3759,3762],{"className":3754},[414],[326,3756],{"className":3757,"style":3758},[418],"height:0.7719em;vertical-align:-0.136em;",[326,3760,3738],{"className":3761},[504],[326,3763],{"className":3764,"style":500},[499],[326,3766,3768,3772],{"className":3767},[414],[326,3769],{"className":3770,"style":3771},[418],"height:0.9694em;vertical-align:-0.2861em;",[326,3773,3775,3778],{"className":3774},[423],[326,3776,2487],{"className":3777,"style":2629},[423,427],[326,3779,3781],{"className":3780},[431],[326,3782,3784,3806],{"className":3783},[435,436],[326,3785,3787,3803],{"className":3786},[440],[326,3788,3791],{"className":3789,"style":3790},[444],"height:0.1514em;",[326,3792,3794,3797],{"style":3793},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[326,3795],{"className":3796,"style":453},[452],[326,3798,3800],{"className":3799},[457,458,459,460],[326,3801,3745],{"className":3802,"style":2032},[423,427,460],[326,3804,486],{"className":3805},[485],[326,3807,3809],{"className":3808},[440],[326,3810,3812],{"className":3811,"style":493},[444],[326,3813],{}," directly excite an electron from the valence band ",[326,3816,3818,3836],{"className":3817},[329],[326,3819,3821],{"className":3820},[333],[335,3822,3823],{"xmlns":337},[339,3824,3825,3833],{},[342,3826,3827],{},[345,3828,3829,3831],{},[348,3830,2487],{},[348,3832,2931],{},[402,3834,3835],{"encoding":404},"E_v",[326,3837,3839],{"className":3838,"ariaHidden":410},[409],[326,3840,3842,3845],{"className":3841},[414],[326,3843],{"className":3844,"style":3141},[418],[326,3846,3848,3851],{"className":3847},[423],[326,3849,2487],{"className":3850,"style":2629},[423,427],[326,3852,3854],{"className":3853},[431],[326,3855,3857,3877],{"className":3856},[435,436],[326,3858,3860,3874],{"className":3859},[440],[326,3861,3863],{"className":3862,"style":3790},[444],[326,3864,3865,3868],{"style":3793},[326,3866],{"className":3867,"style":453},[452],[326,3869,3871],{"className":3870},[457,458,459,460],[326,3872,2931],{"className":3873,"style":2032},[423,427,460],[326,3875,486],{"className":3876},[485],[326,3878,3880],{"className":3879},[440],[326,3881,3883],{"className":3882,"style":729},[444],[326,3884],{}," to the conduction band ",[326,3887,3889,3908],{"className":3888},[329],[326,3890,3892],{"className":3891},[333],[335,3893,3894],{"xmlns":337},[339,3895,3896,3905],{},[342,3897,3898],{},[345,3899,3900,3902],{},[348,3901,2487],{},[348,3903,3904],{},"c",[402,3906,3907],{"encoding":404},"E_c",[326,3909,3911],{"className":3910,"ariaHidden":410},[409],[326,3912,3914,3917],{"className":3913},[414],[326,3915],{"className":3916,"style":3141},[418],[326,3918,3920,3923],{"className":3919},[423],[326,3921,2487],{"className":3922,"style":2629},[423,427],[326,3924,3926],{"className":3925},[431],[326,3927,3929,3949],{"className":3928},[435,436],[326,3930,3932,3946],{"className":3931},[440],[326,3933,3935],{"className":3934,"style":3790},[444],[326,3936,3937,3940],{"style":3793},[326,3938],{"className":3939,"style":453},[452],[326,3941,3943],{"className":3942},[457,458,459,460],[326,3944,3904],{"className":3945},[423,427,460],[326,3947,486],{"className":3948},[485],[326,3950,3952],{"className":3951},[440],[326,3953,3955],{"className":3954,"style":729},[444],[326,3956],{},", creating an electron–hole pair.\n",[255,3959,3960,3966],{},[258,3961,3962,3965],{},[242,3963,3964],{},"Thermal",": energy comes from lattice vibrations (heat\u002Fphonons).",[258,3967,3968,3971,3972,3975,3976,3978],{},[242,3969,3970],{},"Optical (photogeneration)",": energy comes from absorbed photons(注意这是",[242,3973,3974],{},"photon","不是",[242,3977,652],{},").\n然后可以画个图：",[231,3980,3981],{},[3982,3983],"img",{"alt":3984,"src":3985},"PixPin_2025-11-13_10-50-32.png","\u002Fimg\u002FMicroelectronicDevices\u002FMidtermExam-02.png",[255,3987,3988,4284],{},[258,3989,3990,3993,3996,3997,3723,4000,3723,4070,4073,4074,4077,4078,4081,4082,4279,4280],{},[242,3991,3992],{},"R-G Center Generation（通过 R-G 中心产生）",[242,3994,3995],{},"Recombination–generation (R-G) centers"," are defect(缺陷)\u002Fimpurity(杂质)\u002Fsurface states(表面态) that ",[242,3998,3999],{},"introduce an energy level",[326,4001,4003,4021],{"className":4002},[329],[326,4004,4006],{"className":4005},[333],[335,4007,4008],{"xmlns":337},[339,4009,4010,4018],{},[342,4011,4012],{},[345,4013,4014,4016],{},[348,4015,2487],{},[348,4017,377],{},[402,4019,4020],{"encoding":404},"E_T",[326,4022,4024],{"className":4023,"ariaHidden":410},[409],[326,4025,4027,4030],{"className":4026},[414],[326,4028],{"className":4029,"style":3141},[418],[326,4031,4033,4036],{"className":4032},[423],[326,4034,2487],{"className":4035,"style":2629},[423,427],[326,4037,4039],{"className":4038},[431],[326,4040,4042,4062],{"className":4041},[435,436],[326,4043,4045,4059],{"className":4044},[440],[326,4046,4048],{"className":4047,"style":2865},[444],[326,4049,4050,4053],{"style":3793},[326,4051],{"className":4052,"style":453},[452],[326,4054,4056],{"className":4055},[457,458,459,460],[326,4057,377],{"className":4058,"style":521},[423,427,460],[326,4060,486],{"className":4061},[485],[326,4063,4065],{"className":4064},[440],[326,4066,4068],{"className":4067,"style":729},[444],[326,4069],{},[242,4071,4072],{},"inside the bandgap",". With ",[242,4075,4076],{},"thermal energy",", carriers are generated in ",[242,4079,4080],{},"two steps"," via this level (e.g. ",[326,4083,4085,4120],{"className":4084},[329],[326,4086,4088],{"className":4087},[333],[335,4089,4090],{"xmlns":337},[339,4091,4092,4117],{},[342,4093,4094,4100,4103,4109,4111],{},[345,4095,4096,4098],{},[348,4097,2487],{},[348,4099,2931],{},[369,4101,4102],{},"→",[345,4104,4105,4107],{},[348,4106,2487],{},[348,4108,377],{},[369,4110,4102],{},[345,4112,4113,4115],{},[348,4114,2487],{},[348,4116,3904],{},[402,4118,4119],{"encoding":404},"E_v \\rightarrow E_T \\rightarrow E_c",[326,4121,4123,4178,4233],{"className":4122,"ariaHidden":410},[409],[326,4124,4126,4129,4169,4172,4175],{"className":4125},[414],[326,4127],{"className":4128,"style":3141},[418],[326,4130,4132,4135],{"className":4131},[423],[326,4133,2487],{"className":4134,"style":2629},[423,427],[326,4136,4138],{"className":4137},[431],[326,4139,4141,4161],{"className":4140},[435,436],[326,4142,4144,4158],{"className":4143},[440],[326,4145,4147],{"className":4146,"style":3790},[444],[326,4148,4149,4152],{"style":3793},[326,4150],{"className":4151,"style":453},[452],[326,4153,4155],{"className":4154},[457,458,459,460],[326,4156,2931],{"className":4157,"style":2032},[423,427,460],[326,4159,486],{"className":4160},[485],[326,4162,4164],{"className":4163},[440],[326,4165,4167],{"className":4166,"style":729},[444],[326,4168],{},[326,4170],{"className":4171,"style":500},[499],[326,4173,4102],{"className":4174},[504],[326,4176],{"className":4177,"style":500},[499],[326,4179,4181,4184,4224,4227,4230],{"className":4180},[414],[326,4182],{"className":4183,"style":3141},[418],[326,4185,4187,4190],{"className":4186},[423],[326,4188,2487],{"className":4189,"style":2629},[423,427],[326,4191,4193],{"className":4192},[431],[326,4194,4196,4216],{"className":4195},[435,436],[326,4197,4199,4213],{"className":4198},[440],[326,4200,4202],{"className":4201,"style":2865},[444],[326,4203,4204,4207],{"style":3793},[326,4205],{"className":4206,"style":453},[452],[326,4208,4210],{"className":4209},[457,458,459,460],[326,4211,377],{"className":4212,"style":521},[423,427,460],[326,4214,486],{"className":4215},[485],[326,4217,4219],{"className":4218},[440],[326,4220,4222],{"className":4221,"style":729},[444],[326,4223],{},[326,4225],{"className":4226,"style":500},[499],[326,4228,4102],{"className":4229},[504],[326,4231],{"className":4232,"style":500},[499],[326,4234,4236,4239],{"className":4235},[414],[326,4237],{"className":4238,"style":3141},[418],[326,4240,4242,4245],{"className":4241},[423],[326,4243,2487],{"className":4244,"style":2629},[423,427],[326,4246,4248],{"className":4247},[431],[326,4249,4251,4271],{"className":4250},[435,436],[326,4252,4254,4268],{"className":4253},[440],[326,4255,4257],{"className":4256,"style":3790},[444],[326,4258,4259,4262],{"style":3793},[326,4260],{"className":4261,"style":453},[452],[326,4263,4265],{"className":4264},[457,458,459,460],[326,4266,3904],{"className":4267},[423,427,460],[326,4269,486],{"className":4270},[485],[326,4272,4274],{"className":4273},[440],[326,4275,4277],{"className":4276,"style":729},[444],[326,4278],{},"), producing an electron–hole pair.\nR-G centers are a major source of thermal generation and of reverse saturation current in devices.\n",[3982,4281],{"alt":4282,"src":4283},"PixPin_2025-11-13_10-54-26.png","\u002Fimg\u002FMicroelectronicDevices\u002FMidtermExam-05.png",[258,4285,4286,4289,4290,4293,4294,4297,4298],{},[242,4287,4288],{},"Impact Ionization（碰撞电离）","\nIn a ",[242,4291,4292],{},"strong electric field",", carriers are accelerated and gain high kinetic energy between collisions. A “hot” carrier can ",[242,4295,4296],{},"collide with the lattice and knock an electron from the valence band to the conduction band",", creating a new electron–hole pair.\nThis is the basic mechanism behind avalanche multiplication and avalanche breakdown.\n",[3982,4299],{"alt":4300,"src":4301},"PixPin_2025-11-13_10-59-52.png","\u002Fimg\u002FMicroelectronicDevices\u002FMidtermExam-03.png",[4303,4304,4306,4309,4312],"alert",{"type":4305},"tip",[231,4307,4308],{},"原答案",[231,4310,4311],{},"Carrier generation is the process that creates electron-hole pairs in a semiconductor, where an electron is excited from the valence band to the conduction band.",[255,4313,4314,4325,4335,4345],{},[258,4315,4316,3723,4322],{},[4317,4318,4319],"mark",{},[242,4320,4321],{},"Thermal Generation:",[4317,4323,4324],{},"Energy from lattice vibrations (heat\u002Fphonons) excites an electron across the band gap.",[258,4326,4327,3723,4332],{},[4317,4328,4329],{},[242,4330,4331],{},"Optical Generation (Photogeneration):",[4317,4333,4334],{},"A photon with energy greater than the band gap is absorbed, creating an electron.",[258,4336,4337,3723,4342],{},[4317,4338,4339],{},[242,4340,4341],{},"Impact Ionization:",[4317,4343,4344],{},"A high-energy carrier collides with the lattice and uses its kinetic energy to excite a new electron-hole pair.",[258,4346,4347,3723,4352,4355],{},[4317,4348,4349],{},[242,4350,4351],{},"Electric field:",[4317,4353,4354],{},"The field makes the energy gap thin,so that the electrons can be more easily excited.","\n（好像这三个机制吧）",[279,4357],{},[235,4359,4361],{"id":4360},"_9in-a-pn-junctionwhat-conditions-must-be-metin-terms-of-carrier-concentrationsso-thatathe-n-sideandbthe-p-side-can-be-considered-aslow-level-injectionrespectively","9.In a pn junction,what conditions must be met(in terms of carrier concentrations)so that(a)the n-side,and(b)the p-side can be considered as“low-level injection”,respectively?",[255,4363,4364],{},[258,4365,4366,4369,4370,4373,4374,4377,4378,2377],{},[242,4367,4368],{},"On the n-side (n-type region):","\nThe ",[242,4371,4372],{},"injected excess hole concentration","(注入过剩空穴浓度) is ",[242,4375,4376],{},"much smaller"," than the ",[242,4379,4380],{},"equilibrium majority electron concentration",[231,4382,4383,4384,2382],{},"so the total electron concentration is essentially unchanged, ",[326,4385,4387,4419],{"className":4386},[329],[326,4388,4390],{"className":4389},[333],[335,4391,4392],{"xmlns":337},[339,4393,4394,4416],{},[342,4395,4396,4402,4405],{},[345,4397,4398,4400],{},[348,4399,363],{},[348,4401,363],{},[369,4403,4404],{},"≈",[345,4406,4407,4409],{},[348,4408,363],{},[342,4410,4411,4413],{},[348,4412,363],{},[388,4414,4415],{},"0",[402,4417,4418],{"encoding":404},"n_n \\approx n_{n0}",[326,4420,4422,4478],{"className":4421,"ariaHidden":410},[409],[326,4423,4425,4429,4469,4472,4475],{"className":4424},[414],[326,4426],{"className":4427,"style":4428},[418],"height:0.6331em;vertical-align:-0.15em;",[326,4430,4432,4435],{"className":4431},[423],[326,4433,363],{"className":4434},[423,427],[326,4436,4438],{"className":4437},[431],[326,4439,4441,4461],{"className":4440},[435,436],[326,4442,4444,4458],{"className":4443},[440],[326,4445,4447],{"className":4446,"style":3790},[444],[326,4448,4449,4452],{"style":448},[326,4450],{"className":4451,"style":453},[452],[326,4453,4455],{"className":4454},[457,458,459,460],[326,4456,363],{"className":4457},[423,427,460],[326,4459,486],{"className":4460},[485],[326,4462,4464],{"className":4463},[440],[326,4465,4467],{"className":4466,"style":729},[444],[326,4468],{},[326,4470],{"className":4471,"style":500},[499],[326,4473,4404],{"className":4474},[504],[326,4476],{"className":4477,"style":500},[499],[326,4479,4481,4484],{"className":4480},[414],[326,4482],{"className":4483,"style":1075},[418],[326,4485,4487,4490],{"className":4486},[423],[326,4488,363],{"className":4489},[423,427],[326,4491,4493],{"className":4492},[431],[326,4494,4496,4523],{"className":4495},[435,436],[326,4497,4499,4520],{"className":4498},[440],[326,4500,4503],{"className":4501,"style":4502},[444],"height:0.3011em;",[326,4504,4505,4508],{"style":448},[326,4506],{"className":4507,"style":453},[452],[326,4509,4511],{"className":4510},[457,458,459,460],[326,4512,4514,4517],{"className":4513},[423,460],[326,4515,363],{"className":4516},[423,427,460],[326,4518,4415],{"className":4519},[423,460],[326,4521,486],{"className":4522},[485],[326,4524,4526],{"className":4525},[440],[326,4527,4529],{"className":4528,"style":729},[444],[326,4530],{},[255,4532,4533],{},[258,4534,4535,4538,4539,4542],{},[242,4536,4537],{},"On the p-side (p-type region):","\nThe injected excess electron concentration is much smaller than the equilibrium majority ",[242,4540,4541],{},"hole"," concentration:",[231,4544,4545,4546],{},"so the total hole concentration is essentially unchanged, ",[326,4547,4549,4579],{"className":4548},[329],[326,4550,4552],{"className":4551},[333],[335,4553,4554],{"xmlns":337},[339,4555,4556,4576],{},[342,4557,4558,4564,4566],{},[345,4559,4560,4562],{},[348,4561,231],{},[348,4563,231],{},[369,4565,4404],{},[345,4567,4568,4570],{},[348,4569,231],{},[342,4571,4572,4574],{},[348,4573,231],{},[388,4575,4415],{},[402,4577,4578],{"encoding":404},"p_p \\approx p_{p0}",[326,4580,4582,4638],{"className":4581,"ariaHidden":410},[409],[326,4583,4585,4589,4629,4632,4635],{"className":4584},[414],[326,4586],{"className":4587,"style":4588},[418],"height:0.7692em;vertical-align:-0.2861em;",[326,4590,4592,4595],{"className":4591},[423],[326,4593,231],{"className":4594},[423,427],[326,4596,4598],{"className":4597},[431],[326,4599,4601,4621],{"className":4600},[435,436],[326,4602,4604,4618],{"className":4603},[440],[326,4605,4607],{"className":4606,"style":3790},[444],[326,4608,4609,4612],{"style":448},[326,4610],{"className":4611,"style":453},[452],[326,4613,4615],{"className":4614},[457,458,459,460],[326,4616,231],{"className":4617},[423,427,460],[326,4619,486],{"className":4620},[485],[326,4622,4624],{"className":4623},[440],[326,4625,4627],{"className":4626,"style":493},[444],[326,4628],{},[326,4630],{"className":4631,"style":500},[499],[326,4633,4404],{"className":4634},[504],[326,4636],{"className":4637,"style":500},[499],[326,4639,4641,4644],{"className":4640},[414],[326,4642],{"className":4643,"style":419},[418],[326,4645,4647,4650],{"className":4646},[423],[326,4648,231],{"className":4649},[423,427],[326,4651,4653],{"className":4652},[431],[326,4654,4656,4682],{"className":4655},[435,436],[326,4657,4659,4679],{"className":4658},[440],[326,4660,4662],{"className":4661,"style":4502},[444],[326,4663,4664,4667],{"style":448},[326,4665],{"className":4666,"style":453},[452],[326,4668,4670],{"className":4669},[457,458,459,460],[326,4671,4673,4676],{"className":4672},[423,460],[326,4674,231],{"className":4675},[423,427,460],[326,4677,4415],{"className":4678},[423,460],[326,4680,486],{"className":4681},[485],[326,4683,4685],{"className":4684},[440],[326,4686,4688],{"className":4687,"style":493},[444],[326,4689],{},[279,4691],{},[235,4693,4695],{"id":4694},"_10what-are-excessive-carriers-in-a-semiconductorwhat-causes-them","10.What are excessive carriers in a semiconductor?what causes them?",[231,4697,4698,4699,4702],{},"Excess carriers are the ",[242,4700,4701],{},"extra electrons and holes above their thermal-equilibrium values in non-equilibrium concentration",", defined as",[326,4704,4706],{"className":4705},[612],[326,4707,4709,4739],{"className":4708},[329],[326,4710,4712],{"className":4711},[333],[335,4713,4714],{"xmlns":337,"display":621},[339,4715,4716,4736],{},[342,4717,4718,4721,4723,4726,4728,4730],{},[348,4719,4720],{"mathvariant":393},"Δ",[348,4722,363],{},[369,4724,4725],{},"≡",[348,4727,363],{},[369,4729,386],{},[345,4731,4732,4734],{},[348,4733,363],{},[388,4735,4415],{},[402,4737,4738],{"encoding":404},"Δn≡n−n_0",[326,4740,4742,4763,4782],{"className":4741,"ariaHidden":410},[409],[326,4743,4745,4748,4751,4754,4757,4760],{"className":4744},[414],[326,4746],{"className":4747,"style":2782},[418],[326,4749,4720],{"className":4750},[423],[326,4752,363],{"className":4753},[423,427],[326,4755],{"className":4756,"style":500},[499],[326,4758,4725],{"className":4759},[504],[326,4761],{"className":4762,"style":500},[499],[326,4764,4766,4770,4773,4776,4779],{"className":4765},[414],[326,4767],{"className":4768,"style":4769},[418],"height:0.6667em;vertical-align:-0.0833em;",[326,4771,363],{"className":4772},[423,427],[326,4774],{"className":4775,"style":800},[499],[326,4777,386],{"className":4778},[804],[326,4780],{"className":4781,"style":800},[499],[326,4783,4785,4788],{"className":4784},[414],[326,4786],{"className":4787,"style":1075},[418],[326,4789,4791,4794],{"className":4790},[423],[326,4792,363],{"className":4793},[423,427],[326,4795,4797],{"className":4796},[431],[326,4798,4800,4820],{"className":4799},[435,436],[326,4801,4803,4817],{"className":4802},[440],[326,4804,4806],{"className":4805,"style":4502},[444],[326,4807,4808,4811],{"style":448},[326,4809],{"className":4810,"style":453},[452],[326,4812,4814],{"className":4813},[457,458,459,460],[326,4815,4415],{"className":4816},[423,460],[326,4818,486],{"className":4819},[485],[326,4821,4823],{"className":4822},[440],[326,4824,4826],{"className":4825,"style":729},[444],[326,4827],{},[326,4829,4831],{"className":4830},[612],[326,4832,4834,4862],{"className":4833},[329],[326,4835,4837],{"className":4836},[333],[335,4838,4839],{"xmlns":337,"display":621},[339,4840,4841,4859],{},[342,4842,4843,4845,4847,4849,4851,4853],{},[348,4844,4720],{"mathvariant":393},[348,4846,231],{},[369,4848,4725],{},[348,4850,231],{},[369,4852,386],{},[345,4854,4855,4857],{},[348,4856,231],{},[388,4858,4415],{},[402,4860,4861],{"encoding":404},"Δp≡p−p_0",[326,4863,4865,4887,4906],{"className":4864,"ariaHidden":410},[409],[326,4866,4868,4872,4875,4878,4881,4884],{"className":4867},[414],[326,4869],{"className":4870,"style":4871},[418],"height:0.8778em;vertical-align:-0.1944em;",[326,4873,4720],{"className":4874},[423],[326,4876,231],{"className":4877},[423,427],[326,4879],{"className":4880,"style":500},[499],[326,4882,4725],{"className":4883},[504],[326,4885],{"className":4886,"style":500},[499],[326,4888,4890,4894,4897,4900,4903],{"className":4889},[414],[326,4891],{"className":4892,"style":4893},[418],"height:0.7778em;vertical-align:-0.1944em;",[326,4895,231],{"className":4896},[423,427],[326,4898],{"className":4899,"style":800},[499],[326,4901,386],{"className":4902},[804],[326,4904],{"className":4905,"style":800},[499],[326,4907,4909,4912],{"className":4908},[414],[326,4910],{"className":4911,"style":1928},[418],[326,4913,4915,4918],{"className":4914},[423],[326,4916,231],{"className":4917},[423,427],[326,4919,4921],{"className":4920},[431],[326,4922,4924,4944],{"className":4923},[435,436],[326,4925,4927,4941],{"className":4926},[440],[326,4928,4930],{"className":4929,"style":4502},[444],[326,4931,4932,4935],{"style":448},[326,4933],{"className":4934,"style":453},[452],[326,4936,4938],{"className":4937},[457,458,459,460],[326,4939,4415],{"className":4940},[423,460],[326,4942,486],{"className":4943},[485],[326,4945,4947],{"className":4946},[440],[326,4948,4950],{"className":4949,"style":729},[444],[326,4951],{},[231,4953,4954,4955],{},"where in a charge-neutral region ",[326,4956,4958,4980],{"className":4957},[329],[326,4959,4961],{"className":4960},[333],[335,4962,4963],{"xmlns":337},[339,4964,4965,4977],{},[342,4966,4967,4969,4971,4973,4975],{},[348,4968,4720],{"mathvariant":393},[348,4970,363],{},[369,4972,641],{},[348,4974,4720],{"mathvariant":393},[348,4976,231],{},[402,4978,4979],{"encoding":404},"\\Delta n = \\Delta p",[326,4981,4983,5004],{"className":4982,"ariaHidden":410},[409],[326,4984,4986,4989,4992,4995,4998,5001],{"className":4985},[414],[326,4987],{"className":4988,"style":2782},[418],[326,4990,4720],{"className":4991},[423],[326,4993,363],{"className":4994},[423,427],[326,4996],{"className":4997,"style":500},[499],[326,4999,641],{"className":5000},[504],[326,5002],{"className":5003,"style":500},[499],[326,5005,5007,5010,5013],{"className":5006},[414],[326,5008],{"className":5009,"style":4871},[418],[326,5011,4720],{"className":5012},[423],[326,5014,231],{"className":5015},[423,427],[231,5017,5018],{},"Electric field, magnetic field, mechanical stress and light.",[279,5020],{},[235,5022,5024],{"id":5023},"_11in-the-n-side-of-a-pn-junctionwhat-are-majority-carrierand-minority-carrierrespectivelyhow-about-the-p-side","11.In the n-side of a p+n junction,what are “majority carrier”and “minority carrier”,respectively?How about the p-side?",[231,5026,5027],{},"On the n-side, n is the majority carrier, p is the minority carrier.",[231,5029,5030],{},"On the p-side, p is the majority carrier, n is the minority carrier.",[279,5032],{},[235,5034,5036,5037,5106,5107,5188,5189,5188,5269,3015,5339,5408],{"id":5035},"_12what-is-the-meaning-ofquasi-fermi-levelin-a-semiconductor-schematically示意性地-draw-the-band-diagram-of-a-pn-junction-in-aforward-biased-and-breversed-biased-pn-junctionrespectively-in-your-plot-show-ece_cec-efne_fnefnefpe_fpefpeie_iei-and-eve_vevrespectively","12.What is the meaning of“quasi Fermi level”in a semiconductor? Schematically(示意性地) draw the band diagram of a p+n junction in (a)forward-biased and (b)reversed-biased p+n junction,respectively. In your plot, show ",[326,5038,5040,5057],{"className":5039},[329],[326,5041,5043],{"className":5042},[333],[335,5044,5045],{"xmlns":337},[339,5046,5047,5055],{},[342,5048,5049],{},[345,5050,5051,5053],{},[348,5052,2487],{},[348,5054,3904],{},[402,5056,3907],{"encoding":404},[326,5058,5060],{"className":5059,"ariaHidden":410},[409],[326,5061,5063,5066],{"className":5062},[414],[326,5064],{"className":5065,"style":3141},[418],[326,5067,5069,5072],{"className":5068},[423],[326,5070,2487],{"className":5071,"style":2629},[423,427],[326,5073,5075],{"className":5074},[431],[326,5076,5078,5098],{"className":5077},[435,436],[326,5079,5081,5095],{"className":5080},[440],[326,5082,5084],{"className":5083,"style":3790},[444],[326,5085,5086,5089],{"style":3793},[326,5087],{"className":5088,"style":453},[452],[326,5090,5092],{"className":5091},[457,458,459,460],[326,5093,3904],{"className":5094},[423,427,460],[326,5096,486],{"className":5097},[485],[326,5099,5101],{"className":5100},[440],[326,5102,5104],{"className":5103,"style":729},[444],[326,5105],{},", ",[326,5108,5110,5133],{"className":5109},[329],[326,5111,5113],{"className":5112},[333],[335,5114,5115],{"xmlns":337},[339,5116,5117,5130],{},[342,5118,5119],{},[345,5120,5121,5123],{},[348,5122,2487],{},[342,5124,5125,5128],{},[348,5126,5127],{},"F",[348,5129,363],{},[402,5131,5132],{"encoding":404},"E_{Fn}",[326,5134,5136],{"className":5135,"ariaHidden":410},[409],[326,5137,5139,5142],{"className":5138},[414],[326,5140],{"className":5141,"style":3141},[418],[326,5143,5145,5148],{"className":5144},[423],[326,5146,2487],{"className":5147,"style":2629},[423,427],[326,5149,5151],{"className":5150},[431],[326,5152,5154,5180],{"className":5153},[435,436],[326,5155,5157,5177],{"className":5156},[440],[326,5158,5160],{"className":5159,"style":2865},[444],[326,5161,5162,5165],{"style":3793},[326,5163],{"className":5164,"style":453},[452],[326,5166,5168],{"className":5167},[457,458,459,460],[326,5169,5171,5174],{"className":5170},[423,460],[326,5172,5127],{"className":5173,"style":521},[423,427,460],[326,5175,363],{"className":5176},[423,427,460],[326,5178,486],{"className":5179},[485],[326,5181,5183],{"className":5182},[440],[326,5184,5186],{"className":5185,"style":729},[444],[326,5187],{},",",[326,5190,5192,5214],{"className":5191},[329],[326,5193,5195],{"className":5194},[333],[335,5196,5197],{"xmlns":337},[339,5198,5199,5211],{},[342,5200,5201],{},[345,5202,5203,5205],{},[348,5204,2487],{},[342,5206,5207,5209],{},[348,5208,5127],{},[348,5210,231],{},[402,5212,5213],{"encoding":404},"E_{Fp}",[326,5215,5217],{"className":5216,"ariaHidden":410},[409],[326,5218,5220,5223],{"className":5219},[414],[326,5221],{"className":5222,"style":3771},[418],[326,5224,5226,5229],{"className":5225},[423],[326,5227,2487],{"className":5228,"style":2629},[423,427],[326,5230,5232],{"className":5231},[431],[326,5233,5235,5261],{"className":5234},[435,436],[326,5236,5238,5258],{"className":5237},[440],[326,5239,5241],{"className":5240,"style":2865},[444],[326,5242,5243,5246],{"style":3793},[326,5244],{"className":5245,"style":453},[452],[326,5247,5249],{"className":5248},[457,458,459,460],[326,5250,5252,5255],{"className":5251},[423,460],[326,5253,5127],{"className":5254,"style":521},[423,427,460],[326,5256,231],{"className":5257},[423,427,460],[326,5259,486],{"className":5260},[485],[326,5262,5264],{"className":5263},[440],[326,5265,5267],{"className":5266,"style":493},[444],[326,5268],{},[326,5270,5272,5290],{"className":5271},[329],[326,5273,5275],{"className":5274},[333],[335,5276,5277],{"xmlns":337},[339,5278,5279,5287],{},[342,5280,5281],{},[345,5282,5283,5285],{},[348,5284,2487],{},[348,5286,901],{},[402,5288,5289],{"encoding":404},"E_i",[326,5291,5293],{"className":5292,"ariaHidden":410},[409],[326,5294,5296,5299],{"className":5295},[414],[326,5297],{"className":5298,"style":3141},[418],[326,5300,5302,5305],{"className":5301},[423],[326,5303,2487],{"className":5304,"style":2629},[423,427],[326,5306,5308],{"className":5307},[431],[326,5309,5311,5331],{"className":5310},[435,436],[326,5312,5314,5328],{"className":5313},[440],[326,5315,5317],{"className":5316,"style":1094},[444],[326,5318,5319,5322],{"style":3793},[326,5320],{"className":5321,"style":453},[452],[326,5323,5325],{"className":5324},[457,458,459,460],[326,5326,901],{"className":5327},[423,427,460],[326,5329,486],{"className":5330},[485],[326,5332,5334],{"className":5333},[440],[326,5335,5337],{"className":5336,"style":729},[444],[326,5338],{},[326,5340,5342,5359],{"className":5341},[329],[326,5343,5345],{"className":5344},[333],[335,5346,5347],{"xmlns":337},[339,5348,5349,5357],{},[342,5350,5351],{},[345,5352,5353,5355],{},[348,5354,2487],{},[348,5356,2931],{},[402,5358,3835],{"encoding":404},[326,5360,5362],{"className":5361,"ariaHidden":410},[409],[326,5363,5365,5368],{"className":5364},[414],[326,5366],{"className":5367,"style":3141},[418],[326,5369,5371,5374],{"className":5370},[423],[326,5372,2487],{"className":5373,"style":2629},[423,427],[326,5375,5377],{"className":5376},[431],[326,5378,5380,5400],{"className":5379},[435,436],[326,5381,5383,5397],{"className":5382},[440],[326,5384,5386],{"className":5385,"style":3790},[444],[326,5387,5388,5391],{"style":3793},[326,5389],{"className":5390,"style":453},[452],[326,5392,5394],{"className":5393},[457,458,459,460],[326,5395,2931],{"className":5396,"style":2032},[423,427,460],[326,5398,486],{"className":5399},[485],[326,5401,5403],{"className":5402},[440],[326,5404,5406],{"className":5405,"style":729},[444],[326,5407],{},",respectively.",[231,5410,5411,5414,5415,5418,5419,5422],{},[242,5412,5413],{},"Quasi-Fermi levels"," are ",[242,5416,5417],{},"separate effective Fermi levels for electrons and holes"," used when a semiconductor is ",[242,5420,5421],{},"out of thermal equilibrium",". They are defined so that the carrier concentrations can still be written as",[326,5424,5426],{"className":5425},[612],[326,5427,5429,5581],{"className":5428},[329],[326,5430,5432],{"className":5431},[333],[335,5433,5434],{"xmlns":337,"display":621},[339,5435,5436,5578],{},[342,5437,5438,5440,5442,5445,5447,5449,5455,5458,5461,5507,5509,5512,5514,5516,5518,5520,5522,5528,5530,5532],{},[348,5439,363],{},[369,5441,383],{"stretchy":382},[348,5443,5444],{},"x",[369,5446,400],{"stretchy":382},[369,5448,641],{},[345,5450,5451,5453],{},[348,5452,363],{},[348,5454,901],{},[348,5456,5457],{},"exp",[369,5459,5460],{},"⁡",[342,5462,5463,5465,5505],{},[369,5464,383],{"fence":410},[884,5466,5467,5499],{},[342,5468,5469,5479,5481,5483,5485,5487,5493,5495,5497],{},[345,5470,5471,5473],{},[348,5472,2487],{},[342,5474,5475,5477],{},[348,5476,5127],{},[348,5478,363],{},[369,5480,383],{"stretchy":382},[348,5482,5444],{},[369,5484,400],{"stretchy":382},[369,5486,386],{},[345,5488,5489,5491],{},[348,5490,2487],{},[348,5492,901],{},[369,5494,383],{"stretchy":382},[348,5496,5444],{},[369,5498,400],{"stretchy":382},[342,5500,5501,5503],{},[348,5502,2496],{},[348,5504,377],{},[369,5506,400],{"fence":410},[369,5508,5188],{"separator":410},[499,5510],{"width":5511},"1em",[348,5513,231],{},[369,5515,383],{"stretchy":382},[348,5517,5444],{},[369,5519,400],{"stretchy":382},[369,5521,641],{},[345,5523,5524,5526],{},[348,5525,363],{},[348,5527,901],{},[348,5529,5457],{},[369,5531,5460],{},[342,5533,5534,5536,5576],{},[369,5535,383],{"fence":410},[884,5537,5538,5570],{},[342,5539,5540,5546,5548,5550,5552,5554,5564,5566,5568],{},[345,5541,5542,5544],{},[348,5543,2487],{},[348,5545,901],{},[369,5547,383],{"stretchy":382},[348,5549,5444],{},[369,5551,400],{"stretchy":382},[369,5553,386],{},[345,5555,5556,5558],{},[348,5557,2487],{},[342,5559,5560,5562],{},[348,5561,5127],{},[348,5563,231],{},[369,5565,383],{"stretchy":382},[348,5567,5444],{},[369,5569,400],{"stretchy":382},[342,5571,5572,5574],{},[348,5573,2496],{},[348,5575,377],{},[369,5577,400],{"fence":410},[402,5579,5580],{"encoding":404},"n(x) = n_i \\exp \\left(\\frac{E_{Fn}(x) - E_i(x)}{kT}\\right), \\quad p(x) = n_i \\exp \\left(\\frac{E_i(x) - E_{Fp}(x)}{kT}\\right)",[326,5582,5584,5611,5900],{"className":5583,"ariaHidden":410},[409],[326,5585,5587,5590,5593,5596,5599,5602,5605,5608],{"className":5586},[414],[326,5588],{"className":5589,"style":679},[418],[326,5591,363],{"className":5592},[423,427],[326,5594,383],{"className":5595},[549],[326,5597,5444],{"className":5598},[423,427],[326,5600,400],{"className":5601},[560],[326,5603],{"className":5604,"style":500},[499],[326,5606,641],{"className":5607},[504],[326,5609],{"className":5610,"style":500},[499],[326,5612,5614,5618,5658,5661,5664,5667,5865,5868,5872,5876,5879,5882,5885,5888,5891,5894,5897],{"className":5613},[414],[326,5615],{"className":5616,"style":5617},[418],"height:2.4em;vertical-align:-0.95em;",[326,5619,5621,5624],{"className":5620},[423],[326,5622,363],{"className":5623},[423,427],[326,5625,5627],{"className":5626},[431],[326,5628,5630,5650],{"className":5629},[435,436],[326,5631,5633,5647],{"className":5632},[440],[326,5634,5636],{"className":5635,"style":1094},[444],[326,5637,5638,5641],{"style":448},[326,5639],{"className":5640,"style":453},[452],[326,5642,5644],{"className":5643},[457,458,459,460],[326,5645,901],{"className":5646},[423,427,460],[326,5648,486],{"className":5649},[485],[326,5651,5653],{"className":5652},[440],[326,5654,5656],{"className":5655,"style":729},[444],[326,5657],{},[326,5659],{"className":5660,"style":1250},[499],[326,5662,5457],{"className":5663},[1203],[326,5665],{"className":5666,"style":1250},[499],[326,5668,5671,5680,5859],{"className":5669},[5670],"minner",[326,5672,5676],{"className":5673,"style":5675},[549,5674],"delimcenter","top:0em;",[326,5677,383],{"className":5678},[5679,459],"delimsizing",[326,5681,5683,5686,5856],{"className":5682},[423],[326,5684],{"className":5685},[549,921],[326,5687,5689],{"className":5688},[884],[326,5690,5692,5847],{"className":5691},[435,436],[326,5693,5695,5844],{"className":5694},[440],[326,5696,5699,5714,5722],{"className":5697,"style":5698},[444],"height:1.427em;",[326,5700,5702,5705],{"style":5701},"top:-2.314em;",[326,5703],{"className":5704,"style":941},[452],[326,5706,5708,5711],{"className":5707},[423],[326,5709,2496],{"className":5710,"style":2551},[423,427],[326,5712,377],{"className":5713,"style":521},[423,427],[326,5715,5716,5719],{"style":997},[326,5717],{"className":5718,"style":941},[452],[326,5720],{"className":5721,"style":1005},[1004],[326,5723,5725,5728],{"style":5724},"top:-3.677em;",[326,5726],{"className":5727,"style":941},[452],[326,5729,5731,5777,5780,5783,5786,5789,5792,5795,5835,5838,5841],{"className":5730},[423],[326,5732,5734,5737],{"className":5733},[423],[326,5735,2487],{"className":5736,"style":2629},[423,427],[326,5738,5740],{"className":5739},[431],[326,5741,5743,5769],{"className":5742},[435,436],[326,5744,5746,5766],{"className":5745},[440],[326,5747,5749],{"className":5748,"style":2865},[444],[326,5750,5751,5754],{"style":3793},[326,5752],{"className":5753,"style":453},[452],[326,5755,5757],{"className":5756},[457,458,459,460],[326,5758,5760,5763],{"className":5759},[423,460],[326,5761,5127],{"className":5762,"style":521},[423,427,460],[326,5764,363],{"className":5765},[423,427,460],[326,5767,486],{"className":5768},[485],[326,5770,5772],{"className":5771},[440],[326,5773,5775],{"className":5774,"style":729},[444],[326,5776],{},[326,5778,383],{"className":5779},[549],[326,5781,5444],{"className":5782},[423,427],[326,5784,400],{"className":5785},[560],[326,5787],{"className":5788,"style":800},[499],[326,5790,386],{"className":5791},[804],[326,5793],{"className":5794,"style":800},[499],[326,5796,5798,5801],{"className":5797},[423],[326,5799,2487],{"className":5800,"style":2629},[423,427],[326,5802,5804],{"className":5803},[431],[326,5805,5807,5827],{"className":5806},[435,436],[326,5808,5810,5824],{"className":5809},[440],[326,5811,5813],{"className":5812,"style":1094},[444],[326,5814,5815,5818],{"style":3793},[326,5816],{"className":5817,"style":453},[452],[326,5819,5821],{"className":5820},[457,458,459,460],[326,5822,901],{"className":5823},[423,427,460],[326,5825,486],{"className":5826},[485],[326,5828,5830],{"className":5829},[440],[326,5831,5833],{"className":5832,"style":729},[444],[326,5834],{},[326,5836,383],{"className":5837},[549],[326,5839,5444],{"className":5840},[423,427],[326,5842,400],{"className":5843},[560],[326,5845,486],{"className":5846},[485],[326,5848,5850],{"className":5849},[440],[326,5851,5854],{"className":5852,"style":5853},[444],"height:0.686em;",[326,5855],{},[326,5857],{"className":5858},[560,921],[326,5860,5862],{"className":5861,"style":5675},[560,5674],[326,5863,400],{"className":5864},[5679,459],[326,5866],{"className":5867,"style":1250},[499],[326,5869,5188],{"className":5870},[5871],"mpunct",[326,5873],{"className":5874,"style":5875},[499],"margin-right:1em;",[326,5877],{"className":5878,"style":1250},[499],[326,5880,231],{"className":5881},[423,427],[326,5883,383],{"className":5884},[549],[326,5886,5444],{"className":5887},[423,427],[326,588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equilibrium, 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under bias they split and describe non-equilibrium electron and hole populations separately.",[231,6366,6367],{},[3982,6368],{"alt":6369,"src":6370},"image.png","\u002Fimg\u002FMicroelectronicDevices\u002FMidtermExam-04.png",[1040,6372,6373,6707,6872],{},[231,6374,6375,6376,6445,6446,6706],{},"首先画出平衡状态下的能带图，因为thermal equilibrium, 费米能级是相同的，然后越接近",[326,6377,6379,6396],{"className":6378},[329],[326,6380,6382],{"className":6381},[333],[335,6383,6384],{"xmlns":337},[339,6385,6386,6394],{},[342,6387,6388],{},[345,6389,6390,6392],{},[348,6391,2487],{},[348,6393,3904],{},[402,6395,3907],{"encoding":404},[326,6397,6399],{"className":6398,"ariaHidden":410},[409],[326,6400,6402,6405],{"className":6401},[414],[326,6403],{"className":6404,"style":3141},[418],[326,6406,6408,6411],{"className":6407},[423],[326,6409,2487],{"className":6410,"style":2629},[423,427],[326,6412,6414],{"className":6413},[431],[326,6415,6417,6437],{"className":6416},[435,436],[326,6418,6420,6434],{"className":6419},[440],[326,6421,6423],{"className":6422,"style":3790},[444],[326,6424,6425,6428],{"style":3793},[326,6426],{"className":6427,"style":453},[452],[326,6429,6431],{"className":6430},[457,458,459,460],[326,6432,3904],{"className":6433},[423,427,460],[326,6435,486],{"className":6436},[485],[326,6438,6440],{"className":6439},[440],[326,6441,6443],{"className":6442,"style":729},[444],[326,6444],{},"说明电子越多，画出P区与N区，中间弯折，注意一下",[326,6447,6449,6489],{"className":6448},[329],[326,6450,6452],{"className":6451},[333],[335,6453,6454],{"xmlns":337},[339,6455,6456,6486],{},[342,6457,6458,6464,6466],{},[345,6459,6460,6462],{},[348,6461,2487],{},[348,6463,901],{},[369,6465,641],{},[884,6467,6468,6484],{},[342,6469,6470,6476,6478],{},[345,6471,6472,6474],{},[348,6473,2487],{},[348,6475,3904],{},[369,6477,655],{},[345,6479,6480,6482],{},[348,6481,2487],{},[348,6483,2931],{},[388,6485,397],{},[402,6487,6488],{"encoding":404},"E_i=\\frac{E_c+E_v}{2}",[326,6490,6492,6547],{"className":6491,"ariaHidden":410},[409],[326,6493,6495,6498,6538,6541,6544],{"className":6494},[414],[326,6496],{"className":6497,"style":3141},[418],[326,6499,6501,6504],{"className":6500},[423],[326,6502,2487],{"className":6503,"style":2629},[423,427],[326,6505,6507],{"className":6506},[431],[326,6508,6510,6530],{"className":6509},[435,436],[326,6511,6513,6527],{"className":6512},[440],[326,6514,6516],{"className":6515,"style":1094},[444],[326,6517,6518,6521],{"style":3793},[326,6519],{"className":6520,"style":453},[452],[326,6522,6524],{"className":6523},[457,458,459,460],[326,6525,901],{"className":6526},[423,427,460],[326,6528,486],{"className":6529},[485],[326,6531,6533],{"className":6532},[440],[326,6534,6536],{"className":6535,"style":729},[444],[326,6537],{},[326,6539],{"className":6540,"style":500},[499],[326,6542,641],{"className":6543},[504],[326,6545],{"className":6546,"style":500},[499],[326,6548,6550,6554],{"className":6549},[414],[326,6551],{"className":6552,"style":6553},[418],"height:1.2334em;vertical-align:-0.345em;",[326,6555,6557,6560,6703],{"className":6556},[423],[326,6558],{"className":6559},[549,921],[326,6561,6563],{"className":6562},[884],[326,6564,6566,6695],{"className":6565},[435,436],[326,6567,6569,6692],{"className":6568},[440],[326,6570,6573,6587,6595],{"className":6571,"style":6572},[444],"height:0.8884em;",[326,6574,6575,6578],{"style":937},[326,6576],{"className":6577,"style":941},[452],[326,6579,6581],{"className":6580},[457,458,459,460],[326,6582,6584],{"className":6583},[423,460],[326,6585,397],{"className":6586},[423,460],[326,6588,6589,6592],{"style":997},[326,6590],{"className":6591,"style":941},[452],[326,6593],{"className":6594,"style":1005},[1004],[326,6596,6598,6601],{"style":6597},"top:-3.4101em;",[326,6599],{"className":6600,"style":941},[452],[326,6602,6604],{"className":6603},[457,458,459,460],[326,6605,6607,6649,6652],{"className":6606},[423,460],[326,6608,6610,6613],{"className":6609},[423,460],[326,6611,2487],{"className":6612,"style":2629},[423,427,460],[326,6614,6616],{"className":6615},[431],[326,6617,6619,6641],{"className":6618},[435,436],[326,6620,6622,6638],{"className":6621},[440],[326,6623,6626],{"className":6624,"style":6625},[444],"height:0.1645em;",[326,6627,6629,6632],{"style":6628},"top:-2.357em;margin-left:-0.0576em;margin-right:0.0714em;",[326,6630],{"className":6631,"style":974},[452],[326,6633,6635],{"className":6634},[457,978,979,460],[326,6636,3904],{"className":6637},[423,427,460],[326,6639,486],{"className":6640},[485],[326,6642,6644],{"className":6643},[440],[326,6645,6647],{"className":6646,"style":992},[444],[326,6648],{},[326,6650,655],{"className":6651},[804,460],[326,6653,6655,6658],{"className":6654},[423,460],[326,6656,2487],{"className":6657,"style":2629},[423,427,460],[326,6659,6661],{"className":6660},[431],[326,6662,6664,6684],{"className":6663},[435,436],[326,6665,6667,6681],{"className":6666},[440],[326,6668,6670],{"className":6669,"style":6625},[444],[326,6671,6672,6675],{"style":6628},[326,6673],{"className":6674,"style":974},[452],[326,6676,6678],{"className":6677},[457,978,979,460],[326,6679,2931],{"className":6680,"style":2032},[423,427,460],[326,6682,486],{"className":6683},[485],[326,6685,6687],{"className":6686},[440],[326,6688,6690],{"className":6689,"style":992},[444],[326,6691],{},[326,6693,486],{"className":6694},[48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sName":7025},[485],[326,7027,7029],{"className":7028},[440],[326,7030,7032],{"className":7031,"style":729},[444],[326,7033],{},"跟随着往上走",[235,7036,7038],{"id":7037},"q2","Q2",[231,7040,7041],{},[3982,7042],{"alt":6369,"src":7043},"\u002Fimg\u002FMicroelectronicDevices\u002FMidtermExam-01.png",{"title":7045,"searchDepth":7046,"depth":7046,"links":7047},"",4,[7048,7050,7051,7052,7053,7054,7055,7056,7057,7058,7059,7060,7062],{"id":237,"depth":7049,"text":238},2,{"id":607,"depth":7049,"text":608},{"id":2290,"depth":7049,"text":2291},{"id":2707,"depth":7049,"text":2708},{"id":2894,"depth":7049,"text":2895},{"id":3023,"depth":7049,"text":3024},{"id":3053,"depth":7049,"text":3054},{"id":3698,"depth":7049,"text":3699},{"id":4360,"depth":7049,"text":4361},{"id":4694,"depth":7049,"text":4695},{"id":5023,"depth":7049,"text":5024},{"id":5035,"depth":7049,"text":7061},"12.What is the meaning of“quasi Fermi level”in a semiconductor? Schematically(示意性地) draw the band diagram of a p+n junction in (a)forward-biased and (b)reversed-biased p+n junction,respectively. In your plot, show EcE_cEc​, EFnE_{Fn}EFn​,EFpE_{Fp}EFp​,EiE_iEi​ and EvE_vEv​,respectively.",{"id":7037,"depth":7049,"text":7038},[189],"24-25 学年期中复习题：杂质散射与迁移率、Matthiessen 定则、有效质量、速度饱和、漂移与扩散、载流子产生、低水平注入、准费米能级","md",null,{"slots":7068},{},{"text":7070,"minutes":7071,"time":7072,"words":7073},"8 min read",7.635,458100,1527,{"title":166,"description":7064},{"loc":165,"images":7076},[7077,7078,7079,7080,7081],{"loc":3985},{"loc":4283},{"loc":4301},{"loc":6370},{"loc":7043},[176,7083],"课程笔记","tech","FvTTOkT8Te3FTWo7Q7txJXc-GTkJ8SBUUmgwdutE6JI",[7087,7088],{"title":146,"path":145,"stem":144,"date":147,"type":7084,"children":-1},{"title":151,"path":150,"stem":149,"date":152,"type":7084,"children":-1},1789011906832]