1181:
1020:
891:
1029:
688:
In order to simplify the calculation, instead of treating the electrons as fermions, according to the Fermi–Dirac distribution, we instead treat them as a classical non-interacting gas, which is given by the
527:
902:
757:
1698:
190:
1803:, the exact definition of how many "valence electrons" an element should have in elemental form is somewhat arbitrary, but the following table lists the free electron densities given in
1596:
These carrier concentrations will change if these materials are doped. For example, doping pure silicon with a small amount of phosphorus will increase the carrier density of electrons,
750:
1353:
53:, in principle it can depend on position. However, usually carrier concentration is given as a single number, and represents the average carrier density over the whole material.
2355:
Pietro P. Altermatt, Andreas Schenk, Frank
Geelhaar, Gernot Heiser (2003). "Reassessment of the intrinsic carrier density in crystalline silicon in view of band-gap narrowing".
1449:
368:
is the number of holes per unit volume in the valence band. To calculate this number for electrons, we start with the idea that the total density of conduction-band electrons,
293:
221:
447:
87:
If the total number of charge carriers is known, the carrier density can be found by simply dividing by the volume. To show this mathematically, charge carrier density is a
684:
1727:
1254:
1852:
1766:
2390:
2341:
1793:
1394:
1289:
1210:
420:
393:
366:
339:
251:
628:
595:
562:
84:
over the energy range of charge carriers in the material (e.g. integrating over the conduction band for electrons, integrating over the valence band for holes).
1825:
133:
113:
1357:
A similar expression can be derived for holes. The carrier concentration can be calculated by treating electrons moving back and forth across the
454:
752:, which is true for semiconductors near room temperature. This approximation is invalid at very low temperatures or an extremely small band-gap.
1641:
2421:
2325:
1213:
690:
138:
2463:
88:
2501:
1176:{\displaystyle n_{0}=2\left({\frac {m^{*}k_{\text{B}}T}{2\pi \hbar ^{2}}}\right)^{3/2}e^{-{\frac {E_{c}-E_{f}}{k_{\text{B}}T}}}}
395:, is just adding up the conduction electron density across the different energies in the band, from the bottom of the band
1366:
1296:
598:
2279:
are often on the same orders of magnitude, but this simple model cannot predict carrier density to very high accuracy.
1401:
19:
This article is about the number of individual electrons or holes per volume. For the electric charge per volume, see
2404:
Rössler, U. (2002). "Gallium arsenide (GaAs), intrinsic carrier concentration, electrical and thermal conductivity".
256:
1015:{\displaystyle g(E)={\frac {1}{2\pi ^{2}}}\left({\frac {2m^{*}}{\hbar ^{2}}}\right)^{\frac {3}{2}}{\sqrt {E-E_{0}}}}
886:{\displaystyle f(E)={\frac {1}{1+e^{\frac {E-E_{f}}{k_{\text{B}}T}}}}\approx e^{-{\frac {E-E_{f}}{k_{\text{B}}T}}}}
633:
1636:. In this case, the carrier density (in this context, also called the free electron density) can be estimated by:
696:
2562:
1609:
1454:
57:
2406:
Group IV Elements, IV-IV and III-V Compounds. Part b – Electronic, Transport, Optical and Other
Properties
2310:
Group IV Elements, IV-IV and III-V Compounds. Part b – Electronic, Transport, Optical and Other
Properties
307:
2384:
1612:. Doping pure silicon with a small amount of boron will increase the carrier density of holes, so then
2364:
195:
61:
425:
1804:
1362:
1705:
2529:
2521:
2335:
1219:
1830:
1807:, which were calculated using the formula above based on reasonable assumptions about valence,
1744:
2459:
2417:
2321:
2308:
O. Madelung, U. Rössler, M. Schulz (2002). "Germanium (Ge), intrinsic carrier concentration".
1730:
896:
565:
81:
24:
2557:
2513:
2451:
2409:
2372:
2313:
1738:
1503:
1771:
1372:
1267:
1188:
398:
371:
344:
317:
229:
2446:
Gachovska, Tanya K.; Hudgins, Jerry L. (2018). "SiC and GaN Power
Semiconductor Devices".
1855:
1800:
1563:
1547:
1531:
1519:
1257:
604:
571:
538:
38:
2368:
2455:
1810:
303:
118:
98:
20:
2537:
630:
which tells us the portion of those states which will actually have electrons in them
2551:
2533:
65:
1453:
The following table lists a few values of the intrinsic carrier concentration for
2288:
2276:
1796:
1633:
1261:
311:
2497:
226:
If the density does not depend on position and is instead equal to a constant
2065:
1989:
1951:
1932:
1471:
341:
is number of electrons per unit volume in the conduction band. For holes,
2413:
2317:
2287:
The density of charge carriers can be determined in many cases using the
2255:
2179:
2122:
1396:
called the intrinsic carrier concentration, which for undoped materials:
92:
77:
46:
2525:
2236:
2141:
2103:
2027:
1970:
1579:
1487:
1358:
532:
50:
2376:
16:
Charge carriers per volume; such as electrons, ions, "holes" or others
2160:
2008:
1894:
1875:
1629:
42:
2517:
1216:
of the electrons in that particular semiconductor, and the quantity
2291:, the voltage of which depends inversely on the carrier density.
1024:
After combination and simplification, these expressions lead to:
2408:. Landolt-Börnstein – Group III Condensed Matter. pp. 1–8.
2312:. Landolt-Börnstein – Group III Condensed Matter. pp. 1–3.
2217:
2084:
2046:
1913:
535:, the density of conduction electrons at any particular energy,
693:. This approximation has negligible effects when the magnitude
2198:
522:{\displaystyle n_{0}=\int _{E_{c}}^{E_{\text{top}}}N(E)\,dE}
2275:
The values for n among metals inferred for example by the
56:
Charge carrier densities involve equations concerning the
23:. For the number of possible states per energy range, see
1693:{\displaystyle n={\frac {N_{\text{A}}Z\rho _{m}}{m_{a}}}}
76:
The carrier density is usually obtained theoretically by
306:, where it is an important quantity for the process of
1833:
1813:
1774:
1747:
1708:
1644:
1404:
1375:
1299:
1270:
1222:
1191:
1032:
905:
760:
699:
636:
607:
597:
or how many conducting states are possible, with the
574:
541:
457:
428:
401:
374:
347:
320:
259:
232:
198:
141:
121:
101:
2502:"On a New Action of the Magnet on Electric Currents"
1620:, and it will be a p-type extrinsic semiconductor.
1846:
1819:
1787:
1760:
1721:
1692:
1443:
1388:
1347:
1283:
1248:
1204:
1175:
1014:
885:
744:
678:
622:
589:
556:
521:
441:
414:
387:
360:
333:
287:
245:
223:is the position-dependent charge carrier density.
215:
184:
127:
107:
2441:
2439:
2437:
2435:
2433:
185:{\displaystyle N=\int _{V}n(\mathbf {r} )\,dV.}
8:
2389:: CS1 maint: multiple names: authors list (
2340:: CS1 maint: multiple names: authors list (
1632:, where it can be estimated from the simple
2477:
2475:
1628:The carrier density is also applicable to
745:{\displaystyle |E-E_{f}|\gg k_{\text{B}}T}
1838:
1832:
1812:
1779:
1773:
1752:
1746:
1713:
1707:
1682:
1671:
1658:
1651:
1643:
1435:
1422:
1409:
1403:
1380:
1374:
1369:. The mass action law defines a quantity
1336:
1323:
1304:
1298:
1275:
1269:
1240:
1227:
1221:
1196:
1190:
1159:
1147:
1134:
1127:
1123:
1109:
1105:
1092:
1071:
1061:
1054:
1037:
1031:
1004:
992:
981:
969:
958:
948:
934:
921:
904:
869:
857:
844:
840:
817:
805:
792:
776:
759:
733:
721:
715:
700:
698:
635:
606:
573:
540:
512:
492:
487:
480:
475:
462:
456:
433:
427:
406:
400:
379:
373:
352:
346:
325:
319:
276:
258:
237:
231:
205:
197:
172:
164:
152:
140:
120:
100:
1860:
1459:
1256:is the difference in energy between the
2300:
1089:
966:
2382:
2333:
1608:, the doped silicon will be a n-type
302:The carrier density is important for
7:
1799:. Since metals can display multiple
1768:is the density of the material, and
1348:{\displaystyle E_{g}=2(E_{c}-E_{f})}
115:gives the number of charge carriers
1457:, in order of increasing band gap.
49:, it is measured in m. As with any
2456:10.1016/b978-0-12-811407-0.00005-2
14:
1444:{\displaystyle n_{i}=n_{0}=p_{0}}
206:
165:
2506:American Journal of Mathematics
1870:Carrier density (1/cm) at 300K
1466:Carrier density (1/cm) at 300K
1361:just like the equilibrium of a
288:{\displaystyle N=V\cdot n_{0}.}
216:{\displaystyle n(\mathbf {r} )}
1365:from chemistry, leading to an
1342:
1316:
1264:, which is half the band gap,
915:
909:
770:
764:
722:
701:
691:Maxwell–Boltzmann distribution
673:
667:
661:
655:
646:
640:
617:
611:
584:
578:
551:
545:
509:
503:
442:{\displaystyle E_{\text{top}}}
210:
202:
169:
161:
1:
1854:calculated from experimental
679:{\displaystyle N(E)=g(E)f(E)}
60:, related phenomena like the
1867:Number of valence electrons
1722:{\displaystyle N_{\text{A}}}
253:this equation simplifies to
1827:, and with mass densities,
1249:{\displaystyle E_{c}-E_{f}}
64:, and chemicals bonds like
2579:
2448:Power Electronics Handbook
2357:Journal of Applied Physics
1367:electronic mass action law
18:
1847:{\displaystyle \rho _{m}}
1761:{\displaystyle \rho _{m}}
2450:. Elsevier. p. 98.
1455:intrinsic semiconductors
599:Fermi–Dirac distribution
37:, denotes the number of
1610:extrinsic semiconductor
422:to the top of the band
314:, the electron density,
58:electrical conductivity
1848:
1821:
1789:
1762:
1723:
1694:
1445:
1390:
1349:
1285:
1250:
1206:
1177:
1016:
895:The three-dimensional
887:
746:
680:
624:
591:
564:is the product of the
558:
531:Because electrons are
523:
443:
416:
389:
362:
335:
289:
247:
217:
186:
129:
109:
31:Charge carrier density
1849:
1822:
1790:
1788:{\displaystyle m_{a}}
1763:
1724:
1695:
1446:
1391:
1389:{\displaystyle n_{i}}
1350:
1286:
1284:{\displaystyle E_{g}}
1251:
1207:
1205:{\displaystyle m^{*}}
1178:
1017:
888:
747:
681:
625:
592:
559:
524:
444:
417:
415:{\displaystyle E_{c}}
390:
388:{\displaystyle n_{0}}
363:
361:{\displaystyle p_{0}}
336:
334:{\displaystyle n_{0}}
290:
248:
246:{\displaystyle n_{0}}
218:
187:
130:
110:
35:carrier concentration
2414:10.1007/10832182_196
2318:10.1007/10832182_503
1831:
1811:
1772:
1745:
1706:
1642:
1402:
1373:
1297:
1268:
1220:
1189:
1030:
903:
758:
697:
634:
623:{\displaystyle f(E)}
605:
590:{\displaystyle g(E)}
572:
557:{\displaystyle N(E)}
539:
455:
426:
399:
372:
345:
318:
257:
230:
196:
139:
119:
99:
62:thermal conductivity
2484:Solid State Physics
2369:2003JAP....93.1598A
1805:Ashcroft and Mermin
1363:reversible reaction
499:
2482:Ashcroft, Mermin.
1844:
1817:
1785:
1758:
1719:
1690:
1441:
1386:
1345:
1281:
1246:
1202:
1173:
1012:
883:
742:
676:
620:
587:
554:
519:
471:
439:
412:
385:
358:
331:
285:
243:
213:
182:
125:
105:
2423:978-3-540-42876-3
2377:10.1063/1.1529297
2327:978-3-540-42876-3
2273:
2272:
1820:{\displaystyle Z}
1801:oxidation numbers
1739:valence electrons
1737:is the number of
1731:Avogadro constant
1716:
1688:
1661:
1594:
1593:
1169:
1162:
1099:
1074:
1010:
989:
975:
941:
897:density of states
879:
872:
831:
827:
820:
736:
566:density of states
495:
436:
128:{\displaystyle N}
108:{\displaystyle V}
95:it over a volume
82:density of states
25:density of states
2570:
2542:
2541:
2540:on 27 July 2011.
2536:. Archived from
2494:
2488:
2487:
2479:
2470:
2469:
2443:
2428:
2427:
2401:
2395:
2394:
2388:
2380:
2352:
2346:
2345:
2339:
2331:
2305:
2269:
2267:
2250:
2248:
2231:
2229:
2212:
2210:
2193:
2191:
2174:
2172:
2155:
2153:
2136:
2134:
2117:
2115:
2098:
2096:
2079:
2077:
2060:
2058:
2041:
2039:
2022:
2020:
2003:
2001:
1984:
1982:
1965:
1963:
1946:
1944:
1927:
1925:
1908:
1906:
1889:
1887:
1861:
1853:
1851:
1850:
1845:
1843:
1842:
1826:
1824:
1823:
1818:
1794:
1792:
1791:
1786:
1784:
1783:
1767:
1765:
1764:
1759:
1757:
1756:
1728:
1726:
1725:
1720:
1718:
1717:
1714:
1699:
1697:
1696:
1691:
1689:
1687:
1686:
1677:
1676:
1675:
1663:
1662:
1659:
1652:
1590:
1588:
1574:
1572:
1558:
1556:
1542:
1540:
1526:
1514:
1512:
1504:Gallium Arsenide
1498:
1496:
1482:
1480:
1460:
1450:
1448:
1447:
1442:
1440:
1439:
1427:
1426:
1414:
1413:
1395:
1393:
1392:
1387:
1385:
1384:
1354:
1352:
1351:
1346:
1341:
1340:
1328:
1327:
1309:
1308:
1290:
1288:
1287:
1282:
1280:
1279:
1255:
1253:
1252:
1247:
1245:
1244:
1232:
1231:
1211:
1209:
1208:
1203:
1201:
1200:
1182:
1180:
1179:
1174:
1172:
1171:
1170:
1168:
1164:
1163:
1160:
1153:
1152:
1151:
1139:
1138:
1128:
1118:
1117:
1113:
1104:
1100:
1098:
1097:
1096:
1080:
1076:
1075:
1072:
1066:
1065:
1055:
1042:
1041:
1021:
1019:
1018:
1013:
1011:
1009:
1008:
993:
991:
990:
982:
980:
976:
974:
973:
964:
963:
962:
949:
942:
940:
939:
938:
922:
892:
890:
889:
884:
882:
881:
880:
878:
874:
873:
870:
863:
862:
861:
845:
832:
830:
829:
828:
826:
822:
821:
818:
811:
810:
809:
793:
777:
751:
749:
748:
743:
738:
737:
734:
725:
720:
719:
704:
685:
683:
682:
677:
629:
627:
626:
621:
596:
594:
593:
588:
563:
561:
560:
555:
528:
526:
525:
520:
498:
497:
496:
493:
486:
485:
484:
467:
466:
448:
446:
445:
440:
438:
437:
434:
421:
419:
418:
413:
411:
410:
394:
392:
391:
386:
384:
383:
367:
365:
364:
359:
357:
356:
340:
338:
337:
332:
330:
329:
294:
292:
291:
286:
281:
280:
252:
250:
249:
244:
242:
241:
222:
220:
219:
214:
209:
191:
189:
188:
183:
168:
157:
156:
134:
132:
131:
126:
114:
112:
111:
106:
89:particle density
33:, also known as
2578:
2577:
2573:
2572:
2571:
2569:
2568:
2567:
2563:Charge carriers
2548:
2547:
2546:
2545:
2518:10.2307/2369245
2496:
2495:
2491:
2486:. pp. 4–5.
2481:
2480:
2473:
2466:
2445:
2444:
2431:
2424:
2403:
2402:
2398:
2381:
2354:
2353:
2349:
2332:
2328:
2307:
2306:
2302:
2297:
2285:
2265:
2263:
2246:
2244:
2227:
2225:
2208:
2206:
2189:
2187:
2170:
2168:
2151:
2149:
2132:
2130:
2113:
2111:
2094:
2092:
2075:
2073:
2056:
2054:
2037:
2035:
2018:
2016:
1999:
1997:
1980:
1978:
1961:
1959:
1942:
1940:
1923:
1921:
1904:
1902:
1885:
1883:
1856:crystallography
1834:
1829:
1828:
1809:
1808:
1775:
1770:
1769:
1748:
1743:
1742:
1709:
1704:
1703:
1678:
1667:
1654:
1653:
1640:
1639:
1626:
1586:
1584:
1570:
1568:
1564:Gallium nitride
1554:
1552:
1538:
1536:
1524:
1510:
1508:
1494:
1492:
1478:
1476:
1431:
1418:
1405:
1400:
1399:
1376:
1371:
1370:
1332:
1319:
1300:
1295:
1294:
1271:
1266:
1265:
1258:conduction band
1236:
1223:
1218:
1217:
1192:
1187:
1186:
1155:
1154:
1143:
1130:
1129:
1119:
1088:
1081:
1067:
1057:
1056:
1050:
1049:
1033:
1028:
1027:
1000:
965:
954:
950:
944:
943:
930:
926:
901:
900:
865:
864:
853:
846:
836:
813:
812:
801:
794:
788:
781:
756:
755:
729:
711:
695:
694:
632:
631:
603:
602:
570:
569:
537:
536:
488:
476:
458:
453:
452:
429:
424:
423:
402:
397:
396:
375:
370:
369:
348:
343:
342:
321:
316:
315:
308:chemical doping
300:
272:
255:
254:
233:
228:
227:
194:
193:
148:
137:
136:
135:in that volume
117:
116:
97:
96:
74:
39:charge carriers
28:
17:
12:
11:
5:
2576:
2574:
2566:
2565:
2560:
2550:
2549:
2544:
2543:
2489:
2471:
2464:
2429:
2422:
2396:
2347:
2326:
2299:
2298:
2296:
2293:
2284:
2281:
2271:
2270:
2261:
2258:
2252:
2251:
2242:
2239:
2233:
2232:
2223:
2220:
2214:
2213:
2204:
2201:
2195:
2194:
2185:
2182:
2176:
2175:
2166:
2163:
2157:
2156:
2147:
2144:
2138:
2137:
2128:
2125:
2119:
2118:
2109:
2106:
2100:
2099:
2090:
2087:
2081:
2080:
2071:
2068:
2062:
2061:
2052:
2049:
2043:
2042:
2033:
2030:
2024:
2023:
2014:
2011:
2005:
2004:
1995:
1992:
1986:
1985:
1976:
1973:
1967:
1966:
1957:
1954:
1948:
1947:
1938:
1935:
1929:
1928:
1919:
1916:
1910:
1909:
1900:
1897:
1891:
1890:
1881:
1878:
1872:
1871:
1868:
1865:
1841:
1837:
1816:
1782:
1778:
1755:
1751:
1712:
1685:
1681:
1674:
1670:
1666:
1657:
1650:
1647:
1625:
1622:
1600:. Then, since
1592:
1591:
1582:
1576:
1575:
1566:
1560:
1559:
1550:
1544:
1543:
1534:
1528:
1527:
1522:
1516:
1515:
1506:
1500:
1499:
1490:
1484:
1483:
1474:
1468:
1467:
1464:
1438:
1434:
1430:
1425:
1421:
1417:
1412:
1408:
1383:
1379:
1344:
1339:
1335:
1331:
1326:
1322:
1318:
1315:
1312:
1307:
1303:
1278:
1274:
1243:
1239:
1235:
1230:
1226:
1214:effective mass
1199:
1195:
1167:
1158:
1150:
1146:
1142:
1137:
1133:
1126:
1122:
1116:
1112:
1108:
1103:
1095:
1091:
1087:
1084:
1079:
1070:
1064:
1060:
1053:
1048:
1045:
1040:
1036:
1007:
1003:
999:
996:
988:
985:
979:
972:
968:
961:
957:
953:
947:
937:
933:
929:
925:
920:
917:
914:
911:
908:
877:
868:
860:
856:
852:
849:
843:
839:
835:
825:
816:
808:
804:
800:
797:
791:
787:
784:
780:
775:
772:
769:
766:
763:
741:
732:
728:
724:
718:
714:
710:
707:
703:
675:
672:
669:
666:
663:
660:
657:
654:
651:
648:
645:
642:
639:
619:
616:
613:
610:
586:
583:
580:
577:
553:
550:
547:
544:
518:
515:
511:
508:
505:
502:
491:
483:
479:
474:
470:
465:
461:
432:
409:
405:
382:
378:
355:
351:
328:
324:
304:semiconductors
299:
298:Semiconductors
296:
284:
279:
275:
271:
268:
265:
262:
240:
236:
212:
208:
204:
201:
181:
178:
175:
171:
167:
163:
160:
155:
151:
147:
144:
124:
104:
73:
70:
21:charge density
15:
13:
10:
9:
6:
4:
3:
2:
2575:
2564:
2561:
2559:
2556:
2555:
2553:
2539:
2535:
2531:
2527:
2523:
2519:
2515:
2512:(3): 287–92.
2511:
2507:
2503:
2499:
2493:
2490:
2485:
2478:
2476:
2472:
2467:
2465:9780128114070
2461:
2457:
2453:
2449:
2442:
2440:
2438:
2436:
2434:
2430:
2425:
2419:
2415:
2411:
2407:
2400:
2397:
2392:
2386:
2378:
2374:
2370:
2366:
2362:
2358:
2351:
2348:
2343:
2337:
2329:
2323:
2319:
2315:
2311:
2304:
2301:
2294:
2292:
2290:
2282:
2280:
2278:
2262:
2259:
2257:
2254:
2253:
2243:
2240:
2238:
2235:
2234:
2224:
2221:
2219:
2216:
2215:
2205:
2202:
2200:
2197:
2196:
2186:
2183:
2181:
2178:
2177:
2167:
2164:
2162:
2159:
2158:
2148:
2145:
2143:
2140:
2139:
2129:
2126:
2124:
2121:
2120:
2110:
2107:
2105:
2102:
2101:
2091:
2088:
2086:
2083:
2082:
2072:
2069:
2067:
2064:
2063:
2053:
2050:
2048:
2045:
2044:
2034:
2031:
2029:
2026:
2025:
2015:
2012:
2010:
2007:
2006:
1996:
1993:
1991:
1988:
1987:
1977:
1974:
1972:
1969:
1968:
1958:
1955:
1953:
1950:
1949:
1939:
1936:
1934:
1931:
1930:
1920:
1917:
1915:
1912:
1911:
1901:
1898:
1896:
1893:
1892:
1882:
1879:
1877:
1874:
1873:
1869:
1866:
1863:
1862:
1859:
1857:
1839:
1835:
1814:
1806:
1802:
1798:
1780:
1776:
1753:
1749:
1740:
1736:
1732:
1710:
1700:
1683:
1679:
1672:
1668:
1664:
1655:
1648:
1645:
1637:
1635:
1631:
1623:
1621:
1619:
1615:
1611:
1607:
1603:
1599:
1583:
1581:
1578:
1577:
1567:
1565:
1562:
1561:
1551:
1549:
1546:
1545:
1535:
1533:
1530:
1529:
1523:
1521:
1518:
1517:
1507:
1505:
1502:
1501:
1491:
1489:
1486:
1485:
1475:
1473:
1470:
1469:
1465:
1462:
1461:
1458:
1456:
1451:
1436:
1432:
1428:
1423:
1419:
1415:
1410:
1406:
1397:
1381:
1377:
1368:
1364:
1360:
1355:
1337:
1333:
1329:
1324:
1320:
1313:
1310:
1305:
1301:
1292:
1276:
1272:
1263:
1259:
1241:
1237:
1233:
1228:
1224:
1215:
1197:
1193:
1183:
1165:
1156:
1148:
1144:
1140:
1135:
1131:
1124:
1120:
1114:
1110:
1106:
1101:
1093:
1085:
1082:
1077:
1068:
1062:
1058:
1051:
1046:
1043:
1038:
1034:
1025:
1022:
1005:
1001:
997:
994:
986:
983:
977:
970:
959:
955:
951:
945:
935:
931:
927:
923:
918:
912:
906:
898:
893:
875:
866:
858:
854:
850:
847:
841:
837:
833:
823:
814:
806:
802:
798:
795:
789:
785:
782:
778:
773:
767:
761:
753:
739:
730:
726:
716:
712:
708:
705:
692:
686:
670:
664:
658:
652:
649:
643:
637:
614:
608:
600:
581:
575:
567:
548:
542:
534:
529:
516:
513:
506:
500:
489:
481:
477:
472:
468:
463:
459:
450:
430:
407:
403:
380:
376:
353:
349:
326:
322:
313:
309:
305:
297:
295:
282:
277:
273:
269:
266:
263:
260:
238:
234:
224:
199:
179:
176:
173:
158:
153:
149:
145:
142:
122:
102:
94:
90:
85:
83:
79:
71:
69:
67:
66:covalent bond
63:
59:
54:
52:
48:
44:
40:
36:
32:
26:
22:
2538:the original
2509:
2505:
2492:
2483:
2447:
2405:
2399:
2385:cite journal
2360:
2356:
2350:
2309:
2303:
2286:
2274:
1734:
1701:
1638:
1627:
1617:
1613:
1605:
1601:
1597:
1595:
1452:
1398:
1356:
1293:
1184:
1026:
1023:
894:
754:
687:
530:
451:
301:
225:
86:
75:
55:
34:
30:
29:
2363:(3): 1598.
2289:Hall effect
2283:Measurement
2277:Hall effect
1797:atomic mass
1634:Drude model
1262:Fermi level
312:band theory
93:integrating
78:integrating
72:Calculation
2552:Categories
2498:Edwin Hall
2295:References
2534:107500183
2336:cite book
2066:Manganese
1990:Strontium
1952:Magnesium
1933:Beryllium
1864:Material
1836:ρ
1750:ρ
1669:ρ
1472:Germanium
1463:Material
1330:−
1234:−
1198:∗
1141:−
1125:−
1090:ℏ
1086:π
1063:∗
998:−
967:ℏ
960:∗
932:π
851:−
842:−
834:≈
799:−
727:≫
709:−
473:∫
270:⋅
150:∫
2500:(1879).
2256:Antimony
2180:Thallium
2123:Aluminum
1260:and the
533:fermions
310:. Using
47:SI units
2558:Density
2526:2369245
2365:Bibcode
2237:Bismuth
2142:Gallium
2104:Cadmium
2028:Niobium
1971:Calcium
1795:is the
1729:is the
1580:Diamond
1488:Silicon
1359:bandgap
1212:is the
51:density
2532:
2524:
2462:
2420:
2324:
2161:Indium
2009:Barium
1895:Silver
1876:Copper
1858:data.
1702:Where
1630:metals
1624:Metals
1548:4H-SiC
1532:6H-SiC
1520:3C-SiC
192:where
43:volume
2530:S2CID
2522:JSTOR
1616:>
1604:>
1185:Here
91:, so
45:. In
2460:ISBN
2418:ISBN
2391:link
2342:link
2322:ISBN
2264:1.65
2245:1.41
2226:1.32
2218:Lead
2207:1.48
2188:1.05
2169:1.15
2150:1.54
2131:1.81
2112:9.27
2093:1.32
2085:Zinc
2074:1.65
2055:1.70
2047:Iron
2036:5.56
2017:3.15
1998:3.55
1979:4.61
1960:8.61
1941:2.47
1922:5.90
1914:Gold
1903:5.86
1884:8.47
1493:9.65
1477:2.33
899:is:
80:the
41:per
2514:doi
2452:doi
2410:doi
2373:doi
2314:doi
2199:Tin
1585:1.6
1569:1.9
1553:8.2
1537:2.3
1509:2.1
494:top
435:top
2554::
2528:.
2520:.
2508:.
2504:.
2474:^
2458:.
2432:^
2416:.
2387:}}
2383:{{
2371:.
2361:93
2359:.
2338:}}
2334:{{
2320:.
2268:10
2260:5
2249:10
2241:5
2230:10
2222:4
2211:10
2203:4
2192:10
2184:3
2173:10
2165:3
2154:10
2146:3
2135:10
2127:3
2116:10
2108:2
2097:10
2089:2
2078:10
2070:2
2059:10
2051:2
2040:10
2032:1
2021:10
2013:2
2002:10
1994:2
1983:10
1975:2
1964:10
1956:2
1945:10
1937:2
1926:10
1918:1
1907:10
1899:1
1888:10
1880:1
1741:,
1733:,
1589:10
1573:10
1557:10
1541:10
1525:10
1513:10
1497:10
1481:10
1291::
601:,
568:,
449:.
68:.
2516::
2510:2
2468:.
2454::
2426:.
2412::
2393:)
2379:.
2375::
2367::
2344:)
2330:.
2316::
2266:Ă—
2247:Ă—
2228:Ă—
2209:Ă—
2190:Ă—
2171:Ă—
2152:Ă—
2133:Ă—
2114:Ă—
2095:Ă—
2076:Ă—
2057:Ă—
2038:Ă—
2019:Ă—
2000:Ă—
1981:Ă—
1962:Ă—
1943:Ă—
1924:Ă—
1905:Ă—
1886:Ă—
1840:m
1815:Z
1781:a
1777:m
1754:m
1735:Z
1715:A
1711:N
1684:a
1680:m
1673:m
1665:Z
1660:A
1656:N
1649:=
1646:n
1618:n
1614:p
1606:p
1602:n
1598:n
1587:Ă—
1571:Ă—
1555:Ă—
1539:Ă—
1511:Ă—
1495:Ă—
1479:Ă—
1437:0
1433:p
1429:=
1424:0
1420:n
1416:=
1411:i
1407:n
1382:i
1378:n
1343:)
1338:f
1334:E
1325:c
1321:E
1317:(
1314:2
1311:=
1306:g
1302:E
1277:g
1273:E
1242:f
1238:E
1229:c
1225:E
1194:m
1166:T
1161:B
1157:k
1149:f
1145:E
1136:c
1132:E
1121:e
1115:2
1111:/
1107:3
1102:)
1094:2
1083:2
1078:T
1073:B
1069:k
1059:m
1052:(
1047:2
1044:=
1039:0
1035:n
1006:0
1002:E
995:E
987:2
984:3
978:)
971:2
956:m
952:2
946:(
936:2
928:2
924:1
919:=
916:)
913:E
910:(
907:g
876:T
871:B
867:k
859:f
855:E
848:E
838:e
824:T
819:B
815:k
807:f
803:E
796:E
790:e
786:+
783:1
779:1
774:=
771:)
768:E
765:(
762:f
740:T
735:B
731:k
723:|
717:f
713:E
706:E
702:|
674:)
671:E
668:(
665:f
662:)
659:E
656:(
653:g
650:=
647:)
644:E
641:(
638:N
618:)
615:E
612:(
609:f
585:)
582:E
579:(
576:g
552:)
549:E
546:(
543:N
517:E
514:d
510:)
507:E
504:(
501:N
490:E
482:c
478:E
469:=
464:0
460:n
431:E
408:c
404:E
381:0
377:n
354:0
350:p
327:0
323:n
283:.
278:0
274:n
267:V
264:=
261:N
239:0
235:n
211:)
207:r
203:(
200:n
180:.
177:V
174:d
170:)
166:r
162:(
159:n
154:V
146:=
143:N
123:N
103:V
27:.
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