360:
and neutralize opposite charges. The more bias the more neutralization (or screening of ions in the region) occurs. The carriers can be recombined to the ions but thermal energy immediately makes recombined carriers transition back as Fermi energy is in proximity. When bias is strong enough that the depletion region becomes very thin, the diffusion component of the current (through the junction interface) greatly increases and the drift component decreases. In this case, the net current flows from the P-side to the N-side. The carrier density is large (it varies exponentially with the applied bias voltage), making the junction conductive and allowing a large forward current. The mathematical description of the current is provided by the
1936:. A full derivation for the depletion width is presented in reference. This derivation is based on solving the Poisson equation in one dimension – the dimension normal to the metallurgical junction. The electric field is zero outside of the depletion width (seen in above figure) and therefore Gauss's law implies that the charge density in each region balance – as shown by the first equation in this sub-section. Treating each region separately and substituting the charge density for each region into the Poisson equation eventually leads to a result for the depletion width. This result for the depletion width is:
380:(applying a negative voltage to the P-side with respect to the N-side), the potential drop (i.e., voltage) across the depletion region increases. Essentially, majority carriers are pushed away from the junction, leaving behind more charged ions. Thus the depletion region is widened and its field becomes stronger, which increases the drift component of current (through the junction interface) and decreases the diffusion component. In this case, the net current flows from the N-side to the P-side. The carrier density (mostly, minority carriers) is small and only a very small
107:
115:
1497:
1265:
196:
electrons to the P-side and (2) recombination of electrons to holes that are diffused from the P-side. Holes in a P-side region near to the interface are also gone by a similar reason. As a result, majority charge carriers (free electrons for the N-type semiconductor, and holes for the P-type semiconductor) are depleted in the region around the junction interface, so this region is called the
1448:
1019:
75:. The only elements left in the depletion region are ionized donor or acceptor impurities. This region of uncovered positive and negative ions is called the depletion region due to the depletion of carriers in this region, leaving none to carry a current. Understanding the depletion region is key to explaining modern
1472:
region that is insulating because no mobile holes remain; only the immobile, negatively charged acceptor impurities. The greater the positive charge placed on the gate, the more positive the applied gate voltage, and the more holes that leave the semiconductor surface, enlarging the depletion region.
359:
Forward bias (applying a positive voltage to the P-side with respect to the N-side) narrows the depletion region and lowers the barrier to carrier injection (shown in the figure to the right). In more detail, majority carriers get some energy from the bias field, enabling them to go into the region
195:
in the P-side. Likewise, the diffused holes are recombined with free electrons so eliminated in the N-side. The net result is that the diffused electrons and holes are gone. In a N-side region near to the junction interface, free electrons in the conduction band are gone due to (1) the diffusion of
322:
is the hole density (number per unit volume). The electric field makes holes drift along the field direction, and for diffusion holes move in the direction of decreasing concentration, so for holes a negative current results for a positive density gradient. (If the carriers are electrons, the hole
220:
Physically speaking, charge transfer in semiconductor devices is from (1) the charge carrier drift by the electric field and (2) the charge carrier diffusion due to the spatially varying carrier concentration. In the P-side of the depletion region, where holes drift by the electric field with the
188:) compared to the N-type. Therefore, when N-doped and P-doped semiconductors are placed together to form a junction, free electrons in the N-side conduction band migrate (diffuse) into the P-side conduction band, and holes in the P-side valence band migrate into the N-side valence band.
208:
that provides a force opposing the charge diffusion. When the electric field is sufficiently strong to cease further diffusion of holes and electrons, the depletion region reaches the equilibrium. Integrating the electric field across the depletion region determines what is called the
520:
1260:{\displaystyle {\begin{aligned}x_{n}&={\sqrt {{\frac {2\epsilon _{s}}{q}}{\frac {N_{a}}{N_{d}}}{\frac {1}{N_{a}+N_{d}}}(\Delta V)}}\\x_{p}&={\sqrt {{\frac {2\epsilon _{s}}{q}}{\frac {N_{d}}{N_{a}}}{\frac {1}{N_{a}+N_{d}}}(\Delta V)}}\\\end{aligned}}}
1488:
of opposite type to the bulk semiconductor, then a spontaneous depletion region forms if the gate is electrically shorted to the substrate, in much the same manner as described for the p–n junction above. For more on this, see
123:
2449:
2182:
is the applied bias. The depletion region is not symmetrically split between the n and p regions - it will tend towards the lightly doped side. A more complete analysis would take into account that there are still
1459:. It is shown in the figure to the right, for a P-type substrate. Supposing that the semiconductor initially is charge neutral, with the charge due to holes exactly balanced by the negative charge due to
1467:
to the gate, then some positively charged holes in the semiconductor nearest the gate are repelled by the positive charge on the gate, and exit the device through the bottom contact. They leave behind a
840:
281:
204:. Due to the majority charge carrier diffusion described above, the depletion region is charged; the N-side of it is positively charged and the P-side of it is negatively charged. This creates an
1024:
410:
1818:
405:
2101:
1890:
semiconductor, respectively. This condition ensures that the net negative acceptor charge exactly balances the net positive donor charge. The total depletion width in this case is the sum
2304:
because they are oppositely charged to the holes that prevail in a P-type material. When an inversion layer forms, the depletion width ceases to expand with increase in gate charge
962:
1744:
1569:
392:
From a full depletion analysis as shown in figure 2, the charge would be approximated with a sudden drop at its limit points which in reality is gradual and is explained by
2484:
2291:
2130:
1934:
869:
308:
1431:
916:
2160:
118:
Figure 2. From Top to Bottom; Top: hole and electron concentrations through the junction; Second: charge densities; Third: electric field; Bottom: electric potential
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2232:
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1853:
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with negative sign; in some cases, both electrons and holes must be included.) When the two current components balance, as in the p–n junction depletion region at
762:
2180:
1404:
1011:
893:
782:
739:
712:
2517:
2499:
is the meter. This linearly-varying electric field leads to an electrical potential that varies quadratically in space. The energy levels, or energy bands,
2365:
2543:
172:
diffuse into regions with lower concentrations of them, much as ink diffuses into water until it is uniformly distributed. By definition, the
2684:
2570:
2300:
If the depletion width becomes wide enough, then electrons appear in a very thin layer at the semiconductor-oxide interface, called an
340:
2756:
2734:
2709:
2607:
2580:
2553:
2597:
1941:
1474:
2187:
carriers near the edges of the depletion region. This leads to an additional -2kT/q term in the last set of parentheses above.
2659:
2195:
As in p–n junctions, the governing principle here is charge neutrality. Let us assume a P-type substrate. If positive charge
793:
234:
2512:
1481:, near the surface. The above discussion applies for positive voltages low enough that an inversion layer does not form.)
2328:. This effect occurs because the electric field in the depletion layer varies linearly in space from its (maximum) value
1518:
1490:
185:
177:
515:{\displaystyle {\begin{aligned}{\frac {Q_{n}}{x_{n}}}&=qN_{d}\\{\frac {Q_{p}}{x_{p}}}&=-qN_{a}\\\end{aligned}}}
1756:
87:
2248:
20:
1379:
687:
2207:
exposing sufficient negative acceptors to exactly balance the gate charge. Supposing the dopant density to be
1460:
214:
192:
181:
173:
91:
57:
1463:
impurities. If a positive voltage now is applied to the gate, which is done by introducing positive charge
1473:(In this device there is a limit to how wide the depletion width may become. It is set by the onset of an
1383:
691:
135:
923:
364:. The low current conducted under reverse bias and the large current under forward bias is an example of
1697:
1500:
The total width of the depletion region is a function of applied reverse-bias and impurity concentration
875:
of the substance. Integrating electric field with respect to distance determines the electric potential
29:
393:
2313:
2308:. In this case, neutrality is achieved by attracting more electrons into the inversion layer. In the
1640:
are the number of ionized donors and acceptors "per unit of length", respectively. In this way, both
1478:
1434:
2462:
2459:
2108:
1893:
847:
336:
159:
106:
114:
2626:
289:
2730:
2705:
2680:
2655:
2603:
2576:
2549:
1413:
1407:
1324:
are the negative and positive depletion layer width respectively with respect to the center,
898:
715:
315:
191:
Following transfer, the diffused electrons come into contact with holes and are eliminated by
143:
151:
2761:
2135:
2331:
2210:
1858:
1831:
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1354:
1327:
1300:
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969:
662:
635:
608:
581:
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527:
131:
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are the distance for negative and positive charge respectively with zero at the center,
966:
The final equation would then be arranged so that the function of depletion layer width
744:
2165:
1389:
996:
878:
785:
767:
724:
697:
205:
158:: in both of these cases the properties of the system do not vary in time; they are in
72:
64:
2750:
328:
169:
76:
60:
2325:
872:
397:
377:
155:
1496:
154:. It is most easily described when the junction is in thermal equilibrium or in a
110:
Figure 1. Top: p–n junction before diffusion; Bottom: After equilibrium is reached
1694:
can be viewed as doping spatial densities. If we assume full ionization and that
1485:
127:
79:
2444:{\displaystyle E_{m}={Q \over A\epsilon _{0}}=qN_{A}{w \over \epsilon _{0}},\,}
2234:
acceptors per unit volume, then charge neutrality requires the depletion width
365:
139:
1447:
1508:
says the sum of positive charges must equal the sum of negative charges:
165:
68:
95:
2677:
Introduction to
Electrical, Electronics and Communication Engineering
2309:
1456:
146:
for conduction band and valence band in n and p regions (red curves).
122:
2522:
2492:
1495:
1446:
361:
121:
113:
105:
83:
2675:
Sasikala, B; Afzal Khan; S. Pooranchandra; B. Sasikala (2005).
2132:
is the relative dielectric permittivity of the semiconductor,
578:
are the amount of negative and positive charge respectively,
2324:
Associated with the depletion layer is an effect known as
134:
decreases. Both p and n junctions are doped at a 1e15/cm3
2355:
at the gate to zero at the edge of the depletion width:
213:(also called the junction voltage or barrier voltage or
2599:
CMOS Digital
Integrated Circuits Analysis & Design
2465:
2368:
2334:
2251:
2213:
2168:
2138:
2111:
1944:
1896:
1861:
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1451:
Metal–oxide–semiconductor structure on P-type silicon
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1392:
1357:
1330:
1303:
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999:
972:
926:
901:
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850:
835:{\displaystyle E={\frac {\int D\,dx}{\epsilon _{s}}}}
796:
770:
747:
727:
700:
665:
638:
611:
584:
557:
530:
408:
292:
276:{\displaystyle {\bf {J}}=\sigma {\bf {E}}-eD\nabla p}
237:
1455:
Another example of a depletion region occurs in the
2478:
2443:
2347:
2320:Electric field in depletion layer and band bending
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150:A depletion region forms instantaneously across a
788:) creates the second graph as shown in figure 2:
2572:Digital Integrated Circuits: Analysis and Design
1813:{\displaystyle qN_{A}w_{P}\approx qN_{D}w_{N}\,}
1586:are the number of free electrons and holes, and
895:. This would also equal to the built in voltage
184:, and the P-type has an excess of holes (in the
56:, is an insulating region within a conductive,
1433:is the built-in voltage, which is usually the
2312:, this inversion layer is referred to as the
2096:{\displaystyle w\approx \left^{\frac {1}{2}}}
993:would be dependent on the electric potential
8:
2596:Sung-Mo Kang and Yusuf Leblebici (2002).
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239:
238:
236:
721:Taking the integral of the flux density
225:and diffuse with the diffusion constant
176:has an excess of free electrons (in the
98:all rely on depletion region phenomena.
2627:"Electrostatic analysis of a p-n diode"
2534:
229:, the net current density is given by
2203:, then holes are depleted to a depth
388:Determining the depletion layer width
7:
2621:
2619:
16:Insulating region in a semiconductor
2518:Metal–oxide–semiconductor structure
957:{\displaystyle V=\int Edx=\Delta V}
1739:{\displaystyle n,p\ll N_{D},N_{A}}
1564:{\displaystyle n+N_{A}=p+N_{D}\,,}
1417:
1242:
1127:
948:
902:
267:
14:
2727:Electricity, Magnetism, and Light
2652:Semiconductor Device Fundamentals
339:, the current is zero due to the
142:of ~0.59V. Observe the different
2191:Depletion width in MOS capacitor
1477:of carriers in a thin layer, or
295:
253:
240:
2700:Kittel, C; Kroemer, H. (1980).
2503:in response to this potential.
2162:is the built-in voltage, and
1248:
1239:
1133:
1124:
1:
2513:Capacitance voltage profiling
2479:{\displaystyle \epsilon _{0}}
2286:{\displaystyle Q/A=qN_{A}w\,}
2238:to satisfy the relationship:
2125:{\displaystyle \epsilon _{r}}
1929:{\displaystyle w=w_{N}+w_{P}}
1443:Formation in an MOS capacitor
864:{\displaystyle \epsilon _{s}}
2602:. McGraw–Hill Professional.
2199:is placed on gate with area
1882:are depletion widths in the
1491:polysilicon depletion effect
764:to determine electric field
88:bipolar junction transistors
2650:Pierret, Robert F. (1996).
138:level, leading to built-in
102:Formation in a p–n junction
96:variable capacitance diodes
71:away, or forced away by an
2778:
382:reverse saturation current
130:in forward bias mode, the
63:material where the mobile
21:Depletion (disambiguation)
18:
2545:The Mechatronics Handbook
2542:Robert H. Bishop (2002).
1378:are the concentration of
741:with respect to distance
303:{\displaystyle {\bf {E}}}
2757:Semiconductor structures
2725:Wayne M. Saslow (2002).
1484:If the gate material is
1426:{\displaystyle \Delta V}
911:{\displaystyle \Delta V}
221:electrical conductivity
92:field-effect transistors
2654:. pp. 209 to 216.
362:Shockley diode equation
310:is the electric field,
2569:John E. Ayers (2003).
2487: = 8.854×10 F/m,
2480:
2445:
2349:
2287:
2228:
2176:
2156:
2155:{\displaystyle V_{bi}}
2126:
2097:
1930:
1876:
1849:
1814:
1740:
1688:
1661:
1634:
1607:
1565:
1501:
1452:
1427:
1400:
1372:
1345:
1318:
1291:
1261:
1007:
987:
958:
918:as shown in Figure 2.
912:
889:
865:
836:
778:
758:
735:
708:
680:
653:
626:
599:
572:
545:
516:
318:(1.6×10 coulomb), and
304:
277:
147:
119:
111:
2481:
2446:
2350:
2348:{\displaystyle E_{m}}
2288:
2229:
2227:{\displaystyle N_{A}}
2177:
2157:
2127:
2098:
1931:
1877:
1875:{\displaystyle w_{N}}
1850:
1848:{\displaystyle w_{P}}
1815:
1741:
1689:
1687:{\displaystyle N_{A}}
1662:
1660:{\displaystyle N_{D}}
1635:
1633:{\displaystyle N_{A}}
1608:
1606:{\displaystyle N_{D}}
1566:
1499:
1450:
1428:
1401:
1373:
1371:{\displaystyle N_{d}}
1346:
1344:{\displaystyle N_{a}}
1319:
1317:{\displaystyle x_{p}}
1292:
1290:{\displaystyle x_{n}}
1262:
1008:
988:
986:{\displaystyle x_{n}}
959:
913:
890:
866:
837:
779:
759:
736:
709:
681:
679:{\displaystyle N_{d}}
654:
652:{\displaystyle N_{a}}
627:
625:{\displaystyle x_{p}}
600:
598:{\displaystyle x_{n}}
573:
571:{\displaystyle Q_{p}}
546:
544:{\displaystyle Q_{n}}
517:
305:
278:
125:
117:
109:
30:semiconductor physics
2523:Semiconductor diodes
2463:
2366:
2332:
2249:
2211:
2166:
2136:
2109:
1942:
1894:
1859:
1832:
1757:
1698:
1671:
1644:
1617:
1590:
1519:
1436:independent variable
1414:
1390:
1355:
1328:
1301:
1274:
1020:
997:
970:
924:
899:
879:
848:
794:
768:
745:
725:
698:
663:
636:
609:
582:
555:
528:
406:
290:
235:
182:P-type semiconductor
174:N-type semiconductor
50:space charge region,
19:For other uses, see
337:dynamic equilibrium
327:is replaced by the
160:dynamic equilibrium
2679:. Firewall Media.
2476:
2441:
2345:
2283:
2224:
2172:
2152:
2122:
2093:
1926:
1872:
1845:
1810:
1736:
1684:
1657:
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1502:
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1423:
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1368:
1341:
1314:
1287:
1257:
1255:
1003:
983:
954:
908:
885:
861:
832:
774:
757:{\displaystyle dx}
754:
731:
704:
686:are the amount of
676:
649:
622:
595:
568:
541:
512:
510:
394:Poisson's equation
300:
273:
180:) compared to the
148:
144:Quasi Fermi levels
120:
112:
54:space charge layer
2704:. W. H. Freeman.
2686:978-81-7008-639-0
2631:ecee.colorado.edu
2435:
2402:
2175:{\displaystyle V}
2090:
2042:
1987:
1506:charge neutrality
1504:The principle of
1399:{\displaystyle q}
1251:
1237:
1205:
1181:
1136:
1122:
1090:
1066:
1006:{\displaystyle V}
888:{\displaystyle V}
830:
777:{\displaystyle E}
734:{\displaystyle D}
707:{\displaystyle q}
694:respectively and
483:
435:
341:Einstein relation
316:elementary charge
215:contact potential
2769:
2741:
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2716:
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1193:
1184:
1182:
1177:
1176:
1175:
1162:
1160:
1151:
1150:
1137:
1123:
1121:
1120:
1119:
1107:
1106:
1093:
1091:
1089:
1088:
1079:
1078:
1069:
1067:
1062:
1061:
1060:
1047:
1045:
1036:
1035:
1012:
1010:
1009:
1004:
992:
990:
989:
984:
982:
981:
963:
961:
960:
955:
917:
915:
914:
909:
894:
892:
891:
886:
870:
868:
867:
862:
860:
859:
841:
839:
838:
833:
831:
829:
828:
819:
804:
783:
781:
780:
775:
763:
761:
760:
755:
740:
738:
737:
732:
713:
711:
710:
705:
685:
683:
682:
677:
675:
674:
658:
656:
655:
650:
648:
647:
631:
629:
628:
623:
621:
620:
604:
602:
601:
596:
594:
593:
577:
575:
574:
569:
567:
566:
550:
548:
547:
542:
540:
539:
521:
519:
518:
513:
511:
507:
506:
484:
482:
481:
472:
471:
462:
456:
455:
436:
434:
433:
424:
423:
414:
396:. The amount of
343:, which relates
309:
307:
306:
301:
299:
298:
282:
280:
279:
274:
257:
256:
244:
243:
211:built-in voltage
198:depletion region
34:depletion region
2777:
2776:
2772:
2771:
2770:
2768:
2767:
2766:
2747:
2746:
2745:
2744:
2737:
2724:
2723:
2719:
2712:
2702:Thermal Physics
2699:
2698:
2694:
2687:
2674:
2673:
2669:
2662:
2649:
2648:
2644:
2635:
2633:
2625:
2624:
2617:
2610:
2595:
2594:
2590:
2583:
2568:
2567:
2563:
2556:
2541:
2540:
2536:
2531:
2509:
2466:
2461:
2460:
2425:
2410:
2391:
2387:
2369:
2364:
2363:
2335:
2330:
2329:
2322:
2302:inversion layer
2269:
2247:
2246:
2214:
2209:
2208:
2193:
2164:
2163:
2139:
2134:
2133:
2112:
2107:
2106:
2053:
2052:
2048:
2031:
2021:
2020:
2009:
1996:
1995:
1989:
1973:
1963:
1959:
1956:
1952:
1951:
1940:
1939:
1916:
1903:
1892:
1891:
1862:
1857:
1856:
1835:
1830:
1829:
1799:
1789:
1773:
1763:
1755:
1754:
1726:
1713:
1696:
1695:
1674:
1669:
1668:
1647:
1642:
1641:
1620:
1615:
1614:
1593:
1588:
1587:
1547:
1528:
1517:
1516:
1475:inversion layer
1461:acceptor doping
1445:
1412:
1411:
1408:electron charge
1388:
1387:
1358:
1353:
1352:
1331:
1326:
1325:
1304:
1299:
1298:
1277:
1272:
1271:
1268:
1254:
1253:
1226:
1213:
1212:
1195:
1185:
1167:
1163:
1152:
1142:
1139:
1138:
1111:
1098:
1097:
1080:
1070:
1052:
1048:
1037:
1027:
1018:
1017:
995:
994:
973:
968:
967:
922:
921:
897:
896:
877:
876:
851:
846:
845:
820:
805:
792:
791:
766:
765:
743:
742:
723:
722:
716:electron charge
696:
695:
666:
661:
660:
639:
634:
633:
612:
607:
606:
585:
580:
579:
558:
553:
552:
531:
526:
525:
509:
508:
498:
485:
473:
463:
458:
457:
447:
437:
425:
415:
404:
403:
390:
374:
357:
288:
287:
233:
232:
178:conduction band
132:depletion width
104:
65:charge carriers
46:junction region
38:depletion layer
24:
17:
12:
11:
5:
2775:
2773:
2765:
2764:
2759:
2749:
2748:
2743:
2742:
2735:
2717:
2710:
2692:
2685:
2667:
2660:
2642:
2615:
2608:
2588:
2581:
2561:
2554:
2533:
2532:
2530:
2527:
2526:
2525:
2520:
2515:
2508:
2505:
2473:
2469:
2456:
2455:
2454:
2453:
2452:
2451:
2439:
2432:
2428:
2424:
2417:
2413:
2409:
2406:
2398:
2394:
2390:
2386:
2381:
2376:
2372:
2342:
2338:
2321:
2318:
2298:
2297:
2296:
2295:
2294:
2293:
2281:
2276:
2272:
2268:
2265:
2262:
2258:
2254:
2221:
2217:
2192:
2189:
2171:
2149:
2146:
2142:
2119:
2115:
2089:
2086:
2080:
2075:
2071:
2068:
2063:
2060:
2056:
2051:
2046:
2038:
2034:
2028:
2024:
2016:
2012:
2008:
2003:
1999:
1992:
1986:
1980:
1976:
1970:
1966:
1962:
1955:
1950:
1947:
1923:
1919:
1915:
1910:
1906:
1902:
1899:
1869:
1865:
1842:
1838:
1826:
1825:
1824:
1823:
1822:
1821:
1806:
1802:
1796:
1792:
1788:
1785:
1780:
1776:
1770:
1766:
1762:
1733:
1729:
1725:
1720:
1716:
1712:
1709:
1706:
1703:
1681:
1677:
1654:
1650:
1627:
1623:
1600:
1596:
1576:
1575:
1574:
1573:
1572:
1571:
1560:
1554:
1550:
1546:
1543:
1540:
1535:
1531:
1527:
1524:
1444:
1441:
1422:
1419:
1395:
1386:respectively,
1365:
1361:
1338:
1334:
1311:
1307:
1284:
1280:
1250:
1247:
1244:
1241:
1233:
1229:
1225:
1220:
1216:
1211:
1202:
1198:
1192:
1188:
1180:
1174:
1170:
1166:
1158:
1155:
1153:
1149:
1145:
1141:
1140:
1135:
1132:
1129:
1126:
1118:
1114:
1110:
1105:
1101:
1096:
1087:
1083:
1077:
1073:
1065:
1059:
1055:
1051:
1043:
1040:
1038:
1034:
1030:
1026:
1025:
1015:
1002:
980:
976:
953:
950:
947:
944:
941:
938:
935:
932:
929:
907:
904:
884:
858:
854:
827:
823:
818:
815:
811:
808:
802:
799:
773:
753:
750:
730:
703:
673:
669:
646:
642:
619:
615:
592:
588:
565:
561:
538:
534:
505:
501:
497:
494:
491:
488:
486:
480:
476:
470:
466:
460:
459:
454:
450:
446:
443:
440:
438:
432:
428:
422:
418:
412:
411:
400:would then be
389:
386:
373:
370:
356:
353:
297:
272:
269:
266:
263:
260:
255:
250:
247:
242:
206:electric field
202:depletion zone
103:
100:
73:electric field
42:depletion zone
36:, also called
15:
13:
10:
9:
6:
4:
3:
2:
2774:
2763:
2760:
2758:
2755:
2754:
2752:
2738:
2736:0-12-619455-6
2732:
2728:
2721:
2718:
2713:
2711:0-7167-1088-9
2707:
2703:
2696:
2693:
2688:
2682:
2678:
2671:
2668:
2663:
2657:
2653:
2646:
2643:
2632:
2628:
2622:
2620:
2616:
2611:
2609:0-07-246053-9
2605:
2601:
2600:
2592:
2589:
2584:
2582:0-8493-1951-X
2578:
2575:. CRC Press.
2574:
2573:
2565:
2562:
2557:
2555:0-8493-0066-5
2551:
2548:. CRC Press.
2547:
2546:
2538:
2535:
2528:
2524:
2521:
2519:
2516:
2514:
2511:
2510:
2506:
2504:
2502:
2498:
2494:
2490:
2486:
2471:
2467:
2437:
2430:
2426:
2422:
2415:
2411:
2407:
2404:
2396:
2392:
2388:
2384:
2379:
2374:
2370:
2362:
2361:
2360:
2359:
2358:
2357:
2356:
2340:
2336:
2327:
2319:
2317:
2315:
2311:
2307:
2303:
2279:
2274:
2270:
2266:
2263:
2260:
2256:
2252:
2245:
2244:
2243:
2242:
2241:
2240:
2239:
2237:
2219:
2215:
2206:
2202:
2198:
2190:
2188:
2186:
2169:
2147:
2144:
2140:
2117:
2113:
2103:
2087:
2084:
2078:
2073:
2069:
2066:
2061:
2058:
2054:
2049:
2044:
2036:
2032:
2026:
2022:
2014:
2010:
2006:
2001:
1997:
1990:
1984:
1978:
1974:
1968:
1964:
1960:
1953:
1948:
1945:
1937:
1921:
1917:
1913:
1908:
1904:
1900:
1897:
1889:
1885:
1867:
1863:
1840:
1836:
1804:
1800:
1794:
1790:
1786:
1783:
1778:
1774:
1768:
1764:
1760:
1753:
1752:
1751:
1750:
1749:
1748:
1747:
1731:
1727:
1723:
1718:
1714:
1710:
1707:
1704:
1701:
1679:
1675:
1652:
1648:
1625:
1621:
1598:
1594:
1585:
1581:
1558:
1552:
1548:
1544:
1541:
1538:
1533:
1529:
1525:
1522:
1515:
1514:
1513:
1512:
1511:
1510:
1509:
1507:
1498:
1494:
1492:
1487:
1482:
1480:
1476:
1471:
1466:
1462:
1458:
1457:MOS capacitor
1449:
1442:
1440:
1438:
1437:
1420:
1409:
1393:
1385:
1381:
1363:
1359:
1336:
1332:
1309:
1305:
1282:
1278:
1267:
1245:
1231:
1227:
1223:
1218:
1214:
1209:
1200:
1196:
1190:
1186:
1178:
1172:
1168:
1164:
1156:
1154:
1147:
1143:
1130:
1116:
1112:
1108:
1103:
1099:
1094:
1085:
1081:
1075:
1071:
1063:
1057:
1053:
1049:
1041:
1039:
1032:
1028:
1014:
1000:
978:
974:
964:
951:
945:
942:
939:
936:
933:
930:
927:
919:
905:
882:
874:
856:
852:
842:
825:
821:
816:
813:
809:
806:
800:
797:
789:
787:
771:
751:
748:
728:
719:
717:
701:
693:
689:
671:
667:
644:
640:
617:
613:
590:
586:
563:
559:
536:
532:
522:
503:
499:
495:
492:
489:
487:
478:
474:
468:
464:
452:
448:
444:
441:
439:
430:
426:
420:
416:
401:
399:
395:
387:
385:
383:
379:
371:
369:
367:
366:rectification
363:
354:
352:
350:
346:
342:
338:
334:
330:
326:
321:
317:
313:
284:
270:
264:
261:
258:
248:
245:
230:
228:
224:
218:
216:
212:
207:
203:
199:
194:
193:recombination
189:
187:
183:
179:
175:
171:
167:
163:
161:
157:
153:
145:
141:
137:
133:
129:
124:
116:
108:
101:
99:
97:
93:
89:
85:
81:
78:
77:semiconductor
74:
70:
66:
62:
61:semiconductor
59:
55:
51:
47:
43:
39:
35:
31:
26:
22:
2729:. Elsevier.
2726:
2720:
2701:
2695:
2676:
2670:
2651:
2645:
2634:. Retrieved
2630:
2598:
2591:
2571:
2564:
2544:
2537:
2500:
2496:
2488:
2457:
2326:band bending
2323:
2305:
2301:
2299:
2235:
2204:
2200:
2196:
2194:
2184:
2104:
1938:
1887:
1883:
1827:
1583:
1579:
1577:
1505:
1503:
1483:
1469:
1464:
1454:
1435:
1270:In summary,
1269:
1016:
965:
920:
873:permittivity
843:
790:
720:
523:
402:
398:flux density
391:
381:
378:reverse bias
375:
372:Reverse bias
358:
355:Forward bias
348:
344:
332:
324:
319:
311:
285:
231:
226:
222:
219:
210:
201:
197:
190:
186:valence band
164:
156:steady state
152:p–n junction
149:
126:Figure 3. A
53:
49:
45:
41:
37:
33:
27:
25:
1486:polysilicon
1384:donor atoms
786:Gauss's law
692:donor atoms
128:PN junction
80:electronics
2751:Categories
2661:0201543931
2636:2018-09-26
2529:References
2468:ϵ
2427:ϵ
2393:ϵ
2114:ϵ
2067:−
1975:ϵ
1965:ϵ
1949:≈
1784:≈
1711:≪
1418:Δ
1243:Δ
1169:ϵ
1128:Δ
1054:ϵ
949:Δ
934:∫
903:Δ
853:ϵ
822:ϵ
807:∫
493:−
268:∇
259:−
249:σ
166:Electrons
140:potential
2507:See also
1746:, then:
1470:depleted
1380:acceptor
688:acceptor
331:density
329:electron
323:density
69:diffused
2762:MOSFETs
2491:is the
2314:channel
1479:channel
1406:is the
871:is the
714:is the
384:flows.
314:is the
2733:
2708:
2683:
2658:
2606:
2579:
2552:
2458:where
2310:MOSFET
2105:where
1828:where
1578:where
844:where
784:(i.e.
524:where
376:Under
286:where
136:doping
94:, and
84:diodes
32:, the
2493:farad
1855:and
170:holes
67:have
58:doped
2731:ISBN
2706:ISBN
2681:ISBN
2656:ISBN
2604:ISBN
2577:ISBN
2550:ISBN
2501:bend
2495:and
2185:some
1886:and
1667:and
1613:and
1582:and
1410:and
1382:and
1351:and
1297:and
690:and
659:and
605:and
551:and
168:and
347:to
217:).
200:or
52:or
28:In
2753::
2629:.
2618:^
2316:.
1439:.
1013:.
718:.
368:.
351:.
283:,
162:.
90:,
86:,
82::
48:,
44:,
40:,
2739:.
2714:.
2689:.
2664:.
2639:.
2612:.
2585:.
2558:.
2497:m
2489:F
2472:0
2438:,
2431:0
2423:w
2416:A
2412:N
2408:q
2405:=
2397:0
2389:A
2385:Q
2380:=
2375:m
2371:E
2341:m
2337:E
2306:Q
2280:w
2275:A
2271:N
2267:q
2264:=
2261:A
2257:/
2253:Q
2236:w
2220:A
2216:N
2205:w
2201:A
2197:Q
2170:V
2148:i
2145:b
2141:V
2118:r
2088:2
2085:1
2079:]
2074:)
2070:V
2062:i
2059:b
2055:V
2050:(
2045:)
2037:D
2033:N
2027:A
2023:N
2015:D
2011:N
2007:+
2002:A
1998:N
1991:(
1985:q
1979:0
1969:r
1961:2
1954:[
1946:w
1922:P
1918:w
1914:+
1909:N
1905:w
1901:=
1898:w
1888:n
1884:p
1868:N
1864:w
1841:P
1837:w
1820:.
1805:N
1801:w
1795:D
1791:N
1787:q
1779:P
1775:w
1769:A
1765:N
1761:q
1732:A
1728:N
1724:,
1719:D
1715:N
1708:p
1705:,
1702:n
1680:A
1676:N
1653:D
1649:N
1626:A
1622:N
1599:D
1595:N
1584:p
1580:n
1559:,
1553:D
1549:N
1545:+
1542:p
1539:=
1534:A
1530:N
1526:+
1523:n
1493:.
1465:Q
1421:V
1394:q
1364:d
1360:N
1337:a
1333:N
1310:p
1306:x
1283:n
1279:x
1249:)
1246:V
1240:(
1232:d
1228:N
1224:+
1219:a
1215:N
1210:1
1201:a
1197:N
1191:d
1187:N
1179:q
1173:s
1165:2
1157:=
1148:p
1144:x
1134:)
1131:V
1125:(
1117:d
1113:N
1109:+
1104:a
1100:N
1095:1
1086:d
1082:N
1076:a
1072:N
1064:q
1058:s
1050:2
1042:=
1033:n
1029:x
1001:V
979:n
975:x
952:V
946:=
943:x
940:d
937:E
931:=
928:V
906:V
883:V
857:s
826:s
817:x
814:d
810:D
801:=
798:E
772:E
752:x
749:d
729:D
702:q
672:d
668:N
645:a
641:N
618:p
614:x
591:n
587:x
564:p
560:Q
537:n
533:Q
504:a
500:N
496:q
490:=
479:p
475:x
469:p
465:Q
453:d
449:N
445:q
442:=
431:n
427:x
421:n
417:Q
349:σ
345:D
333:n
325:p
320:p
312:e
296:E
271:p
265:D
262:e
254:E
246:=
241:J
227:D
223:σ
23:.
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