1、Semiconductor Physics and Devices: Basic Principles, 4th edition Chapter 7By D. A. Neamen Problem Solutions_1Chapter 77.12lnidatbiNV(a)(i) 21055.l059.biV61(ii) 21065.ln2.biV70(iii) 21075.l59.biV31(b)(i) 21057.ln0259.biV731(ii) 210675.l.biV90(iii) 21077.ln2.biV85_7.2Si: cm10.in3Ge: cm42GaAs: cm68.i 3
2、and V2lnidatbiNV0259.t(a) cm , cm 140d317a3Then Si: V65.biGe: VGaAs: V.i(b) cm , cm1605dN31605aN3Si: V78.biGe: V9GaAs: V2.i(c) cm , cm170d3170a3Si: V84.biGe: VGaAs: V2.i_7.3(a) Silicon ( K)30T2105.ln29.dabi NVFor cm ; V14daN346.bi; V75; V1609.0; V781(b) GaAs ( K)3T260.1ln259.dabi NVFor cm ; V4daN397
3、.bi; V541; V1662.; V708(c) Silicon (400 K), 3.kTcm120in3For cm ; V14daN5.bi; V5047; V1662.; V730GaAs(400 K), cm92.3inFor cm ; V140daN71.bi; V58; V1603.; V79_Semiconductor Physics and Devices: Basic Principles, 4th edition Chapter 7By D. A. Neamen Problem Solutions_27.4(a) n-sideidFinNkTEl105.l0259.o
4、reV34.FiEp-sideiai nNkTl1075.l029.oreV4.FiE(b)07329biVorV6.i(c)2lnidatbiN21057.l059.orV736.bi(d)2/12dadbisn Nex19406.736.85712/15175orcm m4026.nx26.Now194.73.8571p2/15171700orcm m41023.px213.We havesndxeNmax1451908.726.06. orV/cm4max2.3_7.5(a) n-sideidFinNkTEl1065.2l09.oreV36.FiEp-sideiai nNkTl1065.
5、2l09.oreV36.FiE(b)50biVorV7.i(c)2lnidatbiN210665.l09.orV73.bi(d)2/12dadbisn NexSemiconductor Physics and Devices: Basic Principles, 4th edition Chapter 7By D. A. Neamen Problem Solutions_319406.735.857122/1616102orcm m405.nx5.By symmetrycm m1.p.NowsndxeNmax144619085.737206. orV/cm4max5._7.6(b) kTEnN
6、Fiidexp0259.3615.0or cmd698kTEnNFiiaexp0259.315.0or cma2(c) 21065.8ln059.biVV6_7.7200 K; ; cm0172.kT38.in300 K; ; cm596103400 K; ; cm34. 9.iFor 200 K;216158.4ln01726.biVV5For 300 K;2611508.4ln0259.biVV17For 400 K;29161508.34ln0345.biV21_7.8pnnxWx5.0.p27503adnNxnpdxSo 3(a) 2105.l029.dabiV210.3ln.71.
7、aNor 59.7exp05.3212aNwhich yields cm16.a3cm3d2/12dadbisn NeVx19406.7.85712/15.43cm6109.nxor m194.70.8572p2/156.43cm51097.2or mpxSemiconductor Physics and Devices: Basic Principles, 4th edition Chapter 7By D. A. Neamen Problem Solutions_4NowsndxeNmax144619085.793.3206. V/cm4.(b) From part (a), we can
8、 write0259.exp1.3262aNwhich yields cm178a3cm64.d19065132nx2/1527.84cm51032.or mnx1946.0.p2/1527.843cm51097.or mpxsndeNma144619085.332.206. V/cm4._7.9(a) 21056.ln0259.biVorV63.bi(b)2/12dadbisn Nex19406.35.857122/15165orcm m41086.nx8.Now2/12dadbisp NeV19406.35.85712/1516orcm m41086.px84.(c)sndxeNmax14
9、51908.7606.orV/cm4max3._7.10(a) 210675.4ln029.biVV83(b) increases as temperature decreases biAt K, we can writeT21025.in0259.1exp4.8199K6At K, eV27T0278.k31919048. ni2478.exp038115496.2.So 2078inSemiconductor Physics and Devices: Basic Principles, 4th edition Chapter 7By D. A. Neamen Problem Solutio
10、ns_5Then 196708.24ln0247.biVV89We find%30biii08.218.249_7.112lnidatbiNV2151604l3059.0. inTUsing the procedure from Problem 7.10, we can write, for K,2102.in0259.1exp4.8199K65.4At K,30T21056.ln29.biVV68For V, K50.bi 3TAt K, eV3T87.kAlso319192 046.4in287.exp2410.Then2415160.ln387.biVV V5065_7.12(b) Fo
11、r cm ,160dN3idFinkTEl1065.l029.oreV347.FiEFor cm15dN105.ln029.FioreV87.iEThen26034biVorV59.i_7.13(a) 2lnidatbiN21065.l09.orV456.bi(b)1940.56.8712nx2/161260orcm71043.2nx(c)1946.56.08p2/1612orcm3104.2pxSemiconductor Physics and Devices: Basic Principles, 4th edition Chapter 7By D. A. Neamen Problem So
12、lutions_6(d)sndxeNmax147619085.732.orV/cm2max.3_7.14Assume silicon, so2/1dsDNekTL2/12199406. 06.5.857. dor/5.1dDNL(a) cm , m408d3147.0DL(b) cm , m162. 26(c) cm , m7d35.Now(a) V4.0bi(b) V826(c) V91.iAlso19406.57binx2/11778ddNNThen(a) m096.1nx(b) m27(c) m3.Now(a) 10.nDxL(b) 267.(c) 1.0nDxL_7.152/1max2
13、dasbiNeVWe find714910.3085.716s(a)(i) For , ; VaNd65.bi(ii) ; V15940(iii) ; V673.(iv) ; V78(i) For ,170aN; V/cm4dmax4103.(ii) ; V/cm156(iii) ; V/cm64.(iv) ; V/cm702(b)(i) For , ; V14aN14d561.0bi(ii) ; V57(iii) ; V16.(iv) ; V73(i) For ,140aN; V/cmd 4max10265.(ii) ; V/cm 1538(iii) ; V/cm64.(iv) ; V/cm
14、70(c) increases as the doping increases, maxand the electric field extends further into the low-doped side of the pn junction._7.16(a) 21056.ln0259.biVV67(b)/1daRbisNeWSemiconductor Physics and Devices: Basic Principles, 4th edition Chapter 7By D. A. Neamen Problem Solutions_7(i) For ,0RV1946.76.085
15、712W2/1516cm51042.9or m(ii) For V,RV19406.57.87.W2/1516cm410738.2or m(c) WVRbiax(i)For , 0RV/cm44max 103.1952.67(ii)For V,RVV/cm44ax5.0738._7.17(a) 210675.4ln029.biVV81(b)2/12dadRbisn Nex19406.5.8.587.12/16171424cm40987.or mnx2/12dadRbisp NeV19406.5.28.587.12/161717424cm609.5or mpx2/1daRbisNeVW19406
16、.5.8.587.122/161742cm40358.or mWAlso m358.pnx(c) 4max 1022VRbiV/cm510.(d) 2/2daRbisNeAC5.2801.76.1014942/16174F12078.5or pFC_7.18(a) 2lnidatbiNV280lidtWe find tbiidVnNexp20259.7415.20376Semiconductor Physics and Devices: Basic Principles, 4th edition Chapter 7By D. A. Neamen Problem Solutions_8cm150
17、684.2dN3cm7a(b) 2/1dadRbisn NeVx19406.7.857.122/1517084.24. cm2.or m6nx2/1dadRbisp NeV19406.7.857.122/1517084.24. cm683.2or m0px(c) WVRbima410283.6.7V/cm49(d) 2/2 daRbisNVeC1074.85.6.114192/15176.2.2F/cm9054C_7.19(a) abiabiNV322lnlniadtidt N22ll3iadtiadt3ln0259.3lntVV84.(b)/1RbiasNeCSo 732.32/1aa(c)
18、 For a larger doping, the space charge width narrows which results in a larger capacitance._7.20(a) 21075.4ln0259.biVorV76.biNow2/1max2dasRbi Neor14925085.71603RbiV1714orRbiV9102.9so thatV537RbiVwhich yieldsV8.(b) 210765.4ln029biorV86.biWe have14925085.7103RbiV1716so thatV08.RbiVSemiconductor Physic
19、s and Devices: Basic Principles, 4th edition Chapter 7By D. A. Neamen Problem Solutions_9which yieldsV18.7R(c) 210775.4ln029biorV86.biWe have14925085.7103RbiV1717so thatV456.1RbiVwhich yieldsV70_7.21(a)2/12/12dBaRbiBs dAabiAsNeVWor2/1 dABaRbiBAWe findV7543.015.0ln29. 28biAVV819.0.l0. 2168biBWe find1
20、68539.574WA2/150or13.BA(b)RbiBARbiBiAVWV28139.574.or6.0BA(c)2/12/12 dBaRbiBsdAabiAsj NVC2/1 dAabiAdN2/151861650743.90or.BCj_7.22(a) We have2/12/1210 daRbisdabisj NVCor2/113.0bijFor V, we findRV0.2biiorV137bi(b)nppxWx20Semiconductor Physics and Devices: Basic Principles, 4th edition Chapter 7By D. A.
21、 Neamen Problem Solutions_10ThenadnpNx25.0Now2lidtbiVso26108.5ln09.137. aNWe can then write59.37exp25.086aNwhich yieldscm163.a3andcm507.d_7.232615108.ln0259.biVV16RbiCSo 1221bi5.06.50.2RV.1.2which yields V8R_7.24(a) 21065.4ln0259.biVV682/12 daRbisNeACRV689.02105.71.05442/16154RVC689.02(i) For ,RpF57
22、.(ii) For V,pF63.2(b) 2611508.4ln09biVV157.2/12 daRbisNeAC157.08.306.1514942/1642RVC157.0641(i) For ,pF8.(ii) For V,RpF67.2_7.2521057.ln0259.biVV743(a) 2/12 daRbisNeAC107543.8.106.814942/52F1094.C22fCLf Semiconductor Physics and Devices: Basic Principles, 4th edition Chapter 7By D. A. Neamen Problem
23、 Solutions_11261205.094. LH mH36(b)(i) For V, pFRV4.C2/130.1206.2fHz MHz594779(ii) For V, pFR4.2/130.610.2fHz MHz699_7.262/1max2sdRbiNVeLet V75.0bi(a) 21141908.756. dcm1.dN3(b) 25101419085.76. dNcm1.3d3_7.27pnp xWx200x8pn4pdndaN4(a) 2lidatbiV26108.4ln059.d2/1 daRbisNVeAC21085.3106. 494biV2/dN210724.
24、106. biVBy trial and error,cm , 15.dN3cm ,06aV.bi(b) From part (a),51724.1.00bidVNBy trial and error,cm ,1596.dN3cm ,0aV3.bi_7.28(a) 21045.ln0259.biorV74.bi(b)2/12dadbisp Nex19406.57.8712/151454orcm61032.5pxAlso2/1dadbisn NeVSemiconductor Physics and Devices: Basic Principles, 4th edition Chapter 7B
25、y D. A. Neamen Problem Solutions_1219406.57.87122/1514145orcm06.2nx(c) For m, we have3194406.8571RbiV2/1514145which becomesRbiV76029.109We findV47R_7.29An junction with cm ,pn140aN3(a) A one-sided junction and assume . ThenbiRV2/1aRspexor1492406.185705RVwhich yieldsV93R(b)dapnadnpNxxso16405ncm m4.5.
26、(c)4max10.932WVRorV/cm4ax65.7_7.30(a) 21057.ln0259.biVV73(b) /2RbidsNeACbi106.952/151408.7RbiVC132.(i) For V, F14.9(ii) For V, F3063(iii) For V, F5R147._7.31(a) 26108.ln0259. dbi NV.59.exp186dcm153.N3(b) 2/12 daRbisNVAC0.16.10. 92/1516543.85.3cm50.7A2(c) RbiV106 95122/1516543.08.5.3RbiV802.RbiV.16.4
27、V9_Semiconductor Physics and Devices: Basic Principles, 4th edition Chapter 7By D. A. Neamen Problem Solutions_137.32Plot_7.33(a) 2lnidOatbi NV(c) p-regionsasexdor1CNsaOWe haveat 0spaOpxeNx1Then for 0psaOeNn-region, xsdsdx21or21CeNsOn-region, nxsdsdx2or32CeNsOWe have at 0nxsd3so that for , we havenO
28、xeNsd2We also have at 12OxThennsdsOdeCxe2which gives2OnsdxNThen for we haveOx0221nsdsdeN_7.34(a) dxdxs2For m, 1eNSo1CeNdxsdsdAt m , 2Ox0SosdeC1ThenOsdxNAt , , so0x1402sde414598.716orV/cm02.(c) Magnitude of potential difference isdxdxeNOsd22CsLet at , then0OxsOdsd xeNeN222Then we can writeOsdxAt m1x2414519008.726. orV3.1Potential difference across the intrinsic regionSemiconductor Physics and Devices: Basic Principles, 4th edition Chapter 7By D. A. Neamen Problem Solutions_14
