半导体器件物理习题与参考文献 下载本文

2–23.对于下图中的P?v?N二极管,假设P和N区不承受任何外加电压,证明

2A?mqBNvWi?B?exp(?)?1?exp(?)??1 雪崩击穿的条件可表示为2qNvB??m?m?????P+ Nd?Na

v N? ? w?wi ?m

参考文献

1. Shockley, W.:Theory of p-n Junction in Semiconductors and p-n Junction Transistors,

Bell Syst.Tech.J., 28:435(1949). 2. H.Lawrence and R.M.Warner, Jr., Diffused Junction Depletion Layer Caculation, Bell

Syst.Tech.J., 39:389-403(1960).

3. B.Lax and S.F.Neustadter, Transient Response of a p-n Junction, J.Appl.Phys.,

25:1148(1954). 4. J.L.Moll and S.A.Hamilton, Physical Modelling of the Step Recovery Diode for Pulse

and Harmonic Generation Circuits., Proc.IEEE, 57:1250(1969).

5. Dimitrijev, S.Understanding Semiconductor Devices.New York: Oxford University

Press, 2000.

6. Kano, K.Semiconductor Devices.Upper Saddle River, NJ: Prentice Hall, 1998. 7. Li, S.S.Semiconductor Physical Electronics.New York: Plenum Press, 1993. 8. Muller, R.S., and T.I.Kamins.Device Electronics for Integrated Circuits.2nd ed.New

York: Wiley, 1986. 9. Navon, D.H.Semiconductor Micro-devices and Materials.New York: Holt, Rinehart &

Winston, 1986.

10. Neudeck, G.W.The PN Junction Diode.Vol.2 of the Modular Series on Solid State

11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

Devices.2nd ed.Reading, MA: Addison-Wesley, 1989.

Ng, K.K.Complete Guide to Semiconductor Devices. New York: McGraw-Hill, 1995. Pierret,R.F.Semiconductor Device Fundamentals.Reading,MA: Addison-Wesley,1996.

Roulston, D.J.An Introduction to the Physics of Semiconductor Devices.New York: Oxford University Press, 1999.

Shur, M.Introduction to Electronic Devices.New York: John Wiley and Sons, 1996. Shur, M.Physics of Semiconductor Devices.Englewood Cliffs, NJ: Prentice Hall, 1990. Singh, J.Semiconductor Devices: Basic Principles.New York: John Wiley and Sons, 2001.

Sze, S.M.Physics of Semiconductor Devices.2nd ed.New York: Wiley, 1981. Sze, S.M.Semiconductor Devices:Physics and Technology, 2nd ed.New York: John Wiley and Sons, Inc., 2001. Wang, S.Fundamentals of Semiconductor Theory and Device Physics.Englewood Cliffs, NJ: Prentice Hall, 1989.

Yang, E.S.Microelectronic Devices.New York: McGraw-Hill, 1988.

习题

3–1.(1)画出PNP晶体管在平衡时以及在正向有源工作模式下的能带图。

(2)画出晶体管的示意图并表示出所有的电流成分,写出各极电流表达式。 (3)画出发射区、基区、集电区少子分布示意图。 3–2.考虑一个NPN硅晶体管,具有这样一些参数:xB?2?m,在均匀掺杂基区

Na?5?1016cm?3,?n?1?s,A?0.01cm2。若集电结被反向偏置,InE?1mA,

计算在发射结基区一边的过量电子密度、发射结电压以及基区输运因子。 3–3. 在习题3–2的晶体管中,假设发射极的掺杂浓度为10cm,xE?2?m,

18?3?pE?10ns,发射结空间电荷区中,?0?0.1?s。计算在InE?1mA时的发射效

率和hFE。

3-4.(1)根据公式(3-19)或(3-20),证明对于任意的

变成

xBLn值,公式(3-41)和(3-43)

DnxDPE] a11??qAn[(cothB)?NaLnLnNdExE2iqADnni2xa12?a21?cschB

NaLnLn a22??qAni[

(2)证明,若

3–5.证明在有源区晶体管发射极电流–电压特性可用下式表示

2DnDPCx(cothB)?] NaLnLnNdCLPCxB。 Ln<<1,(a)中的表达式约化为(3-41)和(3-43)

IE?qAniWEVE/VTIEB0eVE/VT+e其中IE0为集电极开路时发射结反向饱和电流。

1??F?R2?0提示:首先由EM方程导出IF0?

IEB0。

1??F?R 3–6.(1)忽略空间电荷区的复合电流,证明晶体管共发射极输出特性的精确表达式为

-VCE?VTlnIR0(1??F?R)??FIB?IC(1??F)?+VTlnR

IF0(1??F?R)?IB?IC(1??R)?F提示:首先求出用电流表示结电压的显示解。

(2)若IB>>IE0且?FIB??IR0(1??F?R),证明上式化为

VCE?VTln?F?R1?R?IC/IBhFER, 其中hFEF?,hFER?.

1?IC/IBhFEF1??F1??R?xL3-7.一个用离子注入制造的NPN晶体管,其中性区内浅杂质浓度为Na?x??N0e中N0?2?10cm,l?0.3?m。

(1)求宽度为0.8?m的中性区内单位面积的杂质总量; (2)求出中性区内的平均杂质浓度;

18?3,

19?3(3)若LpE?1?m,NdE?10cm,DpE2,基区内少子平均寿命为?1cm/s10?6s,基区的平均扩散系数和(2)中的 杂质浓度相应,求共发射极电流增益。

3–8.若在公式In?qADnni2?xB0NadxeVEVT中假设IC?In,则可在集电极电流Ic ~VE曲线计

算出根梅尔数。求出图3-12中晶体管中的根梅尔数。采用Dn?35cm2/s、

A?0.1cm2以及ni?1.5?1010cm?3。

13–9.(1)证明对于均匀掺杂的基区,式?T?1?2Ln21xB?T?1?2

2LnxB1(?Na0xB?Nxadx)dx简化为

(2)若基区杂质为指数分布,即Na?N0e??xxB,推导出基区输运因子的表示式。

3-11. 基区直流扩展电阻对集电极电流的影响可表示为

Ic?I0exp???VE?IBrbb??/VT??,用公式以及示于图3-12的数据估算出rbb?

3-12.(1)推导出均匀掺杂基区晶体管的基区渡越时间表达式。假设xBLn<<1。 (2)若基区杂质分布为Na?N0e?axxB,重复(1)

3-13.硅NPN晶体管在300K具有如下参数:IE=1mA,CTE=1pF,xB?0.5?m, Dn=25cm2/S,

xm?0.5?m, rSC=2.4μm, CTC=0,1pF。求发射区-集电区渡越时间和截止频率。

3-14.若实际晶体管的基极电流增益为

, ?T???(/1+?0m)式中?T是共发射极电流增益模量为1时的频率。 3-15.(1)求出图3-23中输出短路时ioutiin的表达式。

???0e

jm?/??/(1+j

?/??),证明

(2)求出??,它相应于ioutiin的数值下降到3dB的情况。 (3)求出?T

3-17.证明均匀基区BJT穿通击穿电压可表示为:

BVBCqWB2Na(Na?Ndc) ?N2k?0dc3-18.一均匀基区硅BJT,基区宽度为0.5?m,基区杂质浓度Na?1016cm?3。若穿通电压期望值为BVBC=25V,集电区掺杂浓度为若干?如果不使集电区穿通,集电区宽度至

少应大于多少?

3-19.证明平面型双扩散晶体管的穿透电压可用下式表示

BVBC?qG?Gx??Bks?0?2NdC?? ?式中G为根梅尔数。

参考文献 1. R.Beaufoy and J.J.Sparks, The Junction Transistor as a Charge controlled Device, ATE

J.(GB), 13:310(October 1957).

2. Kano, K.Semiconductor Devices.Upper Saddle River, NJ: Prentice Hall, 1998. 3. Muller, R.S., and T.I.Kamins.Device Electronics for Integrated Circuits.2nd ed.New

York: Wiley, 1986. 4. Navon, D.H.Semiconductor Microdevices and Materials.New York: Holt, Rinehart &

Winston, 1986.

5. Neudeck, G.W.The PN Junction Diode.Vol.2 of the Modular Series on Solid State

Devices.2nd ed.Reading, MA: Addison-Wesley, 1989.

6. Ng, K.K.Complete Guide to Semiconductor Devices. New York: McGraw-Hill, 1995. 7. Ning, T.H., and R.D.lsaac.“Effect of Emitter Contact on Current Gain of Silicon

Bipolar Devices.” Polysilicon Emitter Bipolar Transistors.eds.A.K.Kapoor and D.J.Roulston.New York: IEEE Press, 1989.

8. Pierret,R.F.Semiconductor Device Fundamentals.Reading,MA: Addison-Wesley,

1996.

9. Roulston, D.J.Bipolar Semiconductor Devices.New York: McGraw-Hill, 1990 10. Roulston, D.J.An Introduction to the Physics of Semiconductor Devices.New York:

Oxford University Press, 1999.

11. Shur, M.GaAs Devices and Circuits.New York: Plenum Press, 1987.

12. Shur, M.Introduction to Electronic Devices.New York: John Wiley and Sons, 1996. 13. Shur, M.Physics of Semiconductor Devices.Englewood Cliffs, NJ: Prentice Hall, 1990.