半导体导论翻译

半导体导论 P124-125

CHAPTER 3 The Semiconductor in Equilibrium

(d) T = 400 K, Nd = 0, Na = 1014 cm-3 (e) T = 500 K, Nd = 1014 cm-3, Na = 0 3.37 Repeat problem 3.36 for GaAs.

3.38 Assume that silicon, germanium, and gallium arsenide each have dopant concentrations of Nd = 1X1013 cm-3 and Na = 2.5 x 1014 cm-3 at T=300K.For each of the three materials(a) Is this material n type or p type?(b) Calculate n0 and p0.

3.39 A sample of silicon at T =450K is doped with boron at a concentration 0f 1.5x1015 cm-3and with arsenic at a concentration of 8 X 1014 cm-3 .(a) Is the material n type or p type? (b) Determine the electron and hole concentrations .(c) Calculate the total ionized impurity concentration.

3.40 The thermal equilibrium hole concentration in silicon at T = 300 K is p0=2x1015 cm-3 .Determine the thermal-equilibrium electron concentration .Is the material n type or p type?

3.41 In a sample of GaAs at T = 200 K, we have experimentally determined that n0 = 5 p0 and that Na = 0. Calculate n0, p0, and Nd.

3.42 Consider a sample of silicon doped at Nd = 1014 cm-3 and Na = 0 Calcu1ate the majority-carrier concentration at (a) T = 300 K, (b) T = 350 K,(C ) T = 400 K (d) T = 450 K, and (e) T = 500 K.

3.43 Consider a sample of silicon doped at Nd = 0 and Na = 1014 cm-3 .Plot the majority-carrier concentration versus temperature over the range 200≤T≤500K.

3.44 The temperature of a sample of silicon is T = 300 K and the acceptor doping concentration is Na = 0. Plot the minority-carrier concentration (on a log-log plot) versus Nd over the range 1015 ≤Nd≤1018 cm-3.

3.45 Repeat problem 3.44 for GaAs.

3.46 A particular semiconductor material is doped at Nd = 2 x 1013 cm-3, Na = 0, and the intrinsic carrier concentration is ni = 2 x 1013 cm-3. Assume complete ionization. Determine the thermal-equilibrium majority-and minority-carrier concentrations.

3.47 (a) Silicon at T = 300 K is uniformly doped with arsenic atoms at a concentration of 2 x 1016 cm-3 and boron atoms at a concentration of 1 x1013 cm-3. Determine the thermal-equilibrium concentrations of majority and minority carriers. (b) Repeat part (a) if the impurity concentrations are 2 x1015 cm-3 phosphorus atoms and 3 x 1016 cm-3 boron atoms.

3.48 In silicon at T = 300 K, we have experimentally found that n0 = 4.5 x 104 cm-3and Nd =5x1015 cm-3. (a) Is the material n type or p type? (b) Determine the majority and minority-carrier concentrations. (c) What types and concentrations of impurity atoms exist in the material?

Section 3.6 Position of Fermi Energy Level

3.49 Consider germanium with an acceptor concentration of Na = 1015 cm-3 and a donor concentration of Nd = 0. Consider temperatures of T = 200, 400,and 600 K. Calculate the position of the Fermi energy with respect to the intrinsic Ferrni level at these temperatures.

3.50 Consider germanium at T = 300 K with donor concentrations of Nd = 104, 1016and1018 cm-3 .Let Na = 0. Calculate the position of the Fermi energy level with respect to the intrinsic Fermi level for these doping concentrations.

3.51 A GaAs device is doped with a donor concentration of 3X1015 cm-3 .For the device to operate properly ,the intrinsic carrier concentration must remain less than 5 percent of the total electron concentration .What is the maximum temperature that the device may operate?

3.52 Consider germanium with an concentration of Na=1015cm-3and a donor concentration of Nd=0.Plot the position of the Fermi energy with respect to the intrinsic Fermi level as a function of temperature over the range 200 ≤T ≤ 600 K.

3,53 Consider silicon at T =300K with Na=0. Plot the position of the Fermi energy with respect to the intrinsic Fermi level as a function of the donor doping concentration over the range 1014≤Nd≤1018cm-3.

3.54 For a particular semiconductor,Eg=1.50eV,m*p=10m*n，T=300K，and ni=105cm-3. (a)Determine the position of the intrinsic Fermi energy level with respect to the center of the bandgap. (b)Impurity atoms are added so that the Fermi energy level is 0.45eV below the center of the bandgap .(i)Are acceptor or donor atoms added? (ii)What is the concentration if impurity atoms added?

3.55 Silicon at T = 300 K contains acceptor atoms at a concentration of Na = 5 x1015cm-3 . Donor atoms are add forming an n-type compensated semiconductor such that the Fermi level is 0.215 eV below the conduction band edge .What concentration of donor atoms are added?

3.56 Silicon at T = 300 K is doped with acceptor atoms at a concentration of Na = 7 x1015cm-3. (a) Determine Ef-Ev. (b) Calculate the concentration of additional acceptor atoms that must be added to move the Fermi level a distance kT closer to the

valence-band edge.

3.57 (a) Determine the position of the Fermi level with respect to the intrinsic Fermi level in silicon at T = 300 K that is doped with phosphorus atoms at a concentration of 1015cm-3. (b) Repeat part (a) if the silicon is doped with boron atoms at a concentration of 1015cm-3. (c) Calculate the electron concentration in the silicon for parts (a) and (b).

3.58 Gallium arsenide at T = 300 K contains acceptor impurity atoms at a density of 1015cm-3. Additional impurity atoms are to be added so that the Fermi level is 0.45 eV below the intrinsic level. Determine the concentration and type (donor or acceptor) of impurity atoms to be added.

3.59 Determine the Fermi energy level with respect to the intrinsic Fermi level for each condition given in Problem 3.36.

3.60 Find the Fermi energy level with respect to the valence band energy for the conditions given in Problem 3.37.

3.61 Calculate the position of the Fermi energy level with respect to the intrinsic Fermi for the conditions given in Problem 3.48.

Summary and Review

3.62 A special semiconductor material is to be “designed. ” The semiconductor is to

be n type and doped with 1 x 1015 cm -3 donor atoms . Assume complete ionization and assume Na=0. The effective density of states functions are given by Nc=Nv=1.5x1019cm-3 and ate independent of temperature .A particular semiconductor device fabricated with this material requires the electron concentration to be no greater than 1.01x1019cm-3 at T=400K. What is the minimum value of the bandgap energy ? 译文

第三章 半导体的平衡

(d) T = 400 K, Nd = 0, Na = 1014 cm-3 (e) T = 500 K, Nd = 1014 cm-3, Na = 0

3.37 重复3.36砷化镓的问题

3.38 假设硅，锗，镓砷化物各有厘米的Nd = 1X10 cm掺杂浓度和Na = 2.5 ×10 cm

在T = 300K. 对于每三种材料（一）这是N型还是P型材料？（二）计算N0和P0。

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3.39 甲硅样品在T = 450K与硼掺杂浓度1.5x10 cm和砷浓度在8 ×1.5x10 cm。（a）

是n型或p物质类型？ （二）确定的电子和空穴浓度。（c）计算的总电离杂质浓度。 3.40 在硅中的热平衡孔在T = 300 K的浓度为P0 = 2x10 cm。确定热平衡电子浓度。材料是N型或P型？

3.41 在砷化镓在T = 200 K的样品，我们已经确定，N0的实验= 5 ,P0和Na= 0. 计算n0时，

P0和Nd。

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3.42 考虑一个硅样品在Nd=10 cm掺杂和Na= 0。 计算多数载流子浓度（一）当T = 300

K时，（二）T= 350 K时，（三）T= 400 K时（四）T= 450 K和（五）T= 500K。

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3.43 考虑一个硅样品在掺Nd= 0和Na =10 cm。多数载流子浓度范围内与超过200≤T

≤500K的温度。

3.44 一类硅样品的温度为T = 300 K和受体掺杂浓度为Na = 0。少数载流子浓度（以对数3.45 3.46 3.47

图）范围内与超过10≤Nd≤10 cm。 为砷化镓3.44重复问题。

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一个特殊的半导体材料掺杂Nd= 2 ×10 cm，而Na= 0，本征载流子浓度是ni = 2 x 1013 cm-3。假设完全电离。确定热平衡多数和少数载流子浓度。

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（一）硅在T = 300 K是均匀掺砷原子在一个2 ×10 cm和硼原子以1 x10 cm的浓度。确定多数与少数载流子的热平衡浓度。 （二）重复第（一）如果杂质浓度

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为2 x10 cm磷原子和3 x 10 cm硼原子。

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硅在T= 300 K，我们实验发现，n0= 4.5 × 10 cm和Nd= 5x10 cm。（a）是n型或p物质类型？ （二）确定的多数和少数载流子浓度。 （三）什么类型和浓度的杂质原子在物质中存在吗？

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3.48

第3.6节费米能级的位置

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3.49 考虑与Na= 10 cm受体浓度和Nd施主浓度= 0。考虑温度的T = 200, 400,和600 K

的温度计算费米能级的位置相对于这些内在的费米水平。 3.50 考虑锗在T = 300 K的施主浓度Nd= 10，10 和10 cm。让Na= 0。计算相对于

这些内在的费米掺杂浓度水平费米能级的位置。 3.51 砷化镓是一个掺杂了3X10 cm施主浓度。对于设备正常运作，内在载流子浓度必

须保持不少于总数的5电子浓度百分比。什么是最高温度，该装置可以操作？

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3.52 考虑浓度锗与Na=10cm和一对Nd = 0施主浓度。画出相对于费米能级位置，关

于费米能级以上的内在范围温度：T≤200≤600作为温度函数光。

3.53 考虑硅在T = 300K与Na = 0的情况下。绘制的费米能量本征费米方面作为施主掺杂在范围10≤ Nd≤10cm浓度的功能级别的地位。

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3.54 对于一个特定的半导体，如Eg=1.50eV, m*p=10m*n， T=300K， ni=10cm.

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（一）确定的内在费米就到了带隙中心的能级位置。 （二）添加杂质原子，使费米能级低于带隙中心0.45eV. （i）是否受体或施主原子加入？ （ii）什么是杂质原子的浓度增加？

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3.55 硅在T = 300 K的含有的Na = 5 x10cm浓度受体原子。供体原子形成一个添加n

型半导体，这样的补偿费米能级低于0.215 eV的导带的边缘。什么样的施主浓度增加？ 3.56 硅在T= 300 K与受体原子掺杂的Na = 7 x10cm浓度。（一）确定Ef—Ev. （b）

计算的受体必须添加到移动的距离kT的费米能级靠近价带边缘的原子浓度。

3.57 （一）确定相对于费米能级位置，在硅的内在费米= 300 K的水平是与磷原子掺杂在

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一个10cm浓度的T （二）重复第（一）如果是在一个硅的10cm浓度的硼原子掺杂。 （三）计算硅在电子浓度的（a）及（b）。 3.58 砷化镓在T = 300 K的包含了10cm密度受主杂质原子。额外的杂质原子是要添加，使费米能级为0.45电子伏特以下的内在水平。确定浓度和类型杂质原子（供体或受体）以复加。

3.59 确定与费米能级方面的内在费米水平,每一个给定的条件在第3.36个问题。 3.60 发现费米能级关于在给的条件的化学价带能量在第3.37个问题。 3.61 计算费米能级的位置关于指定的条件的内在费米在第3.48个问题。

总结和回顾

3.62 一种特殊的半导体材料是“设计的。”半导体是为n型和1 ×10cm 的施主原子

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掺杂。假设完全电离并且假设Na=0。Nc=Nv=1.5x10cm 测量有效的密度态函数并且说明和温度无关。某特定半导体器件用这种材料制作的电子浓度要求不大于1.01x1015 cm -3在T = 400K的情况下。什么是带隙能量的最小值？

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