Homework description
This is an extra exercise for Chapter 7, and you don’t need to hand in.
Exercise 5.1
(a) Consider a uniformly doped silicon pn junction at T = 300 K. At zero bias, 25 percent of the total space charge region is in the n-region. The built-in potential barrier is Vbi = 0.710 V. Determine (i)Na, (ii)Nd, (iii) xn, (iv) xp, and (v) |Emax| .
(b) Repeat part (a) for a GaAs pn junction with Vbi = 1.180 V.
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Exercise 5.2
An ”isotype” step junction is one in which the same impurity type doping changes from one concentration value to another value. An n-n isotype doping profile is shown in Figure 1.
(a) Sketch the thermal equilibrium energy-band diagram of the isotype junction. (b) Using the energy-band diagram, determine the built-in potential barrier.
(c) Discuss the charge distribution through the junction.
Figure 1: Figure for Problem 5.2
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Exercise 5.3
An ideal one-sided silicon p+n junction at T = 300 K is uniformly doped on both sides of the metallurgical junction. It is found that the doping relation is Na = 80Nd and the built-in potential barrier is Vbi = 0.740 V. A reverse-biased voltage of VR = 10 V is applied. Determine
(a)Na,Nd ; (b)xp,xn ; (c)|Emax| ; (d) Cj′.
Exercise 5.4
A silicon p+n junction has doping concentrations of Na = 2 × 1017 cm−3 and Nd = 2 × 1015 cm−3. The cross-sectional area is 10−5 cm2. Calculate
(a) Vbi
(b)thejunctioncapacitanceat( i)VR =1V,(ii)VR =3V,and(iii)VR =5V.
(c) Plot 1/C2 versus VR and show that the slope can be used to find Nd and the intercept
at the voltage axis yields Vbi.
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Exercise 5.5
A silicon pn junction at T = 300 K has the doping profile shown in Figure 2. Calculate (a) Vbi,
(b) xn and xp at zero bias, and
(c) the applied bias required so that xn = 30μm
Figure 2: Figure for Problem 5.5
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Exercise 5.6
Consider a silicon pn junction with the doping profile shown in Figure 3. T = 300 K.
(a) Calculate the applied reverse-biased voltage required so that the space charge region extends entirely through the p region.
(b) Determine the space charge width into the n+region with the reverse-biased voltage calculated in part (a).
(c) Calculate the peak electric field for this applied voltage.
Figure 3: Figure for Problem 5.6
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Exercise 5.7
Consider a silicon n+p junction diode. The critical electric field for breakdown in silicon is approximately Ecrit = 4 × 105 V/cm. Determine the maximum p-type doping concentration such that the breakdown voltage is
(a) 40 V and (b) 20 V.
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Reference
1. Neamen, Donald A. Semiconductor physics and devices: basic principles. McGraw- hill, 2003.
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