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.
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
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) the junction capacitance at ( i) VR = 1 V, (ii) VR = 3 V, and (iii) VR = 5 V.
(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.
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
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 regionextends 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
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.
Reference
1. Neamen, Donald A. Semiconductor physics and devices: basic principles. McGrawhill, 2003.
