VE320 Extra -Solved

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.