# VE320 Introduction of Semiconductor Device Homework 5 solved

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5.1 An abrupt silicon pn junction at zero bias has dopant concentrations of Na = 1017 cm-3
and
Nd = 5*1015 cm-3
. T = 300 K.
(a) Calculate the Fermi level on each side of the junction with respect to the intrinsic Fermi
level.
(b) Sketch the equilibrium energy-band diagram for the junction and determine Vbi from the
diagram and the results of part (a).
(c) Calculate Vbi using Equation (7.10), and compare the results to part (b).
(d) Determine xn, xp, and the peak electric field for this junction
5.2 A silicon pn junction in thermal equilibrium at T =300 K is doped such that
EF – EFi = 0.365 eV in the n region and EFi – EF = 0.330 eV in the p region.
(a) Sketch the energy-band diagram for the pn junction.
(b) Find the impurity doping concentration in each region.
(c) Determine Vbi.
5.3 (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.
5.4 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
5.5 An abrupt silicon pn junction at T = 300 K has impurity doping concentrations of
Na = 5*1016 cm-3
and Nd = 1015 cm-3
. Calculate (a) Vbi, (b) W at (i) VR = 0 and (ii) VR = 5 V, and
(c) |Emax| at (i) VR = 0 and (ii) VR = 5V.
5.6 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|, and (d)Cj

.
5.7 Consider a silicon pn junction with the doping profile shown in Figure 2. 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.(You can ignore the influence of p+
)
Figure 2