[SOLVED] VE320 Homework 2

Exercise 2.1

Two possible valence bands are shown in the E versus k diagram given in Figure 1. State which band will result in the heavier hole effective mass; state why.

Figure 1: Valence bands for Problem 2.1.

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Exercise 2.2

(a) The forbidden bandgap energy in GaAs is 1.42eV. (i) Determine the minimum frequency of an incident photon that can interact with a valence electron and elevate the electron to the conduction band. (ii) What is the corresponding wavelength?

(b) Repeat part ( a ) for silicon with a bandgap energy of 1.12eV.

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Exercise 2.3

The energy-band diagram for silicon is shown in Figure 2. The minimum energy in the conduction band is in the [100] direction. The energy in this one-dimensional direction near the minimum value can be approximated by

E = E0 − E1 cos α (k − k0)
where k0 is the value of k at the minimum energy. Determine the effective mass of the

particle at k = k0 in terms of the equation parameters.

Figure 2: Energy-band structures of Si

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Exercise 2.4

(a) Determine the total number (#/cm3) of energy states in silicon between Ev and Ev −3kT at(i)T =300Kand(ii)T =400K.

(b) Repeat part (a) for GaAs.

Exercise 2.5

(a) For silicon, find the ratio of the density of states in the conduction band at E = Ec + kT to the density of states in the valence band at E = Ev − kT .

(b) Repeat part (a) for GaAs.

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Exercise 2.6

Consider the energy levels shown in Figure 3. Let T = 300 K.

(a) If E1 − EF = 0.30eV, determine the probability that an energy state at E = E1 is occupied by an electron and the probability that an energy state at E = E2 is empty.

(b) Repeat part (a) if EF − E2 = 0.40eV.

Figure 3: Energy levels for Problem 2.6

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Exercise 2.7

(a) The carrier effective masses in a semiconductor are m∗n = 1.21m0 and m∗p = 0.70m0. Determine the position of the intrinsic Fermi level with respect to the center of the bandgap atT =300K.

(b) Repeat part (a) if m∗n = 0.080m0 and m∗p = 0.75m0.

Exercise 2.8

Silicon at T = 300 K is doped with boron atoms such that the concentration of holes is p0 = 5 × 1015 cm−3.

(a)FindEF −Ev.
(b) Determine Ec − EF .
(c) Determine n0.
(d) Which carrier is the majority carrier? (e) Determine EF i − EF .

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Reference

1. Neamen, Donald A. Semiconductor physics and devices: basic principles. McGraw- hill, 2003.

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