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.
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.
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 cosα(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
Exercise 2.4
(a) Determine the total number (#/cm3) of energy states in silicon between Ev and Ev − 3kT at (i) T = 300 K and (ii) T = 400 K.
(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.
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
Exercise 2.7
(a) The carrier effective masses in a semiconductor are and .
Determine the position of the intrinsic Fermi level with respect to the center of the bandgap at T = 300 K.
(b) Repeat part (a) if and .
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) Find EF − Ev.
(b) Determine Ec − EF.
(c) Determine n0.
(d) Which carrier is the majority carrier?(e) Determine EFi − EF.
