2.14. PROBLEMS 87
data:
Si :m∗ 1 = m∗=0. 98 m 0
m∗ 2 = m∗ 3 =m∗t=0. 19 m 0
m∗hh =0. 49 m 0
m∗h =0. 16 m 0
GaAs :m∗e = m∗dos=0. 067 m 0
m∗hh =0. 45 m 0
m∗h =0. 08 m 0
The wavevector of a conduction band electron in GaAs isk=
(0. 1 , 0. 1 , 0 .0)A ̊−^1. Calculate the energy of the electron measured from the conduction
bandedge.
Problem 2.2Calculate the lattice constant, bandgap, and electron effective mass of the
alloy InxGa 1 −xAs as a function of composition fromx=0tox=1.
Problem 2.3Calculate the effective density of states at the conduction and valence bands
of Si GaAs, and GaN at 77 K, 300 K, and 500 K.
Problem 2.4Estimate the intrinsic carrier concentration of diamond at 700 K. You can
assume that the carrier masses are similar to those in Si. Compare the results with those
for GaAs, Si, SiC and GaN.
Problem 2.5Estimate the change in intrinsic carrier concentration per K change in
temperature for InAs, Si, and GaAs at near room temperature.
Problem 2.6Calculate the Fermi energy and Fermi velocity for the following metals: Ag,
Au,Ca,Cs,Cu,Na.
Problem 2.7Calculate the change in the Fermi level as temperature changes from 0 to
1000 K for Al and Cu.
Problem 2.8Consider a donor an energy EDfrom the conduction band as shown in
figure 2.40. If the density of the donor device is ND(cm−^3 ) derive a relationship for the
position of the fermi level as a function of temperature in terms of NCand NV.Plotthe
fermi level as a function of temperature for the case ND=NA=NV. Physically explain
your result. Repeat for the case of a donor and an acceptor of densities NDand NA
respectively. What will be the dependence of the fermi level on temperature if (i) ND=
NA, (ii) ND>NA, and (iii) ND<NA. Explain.
Problem 2.9Consider a slab of GaAs that is doped n-type with 1017 cm−^3.
- Consider the case where there is a surface donor state 0.5 eV from the conduction
band. What is the fermi level at the surface as the density of this level is increased
from 1010 cm−^2 to 1014 cm−^2?
