EN 204: Materials for Energy Applications
Quiz 2
14.02.2021
Time: 90 minutes
Instructions:
1. This test consists of five questions and two bonus questions, all having equal weightage.
2. Wherever needed, take reasonable assumptions and state them clearly.
3. You are allowed a single A4 paper formula sheet. This should be the first page of your answer sheet.
Note:
1. (ni)Si = 1.5 x 1010 cm-3 at 300 K; (Eg)Si = 1.1 eV
2. (ni)Ge = 2.3 x 1013 cm-3 at 300 K; (Eg)Ge = 0.66 eV
3. Law of mass action: np=ni2
QUESTIONS
1.
a. For a material that has a donor density of Nd and an acceptor density of Na, assuming complete ionisation,
calculate the carrier concentrations for a
i. p-type material
ii. n-type material
b. A hypothetical semiconductor has a ni of 1010 cm-3. At 300 K, it has valence and conduction band
densities of states Nv and Nc as equal to 1019 cm-3. What is the bandgap for this material?
2. A Si sample is doped with 1017 atoms of N per cm3. What is the equilibrium carrier concentrations at 300 K?
Where is EF relative to Ei for this material? Draw the resultant band diagram.
3. For a non-degenerate semiconductor, show that the electron concentration peaks at Ec + 0.5kT. As a fraction of
the peak population Np, what is the electron concentration at Ec + 5kT?
4.
a. An electron is confined to a 5 µm thin layer of Si. Assuming that the system can be adequately
represented by the particle in a 1D infinite potential well model, what is the velocity that the electron can
occupy at the ground state? Assume the m*Si = 0.26me
b. For a material having an EF of 7.5 eV, what is the temperature at which there is a 1 % probability of a
state at 6.25 eV being empty?
5. A Ge wafer is doped with As having a density of 2.5ni. What is the number of empty donor states at an energy 10
meV above the fermi level? Calculate the equilibrium electron and hole density at 300 K. How do your answers
change if EF-Ed is 100 meV?
BONUS
A. For an unknown semiconductor, Eg is 1.1 eV and Nc=Nv. It is doped with 1015 cm-3 donors, with the donor levels
0.2 eV below Ec. If EF is 0.25 eV below Ec, calculate ni and the carrier densities in the semiconductor at 300 K.
B. A sample of Si contains 1016 cm-3 boron atoms and a number of shallow donors. If the fermi level is 0.36 eV
above the Ei at 300 K, what is the donor density Nd?
…..o000o.....