solid states device

Sept.13, 2016

EECS 4600: Solid State Devices, Fall 2015

Homework Assignment # 2

The assignment is due on Tuesday Sept. 20, 2016, before the class at 5:45 pm

Where applicable, always first obtain symbolic expressions for the required quantities or parameters and then calculate

their numerical values. Do not skip intermediate steps. Please write as legibly as possible.

1. The wavefunction of a 1-D particle is:  = Be -2x

for x ≥ 0 and  = Ce 3x

for x < 0, where B and C

are real constants. Find the values of B and C to make y a valid wavefunction. Also, where in space is

the particle most likely to be?

2. A particle is described by a plane-wave wavefunction x,t= Ae j(10x + 3y – 4t)

. You need to calculate

the expectation value of a physical quantity U, which is given by the function

U = 4px 2 + 2pz

2 + 7mE. Here px and pz are the x and z components of the momentum, m is the mass

and E is the energy of the particle and your result should be be given in terms of the Plank’s constant.

3. Calculate the first 3 energy levels for an electron in a 1-D quantum well with width of 2nm and

infinitely high and steep walls.

4. Schematically show the number of electrons in the various subshells of an atom with the electronic

shell structure 1s22s22p4 and an atomic weight of 21. How many protons and neutrons are in the

nucleus of this atom? Is this atom chemically reactive or chemically inert and why?

5. Calculate the values for the Fermi-Dirac distribution function f(E) at 300K and plot (preferably by

using Matlab) these values vs. the energy in eV. Choose the Fermi level to be EF = 1eV and make the

calculated points closer together in the vicinity of EF to obtain a smooth curve. You will notice that

f(E) varies quite rapidly within a few kT of EF. Since f(E) is related to the probability that an energy

level at E is occupied, show that the probability that a state located E above EF is occupied is the

same as the probability that a state located E bellow EF is empty.