Chapter 17: Band Theory of Solids

Example 17.1, Page 17.18

In [2]:
 
# Given 
a = 3e-10 # side of square lattice in m
h = 6.62e-34 # Planck constant in J sec
e = 1.6e-19 # charge on an electron in C
m = 9.1e-31 # mass of electron in kg

#Calculations
p = (h / (2 * a))
E = (p**2 / (2 * m)) * (1. / e)

#Result
print "Electron momentum value at the sides of first Brilloin zone is %.1e kg-m/sec\nEnergy of free electron is %.1f eV"%(p,E)

Electron momentum value at the sides of first Brilloin zone is 1.1e-24 kg-m/sec
Energy of free electron is 4.2 eV

Example 17.2, Page 17.19

In [3]:
from math import log,pi

# Given 
n = 5e22 # no. of atoms per m^3
t = 300 # room temperature in K
k = 1.37e-23 # Boltzmann's constant in J/K
h = 6.62e-34 # Planck constant in J sec
e = 1.6e-19 # charge on an electron in C
m = 9.1e-31 # mass of electron in kg

#Calculations
d = (k * t) * log(n * h**3 / (2 * (2 * pi * m * k * t)**(3./2)))

#Result
print "Position of fermi level is %.3f eV"%(-d/e)
#Answer varies due to round-off errors

Position of fermi level is 0.159 eV

Example 17.3, Page 17.19

In [4]:
 
# Given 
E = 0.3 # Fermi energy in eV
T = 330 # temperature in K
t = 300 # room temperature in K
k = 1.37e-23 # Boltzmann's constant in J/K
h = 6.62e-34 # Planck constant in J sec
e = 1.6e-19 # charge on an electron in C
m = 9.1e-31 # mass of electron in kg

#Calculations
d = (T / t) * (E)

print "New position of fermi level is %.2f eV"%d

New position of fermi level is 0.30 eV

Example 17.4, Page 17.20

In [5]:
from math import *

# Given
E = 0.7 # band gap for semiconductor in eV
t = 300 # room temperature in K
k = 1.38e-23 # Boltzmann's constant in J/K
h = 6.62e-34 # Planck constant in J sec
e = 1.6e-19 # charge on an electron in C
m = 9.1e-31 # mass of electron in kg

#Calculations
n = 2 * ((2 * pi * k * t * m) / h**2)**(3./2) * exp(-(E * e / (2 * k * t)))

#Result
print "Density of holes and electron is %.1e per m^3"%n

Density of holes and electron is 3.4e+19 per m^3

Example 17.5, Page 17.20

In [6]:
 
# Given 
n = 5e28 # no. of atoms in per m^3
e = 1.6e-19 # charge on an electron in C

#Calculations
R = -(1 / (n * e))

#Resilt
print "Hall coefficient is %.3e m^3/C"%R

Hall coefficient is -1.250e-10 m^3/C

Example 17.6, Page 17.20

In [7]:
 
# Given 
a = 4.28e-10 # cell side of Na in m
e = 1.6e-19 # charge on an electron in C

#Calculations
n = (2 / a**3)
R = -(1 / (n * e))

#Result
print "Hall coefficient is %.3e m^3/C"%R

Hall coefficient is -2.450e-10 m^3/C