12: Band theory of solids

Example number 12.1, Page number 243

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
EF=8;     #fermi energy(eV)
e=1.6*10**-19;   #conversion factor from J to eV
m=9.1*10**-31;    #mass of electron(kg)

#Calculation
E0bar=3*EF/5;   
v=math.sqrt(2*E0bar*e/m);     #speed of electron(m/s)

#Result
print "speed of electron is",round(v/10**6,1),"*10**6 m/s"

speed of electron is 1.3 *10**6 m/s

Example number 12.2, Page number 244

In [6]:
#importing modules
import math
from __future__ import division

#Variable declaration
I=8;    #current(ampere)
r=9*10**-4;   #radius(m)
V=5;   #potential difference(V)
L=1;   #length(m)

#Calculation
A=math.pi*r**2;    #area of wire(m**2)
E=V/L;
J=I/A;   #current density(V/m)
rho=E/J;    #resistivity(ohm m)

#Result
print "current density is",round(J/10**6,3),"*10**6 V/m"
print "resistivity is",round(rho*10**6,2),"*10**-6 ohm m"

current density is 3.144 *10**6 V/m
resistivity is 1.59 *10**-6 ohm m

Example number 12.3, Page number 245

In [8]:
#importing modules
import math
from __future__ import division

#Variable declaration
n=1;
a=4*10**-10;   #lattice parameter(m)
N=1.56*10**28;  
e=1.6*10**-19;   #conversion factor from J to eV
tow=10**-15;    #collision time(s)
m=9.1*10**-31;    #mass of electron(kg)

#Calculation
N=n/(a**3);    #number of electrons per unit volume(per m**3)
sigma=N*e**2*tow/m;   #conductivity(per ohm m)
rho=1/sigma;   #resistivity(ohm m)

#Result
print "conductivity is",round(sigma/10**6,2),"*10**6 ohm m"
print "resistivity is",rho,"ohm m"

conductivity is 0.44 *10**6 ohm m
resistivity is 2.275e-06 ohm m

Example number 12.4, Page number 247

In [10]:
#importing modules
import math
from __future__ import division

#Variable declaration
k=1.38*10**-23;   #boltzmann constant(J/K)
NA=6.02*10**26;   #avagadro number(k/mole)
T=300;     #temperature(K)
EF=2;   #fermi energy(eV)
e=1.6*10**-19;   #conversion factor from J to eV

#Calculation
C=math.pi**2*k**2*NA*T/(2*EF*e);    #electronic specific heat(J/kmol/K)

#Result
print "electronic specific heat is",int(C),"J/kmol/K"

electronic specific heat is 530 J/kmol/K

Example number 12.5, Page number 247

In [12]:
#importing modules
import math
from __future__ import division

#Variable declaration
K=327;    #thermal conductivity(W/mK)
T=300;   #temperature(K)
rho=7.13*10**3;    #density(kg/m**3)
NA=6.02*10**26;   #avagadro number(k/mole)
w=65.38;   #atomic weight
e=1.6*10**-19;   #conversion factor from J to eV
tow=2.5*10**-14;   #relaxation time(s)
m=9.1*10**-31;    #mass of electron(kg)

#Calculation
N=2*rho*NA/w;     #number of electrons per unit volume(per m**3)
sigma=N*e**2*tow/m;   #conductivity(per ohm m)
L=K/(sigma*T);    #lorentz number(W ohm/K**2)

#Result
print "lorentz number is",round(L*10**8,4),"*10**-8 W ohm/K**2"

lorentz number is 1.1804 *10**-8 W ohm/K**2

Example number 12.6, Page number 248

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=1.6*10**-19;   #conversion factor from J to eV
n=5*10**28;    #number of atoms(/m**3)

#Calculation
RH=-1/(n*e);    #hall coefficient(m**3/C)

#Result
print "hall coefficient is",round(RH*10**9,3),"*10**-9 m**3/C"

hall coefficient is -0.125 *10**-9 m**3/C