16: Electron theory of solids

Example number 16.1, Page number 10

In [2]:
#importing modules
import math
from __future__ import division

#Variable declaration
sigma=5.87*10**7;   #electrical conductivity of Cu(per ohm m)
K=390;   #thermal conductivity(W/mK)
T=20+273;   #temperature(K)

#Calculation
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 2.2676 *10**-8 W ohm/K**2

Example number 16.2, Page number 11

In [7]:
#importing modules
import math
from __future__ import division

#Variable declaration
tow_r=10**-14;   #relaxation time(s)
T=300;   #temperature(K)
kB=1.38*10**-23;   #boltzmann constant
e=1.6*10**-19;   #charge of electron(c)
m=9.1*10**-31;   #mass of electron(kg)
n=6*10**28;   #electron concentration(per m**3)

#Calculation	
sigma=n*e**2*tow_r/m;   #electrical conductivity(per ohm m)
K=n*math.pi**2*kB**2*T*tow_r/(3*m);   #thermal conductivity(W/mK)
L=K/(sigma*T);   #Lorentz number(W ohm/K**2)

#Result
print "electrical conductivity is",round(sigma/10**7,4),"*10**7 per ohm m"
print "thermal conductivity is",round(K,4),"W/mK"
print "Lorentz number is",round(L*10**8,4),"*10**-8 W ohm/K**2"

electrical conductivity is 1.6879 *10**7 per ohm m
thermal conductivity is 123.9275 W/mK
Lorentz number is 2.4474 *10**-8 W ohm/K**2

Example number 16.3, Page number 11

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

#Variable declaration
tow_r=10**-14;   #relaxation time(s)
rho=8900;   #density of Cu(kg/m**3)
aw=63.5;   #atomic weight of Cu
N=6.022*10**23;   #avagadro constant
f=1*10**3;   #number of free electrons per atom
e=1.6*10**-19;   #charge of electron(c)
m=9.1*10**-31;   #mass of electron(kg)

#Calculation	
n=N*rho*f/aw;    #electron concentration(per m**3)
sigma=n*e**2*tow_r/m;   #electrical conductivity(per ohm m)

#Result
print "electrical conductivity is",round(sigma/10**7,3),"*10**7 per ohm m"

electrical conductivity is 2.374 *10**7 per ohm m

Example number 16.4, Page number 12

In [15]:
#importing modules
import math
from __future__ import division

#Variable declaration
rho=1.54*10**-8;   #resistivity(ohm m)
EF=5.5;   #fermi energy(eV)
e=1.6*10**-19;   #charge of electron(c)
m=9.1*10**-31;   #mass of electron(kg)
E=100;
n=5.8*10**28;   #electron concentration(per m**3)

#Calculation	
tow_r=m/(rho*n*e**2);   #relaxation time(s)
mew=e*tow_r/m;   #mobility of electrons(m**2/Vs)
v=e*tow_r*E/m;   #drift velocity(m/s)
EF=EF*e;   #fermi energy(J)
vF=math.sqrt(2*EF/m);   #fermi velocity(m/s)
lamda=vF*tow_r;   #mean free path(m)

#Result
print "relaxation time is",round(tow_r*10**14,2),"*10**-14 s"
print "mobility of electrons is",round(mew*10**3,3),"*10**-3 m**2/Vs"
print "drift velocity is",round(v,4),"m/s"
print "fermi velocity is",round(vF/10**6,2),"*10**6 m/s"
print "mean free path is",round(lamda*10**8,2),"*10**-8 m"

relaxation time is 3.98 *10**-14 s
mobility of electrons is 6.997 *10**-3 m**2/Vs
drift velocity is 0.6997 m/s
fermi velocity is 1.39 *10**6 m/s
mean free path is 5.53 *10**-8 m