7: Band Theory of Solids

Example number 7.1, Page number 7.5

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
rho_s=10.5*10**3;     #density(kg/m**3)
NA=6.02*10**26;       #avagadro number(per k mol)
MA=107.9;      #atomic mass
sigma=6.8*10**7;     #conductance(ohm-1 m-1)
e=1.6*10**-19;     #charge(coulomb)

#Calculation
n=rho_s*NA/MA;     #density of electrons
mew=sigma/(n*e);    #mobility of electrons(m**2/Vs)

#Result
print "density of electrons is",round(n/10**28,2),"*10**28"
print "mobility of electrons is",round(mew*10**2,3),"*10**-2 m**2 V-1 s-1"

density of electrons is 5.86 *10**28
mobility of electrons is 0.725 *10**-2 m**2 V-1 s-1

Example number 7.2, Page number 7.6

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=8.92*10**3;     #density(kg/m**3)
rho=1.73*10**-8;     #resistivity of copper(ohm m)
NA=6.02*10**26;       #avagadro number(per k mol)
Aw=63.5;      #atomic weight
m=9.1*10**-31;     #mass(kg)
e=1.6*10**-19;     #charge(coulomb)

#Calculation
n=d*NA/Aw;     #density of electrons
mew=1/(rho*n*e);    #mobility of electrons(m**2/Vs)
t=m/(n*e**2*rho);    #average time of collision(s)

#Result
print "mobility of electrons is",round(mew*10**2,3),"*10**-2 m V-1 s-1"
print "average time of collision is",round(t*10**14,2),"*10**-14 s"

mobility of electrons is 0.427 *10**-2 m V-1 s-1
average time of collision is 2.43 *10**-14 s

Example number 7.3, Page number 7.7

In [11]:
#importing modules
import math
from __future__ import division

#Variable declaration
P=1.54*10**-8;     #resistance(ohm m)
n=5.8*10**28;      #number of electrons(per m**3)
m=9.108*10**-31;     #mass(kg)
e=1.602*10**-19;     #charge(coulomb)

#Calculation
t=m/(n*e**2*P);      #relaxation time of conduction electrons(s) 

#Result
print "relaxation time of conduction electrons is",round(t*10**14,2),"*10**-14 s"

relaxation time of conduction electrons is 3.97 *10**-14 s

Example number 7.4, Page number 7.8

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

#Variable declaration
R=0.06;    #resistance(ohm)
I=15;      #current(A)
D=5;     #length(m)
MA=26.98;       #atomic mass
rho_s=2.7*10**3;    #density(kg/m**3)
NA=6.025*10**26;       #avagadro number(per k mol)
e=1.602*10**-19;     #charge(coulomb)

#Calculation
n=3*rho_s*NA/MA;     #free electron concentration(electrons/m**2)
mew=1/(n*e*rho_s*10**-11);     #mobility(m s-1 V-1)
E=I*R/D;     #electric field(V/m)
vd=mew*E;    #drift velocity of electrons(m/s)

#Result
print "free electron concentration is",round(n/10**29,4),"*10**29 electrons/m**2"
print "mobility is",round(mew*10**3,3),"*10**-3 m s-1 V-1"
print "drift velocity of electrons is",round(vd*10**3,2),"*10**-3 m s-1"

free electron concentration is 1.8088 *10**29 electrons/m**2
mobility is 1.278 *10**-3 m s-1 V-1
drift velocity of electrons is 0.23 *10**-3 m s-1