# Chapter 21 Band theory of solids¶

## Example 21.1 Page no 228¶

In [12]:
#Given
T=300                   #K
Er=0.7                  #ev
K=0.025                  #ev
a=4.83*10**21

#Calculation
import math
ni=a*T**1.5*math.exp(Er/K)

#Result
print"Density of holes and electron is",round(ni*10**-37,1)*10**19,"/m**3"
Density of holes and electron is 3.6e+19 /m**3

## Example 21.2 Page no 229¶

In [20]:
#Given
T=300                  #K
nd=5*10**22                #/m**3
K=0.025                     #ev
a=4.83*10**21

#Calculation
import math
E=(a*T**1.5)/nd
E1=K*math.log(E)

#Result
print"Position of fermi level is", round(E1,2),"ev"
Position of fermi level is 0.16 ev

## Example 21.3 Page no 229¶

In [22]:
#Given
E=0.3                         #ev
T1=300.0
T2=330                         #K

#Calculation
E1=E*T2/T1

#Result
print"New position of fermi level is",E1,"ev"
New position of fermi level is 0.33 ev

## Example 21.4 Page no 230¶

In [51]:
#Given
Kb=9.1*10**-31
m=1.38*10**-23
h=6.6*10**-34
uh=0.17                       #m**2/Volt/sec
a=2.12                        #/ohm/m
ue=0.36
e=1.2*10**-19
T=300
T1=13.8

#Calculation
import math
C=2*((2*math.pi*Kb*m)/h**2)**1.5
ni=a/(e*(ue+uh))
A=(C*T**1.5)/ni
K=math.log(A)*T
Eb=2*Kb*T1

#Result
print round(Eb*10**28,2),"ev"
0.25 ev

## Example 21.5 Page no 231¶

In [55]:
#Given
E=0.4                                    #ev
T=0.03                                   #ev

#Calculation
import math
E1=E-(T*math.log(3))

#Result
print"New position of fermi level is", round(E1,3),"ev"
New position of fermi level is 0.367 ev

## Example 21.6 Page no 231¶

In [64]:
#Given
h=6.626*10**-34                           #J-s
m=9.1*10**-31                               #Kg
a=0.3*10**-9                                #m
e=1.6*10**-19

#Calculation
p=h/(2*a)
E=p**2/(2*m*e)

#Result
print"Electron momentum is",round(p*10**24,1)*10**-24,"Kg m/s"
print"Energy of free electron is",round(E,1),"ev"
Electron momentum is 1.1e-24 Kg m/s
Energy of free electron is 4.2 ev

## Example 21.7 Page no 232¶

In [11]:
#Given
P=0.35                          #Volt
T=300                           #K
e=1.6*10**-19
K=1.38*10**-23

#Calculation
import math
Iv=math.exp(e*P/(K*T))

#Result
print"Forward current is", round(Iv*10**-5,2),"*10**5 I0"
Forward current is 7.49 *10**5 I0

## Example 21.8 Page no 232¶

In [17]:
#Given
Kb=1.38*10**-23
T=300
e=1.6*10**-19

#Calculation
import math
V=math.log(10)*math.log10(1.9)*Kb*T/e

#Result
print"Voltage is", round(V,4),"Volts"
Voltage is 0.0166 Volts

## Example 21.9 Page no 232¶

In [43]:
#Given
a=0.428*10**-9
n=2.55*10**28
e=1.6*10**-19
m=0.014
m1=0.18
me=9.1*10**-31                      #kg
T=300                               #K
K=0.025                             #ev
Eg=0.15                             #ev
n1=1.535*10**22
Ix=100*10**-3
b=10**-3                          #Web/m**3
B=0.1

#Calculation
n=2/a**3
Rh=1/(n*e)
me1=m*me
mh=m1*me
RH=1/(n1*e)
Vh=(Rh*Ix*B)/b
VH=Ix*B*RH/b

#Result
print"Hall coefficient of sodium is", round(Rh*10**9,3),"*10**-9 m**3/C"
print"Hall coefficient of pure InSb is",round(RH*10**4,2),"*10**-4 m**3/C"
print"Hall voltage for sodium is",round(Vh*10**9,2)*10**-9,"V"
print"Hall voltage for InSb is",round(VH*10**3,2),"*10**-3 V"
Hall coefficient of sodium is 0.245 *10**-9 m**3/C
Hall coefficient of pure InSb is 4.07 *10**-4 m**3/C
Hall voltage for sodium is 2.45e-09 V
Hall voltage for InSb is 4.07 *10**-3 V

## Example 21.10 Page no 233¶

In [52]:
#Given
n=5*10**25                       #atoms/m**3
e=1.6*10**-19                    #C

#Calculation
Rh=1/(n*e)

#Result
print"Hall coefficient is",Rh*10**8,"*10**-4 m**3"
Hall coefficient is 12.5 *10**-4 m**3