# 8: Semiconductor Physics¶

## Example number 8.1, Page number 229¶

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration
ni=2.5*10**19;     #concentration(per m**3)
d=4.4*10**28;    #density(per m**3)
n=4*10**8;      #number of Ge atoms

#Calculation
Na=d/n;     #density of acceptor atoms
np=ni**2/Na;
npbyni=np/ni;     #ratio of density of electrons

#Result
print "ratio of density of electrons is",round(npbyni,3)

ratio of density of electrons is 0.227


## Example number 8.2, Page number 230¶

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

#Variable declaration
ni=2.4*10**19;     #concentration(per m**3)
d=4*10**28;    #density(per m**3)
n=10**6;      #number of Ge atoms

#Calculation
Nd=d/n;     #density of acceptor atoms
np=ni**2/Nd;     #hole concentration(holes/m**3)

#Result
print "hole concentration is",np,"holes/m**3"

hole concentration is 1.44e+16 holes/m**3


## Example number 8.3, Page number 230¶

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration
me=9.1*10**-31;          #mass of electron(kg)
kb=1.38*10**-23;      #boltzmann constant
T=300;      #temperature(K)
h=6.62*10**-34;      #planck's constant
Eg=0.7;     #band gap(eV)
e=1.6*10**-19;      #charge(c)

#Calculation
x=2*math.pi*me*kb*T/(h**2);
n=2*(x**(3/2))*math.exp(-Eg*e/(2*kb*T));       #density of holes and electrons(per m**3)

#Result
print "density of holes and electrons is",round(n/10**19,3),"*10**19 per m**3"

density of holes and electrons is 3.352 *10**19 per m**3


## Example number 8.4, Page number 231¶

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
kb=1.38*10**-23;      #boltzmann constant
T=300;      #temperature(K)
m=6;
Eg=0.7;     #band gap(eV)

#Calculation
x=3*kb*T*math.log(m)/4;
EF=(Eg/2)+x;            #position of Fermi level(eV)

#Result
print "position of Fermi level is",EF,"eV"
print "answer in the book is wrong"

position of Fermi level is 0.35 eV
answer in the book is wrong


## Example number 8.5, Page number 231¶

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

#Variable declaration
T1=300;      #temperature(K)
T2=330;      #temperature(K)
E=0.3;     #band gap(eV)

#Calculation
Ec_Ef=T2*E/T1;     #position of Fermi level(eV)

#Result
print "position of Fermi level is",Ec_Ef,"eV"

position of Fermi level is 0.33 eV


## Example number 8.6, Page number 239¶

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

#Variable declaration
n=2.05*10**22;           #charge carrier density
e=1.602*10**-19;         #charge of electron

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

#Result
print "hall coefficient is",round(RH*10**4,3),"*10**-4 m**3/C"

hall coefficient is 3.045 *10**-4 m**3/C


## Example number 8.7, Page number 239¶

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

#Variable declaration
n=5*10**28;           #charge carrier density
e=1.6*10**-19;         #charge of electron

#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


## Example number 8.8, Page number 240¶

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

#Variable declaration
a=4.28*10**-10;           #side(m)
e=1.6*10**-19;         #charge of electron

#Calculation
n=2/(a**3);
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 -0.245 *10**-9 m**3/C


## Example number 8.9, Page number 240¶

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

#Variable declaration
rho=9*10**-3;       #resistivity(ohm m)
mew=0.03;     #mobility(m**2/Vs)

#Calculation
sigma=1/rho;
RH=mew/sigma;     #hall coefficient(m**3/C)

#Result
print "hall coefficient is",RH*10**4,"*10**-4 m**3/C"

hall coefficient is 2.7 *10**-4 m**3/C


## Example number 8.10, Page number 240¶

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

#Variable declaration
rho=9*10**-3;       #resistivity(ohm m)
RH=3.6*10**-4;      #hall coefficient(m**3/C)
e=1.6*10**-19;         #charge of electron

#Calculation
sigma=1/rho;
rho=1/RH;
n=rho/e;        #density of charge carrier(per m**3)
mew=sigma*RH;      #mobility(m**2/Vs)

#Result
print "density of charge carrier is",round(n/10**22,5),"*10**22 per m**3"
print "mobility is",mew,"m**2/Vs"

density of charge carrier is 1.73611 *10**22 per m**3
mobility is 0.04 m**2/Vs


## Example number 8.11, Page number 241¶

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

#Variable declaration
e=1.6*10**-19;         #charge of electron
z=0.3*10**-3;     #thickness(m)
VH=1*10**-3;      #hall voltage(V)
Ix=10*10**-3;     #current(A)
Bz=0.3;           #magnetic field(T)

#Calculation
n=Ix*Bz/(VH*z*e);      #charge carrier concentration(m**-3)

#Result
print "charge carrier concentration is",n,"m**-3"

charge carrier concentration is 6.25e+22 m**-3


## Example number 8.12, Page number 241¶

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

#Variable declaration
rho=0.00912;       #resistivity(ohm m)
RH=3.55*10**-4;      #hall coefficient(m**3/C)
B=0.48;        #flux density(Wb/m**2)

#Calculation
sigma=1/rho;

hall angle is 1.0704 degrees