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;
theta_H=math.atan(sigma*B*RH);      #hall angle(radian)
theta_H=theta_H*180/math.pi;       #hall angle(degrees)

#Result
print "hall angle is",round(theta_H,4),"degrees"

hall angle is 1.0704 degrees