8: Semiconductors

Example number 8.1, Page number 8.11

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
ni=2.37*10**19;     #carrier density(per m**3)
mew_e=0.38;     #electron mobility(m**2/Vs)
mew_h=0.18;     #hole mobility(m**2/Vs)
e=1.6*10**-19;   

#Calculation
sigma_i=ni*e*(mew_e+mew_h);     
rho=1/sigma_i;      #resistivity(ohm m)

#Result
print "resistivity is",round(rho,3),"ohm m"
resistivity is 0.471 ohm m

Example number 8.2, Page number 8.11

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

#Variable declaration
Eg=1.12;    #band gap(eV)
T=300;      #temperature(K)
m0=1;    #assume
me=0.12*m0;
mh=0.28*m0;
k=1.38*10**-23;   #boltzmann constant
e=1.6*10**-19;  

#Calculation
EF=(Eg/2)+(3*k*T*math.log(mh/me)/(4*e));    #position of fermi level(eV)

#Result
print "position of fermi level is",round(EF,3),"eV"
position of fermi level is 0.576 eV

Example number 8.3, Page number 8.12

In [13]:
#importing modules
import math
from __future__ import division

#Variable declaration
T=300;      #temperature(K)
k=1.38*10**-23;   #boltzmann constant
m=9.109*10**-31;    #mass(kg)
h=6.626*10**-34;    #plancks constant
Eg=0.7;     #energy(eV)
e=1.6*10**-19;  

#Calculation
x=(2*math.pi*m*k/h**2)**(3/2);
y=math.exp(-Eg*e/(2*k*T));
ni=2*x*(T**(3/2))*y;             #concentration of intrinsic charge carriers(per m**3)

#Result
print "concentration of intrinsic charge carriers is",round(ni/10**18,2),"*10**18 per m**3"
concentration of intrinsic charge carriers is 33.48 *10**18 per m**3

Example number 8.4, Page number 8.13

In [20]:
#importing modules
import math
from __future__ import division

#Variable declaration
ni=2.4*10**19;     #carrier density(per m**3)
mew_e=0.39;     #electron mobility(m**2/Vs)
mew_h=0.19;     #hole mobility(m**2/Vs)
e=1.6*10**-19;   

#Calculation
sigma_i=ni*e*(mew_e+mew_h);     
rhoi=1/sigma_i;      #resistivity(ohm m)

#Result
print "resistivity is",round(rhoi,3),"ohm m"
resistivity is 0.449 ohm m

Example number 8.5, Page number 8.13

In [22]:
#importing modules
import math
from __future__ import division

#Variable declaration
ni=2.5*10**19;     #carrier density(per m**3)
mew_e=0.39;     #electron mobility(m**2/Vs)
mew_p=0.19;     #hole mobility(m**2/Vs)
e=1.6*10**-19; 
l=1*10**-2;     #length(m)
A=10**-3*10**-3;     #area(m**2)

#Calculation
R=l/(ni*e*A*(mew_p+mew_e));     #resistance(ohm)

#Result
print "resistance is",round(R/10**3,2),"*10**3 ohm"
resistance is 4.31 *10**3 ohm

Example number 8.6, Page number 8.14

In [28]:
#importing modules
import math
from __future__ import division

#Variable declaration
T=300;      #temperature(K)
k=1.38*10**-23;   #boltzmann constant
m=9.109*10**-31;    #mass(kg)
h=6.626*10**-34;    #plancks constant
Eg=1.1;     #energy(eV)
e=1.6*10**-19;  
mew_e=0.48;     #electron mobility(m**2/Vs)
mew_p=0.013;     #hole mobility(m**2/Vs)

#Calculation
C=2*((2*math.pi*m*k/h**2)**(3/2));
y=math.exp(-Eg*e/(2*k*T));
ni=C*(T**(3/2))*y;             #concentration of intrinsic charge carriers(per m**3)
sigma_i=ni*e*(mew_e+mew_h);     #conductivity(ohm-1 m-1)


#Result
print "conductivity is",round(sigma_i*10**3,3),"*10**-3 ohm-1 m-1"
print "answer given in the book is wrong"
conductivity is 1.578 *10**-3 ohm-1 m-1
answer given in the book is wrong

Example number 8.7, Page number 8.15

In [33]:
#importing modules
import math
from __future__ import division

#Variable declaration
T=300;      #temperature(K)
k=1.38*10**-23;   #boltzmann constant
m=9.109*10**-31;    #mass(kg)
h=6.626*10**-34;    #plancks constant
Eg=0.7;     #energy(eV)
e=1.6*10**-19;  
mew_e=0.48;     #electron mobility(m**2/Vs)
mew_p=0.013;     #hole mobility(m**2/Vs)

#Calculation
C=2*((2*math.pi*m*k/h**2)**(3/2));
y=math.exp(-Eg*e/(2*k*T));
ni=C*(T**(3/2))*y;             #concentration of intrinsic charge carriers(per m**3)
sigma_i=ni*e*(mew_e+mew_h);     #conductivity(ohm-1 m-1)

#Result
print "concentration of intrinsic charge carriers is",round(ni/10**19,2),"*10**19 per m**3"
print "conductivity is",round(sigma_i,3),"ohm-1 m-1"
print "answer in the book varies due to rounding off errors"
concentration of intrinsic charge carriers is 3.35 *10**19 per m**3
conductivity is 3.589 ohm-1 m-1
answer in the book varies due to rounding off errors

Example number 8.8, Page number 8.15

In [45]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=1.6*10**-19;  
mew_e=0.36;     #electron mobility(m**2/Vs)
mew_h=0.17;     #hole mobility(m**2/Vs)
rho=2.12;       #resistivity(ohm m)
T=300;      #temperature(K)
k=1.38*10**-23;   #boltzmann constant
m=9.109*10**-31;    #mass(kg)
h=6.626*10**-34;    #plancks constant

#Calculation
sigma=1/rho;
ni=sigma/(e*(mew_e+mew_h));
C=2*((2*math.pi*m*k/h**2)**(3/2));
y=C*T**(3/2)/ni;
z=math.log(y);
Eg=2*k*T*z/(1.6*10**-19);        #forbidden energy gap(eV)

#Result
print "forbidden energy gap is",round(Eg,3),"eV"
print "answer varies due to rounding off errors"
forbidden energy gap is 0.793 eV
answer varies due to rounding off errors

Example number 8.9, Page number 8.16

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
x=0.6532;
y=0.3010;
T1=273+20;    #temperature(K)
T2=273+32;    #temperature(K)
k=8.616*10**-5;

#Calculation
dy=x-y;
dx=(1/T1)-(1/T2);
Eg=2*k*dy/dx;      #energy band gap(eV)

#Result
print "energy band gap is",round(Eg,3),"eV"
print "answer varies due to rounding off errors"
energy band gap is 0.452 eV
answer varies due to rounding off errors

Example number 8.10, Page number 8.17

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

#Variable declaration
k=1.38*10**-23;   #boltzmann constant
EF=0.18;      #fermi shift(eV)
E=1.2;       #energy gap(eV)
e=1.6*10**-19;  
r=5;   

#Calculation
T=EF*e*4/(3*k*math.log(r));    #temperature(K)

#Result
print "temperature is",round(T),"K"
temperature is 1729.0 K

Example number 8.11, Page number 8.17

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

#Variable declaration
Na=5*10**23;     #number of atoms(atoms)
Nd=3*10**23;     #number of atoms(atoms)
ni=2*10**16;    #intrinsic charge carriers(per m**3)

#Calculation
p=2*(Na-Nd)/2;    #hole concentration(per m**3)
n=ni**2/p;       #electron concentration(per m**3)

#Result
print "electron concentration is",n/10**9,"*10**9 per m**3"
electron concentration is 2.0 *10**9 per m**3

Example number 8.12, Page number 8.18

In [18]:
#importing modules
import math
from __future__ import division

#Variable declaration
ni=1.5*10**16;     #carrier density(per m**3)
mew_e=0.13;     #electron mobility(m**2/Vs)
mew_h=0.05;     #hole mobility(m**2/Vs)
e=1.6*10**-19;   
d=2.33*10**3;    #density(kg/m**3)
n=28.1;
na=6.02*10**26;     #number of atoms

#Calculation
sigma=ni*e*(mew_e+mew_h);     #conductivity(ohm-1 m-1)
Nd=d*na/(n*10**8);
p=ni**2/Nd;    
sigma_ex1=Nd*e*mew_e;     #conductivity(ohm-1 m-1)
n=p;
Na=Nd;
sigma_ex2=Na*e*mew_h;     #conductivity(ohm-1 m-1)

#Result
print "conductivity is",sigma*10**3,"*10**-3 ohm-1 m-1"
print "conductivity is",round(sigma_ex1,2),"ohm-1 m-1"
print "conductivity is",round(sigma_ex2,2),"ohm-1 m-1"
conductivity is 0.432 *10**-3 ohm-1 m-1
conductivity is 10.38 ohm-1 m-1
conductivity is 3.99 ohm-1 m-1

Example number 8.13, Page number 8.20

In [28]:
#importing modules
import math
from __future__ import division

#Variable declaration
ni=1.5*10**16;     #carrier density(per m**3)
mew_e=0.135;     #electron mobility(m**2/Vs)
mew_h=0.048;     #hole mobility(m**2/Vs)
e=1.6*10**-19;  
Nd=10**23;      
T=300;    #temperature(K)
k=1.38*10**-23;

#Calculation
sigma=ni*e*(mew_e+mew_h);     #conductivity(ohm-1 m-1)
p=ni**2/Nd;     #hole concentration(per m**3)
sigma_ex=Nd*e*mew_e;      #conductivity(ohm-1 m-1)
x=3*k*T*math.log(mew_e/mew_h)/4;

#Result
print "conductivity is",sigma*10**3,"*10**-3 ohm-1 m-1"
print "hole concentration is",p,"per m**3"
print "conductivity is",sigma_ex/10**3,"*10**3 ohm-1 m-1"
print "position of fermi level is",round(x/(1.6*10**-19),2),"eV"
conductivity is 0.4392 *10**-3 ohm-1 m-1
hole concentration is 2250000000.0 per m**3
conductivity is 2.16 *10**3 ohm-1 m-1
position of fermi level is 0.02 eV

Example number 8.14, Page number 8.35

In [33]:
#importing modules
import math
from __future__ import division

#Variable declaration
mew_e=0.19;     #electron mobility(m**2/Vs)
e=1.6*10**-19;        
T=300;    #temperature(K)
k=1.38*10**-23;

#Calculation
Dn=mew_e*k*T/e;     #diffusion coefficient(m**2 s-1)

#Result
print "diffusion coefficient is",round(Dn*10**4,3),"*10**-4 m**2 s-1"
print "answer varies due to rounding off errors"
diffusion coefficient is 49.162 *10**-4 m**2 s-1
answer varies due to rounding off errors

Example number 8.15, Page number 8.44

In [37]:
#importing modules
import math
from __future__ import division

#Variable declaration
RH=3.66*10**-4;   #hall coefficient(m**3/coulomb)
I=10**-2;     #current(amp)
B=0.5;     #magnetic field(wb/m**2)
t=1*10**-3;    #thickness(m)

#Calculation
VH=RH*I*B*10**3/t;     #hall voltage(mV)

#Result
print "hall voltage is",VH,"mV"
hall voltage is 1.83 mV

Example number 8.16, Page number 8.45

In [40]:
#importing modules
import math
from __future__ import division

#Variable declaration
Vy=37*10**-6;     #voltage(V)
t=10**-3;    #thickness(m)
Bz=0.5;      #magnetic field(wb/m**2)
Ix=20*10**-3;   #current(A)

#Calculation
RH=Vy*t/(Ix*Bz);     #hall coefficient(m**3/coulomb)

#Result
print "hall coefficient is",RH,"C-1 m**3"
hall coefficient is 3.7e-06 C-1 m**3

Example number 8.17, Page number 8.46

In [44]:
#importing modules
import math
from __future__ import division

#Variable declaration
RH=6.85*10**-5;   #hall coefficient(m**3/coulomb)
e=1.6*10**-19; 
sigma=250;      #conductivity(m-1 ohm-1)

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

#Result
print "density of charge carriers is",round(n/10**22,3),"*10**22 m**3"
print "mobility of charge carriers is",mew*10**3,"*10**-3 m**2 V-1 s-1"
density of charge carriers is 9.124 *10**22 m**3
mobility of charge carriers is 17.125 *10**-3 m**2 V-1 s-1

Example number 8.18, Page number 8.46

In [48]:
#importing modules
import math
from __future__ import division

#Variable declaration
I=30;    #current(A)
B=1.75;   #magnetic field(T)
n=6.55*10**28;    #electron concentration(/m**3)
t=0.35*10**-2;    #thickness(m)
e=1.6*10**-19; 

#Calculation
VH=I*B*10**6/(n*e*t);     #hall voltage(micro V)

#Result
print "hall voltage is",round(VH,3),"micro V"
hall voltage is 1.431 micro V

Example number 8.19, Page number 8.47

In [55]:
#importing modules
import math
from __future__ import division

#Variable declaration
RH=3.66*10**-4;   #hall coefficient(m**3/coulomb)
e=1.6*10**-19;
Pn=8.93*10**-3;    #resistivity(ohm m)

#Calculation
n=1/(RH*e);      #density of charge carriers(per m**3)
mew_e=RH/Pn;    #mobility of charge carriers(m**2/Vs)

#Result
print "density of charge carriers is",round(n/10**22,3),"*10**22 per m**3"
print "mobility of charge carriers is",round(mew_e,3),"m**2 V-1 s-1"
density of charge carriers is 1.708 *10**22 per m**3
mobility of charge carriers is 0.041 m**2 V-1 s-1