# 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