11: Extrinsic Semiconductors

Example number 11.1, Page number 307

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

#Variable declaration
ni=2.1*10**19;   #intrinsic charge carriers(m^-3)
me=0.4;   #electron mobility(m^2 V^-1 s^-1)
mh=0.2;   #hole mobility(m^2 V^-1 s^-1)
d=4.5*10**23;   #density of boron(m^-3)
e=1.6*10**-19;   #charge of electron(c)

#Calculation
C=ni*e*(me+mh);   #conductivity before adding boron atoms(ohm^-1 m^-1)
c=d*e*mh;   #conductivity after adding boron atoms(ohm^-1 m^-1)

#Result
print "Before adding boron atoms,the semiconductor is an intrinsic semiconductor"
print "conductivity before adding boron atoms is",C,"ohm^-1 m^-1"
print "After adding boron atoms,the semiconductor becomes a P-type semiconductor"
print "conductivity after adding boron atoms is",c/10**4,"*10**4 ohm^-1 m^-1"

Before adding boron atoms,the semiconductor is an intrinsic semiconductor
conductivity before adding boron atoms is 2.016 ohm^-1 m^-1
After adding boron atoms,the semiconductor becomes a P-type semiconductor
conductivity after adding boron atoms is 1.44 *10**4 ohm^-1 m^-1

Example number 11.2, Page number 307

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

#Variable declaration
ni=1.5*10**16;   #intrinsic charge carriers(m^-3)
me=1300*10**-4;   #electron mobility(m^2 V^-1 s^-1)
mh=500*10**-4;    #hole mobility(m^2 V^-1 s^-1)
c=3*10**4;     #conductivity of n-tpye silicon(ohm^-1 m^-1)
e=1.6*10**-19;   #charge of electron(c)

#Calculation
ne=c/(e*me);    #DensiTy of electrons in n-type silicon(electrons/m^3)
nh=ni**2/ne;   #Density of holes in n-type silicon(holes/m^3)
Ne=c/(e*mh);    #Density of holes in p-type silicon(holes/m^3)
Nh=ni**2/Ne;   #Density of electrons in p-type silicon(holes/m^3)

#Result
print "DensiTy of electrons in n-type silicon is",round(ne/10**24,4),"*10**24 electrons/m^3"
print "DensiTy of holes in n-type silicon is",nh/10**8,"*10**8 holes/m^3"
print "DensiTy of holes in p-type silicon is",Ne,"holes/m^3"
print "DensiTy of electrons in p-type silicon is",Nh/10**7,"*10**7 electrons/m^3"

DensiTy of electrons in n-type silicon is 1.4423 *10**24 electrons/m^3
DensiTy of holes in n-type silicon is 1.56 *10**8 holes/m^3
DensiTy of holes in p-type silicon is 3.75e+24 holes/m^3
DensiTy of electrons in p-type silicon is 6.0 *10**7 electrons/m^3

Example number 11.3, Page number 308

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

#Variable declaration
ni=2*10**16;    #intrinsic charge carriers(m^-3)
Na=5*10**23;    #density of acceptor concentration of silicon with arsenic(atoms)
Nd=3*10**23;    #density of donor concentration of silicon with arsenic(atoms)

#Calculation
nh=Na-Nd;   #density of hole(m^-3)
ne=ni**2/nh;   #The electron concentration(electrons/m^3)

#Result
print "The electron concentration is",ne/10**9,"*10**9 electrons/m^3"

The electron concentration is 2.0 *10**9 electrons/m^3

Example number 11.4, Page number 309

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=5*10**28;    #density of silicon atom(atoms/m^3)
nd=2.5*10**7;   #donor concentration in 1 atom per si atom
T=300;    #Temperature(K)
Eg=1.1*1.6*10**-19;   #Eg for silicon(eV)
kb=1.38*10**-23;    #Boltzmann's Constant(m^2 Kg s^-2 k^-1)
m=9.11*10**-31;   #mass of electon(kg)
h=6.625*10**-34;   #plank's constant(m^2 Kg/sec)

#Calculation
Nd=d/nd;     #The donor concentration(atoms/m^3)
Ef=(Eg/2)+(kb*T*(math.log(Nd/(2*((2*math.pi*m*kb*T)/h**2)**(3/2)))));    #The position of fermi level at 300K(J)

#Result
print "The position of fermi level is",round(Ef*10**20,3),"*10**-20 J or",round(Ef/(1.6*10**-19),4),"eV"

The position of fermi level is 4.893 *10**-20 J or 0.3058 eV

Example number 11.5, Page number 310

In [17]:
#importing modules
import math
from __future__ import division

#Variable declaration
ni=1.5*10**16;   #intrinsic charge carriers(m^-3)
r1=10*10**-2;    #resistivity of p-type silicon(ohm m)
r2=10*10**-2;    #resistivity of n-type silicon(ohm m)
me=1350*10**-4;   #The mobility of the charge carrier(m^2 V^-1 s^-1)
mh=480*10**-4;    #The hole charge carrier(m^2 V^-1 s^-1)
e=1.6*10**-19;    #charge of electron(c)

#Calculation
Na=1/(r1*e*mh);    #The density of the intrinsic crystal for p-type(m^-3)
ne=ni**2/Na;    #The minor carrier concentration for p-type(electrons/m^3)
Nd=1/(r2*e*me);    #The density of the intrinsic crystal for n-type(m^-3)
nh=ni**2/Nd;       #The minor carrier concentration for n-type(electrons/m^3)

#Result
print "The density of the intrinsic crystal for p-type is",round(Na/10**21,3),"*10**21 m^-3"
print "The minor carrier concentration for p-type is",ne,"electrons/m^3"
print "The density of the intrinsic crystal for n-type is",round(Nd/10**20,4),"*10**20 m^-3"
print "The minor carrier concentration for n-type is",nh,"holes/m^3"

The density of the intrinsic crystal for p-type is 1.302 *10**21 m^-3
The minor carrier concentration for p-type is 1.728e+11 electrons/m^3
The density of the intrinsic crystal for n-type is 4.6296 *10**20 m^-3
The minor carrier concentration for n-type is 4.86e+11 holes/m^3

Example number 11.6, Page number 315

In [19]:
#importing modules
import math
from __future__ import division

#Variable declaration
c=112;   #conductivity of a n-type silicon specimen(ohm^-1 m^-1)
RH=1.25*10**-3;   #Hall coefficient of a n-type silicon specimen(m^3 C^-1)
e=1.6*10**-19;    #charge of electron(c)

#Calculation
me=c*RH;     #electron mobility(m^2 V^-1 s^-1)
ne=c/(me*e);    #The charge carrier density(electrons/m^3)

#Result
print "The electron mobility is",me,"m^2 V^-1 s^-1"
print "The charge carrier density is",ne,"electrons/m^3"

The electron mobility is 0.14 m^2 V^-1 s^-1
The charge carrier density is 5e+21 electrons/m^3

Example number 11.7, Page number 315

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

#Variable declaration
l=12*10**-3;    #length of semi conductor crystal(m)
b=1*10**-3;     #breadth of semi conductor crystal(m)
t=1*10**-3;     #thickness of semi conductor crystal(m)
I=20*10**-3;    #current(A)
Vh=37*10**-6;    #voltage measured across the width(V)
B=0.5;   #magnetic flux density(Wb/m^2)
e=1.6*10**-19;    #charge of electron(c)

#Calculation
RH=Vh*t/(I*B);    #Hall coefficient of semiconductor(C^-1 m^3)
ne=1/(RH*e);      #The density of the charge carrier(electrons/m^3)

#Result
print "Hall coefficient of semiconductor is",RH,"C^-1 m^3"
print "The density of the charge carrier is",round(ne/10**24,3),"*10**24 electrons/m^3"

Hall coefficient of semiconductor is 3.7e-06 C^-1 m^3
The density of the charge carrier is 1.689 *10**24 electrons/m^3

Example number 11.8, Page number 315

In [24]:
#importing modules
import math
from __future__ import division

#Variable declaration
l=100*10**-3;   #length of silicon plate(m)
b=10*10**-3;    #breadth of silicon plate(m)
t=1*10**-3;    #thickness of silicon plate(m)
I=10**-2;   #current(A)
Vh=1.83*10**-3;   #voltage measured across the width(V)
B=0.5;    #magnetic flux density(Wb/m^2)

#Calculation
RH=Vh*t/(I*B);     #Hall coefficient of silicon plate(m^3 C^-1)

#Result
print "Hall coefficient of silicon plate is",RH*10**4,"*10**-4 m^3 C^-1"

Hall coefficient of silicon plate is 3.66 *10**-4 m^3 C^-1

Example number 11.9, Page number 316

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

#Variable declaration
RH=7.35*10**-5;   #Hall coefficient of silicon specimen(m^3 C^-1)
rh=-7.35*10**-5;   #Hall coefficient of silicon specimen(m^3 C^-1)
c=200;   #conductivity(ohm^-1 m^-1)
e=1.6*10**-19;   #charge of electron(c)

#Calculation
ne=1/(RH*e);    #The density of the charge carrier(electrons/m^3)
me=c*RH;      #The mobility of the charge carrier(m^2 V^-1 s^-1)

#Result
print "The negative sign of the Hall coefficient indicates that the nature of the semiconductor is n-type"
print "The density of the charge carrier is",round(ne/10**22,3),"*10**22 electrons/m^3"
print "The mobility of the charge carrier is",me*10**3,"*10**-3 m^2 V^-1 s^-1"

The negative sign of the Hall coefficient indicates that the nature of the semiconductor is n-type
The density of the charge carrier is 8.503 *10**22 electrons/m^3
The mobility of the charge carrier is 14.7 *10**-3 m^2 V^-1 s^-1

Example number 11.10, Page number 316

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

#Variable declaration
RH=4.16*10**-4;    #Hall coefficient of n-type semiconductor(m^3 C^-1)
c=180;    #conductivity(ohm^-1 m^-1)
e=1.6*10**-19;   #charge of electron(c)
x=1.18;    #correction factor for RH

#Calculation
ne=x/(RH*e);    #The density of the charge carrier(electrons/m^3)
me=c/(ne*e);    #The mobility of the charge carrier(m^2 V^-1 s^-1)

#Result
print "The density of the charge carrier is",round(ne/10**22,4),"*10**22 electrons/m^3"
print "The mobility of the charge carrier is",round(me,5),"m^2 V^-1 s^-1"
print "answer given in the book is wrong"

The density of the charge carrier is 1.7728 *10**22 electrons/m^3
The mobility of the charge carrier is 0.06346 m^2 V^-1 s^-1
answer given in the book is wrong

Example number 11.11, Page number 317

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

#Variable declaration
l=1*10**-3;    #length of rectangular plane sheet of doped silicon(m)
b=1*10**-3;    #breadth of semi rectangular plane sheet of doped silicon(m)
t=0.5*10**-3;    #thickness of rectangular plane sheet of doped silicon(m)
RH=1.25*10**-3;    #Hall coefficient of the material(m^3 C^-1)
I=1*10**-3;    #current(A)
B=0.7;     #magnetic flux density(Wb/m^2)
e=1.6*10**-19;   #charge of electron(c)

#Calculation
Vh=RH*I*B/t;     #The hall coefficient measured by the probes(mV)

#Result
print "The hall coefficient measured by the probes is",Vh*10**3,"mV"

The hall coefficient measured by the probes is 1.75 mV

Example number 11.12, Page number 317

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

#Variable declaration
RH=3.66*10**-4;    #Hall coefficient of a doped silicon(m^3 C^-1)
r=8.93*10**-3;     #The resistivity(ohm m)
e=1.6*10**-19;    #charge of electron(c)

#Calculation
n=1/(RH*e);     #The density of the charge carrier(m^-3)
me=RH/r;        #The mobility(m^2 V^-1 s^-1)

#Result
print "The density of the charge carrier is",round(n/10**22,5),"*10**22 m^-3"
print "The mobility is",round(me,5),"m^2 V^-1 s^-1"

The density of the charge carrier is 1.70765 *10**22 m^-3
The mobility is 0.04099 m^2 V^-1 s^-1

Example number 11.13, Page number 317

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

#Variable declaration
RH=0.0125;    #Hall coefficient of a sample n-type semiconductor(m^3 C^-1)
rh=-0.0125;   #Hall coefficient of a sample n-type semiconductor(m^3 C^-1)
me=0.36;      #electron mobility(m^2 V^-1 s^-1)
EH=100;       #electric field(V/m)
e=1.6*10**-19;    #charge of electron(c)

#Calculation
n=1/(RH*e);    #The density of the charge carrier(m^-3)
c=n*e*me;      #conductivity of n-type semiconductor(ohm^-1 m^-1)
J=c*EH;        #The current density(A/m^2)

#Result
print "The current density is",J,"A/m^2"

The current density is 2880.0 A/m^2