# Chapter 3 : Energy Bands and Charge Carriers in Semiconductors¶

## Example number 3.1 , Page number 75¶

In [31]:
#importing module
import math
from __future__ import division

#Variable declaration
v=5*10**5 #velocity of electron in cm/s
m=9.11*10**-31 #mass of electron in kg
const=1.6*10**-19 #in eV

#Calculations
delv=0.02 #change in speed in cm/s
delE=(m*v*delv)/const

#Result
print("Increase in kinetic energy of electron= %1.1f*10**-8 eV" %(delE/10**-8))

Increase in kinetic energy of electron= 5.7*10**-8 eV


## Example number 3.2 , Page number¶

In [32]:
#importing module
import math
from __future__ import division

#Variable declaration
epsilon_r=13.2
m0=9.11*10**-31 #in kg
q=1.6*10**-19 #in eV
epsilon_0=8.85*10**-12 #in F/m
h=6.63*10**-34 #planck's constant in J/s

#Calculations
mn=0.067*m0 #in kg
E=((mn*q**4)/(8*(epsilon_0*epsilon_r)**2*h**2))
E1=E/q

#Result
print("Energy required to excite the donor electron= %.2f*10**-22 J\n" %(E/10**-22))
print("Energy required to excite the donor electron= %.4f eV" %E1)

Energy required to excite the donor electron= 8.34*10**-22 J

Energy required to excite the donor electron= 0.0052 eV


## Example number 3.3 , Page number 110¶

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

#Variable declaration
ml=0.98#*m0
mt=0.19#*m0
#rest mass m0 = 9.1*10**-31 kg

#Calculations
mn=6**(2/3)*(ml*mt**2)**(1/3)

#Result
print("Density of states effective mass of electrons in silicon= %1.1f m0" %mn)

Density of states effective mass of electrons in silicon= 1.1 m0


## Example number 3.4 , Page number 110¶

In [34]:
#importing module
import math
from __future__ import division

#Variable declaration
n0=10**16 #doping atoms of P in atoms/cm**3
ni=1.5*10**10 #in cm**-3
Const=0.0259 #constant value for kT in eV

#Calculations
p0=(ni**2)/n0 #in cm**-3
x=(n0/ni)
delE=Const*math.log(x) #difference between energy bands Ef-Ei

#Result
print("Ef-Ei= %.3f eV" %delE)

Ef-Ei= 0.347 eV


## Example number 3.5 , Page number 111¶

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

#Variable declaration
ml=0.98#*m0
mt=0.19#*m0
#rest mass m0 = 9.1*10**-31 kg

#Calculations
mnc=0.33*(1/ml+2/mt)

#Result
print("1/mnc*= %1.2f m0" %(1/mnc))

1/mnc*= 0.26 m0


## Example number 3.6 , Page number 111¶

In [36]:
#importing module
import math
from __future__ import division

#Variable declaration
Nd=10**14 #in cm**-3
myu_n=3900 #in cm**2/V
e=1.6*10**-19 #in J

#Calculations
p=1/(Nd*e*myu_n)

#Result
print("Resistivity of the sample p= %.2f ohm-cm" %p)

Resistivity of the sample p= 16.03 ohm-cm


## Example number 3.7 , Page number 111¶

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

#Variable declaration
n0=5*10**16 #doping level of Si with As in cm**-3
myu_n=800 #in cm**2/Vs
Ix=2*10**-3 #in A
Bz=5*10**-5 #in A
d=2*10**-2 #in cm
e=1.6*10**-19 #in J

#Calculations
p=1/(e*myu_n*n0)
RH=-1/(e*n0)
VH=(Ix*Bz*RH)/(d)

#Result
print("Resistivity= %0.3f ohm-cm\n" %p)
print("Hall coefficient= %i cm**3/c\n" %RH)
print("Hall Voltage= %.1f*10**-5 V" %(VH/10**-5))

Resistivity= 0.156 ohm-cm

Hall coefficient= -125 cm**3/c

Hall Voltage= -62.5*10**-5 V


## Example number 3.9 , Page number 111¶

In [38]:
#importing module
import math
from __future__ import division

#Variable declaration
Boron_impurity=10**18 #in cm**-3
Phosphorus_impurity=10**16 #in cm**-3

#Calculations
Density=Boron_impurity-(8*Phosphorus_impurity)

print("Density of majority carriers(holes)= %1.1f*10**17 cm**-3" %(Density/10**17))

Density of majority carriers(holes)= 9.2*10**17 cm**-3


## Example number 3.10 , Page number 115¶

In [39]:
#importing module
import math
from __future__ import division

#Variable declaration
J=14.14*10**-14 #current density in A/cm**2
v1=3*10**7 #hole group drift velocities in cm/s
v2=5*10**8 #in cm/s
v3=6*10**8 #in cm/s
q=1.6*10**-19 #in C
n=1000 #number of holes

#Calculations
x=((J/(n*q))-v1-v2-v3)

#Result
print("Drift velocity of remaining hole group= %.1f*10**8 cm s**-1" %(x/10**8))

Drift velocity of remaining hole group= -11.3*10**8 cm s**-1


## Example number 3.11 , Page number 115¶

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

#Variable declaration
E=1.43 #in eV
h=4.14*10**-15 #plancks constant in e*V*s
c=3*10**8 #in m/s

#Calculations
#a)
v=E/h

#b)
lamda=c/v

#Result
print("a)minimum frequency= %.3f*10**14 Hz\n" %(v/10**14))
print("b)wavelength= %.1f*10**-7 m" %(lamda/10**-7)) #The answers vary due to round off error

a)minimum frequency= 3.454*10**14 Hz

b)wavelength= 8.7*10**-7 m


## Example number 3.12 , Page number 116¶

In [41]:
#importing module
import math
from __future__ import division

#Variable declaration
R=10*10**3 #Resistance in ohm
V=5 #Voltage in V
J=50 #current density in A/cm**2
E=100 #in V/cm
q=1.6*10**10 #in eV
myu_p=410 #in cm**2/V*s
Nd=5*10**15 #in cm**-3

#Calculations
I=V/R #ohms law in mA
A=I/J #Area in cm**2
L=V/E
rho=(R*A)/L
sigma=1/rho #in ohm**-1 cm**-1
Na=(sigma/(myu_p*q))+Nd

#Result
print("a)Limiting electric field= %i V/cm\n" %E)
print("b)Length of resistor= %.1f*10**-2 cm\n" %(L/10**-2))
print("c)Area of cross-section= %.1f*10**-5 cm**2\n" %(A/10**-5))
print("d)Acceptor doping concentration= %.2f*10**15 cm**-3" %(Na/10**15)) #The answer provided in the textbook is wrong

a)Limiting electric field= 100 V/cm

b)Length of resistor= 5.0*10**-2 cm

c)Area of cross-section= 1.0*10**-5 cm**2

d)Acceptor doping concentration= 5.00*10**15 cm**-3


## Example number 3.13 , Page number 117¶

In [42]:
#importing module
import math
from __future__ import division

#Variable declaration
E_fi=0.35 #in eV
ni=1.5*10**10 #in cm**-3
q=1.6*10**-19 #in eV
myu_n=1400 #in cm**2/Vs
myu_p=500 #in cm**2/Vs
Const=0.0259 #constant value for kT in eV

#Calculations
#a)
n0=ni*math.exp((E_fi)/Const)

#c)
#doped substrate
sigma=q*(myu_n*n0) #in ohm**-1 cm**-1
rho=1/sigma

#undoped substrate
sigma1=q*(ni*(myu_n+myu_p))
rho1=1/sigma1

#Result
print("a)Doping value= %1.3f*10**16 cm**-3\n" %(n0/10**16))
print("c)resistivity of the doped pieces of silicon= %.4f ohm-cm\n" %rho)
print("c)resistivity of the undoped pieces of silicon= %.1f*10**5 ohm-cm" %(rho1/10**5)) #The answers vary due to round off error

a)Doping value= 1.109*10**16 cm**-3

c)resistivity of the doped pieces of silicon= 0.4025 ohm-cm

c)resistivity of the undoped pieces of silicon= 2.2*10**5 ohm-cm


## Example number 3.14 , Page number 119¶

In [43]:
#importing module
import math
from __future__ import division

#Variable declaration
ni=1.5*10**10 #in cm**-3
Ex=0.6 #position of energy level in eV
Const=0.0259 #constant value for kT in eV

#Calculations
n0=ni*math.exp(Ex/Const)

#Result
print("concentration of doping= %.3f*10**20 cm**-3" %(n0/10**20)) #The answers vary due to round off error

concentration of doping= 1.726*10**20 cm**-3