Chapter 11: Semiconductors

Example 11.1, Page 343

In [1]:
#Variable Declaration
Pi=0.47;#given resistivity of intrinsic germanium
sigmai=1/Pi;#conductance
e=1.6*1e-19;#charge of electron
ue=0.38;#electron mobility
up=0.18;#hole mobility

#Calculation
ni=sigmai/(e*(ue+up));#intrinsic carrier density at 300K 

#Result
print 'intrinsic carrier density at 300K temp= %.2f*10^19 m^-3'%(ni/1e+19)

intrinsic carrier density at 300K temp= 2.37*10^19 m^-3

Example 11.2, Page 343

In [2]:
#Variable Declaration
e=1.6*1e-19;#charge of electron
ue=0.39;#electron mobility
up=0.19;#hole mobility
ni=2.4*1e19;#intrinsic carrier density 

#calculation
sigma=ni*e*(up+ue);

#Result
print 'conductivity of intrinsic semiconductor= %.2f ohm^-1*m^-1'%sigma

conductivity of intrinsic semiconductor= 2.23 ohm^-1*m^-1

Example 11.3, Page 343

In [3]:
from math import pi,exp

#Variable Declaration
m0=9.1*1e-31;
me=0.12*m0;
mp=0.28*m0;
Eg=0.67*1.6*1e-19
k=1.38*1e-23;#boltzman constant
h=6.62*1e-34;#plank's constant
T=300;

#Calculations
ni=2*((2*pi*k*T/h**2)**(3./2))*((me*mp)**(3./4))*exp(-Eg/(2*k*T));#intrinsic carrier concentration

#Result
print 'intrinsic carrier concentration is= %.1f *10^18 m^-3'%(ni/1e18)

intrinsic carrier concentration is= 4.7 *10^18 m^-3

Example 11.4, Page 343

In [5]:
from math import exp

#Variable Declaration
Eg1=0.36*1.6*1e-19;
Eg2=0.72*1.6*1e-19
k=1.38*1e-23;#boltzman constant
T=300;#tempreture in kelvin

#Calculation
#in this formula ni=2*((2*%pi*k*T/h^2)^(3/2))*((me*mp)^(3/4))*exp(-Eg/(2*k*T))ratio of nip/niq is given by:
x=exp((Eg2-Eg1)/(2*k*T));#ratio of nip/niq

#Result
print 'ratio of nip/niq is= %.f '%x
#Incorrect answer in the textbook

ratio of nip/niq is= 1050

Example 11.5, Page 344

In [6]:
#Variable Declaration
e=1.6*1e-19;#charge of electron
ue=0.39;#electron mobility
up=0.19;#hole mobility
ni=2.5*1e19;#intrinsic carrier density 
l=1e-2;#length of Ge rode
a=1e-4;#area of Ge rode

#Calculations&Results
sigma=ni*e*(up+ue);#conductivity of intrinsic semiconductor
print 'conductivity of intrinsic semiconductor= %.2f ohm^-1*m^-1'%sigma
P=1/sigma;
R=P*l/a;#resistance of Ge rode
print 'resistance of Ge rode =%.1f ohm'%R

conductivity of intrinsic semiconductor= 2.32 ohm^-1*m^-1
resistance of Ge rode =43.1 ohm

Example 11.6, Page 347

In [7]:
#Variable Declaration
ue=3850;#mobility of electron
sigma=5;#conductivity of ntype semiconductor
e=1.6*1e-19;#charge of electron

#Calculation
Nd=sigma/(e*ue);#density of donor atoms

#Result
print 'density of donor atoms is= %.2f*10^16 cm^-3'%(Nd/1e16)

density of donor atoms is= 0.81*10^16 cm^-3

Example 11.7, Page 351

In [8]:
from math import log

#Variable Declaration
#let Ef-Ev=0.4eV=x and Ef1-Ev=y
x=0.4;#Ef-Ev in eV
k=1.38*1e-23;#boltzmann constant
T=300;#tempreture in kelvin

#Calculations
#now p=Nv*exp(-x/(k*T))=Na and p'=Nv*exp(-y/(k*T))=2Na so ratio of this 2 is 2=exp(x-y/(k*T))
y=x-((k*T*log(2))/1.6e-19);#Ef1-Ev in eV

#Result
print 'Ef1-Ev in eV is= %.4feV'%y
#Answer varies due to rounding-off errors

Ef1-Ev in eV is= 0.3821eV

Example 11.8, Page 352

In [9]:
#Variable Declaration
#let Ec1-Ef=0.3eV=x and Ec2-Ef=y
x=0.3;#Ec-Ef in eV
T1=300.;#tempreture in kelvin
T2=330.;#tempreture in kelvin

#Calculation
#Ec-Ef=k*T*log(Nc/Nd) so..
y=T2*x/T1;#Ec2-Ef in eV

#Result
print 'Ec2-Ef in eV is= %.2f eV'%y

Ec2-Ef in eV is= 0.33 eV

Example 11.9, Page 356

In [11]:
#Variable Declaration
B=0.5;#given flux density
d=3*1e-3;#given thickness
J=500.;#given current density
n=1e21;#given donor density
e=1.6*1e-19;#charge of electron

#Calculation
Vh=(B*J*d)/(n*e);#hall voltage

#Result
print 'hall voltage is= %.1f mV'%(Vh/1e-3)

hall voltage is= 4.7 mV

Example 11.10, Page 357

In [12]:
from math import pi

#Variable Declaration
P=8.9*1e-3;#resistivity of doped sillicon
Rh=3.6*1e-4;#hall coefficient
e=1.6*1e-19;#charge of electron

#Calculations&Results
ne=(3*pi)/(8*Rh*e);#carrier density of electron
print 'carrier density of electrons = %.3f*10^22 m^-3'%(ne/1e22)
ue=1./(P*ne*e);#mobility of electon
print 'mobility of charges = %.4f m^2*V^-1*s^-1'%ue

carrier density of electrons = 2.045*10^22 m^-3
mobility of charges = 0.0343 m^2*V^-1*s^-1