# 8: Semiconductors¶

## Example number 8.1, Page number 8.55¶

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

#Variable declaration
ni=2.5*10**19;     #intrinsic concentration(per m**3)
mewn=0.4;     #mobility of electrons(m**2/Vs)
mewp=0.2;    #mobility of holes(m**2/Vs)
e=1.6*10**-19;

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

#Result
print "resistivity is",round(rhoi,5),"ohm m"

resistivity is 0.41667 ohm m


## Example number 8.2, Page number 8.56¶

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

#Variable declaration
mewn=0.3;     #mobility of electrons(m**2/Vs)
rho=0.25;     #resistivity(ohm m)
e=1.6*10**-19;

#Calculation
n=1/(rho*e*mewn);    #number of donor atoms(per m**3)

#Result
print "number of donor atoms is",round(n/10**19,3),"*10**19 per m**3"

number of donor atoms is 8.333 *10**19 per m**3


## Example number 8.3, Page number 8.56¶

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

#Variable declaration
mewn=0.21;     #mobility of electrons(m**2/Vs)
e=1.6*10**-19;
Kb=1.38*10**-23;    #boltzmann constant
T=300;    #temperature(K)

#Calculation
Dn=mewn*Kb*T/e;     #diffusion coefficient of electrons(m**2/s)

#Result
print "diffusion coefficient of electrons is",round(Dn*10**4,2),"*10**-4 m**2/s"

diffusion coefficient of electrons is 54.34 *10**-4 m**2/s


## Example number 8.4, Page number 8.56¶

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

#Variable declaration
Rh=3.22*10**-4;    #hall coefficient(m**3/C)
e=1.6*10**-19;
rho=8.5*10**-3;    #resistivity(ohm m)

#Calculation
p=1/(Rh*e);      #carrier concentration(per m**3)
mewp=Rh/rho;     #mobility of holes(m**2/Vs)

#Result
print "carrier concentration is",round(p/10**21,1),"*10**21 per m**3"
print "#mobility of holes is",round(mewp,5),"m**2/Vs"

carrier concentration is 19.4 *10**21 per m**3
#mobility of holes is 0.03788 m**2/Vs


## Example number 8.5, Page number 8.57¶

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

#Variable declaration
mewe=0.36;     #mobility of electrons(m**2/Vs)
mewh=0.17;    #mobility of holes(m**2/Vs)
e=1.6*10**-19;
rhoi=2.12;    #resistivity(ohm m)

#Calculation
ni=1/(rhoi*e*(mewe+mewh));     #intrinsic concentration(per m**3)

#Result
print "intrinsic concentration is",round(ni/10**16,2),"*10**16 per m**3"

intrinsic concentration is 556.25 *10**16 per m**3


## Example number 8.6, Page number 8.57¶

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

#Variable declaration
mewe=0.39;     #mobility of electrons(m**2/Vs)
mewh=0.19;    #mobility of holes(m**2/Vs)
e=1.6*10**-19;
ni=2.4*10**19;     #intrinsic concentration(per m**3)

#Calculation
rhoi=1/(ni*e*(mewe+mewh));           #resistivity(ohm m)

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

resistivity is 0.449 ohm m


## Example number 8.7, Page number 8.57¶

In [49]:
#importing modules
import math
from __future__ import division

#Variable declaration
mewe=0.135;     #mobility of electrons(m**2/Vs)
mewh=0.048;    #mobility of holes(m**2/Vs)
e=1.6*10**-19;
ni=1.5*10**16;     #intrinsic concentration(per m**3)
Nd=10**23;         #doping concentration(per m**3)

#Calculation
sigma=ni*e*(mewe+mewh);     #conductivity(per ohm m)
p=ni**2/Nd;      #hole concentration(per m**3)
sigman=Nd*e*mewe;     #conductivity(per ohm m)

#Result
print "conductivity is",round(sigma*10**3,3),"*10**-3 per ohm m"
print "hole concentration is",p/10**9,"*10**9 per m**3"
print "conductivity is",sigman/10**3,"*10**3 per ohm m"

conductivity is 0.439 *10**-3 per ohm m
hole concentration is 2.25 *10**9 per m**3
conductivity is 2.16 *10**3 per ohm m


## Example number 8.8, Page number 8.58¶

In [50]:
#importing modules
import math
from __future__ import division

#Variable declaration
Rh=3.66*10**-4;    #hall coefficient(m**3/C)
e=1.6*10**-19;
rhoh=8.93*10**-3;    #resistivity(ohm m)

#Calculation
p=1/(Rh*e);      #carrier concentration(per m**3)
mewp=Rh/rhoh;     #mobility of holes(m**2/Vs)

#Result
print "carrier concentration is",round(p/10**22,1),"*10**22 per m**3"
print "#mobility of holes is",round(mewp*10**2,3),"*10**-2 m**2/Vs"

carrier concentration is 1.7 *10**22 per m**3
#mobility of holes is 4.099 *10**-2 m**2/Vs


## Example number 8.9, Page number 8.58¶

In [51]:
#importing modules
import math
from __future__ import division

#Variable declaration
mewe=0.13;     #mobility of electrons(m**2/Vs)
mewh=0.05;    #mobility of holes(m**2/Vs)
e=1.6*10**-19;
ni=1.5*10**16;     #intrinsic concentration(per m**3)

#Calculation
sigma=ni*e*(mewe+mewh);     #conductivity(per ohm m)

#Result
print "conductivity is",sigma*10**4,"*10**-4 per ohm m"

conductivity is 4.32 *10**-4 per ohm m


## Example number 8.10, Page number 8.58¶

In [52]:
#importing modules
import math
from __future__ import division

#Variable declaration
mewe=0.14;     #mobility of electrons(m**2/Vs)
mewh=0.05;    #mobility of holes(m**2/Vs)
e=1.6*10**-19;
ni=1.5*10**16;     #intrinsic concentration(per m**3)
A=28.09;     #atomic weight
D=2.33*10**3;    #density(kg/m**3)

#Calculation
N=Na*D/A;    #number of atoms(per m**3)
n=N/10**8;    #electron concentration(per m**3)
p=ni**2/n;    #hole concentration(per m**3)
sigma=e*((n*mewe)+(p*mewh));     #conductivity(per ohm m)

#Result
print "conductivity is",round(sigma,1),"per ohm m"

conductivity is 11.2 per ohm m


## Example number 8.11, Page number 8.59¶

In [53]:
#importing modules
import math
from __future__ import division

#Variable declaration
mewe=0.36;     #mobility of electrons(m**2/Vs)
mewh=0.18;    #mobility of holes(m**2/Vs)
e=1.6*10**-19;
ni=2.5*10**19;     #intrinsic concentration(per m**3)

#Calculation
n=N/10**6;    #electron concentration(per m**3)
p=ni**2/n;    #hole concentration(per m**3)
rhoi=1/(e*((n*mewe)+(p*mewh)));     #resistivity(per ohm m)

#Result
print "resistivity is",round(rhoi*10**4,2),"*10**-4 per ohm m"

resistivity is 4.13 *10**-4 per ohm m


## Example number 8.12, Page number 8.60¶

In [54]:
#importing modules
import math
from __future__ import division

#Variable declaration
np=2.4*10**9;    #carrier concentration(per m**3)

#Calculation
p=np/2;     #hole concentration(per m**3)

#Result
print "hole concentration is",p/10**9,"*10**9 per m**3"

hole concentration is 1.2 *10**9 per m**3


## Example number 8.13, Page number 8.60¶

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

#Variable declaration
mewn=0.35;     #mobility of electrons(m**2/Vs)
e=1.602*10**-19;
rho=0.2;    #resistivity(ohm m)

#Calculation
n=1/(rho*e*mewn);      #density of donor atoms

#Result
print "density of donor atoms is",round(n/10**19,2),"*10**19 electrons/m**3"

density of donor atoms is 8.92 *10**19 electrons/m**3


## Example number 8.14, Page number 8.60¶

In [56]:
#importing modules
import math
from __future__ import division

#Variable declaration
Kb=1.38*10**-23;    #boltzmann constant
T1=300;    #temperature(K)
T2=320;    #temperature(K)
rho1=5;    #resistivity(ohm m)
rho2=2.5;    #resistivity(ohm m)

#Calculation
Eg=2*Kb*math.log(rho1/rho2)/((1/T1)-(1/T2));     #energy gap(J)

#Result
print "energy gap is",round(Eg/e,3),"eV"

energy gap is 0.573 eV


## Example number 8.15, Page number 8.61¶

In [57]:
#importing modules
import math
from __future__ import division

#Variable declaration
Kb=1.38*10**-23;    #boltzmann constant
T=300;    #temperature(K)
mewe=0.19;     #mobility of electrons(m**2/Vs)
e=1.6*10**-19;

#Calculation
Dn=mewe*Kb*T/e;      #diffusion coefficient(m**2/sec)

#Result
print "diffusion coefficient is",round(Dn*10**3,2),"*10**-3 m**2/sec"

diffusion coefficient is 4.92 *10**-3 m**2/sec


## Example number 8.16, Page number 8.61¶

In [59]:
#importing modules
import math
from __future__ import division

#Variable declaration
Kb=1.38*10**-23;    #boltzmann constant
T1=293;    #temperature(K)
T2=305;    #temperature(K)
rho1=4.5;    #resistivity(ohm m)
rho2=2.0;    #resistivity(ohm m)

#Calculation
Eg=2*Kb*math.log(rho1/rho2)/((1/T1)-(1/T2));     #energy gap(J)

#Result
print "energy gap is",round(Eg/e,2),"eV"

energy gap is 1.04 eV