# 18: Transport properties of semiconductors¶

## Example number 18.1, Page number 26¶

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
T=300;    #temperature(K)
mew_e=0.4;   #electron mobility(m**2/Vs)
mew_h=0.2;      #hole mobility(m**2/Vs)
Eg=0.7;     #band gap(eV)
m0=9.1*10**-31;   #mass of electron(kg)
mestar=0.55*m0;   #electron effective mass(kg)
mhstar=0.37*m0;   #hole effective mass(kg)
k=1.38*10**-23;   #boltzmann constant
h=6.626*10**-34;  #planck's constant
e=1.6*10**-19;    #charge of electron(c)

#Calculation
a=(2*math.pi*k*T/(h**2))**(3/2);
Eg=Eg*e;    #band gap(J)
b=-Eg/(k*T);
ni=2*a*((mhstar*mestar)**(3/4))*math.exp(b);   #intrinsic concentration(per m**3)
sigma=ni*e*(mew_e+mew_h);   #intrinsic conductivity(per ohm m)
rho=1/sigma;   #intrinsic resistivity(ohm m)

#Result
print "intrinsic concentration is",round(ni/10**13,3),"*10**13 per m**3"
print "intrinsic conductivity is",round(sigma*10**6,3),"*10**-6 per ohm m"
print "intrinsic resistivity is",round(rho/10**6,2),"*10**6 ohm m"

intrinsic concentration is 1.352 *10**13 per m**3
intrinsic conductivity is 1.298 *10**-6 per ohm m
intrinsic resistivity is 0.77 *10**6 ohm m


## Example number 18.2, Page number 26¶

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
T=300;    #temperature(K)
k=1.38*10**-23;   #boltzmann constant
Nd=10**16;   #donor concentration(per cm**3)
ni=1.45*10**10;   #intrinsic concentration(per cm**3)
e=1.6*10**-19;    #charge of electron(c)

#Calculation
Efd_Efi=k*T*math.log(Nd/ni);    #fermi energy(J)
Efd_Efi=Efd_Efi/e;   #fermi energy(eV)

#Result
print "fermi energy is",round(Efd_Efi,3),"eV"

fermi energy is 0.348 eV


## Example number 18.3, Page number 27¶

In [13]:
#importing modules
import math
from __future__ import division

#Variable declaration
mew_e=1.35;   #electron mobility(m**2/Vs)
mew_h=0.45;      #hole mobility(m**2/Vs)
ni=1.45*10**13;  #intrinsic concentration(per m**3)
NSi=5*10**28;   #atomic concentration(per m**3)
e=1.6*10**-19;    #charge of electron(c)
LbyA=1;   #Si crystal(cm**3)

#Calculation
sigmai=ni*e*(mew_e+mew_h);   #intrinsic conductivity(per ohm m)
rho=1/sigmai;   #intrinsic resistivity(ohm m)
LbyA=LbyA*10**2;   #Si crystal(m**3)
R1=rho*LbyA;  #resistance(ohm)
Nd=NSi/10**9;   #donor concentration(per m**3)
p=(ni**2)/Nd;   #hole concentration(per m**3)
sigma=Nd*e*mew_e;  #conductivity(per ohm m)
R2=(1/sigma)*100;  #resistance(ohm)

#Result
print "resistance of 1cm**3 pure Si crystal is",round(R1/10**7,2),"*10**7 ohm"
print "resistance when crystal is doped with arsenic is",round(R2,2),"ohm"

resistance of 1cm**3 pure Si crystal is 2.39 *10**7 ohm
resistance when crystal is doped with arsenic is 9.26 ohm


## Example number 18.4, Page number 28¶

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

#Variable declaration
T=300;   #temperature(K)
rho=2.12;   #resistivity(ohm m)
mew_e=0.36;   #electron mobility(m**2/Vs)
mew_h=0.17;      #hole mobility(m**2/Vs)
mestar=0.5*m0;   #electron effective mass(kg)
mhstar=0.37*m0;   #hole effective mass(kg)
m0=9.1*10**-31;   #mass of electron(kg)
k=1.38*10**-23;   #boltzmann constant
h=6.626*10**-34;  #planck's constant
e=1.6*10**-19;    #charge of electron(c)

#Calculation
sigma=1/rho;   #conductivity(per ohm m)
ni=sigma/(e*(mew_e+mew_h));   #intrinsic concentration(per m**3)
a=(2*math.pi*k*T/(h**2))**(3/2);
NC=2*a*(mestar**(3/2));
NV=2*a*(mhstar**(3/2));
b=(NC*NV)**(1/2);
Eg=2*k*T*math.log(b/ni);    #energy gap of semiconductor(J)
Eg=Eg/e;    #energy gap of semiconductor(eV)

#Result
print "energy gap of semiconductor is",round(Eg,3),"eV"

energy gap of semiconductor is 0.727 eV


## Example number 18.5, Page number 29¶

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

#Variable declaration
e=1.6*10**-19;    #charge of electron(c)
mew_e=0.39;   #electron mobility(m**2/Vs)
mew_h=0.19;      #hole mobility(m**2/Vs)
ni=2.4*10**19;  #intrinsic concentration(per m**3)

#Calculation
sigmai=ni*e*(mew_e+mew_h);    #conductivity of Ge(per Wm)

#Result
print "conductivity of Ge is",round(sigmai,3),"per Wm"

conductivity of Ge is 2.227 per Wm


## Example number 18.6, Page number 29¶

In [21]:
#importing modules
import math
from __future__ import division

#Variable declaration
EC_EF300=-0.3;    #position of fermi level(eV)
T1=300;   #temperature(K)
T2=330;   #temperature(K)
k=1.38*10**-23;   #boltzmann constant
e=1.6*10**-19;    #charge of electron(c)

#Calculation
EC_EF330=-EC_EF300*T2/T1;   #new position of fermi level(eV)

#Result
print "new position of fermi level is",EC_EF330,"eV"

new position of fermi level is 0.33 eV


## Example number 18.7, Page number 30¶

In [25]:
#importing modules
import math
from __future__ import division

#Variable declaration
T1=20;    #temperature(C)
T2=40;    #temperature(C)
Eg=0.72;   #energy gap(eV)
e=1.6*10**-19;    #charge of electron(c)
k=1.38*10**-23;   #boltzmann constant
sigmai20=2;    #conductivity(per ohm m)

#Calculation
T1=T1+273;   #temperature(K)
T2=T2+273;   #temperature(K)
Eg=Eg*e;   #energy gap(J)
a=(T2/T1)**(3/2);
b=Eg/(2*k);
c=(1/T1)-(1/T2);
ni40byni20=a*math.exp(b*c);    #ratio of intrinsic concentration
sigmai40=sigmai20*ni40byni20;   #conductivity at 40C(per ohm m)

#Result
print "conductivity at 40C is",round(sigmai40,3),"per ohm m"

conductivity at 40C is 5.487 per ohm m


## Example number 18.8, Page number 30¶

In [27]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=1.6*10**-19;    #charge of electron(c)
k=1.38*10**-23;   #boltzmann constant
T=300;   #temperature(K)
m0=9.1*10**-31;   #mass of electron(kg)
Eg=1.1;   #energy gap(eV)
mestar=0.31*m0;   #effective mass of electron(kg)

#Calculation
Eg=Eg*e;    #energy gap(J)
a=(2*math.pi*k*T*mestar/(h**2))**(3/2);
b=-Eg/(2*k*T);
ni=2*a*math.exp(b);   #intrinsic concentration(per m**3)

#Result
print "intrinsic concentration is",round(ni/10**15,4),"*10**15 per m**3"

intrinsic concentration is 2.5367 *10**15 per m**3


## Example number 18.9, Page number 31¶

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

#Variable declaration
RH=-0.55*10**-10;    #hall coefficient(m**3/As)
sigma=5.9*10**7;    #conductivity(per ohm m)

#Calculation
mewd=-RH*sigma;     #drift mobility(m**2/Vs)

#Result
print "drift mobility is",round(mewd*10**3,1),"*10**-3 m**2/Vs"

drift mobility is 3.2 *10**-3 m**2/Vs


## Example number 18.10, Page number 31¶

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

#Variable declaration
sigma=5.9*10**7;    #conductivity(per ohm m)
e=1.6*10**-19;    #charge of electron(c)
mew=3.2*10**-3;   #drift velocity(m**2/Vs)
ne=8900*10**3;   #number of free electrons per atom
w=63.5;    #atomic weight of Cu(kg)

#Calculation
ni=sigma/(e*mew);   #intrinsic concentration(per m**3)
n=N*ne/w;  #concentration of free electrons(per m**3)
a=ni/n;    #average number of electrons

#Result
print "intrinsic concentration is",round(ni/10**29,2),"*10**29 per m**3"
print "concentration of free electrons is",round(n/10**28,2),"*10**28 per m**3"
print "average number of electrons is",int(a)

intrinsic concentration is 1.15 *10**29 per m**3
concentration of free electrons is 8.44 *10**28 per m**3
average number of electrons is 1


## Example number 18.11, Page number 32¶

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

#Variable declaration
RH=3.66*10**-11;   #hall coefficient(m**3/As)
sigma=112*10**7;   #conductivity(per ohm m)
e=1.6*10**-19;    #charge of electron(c)

#Calculation
n=3*math.pi/(8*RH*e);    #concentration of electrons(per m**3)
mew_e=sigma/(n*e);    #electron mobility(m**2/Vs)

#Result
print "concentration of electrons is",round(n/10**29,1),"*10**29 per m**3"
print "electron mobility is",round(mew_e,3),"m**2/Vs"

concentration of electrons is 2.0 *10**29 per m**3
electron mobility is 0.035 m**2/Vs


## Example number 18.12, Page number 33¶

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

#Variable declaration
i=50;   #current(A)
B=1.5;  #magnetic field(T)
n=8.4*10**28;   #concentration of electrons(per m**3)
t=0.5;   #thickness(cm)
w=2;   #width of slab(cm)
e=1.6*10**-19;    #charge of electron(c)

#Calculation
w=w*10**-2;   #width of slab(m)
VH=B*i/(n*e*w);    #hall voltage(V)

#Result
print "hall voltage is",round(VH*10**7,2),"*10**-7 V"

hall voltage is 2.79 *10**-7 V