Chapter 3: Properties of Semiconductors

Example 1, Page 40

In [4]:
#Variable declaration
T=300;  #K
ni=1.5*10**16;    #Intrinsic carrier concentartion per m^3
yn=0.13;    #Electron mobility in m^2/(V*s)
yp=0.05;   #Hole mobility in m^2/(V*s)
e=1.6*10**-19;   #Charge of electron in C

#Calculations
Gi=e*ni*(yn+yp);    #Intrinsic conductivity
Ri=1/Gi;    #Intrinsic resistivity

#Results
print 'Intrinsic conductivity=%.3e S/m'%Gi;   #incorrect answer in textbook for Gi
print 'Intrinsic resistivity=%.3e ohm*meter'%Ri;

Intrinsic conductivity=4.320e-04 S/m
Intrinsic resistivity=2.315e+03 ohm*meter

Example 2, Page 40

In [6]:
#Variable declaration
Sn=480;     #Conductivity in S/m
yn=0.38;    #Electron mobility in m^2/(V*s)
e=1.6*10**-19;   #Charge of electron in C

#Calculations
Nd=Sn/(e*yn);   #Concentration of donor atoms per m^3

#Result
print 'Concentration of donor atoms = %.1e m^-3'%Nd;

Concentration of donor atoms = 7.9e+21 m^-3

Example 4, Page 41

In [11]:
#Variable declaration
T=300;  #K
ni=1.5*10**16;    #Intrinsic carrier concentartion per m^3
yn=0.13;    #Electron mobility in m^2/(V*s)
yp=0.05;   #Hole mobility in m^2/(V*s)
e=1.6*10**-19;   #Charge of electron in C
l=0.01;    #length in m
a=10**-6;    #cross sectional area in m^2

#Calculations
Gi=e*ni*(yn+yp);    #Intrinsic conductivity
Ri=l/(Gi*a);    #Required resistance

#Results
print 'Intrinsic conductivity=%.2e S/m'%Gi;
print 'required resistance = %.2f Mohm'%(Ri*10**-6);

Intrinsic conductivity=4.32e-04 S/m
required resistance = 23.15 Mohm

Example 5, Page 41

In [13]:
import math

#Variable declaration
z=(100./60);#z=conductiarrier concentration in /(m^3)
ni=2.5*10**(19);#ni=intrinsic conductivity of intrinsic material in S/m
#(P/N)=(1./2);#(P/N)=ratio of hole mobility(P) to electron mobility(N)
e=1.6*(10**-19);#e=charge of electron in Coulomb

#Calculations&Results
N=(z/(e*ni*(1+(1./2))))
print "N=%.4f (m^2)/(V.s)"%N
P=(N/2)
print "P=%.4f (m^2)/(V.s)"%P
#Nd+p=Na+n;n=electron concentration;p=hole concentration
#np=(ni^2)
Nd=(10**20)#Nd=donor concentration in /(m^3)
Na=5*(10**19)#Na=acceptor concentration in /(m^3)
n=(1./2)*((Nd-Na)+math.sqrt(((Nd-Na)**2)+(4*(ni**2))))
print "n=%.3e /(m**3)"%n
p=(ni**2)/n
print "p=%.3e /(m^3)"%p
Z=e*((n*N)+(p*P))#Z=conductivity of doped sample in S/m
print "Z=%.1f S/m"%Z
F=200#F=applied electric field in V/cm
J=Z*F#J=total conduction current density in A/(m^2)
print "J=%.f A/(m^2)"%J

N=0.2778 (m^2)/(V.s)
P=0.1389 (m^2)/(V.s)
n=6.036e+19 /(m**3)
p=1.036e+19 /(m^3)
Z=2.9 S/m
J=583 A/(m^2)

Example 6, Page 42

In [15]:
import math

#Variable declaration
ni=2.5*10**(19);#ni=intrinsic conductivity of intrinsic material in S/m
Nd=5*(10**19)#Nd=donor concentration in /(m^3)

#Calculations&Results
n=(1./2)*(Nd+math.sqrt((Nd**2)+(4*(ni**2))))#n=electron concentration
print "n=%.3e /(m^3)"%n
p=(ni**2)/n#p=hole concentration
print "p=%.3e /(m^3)"%p
N=0.38#N=electron mobility in (m^2)/(V.s)
P=0.18#P=hole mobility in (m^2)/(V.s)
e=1.6*(10**-19)#e=electronic charge in Coulomb
Z=e*((n*N)+(p*P))#Z=conductivity of doped sample in S/m
print "Z=%.3f S/m"%Z

n=6.036e+19 /(m^3)
p=1.036e+19 /(m^3)
Z=3.968 S/m

Example 7, Page 43

In [17]:
#Variable declaration
c=3*(10**8);#c=velocity of light in vacuum in m/s
h=6.6*(10**-34);#h=Planck's constant in J.s
Eg=1.98*1.6*(10**-19)#Eg=band gap in J

#Calculations
#calculating Y=required wavelength
Y=((c*h)/Eg)/(10**-9)

#Result
print "Y=%.f nm"%Y

Y=625 nm

Example 8, Page 43

In [19]:
#Variable declaration
RH=(10**-2);#RH=Hall coefficient in (m^3)/C
VH=(10**-3);#VH=Hall Voltage in V
b=2*(10**-3);#b=width in m
I=(10**-3);#I=current in A

#Calculations&Results
#RH=(VH*b)/(I*B)
B=(VH*b)/(I*RH)#B=magnetic field
print "B= %.1f T"%B
t=(10**-3)#t=thickness in m
FH=(VH/t)#FH=Hall field
print "FH=%.f V/m"%FH

B= 0.2 T
FH=1 V/m