# Chapter 2: Fundamental of Semiconductor Theory¶

## Example 2.1,Page number 43¶

In [1]:
import math

#given

n=1;
Ne=2*n**2;
print"Maximum number of electron in 1st shell is ",Ne;  #Result
n2=2;  #shell no
Ne2=2*n2**2;  #shell no
print"Maximum number of electron in 2nd shell is ",Ne2; #Result

Maximum number of electron in 1st shell is  2
Maximum number of electron in 2nd shell is  8


## Example 2.2,Page number 45¶

In [12]:
import math

#given

#Given  for silicon for temp 0-400K
Eg0_Si=1.17;         #in eV
A=4.73*10**-4;       #in eV/K
B=636;
for i in range(1,9):
T=50*i;          #degree/Kelvin
Eg_Si=Eg0_Si-(A*T**2)/(B+T);
print"Band gap energy of silicon at ",T," K is ",round(Eg_Si,3),"eV ";  #result

#Given  for Germanium for temp 0-400K
print"\n"
Eg0_Ge=0.7437;           #in eV
A_Ge=4.774*10**-4;       #in eV/K
B_Ge=235;
for i in range(1,9):
T=50*i;              #degree/Kelvin
Eg_Ge=Eg0_Ge-(A_Ge*T**2)/(B_Ge+T);
print"Band gap energy of germanium at ",T," K is ",round(Eg_Ge,3),"eV "; #result

#Given  for GaAs for temp 0-400K
print"\n"
Eg0_Ga=1.519;       #in eV
A_Ga=5.405*10**-4;  #in eV/K
B_Ga=204;
for i in range(1,9):
T=50*i;         #degree/Kelvin
Eg_Ga=Eg0_Ga-(A_Ga*T**2)/(B_Ga+T);
print"Band gap energy of GaAs at ",T ,"K is ",round(Eg_Ga,3),"eV";  #result

Band gap energy of silicon at  50  K is  1.168 eV
Band gap energy of silicon at  100  K is  1.164 eV
Band gap energy of silicon at  150  K is  1.156 eV
Band gap energy of silicon at  200  K is  1.147 eV
Band gap energy of silicon at  250  K is  1.137 eV
Band gap energy of silicon at  300  K is  1.125 eV
Band gap energy of silicon at  350  K is  1.111 eV
Band gap energy of silicon at  400  K is  1.097 eV

Band gap energy of germanium at  50  K is  0.74 eV
Band gap energy of germanium at  100  K is  0.729 eV
Band gap energy of germanium at  150  K is  0.716 eV
Band gap energy of germanium at  200  K is  0.7 eV
Band gap energy of germanium at  250  K is  0.682 eV
Band gap energy of germanium at  300  K is  0.663 eV
Band gap energy of germanium at  350  K is  0.644 eV
Band gap energy of germanium at  400  K is  0.623 eV

Band gap energy of GaAs at  50 K is  1.514 eV
Band gap energy of GaAs at  100 K is  1.501 eV
Band gap energy of GaAs at  150 K is  1.485 eV
Band gap energy of GaAs at  200 K is  1.465 eV
Band gap energy of GaAs at  250 K is  1.445 eV
Band gap energy of GaAs at  300 K is  1.422 eV
Band gap energy of GaAs at  350 K is  1.399 eV
Band gap energy of GaAs at  400 K is  1.376 eV


## Example 2.3,Page number 52¶

In [14]:
import math

#given

l=10*10**-3;        #in m
w=2*10**-3;         #in m
h=2*10**-3;         #in m
V=12;               #in V
u_n=0.14;          #in  m*m/V*s
u_p=0.05;          #in m*m/V*s
q_n=1.6*10**-19;     #in Columbs
q_p=1.6*10**-19;     #in Columbs
p_i=2.4*10**19;      #in columbs
n_i=2.4*10**19;      #in columbs
E=V/l;
v_n=E*u_n;
v_p=E*u_p;
J_n=n_i*q_n*v_n;
J_p=p_i*q_p*v_p;
J=J_n+J_p;
print"Electron velocity :vn is ",v_n,"m/s";      #result
print"Hole velocity :vp is  ",v_p/1000,"km/s";  #result
print"Current density : Jn ",J,"A/m^2";           #result
A=88*10**-6;
I_T=J*A;
print"Total current :I_T is",round(I_T*1000,4),"mA";      #result

Electron velocity :vn is  168.0 m/s
Hole velocity :vp is   0.06 km/s
Current density : Jn  875.52 A/m^2
Total current :I_T is 77.0458 mA


## Example 2.4,Page number 53¶

In [17]:
import math

#given

n_i=2*10**17;          #electron/m*m*m
p=5.7*10**20;          #holes/m*m*m
u_n=0.14;           #in  m*m/V*s
u_p=0.05;           #in m*m/V*s
q_n=1.6*10**-19;     #in Columbs
q_p=1.6*10**-19;     #in Columbs
n=(n_i)**2/p;
print"Electron :n is ","{0:.3e}".format(n),"electrons ";  #result
n=7*10**13
P=(n*u_n*q_n)+(p*u_p*q_p);
print"Conductivity :P is ",round(P,4),"S/m ";                      #result

Electron :n is  7.018e+13 electrons
Conductivity :P is  4.56 S/m


## Example 2.5,Page number 55¶

In [19]:
import math

#given

NA=10**22;           #acceptors/m*m*m
ND=1.2*10**21;       #donors/m*m*m
T=298;               #in Kelvin
k=1.38*10**-23;      #Boltzman Constant in J/K
q=1.6*10**-19;       #charge of electron  in C
Vt=k*T/q;            #thermal voltage  in V
print" VT is ",Vt*1000,"mV";     #result
n_i=2.4*10**17;                  #carrier/m**3 for silicon
VB=Vt*log(NA*ND/n_i**2);         #barrier voltage in V
print" Barrier Voltage of Silicon VB is ",round(VB*1000,4),"mV";     #result

 VT is  25.7025 mV
Barrier Voltage of Silicon VB is  492.3224 mV


## Example 2.6,Page number 56¶

In [22]:
import math

#given

Is=0.12;          #in pAmp
V=0.6;            #in V
T=293;            #in Kelvin
k=1.38*10**-23;      #Boltzmann's Constant in J/K
q=1.6*10**-19;       # charge of electron in C
Vt=k*T/q;            #thermal voltage
print"VT(20 deg Cel) is  ",round(Vt,4),"V";    #result in book is misprint
T1=373;              #in Kelvin
n=1.25;
Vt1=k*T1/q;          #thermal voltage
print"VT(100 deg Cel) is  ",round(Vt1,4),"V";
I=Is*(math.e**(V/(n*Vt1))-1);        #forward biasing current in mircoA
print"I(100 deg Cel) is ",round(I/10**6,4),"microampere";   #result

VT(20 deg Cel) is   0.0253 V
VT(100 deg Cel) is   0.0322 V
I(100 deg Cel) is  0.3622 microampere


## Example 2.7,Page number 56¶

In [23]:
import math

#given

Is=100;          #in nAmp
Ts=100;          #in Kelvin
I_s=Is*10**-9*2**(Ts/10);       #I_s will be in nm
print" I(100 deg Cel) is ",I_s*10**6,"microampere";   #converted to microA from nm
# wrong calculation in the book

 I(100 deg Cel) is  102.4 microampere


## Example 2.8,Page number 59¶

In [25]:
import math

#given

Br_Si=1.79*10**-15;             #Recombination coefficient for Si
Br_Ge=5.25*10**-14;             #Recombination coefficient for Ge
Br_GeAs=7.21*10**-10;           #Recombination coefficient for GeAs
Br_InAs=8.5*10**-11;            #Recombination coefficient for InAs
P_N=2*10**20;                   #per cubic cm

print"T_Ge is ",round(T_Ge/10**-6,4),"micro-s";    #result


T_Ge is  0.0952 micro-s