Chapter No 3 : Excess Carriers In Semiconductors

Example 3.1, Page No 145

In [20]:
#initialisation of variables
n_o = 10**17          #in/cm^3
n_i = 1.5*10**10      #in /cm^3

#CALCULATIONS
p_o = ((n_i)**(2))/n_o      #in holes/cm^3

#RESULTS
print('The hole concentration  is =%.f  in holes/cm^3' %p_o)

The hole concentration  is =2250  in holes/cm^3

Example 3.3, Page No 146

In [21]:
import math
#initialisation of variables
n_i = 1.5 * 10**10              #in /cm^3 for silicon
N_d = 10**17                    #in atoms/cm^3
n_o = 10**17                   #electrons/cm^3
KT = 0.0259

#CALCULATIONS
# E_r - E_i = KT * log(n_o/n_i)
del_E = KT * math.log(n_o/n_i)                 #in eV

#RESULTS
print('The energy band for this type material is Ei =%.2f eV' %del_E)

The energy band for this type material is Ei =0.41 eV

Example 3.4 Page No 147

In [22]:
import math

#initialisation of variables
K = 1.38*10**-23               #in J/K
T = 27                     #in degree C
T = T + 273               #in K
e = 1.6*10**-19          
Miu = 0.17             #in m^2/v-s
Miu1 = 0.025           #in m^2/v-s

#CALCULATIONS
D_n = ((K*T)/e)*Miu        #in m^2/s
D_p = ((K*T)/e)*Miu1    #in m^2/s


#RESULTS
print('The diffusion coefficient  of electrons  is =%.2f X 10^-4 in m^2/s ' %(D_n*(10**4)))
print('The diffusion coefficient  of holes  is =%.2f X 10^-4 in m^2/s ' %(D_p*(10**4)))

The diffusion coefficient  of electrons  is =43.99 X 10^-4 in m^2/s 
The diffusion coefficient  of holes  is =6.47 X 10^-4 in m^2/s

Example 3.5, Page No 147

In [23]:
import math

#initialisation of variables
Miu_n = 0.15           #in m^2/v-s
K = 1.38*10**-23      
T = 300                #in K
e = 1.6*10**-19      #in C

#CALCULATIONS
D_n = Miu_n*((K*T)/e)            #in m^2/s
Torque_n = 10**-7                 #in s
L_n = math.sqrt(D_n*Torque_n)    #in m
del_n = 10**20                   #electrons/m^3
J_n = (e*D_n*del_n)/L_n        #in A/m^2

#RESULTS
print('The diffusion length is =%.2f  X 10^-4 in m' %(L_n*(10**5)))
print('The diffusion current density  is =%.2f X 10^3 in A/m^2 ' %(J_n/(10**3)))

The diffusion length is =1.97  X 10^-4 in m
The diffusion current density  is =3.15 X 10^3 in A/m^2

Example 3.6 Page No 147

In [24]:
import math

#initialisation of variables
Sigma_n = 0.1              #in (ohm-cm)^-1
Miu_n = 1300
q = 1.6*10**-19             #in C

#CALCULATIONS
n_n = Sigma_n/(Miu_n*q)        #in electrons/cm^3 
n_i = 1.5*10**10
p_n = ((n_i)**2)/n_n           #in holes/cm^3
p_n = p_n * 10**6          #in holes/m^3
n_n=n_n*10**6

#RESULTS
print('Concentration of electrons  is =%.2f X 10^20 per m^3 ' %(n_n/(10**20)))
print('Concentration of holes  is =%.2f X 10^11 per m^3 ' %(p_n/(10**11)))

Concentration of electrons  is =4.81 X 10^20 per m^3 
Concentration of holes  is =4.68 X 10^11 per m^3

Example 3.7 Page No 147

In [25]:
import math

#initialisation of variables
L = 100*10**-6         #in m
Miu_e = 0.13          #in m^2/V-s
Torque_h = 10**-6     #in s
Miu_h = 0.05          #in m^2/v-s
V = 12                 #in V

#CALCULATIONS
Torque_n = ((L)**2)/(Miu_e*V)             #in s
P = (Torque_h/Torque_n)*(1+(Miu_h/Miu_e))

#RESULTS
print('Electron transit time  is =%.2f X 10^-9 in sec' %(Torque_n*(10**9)))
print('Photoconductor gain is =%.2f  ' %P)

Electron transit time  is =6.41 X 10^-9 in sec
Photoconductor gain is =216.00

Example 3.8, Page No 147

In [26]:
import math

#initialisation of variables
q = 1.6*10**-19              #in C
n_i = 2.5*10**13
Miu_n = 3800             #in cm^2/V-s
Miu_p = 1800             #in cm^2/V-s

#CALCULATIONS
Sigma = n_i*(Miu_n + Miu_p)*q             #in (ohm-cm)^-1
Rho = 1/Sigma               #in ohm-cm
N_D =4.4*10**22/10**8     #in atoms/cm^3
Sigma_n = N_D * Miu_n*q   #in (ohm-cm)^-1 
Rho1 = 1/Sigma_n     #in ohm cm

#RESULTS
print('The resistivity  is =%.2f in ohm-cm ' %Rho)
print('The resistivity drops  is =%.2f in ohm cm ' %Rho1)

The resistivity  is =44.64 in ohm-cm 
The resistivity drops  is =3.74 in ohm cm

Example 3.9 Page No 148

In [27]:
import math 

#initialisation of variables
n_i = 10**16          #in /m^3
N_D = 10**22       #in /m^3

#CALCULATIONS
n = N_D        #in /m^3
p = ((n_i)**2)/n   #in /m^3


#RESULTS
print('The concentration of  is =%.2f X 10^21  electrons per m^3' %(n/(10**21)))
print('The concentration of  is =%.2f X 10^9 holes per m^3 ' %(p/(10**9)))

The concentration of  is =10.00 X 10^21  electrons per m^3
The concentration of  is =10.00 X 10^9 holes per m^3

Example 3.10 Page No 148

In [28]:
import math

#initialisation of variables
Rho = 9.6*10**-2       #ohm-m
Sigma_n = 1/Rho        #in (ohm-m)^-1
Miu_n = 1300           #in cm^2/V-s

#CALCULATIONS
Miu_n = Miu_n * 10**-4  #in m^2/V-s
q = 1.6*10**-19     #in C
N_D = Sigma_n/(Miu_n*q)           #in atoms/m^3
d = 5*10**22                     #in atoms/cm^3
d = d * 10**6                   #// in atoms/m^3
R_d = N_D/d                   #Ratio 

#RESULTS
print('Ratio of donor atom to silicon atoms per unit volume is =%.2f X 10^-8  ' %(R_d*(10**8)))

Ratio of donor atom to silicon atoms per unit volume is =1.00 X 10^-8

Example 3.11 Page No 148

In [29]:
import math

#initialisation of variables
n_i = 1.5*10**10            #in /cm^3
n_n = 2.25*10**15           #in /cm^3

#CALCULATIONS
p_n = ((n_i)**2)/n_n         #in /cm^3

#RESULTS
print('The concentration of  is =%.2f X 10^5 holes per cm^3 ' %(p_n/(10**5)))
print('Donor impurity per cm^3 is =%.2f X 10^15 ' %(n_n/(10**15)))

The concentration of  is =1.00 X 10^5 holes per cm^3 
Donor impurity per cm^3 is =2.25 X 10^15

Example No 3.12 Page No 149

In [30]:
#initialisation of variables
N_A = 2*10**16           #in /cm^3
N_D = 10**16             #in /cm^3

#CALCULATIONS
C = N_A-N_D             #in /cm^3

#RESULTS
print('Carrier concentration in holes/cm^3 is =%.2f X 10^16 ' %(C/(10**16)))

Carrier concentration in holes/cm^3 is =1.00 X 10^16

Example No 3.13 Page No 149

In [31]:
#initialisation of variables
del_n = 10**15           #in /cm^3
Torque_p = 10*10**-6       #in sec

#CALCULATIONS
R_G = del_n/Torque_p          #in electron hole pairs/sec/cm^3

#RESULTS
print('The rate of generation of minority carrier is : =%.2f X 10^20 electron hole pairs/sec/cm^3 ' %(R_G/(10**20)))

The rate of generation of minority carrier is : =1.00 X 10^20 electron hole pairs/sec/cm^3

Example No 3.14 Page No 149

In [32]:
#initialisation of variables
V = 1/20.0        #in cm/µsec
V=V*10**6       #in cm/sec

#CALCULATIONS
E = 10            #in V/cm
Miu = V/E         #in cm^2/V-sec

#RESULTS
print('The mobility of minority charge carrier is =%.f  cm^2/V-sec' %Miu)

The mobility of minority charge carrier is =5000  cm^2/V-sec

Example No 3.15 Page No 149

In [33]:
import math

#initialisation of variables
q = 1.6 * 10**-19       #in C
N_D = 4.5 * 10**15      #in /cm^3
del_p = 10**21 
e=10                #in cm
A = 1             #in mm^2
A = A * 10**-14        #cm^2
l = 10              #in cm
Torque_p = 1            #in microsec


#CALCULATIONS
Torque_p = Torque_p * 10**-6           #in sec
Torque_n = 1                      #in microsec
Torque_n = Torque_n * 10**-6        #in  sec
n_i = 1.5 * 10**10               #in /cm^3
D_n = 30                   #cm^2/sec
D_p = 12                  #in cm^2/sec
n_o = N_D                #in /cm^3
p_o = ((n_i)**2)/n_o           #in /cm^3
l_n = math.sqrt(D_n * Torque_n)  #in cm
l_p = math.sqrt(D_p * Torque_p)      #in cm
x=34.6*10*8-4            #in cm
e1 = 1.88 * 10**1        #in cm
dnBYdx = del_p * e1        #in cm^4
dpBYdx = del_p *e         #in cm^4

J_P = -(q) * D_p * dpBYdx       #in A/cm^2
J_n = q * D_n * dnBYdx          #in A/cm^2


#RESULTS
print('Hole concentration at thermal equilibrium per cm^3 is =%.1f X 10^5  ' %(p_o/(10**5)))
print('Diffusion length of holes in cm is =%.1f X 10^-3 ' %(l_p*(10**3)))
print('Concentration gradient of holes at distance in cm^4 is =%.f X 10^22 ' %(dpBYdx/(10**22)))
print('Concentration gradient of electrons in per cm^4 is =%.1f X 10^22  ' %(dnBYdx/(10**22)))
print('Current density of holes due to diffusion in A/cm^2 is =%.2f X 10^4 ' %(J_P/(10**4)))
print('Current density of electrons due to diffusion in A/cm^2 is =%.2f X 10^4 ' %(J_n/(10**4)))

Hole concentration at thermal equilibrium per cm^3 is =0.5 X 10^5  
Diffusion length of holes in cm is =3.5 X 10^-3 
Concentration gradient of holes at distance in cm^4 is =1 X 10^22 
Concentration gradient of electrons in per cm^4 is =1.9 X 10^22  
Current density of holes due to diffusion in A/cm^2 is =-1.92 X 10^4 
Current density of electrons due to diffusion in A/cm^2 is =9.02 X 10^4

Example No 3.16 Page No 151

In [34]:
#initialisation of variables
h = 6.626 * 10**-34          #in J-s
q= 1.6*10**-19            #in C

#CALCULATIONS
h= h/q              #in eV
c = 3*10**8
lembda = 5490*10**-10             #in m
E = h*c/lembda                 #in eV

#RESULTS
print('The energy band gap is =%.2f eV ' %E)

The energy band gap is =2.26 eV

Example No 3.17 Page No 151

In [35]:
#initialisation of variables
D_n = 35               #in cm^2/sec
q = 1.6*10**-19        #in C
y2 = 6*10**16          #in /cm^3
y1 = 10**17           #in /cm^3
x2 = 2*10**-4
x1 = 0

#CALCULATIONS
dnBYdx = (y2-y1)/(x2-x1)
J_n = q*D_n*dnBYdx              #in A/cm^2

#RESULTS
print('The current density is =%.f  in A/cm^2' %J_n)

The current density is =-1120  in A/cm^2

Example No 3.18 Page No 151

In [36]:
#initialisation of variables
q = 1.6*10**-19               #in C
n_n = 5*10**20                #in  /m^3
n_n = n_n * 10**-6            #in /cm^3
Miu_n = 0.13                   #in m^2/V-sec


#CALCULATIONS
Miu_n = Miu_n * 10**4       #in cm^2/V-sec
Sigma_n = q*n_n*Miu_n      #in ohm-cm^-1
Rho = 1/Sigma_n
A = 100        # in µm^2
A = A * 10**-8     #in cm^2
l = 0.1           #in cm
R = Rho * (l/A)        #in ohm
R=R*10**-6
#RESULTS
print('The resistance of the bar  is =%.2f in M ohm' %R)

The resistance of the bar  is =0.96 in M ohm

Example No 3.19 Page No 152

In [37]:
#initialisation of variables
w = 3.0              #in µm

#CALCULATIONS
D = w/9          #in µm

#RESULTS
print('Depletion width on P side is =%.2f in µm ' %D)

Depletion width on P side is =0.33 in µm

Example No 3.20 Page No 152

In [38]:
#initialisation of variables
n_i = 1.5*10**16          #in /m^3
n_n = 5*10**20          #in /m^3

#CALCULATIONS
p_n = ((n_i)**2)/n_n          #in /m^3

#RESULTS
print('The minority carrier density per m^3 is =%.2f X 10^11' %(p_n/(10**11)))

The minority carrier density per m^3 is =4.50 X 10^11

Example No 3.21 Page No 152

In [39]:
#initialisation of variables
y2 = 10**14                #in /cm^3
y1 = 0
x1=-0.5                    #in µm

#CALCULATIONS
x1= x1*10**-4             #in cm
x2=0
dnBYdx = (y2-y1)/(x2-x1)     #in /cm^4
q = 1.6*10**-19              #in C
D_n = 25                     #in cm^2/sec
J_n = q*D_n*dnBYdx          #in A/cm^2


#RESULTS
print('The collector current density  is =%.f in A/cm^2' %J_n)

The collector current density  is =8 in A/cm^2

Example No 3.22 Page No 153

In [40]:
#initialisation of variables
h = 6.64*10**-34              ##in J-s
q=1.6*10**-19                #in C

#CALCULATIONS
h= h/q                     #in eV
c = 3*10**8               #in m/s
lembda = 0.87*10**-6        #in m
E_g = (h*c)/lembda         #in eV

#RESULTS
print('The band gap in eV is =%.2f ' %E_g)

The band gap in eV is =1.43

Example No 3.23 Page No 153

In [41]:
import math
#initialisation of variables
alpha = 5*10**4            #in cm^-1
l = 0.46*10**-4            #in cm
hv = 2                    #in eV
I_o = 10**-2             #in W

#CALCULATIONS
I_t = I_o*math.exp(-alpha*l)   #in W
A_p = I_o-I_t            #absorbed power in W or J/s
c = 1.43
A_E = (hv-c)/hv*A_p           # in J/s
e = 1.6*10**-19               #in C
P = A_p/(e*hv)               #Perfect quantum efficiency in photon/s

#RESULTS
print('Total energy absorbed  is =%.f X 10^-3 in J/s' %(A_p*(10**3)))
print('Rate of excess thermal energy  is =%.2f X 10^-3 in J/s' %(A_E*(10**3)))
print('Perfect quantum efficiency  is =%.2f X 10^16 in photon/s' %(P/(10**16)))

Total energy absorbed  is =9 X 10^-3 in J/s
Rate of excess thermal energy  is =2.56 X 10^-3 in J/s
Perfect quantum efficiency  is =2.81 X 10^16 in photon/s

Example No 3.24 Page No 154

In [42]:
import math

#initialisation of variables
Mu_p = 500         #in cm^2/v-s
kT = 0.0259
Toh_p = 10**-10         #in sec
p_o = 10**17           #in cm^-3
q= 1.6*10**-19             # in C
A=0.5             #in square meter
del_p = 5 * 10**16        #in cm^-3
n_i= 1.5*10**10          #in cm^-3    


#CALCULATIONS
D_p = kT * Mu_p          #in cm/s
L_p = math.sqrt(D_p * Toh_p)             # in cm
x = 10**-5            #in cm
p = p_o+del_p*e**(x/L_p)          #in cm^-3
Eip= math.log(p/n_i)*kT              #in eV
Ecp= 1.1/2-Eip                   #value of E_c-E_p in eV
Ip= q*A*D_p/L_p*del_p*e**(x/L_p)         #in A
Qp= q*A*del_p*L_p               #in C

#RESULTS
print('The hole current  is : =%.2f X 10^3 in A ' %(Ip*(10**3)))
print('Approximation error')
print('The value of Qp  is :=%.2f X 10^-7 in C' %(Qp*(10**7)))

#Note: There is a calculation error to evalaute the value of hole current hence the value of hole current in the book is wrong

The hole current  is : =8.61 X 10^3 in A 
Approximation error
The value of Qp  is :=1.44 X 10^-7 in C