Chapter 07 : Integrated Circuit Fabrication and Characteristic

Example 7.1, Page No 215

In [8]:
import math
#initialisation of variables

print('At distance equal to x=xi at which N = concentration n of doped silicon wafers , the net impurity density is zero. Thus xi is the distance at which junction  is formed')
q = 1.6*(10**-19)         #Charge of electron
yn=1300.0        #mobility of silicon
p = 0.5          #resistivity in ohm=cm
y=2.2

#Calculations
t=2.0*3600          #in sec.
xi = 2.7*(10**-4)    #Junction Depth in cm.
n = 1/(p*yn*q)             #Concentration of doped silicon wafer
print("The concentration n = %.2f cm^-3 x 10^16" %(n/10**16))
print('The junction is formed when N = n')

#y = xi/(2*(D*t)^0.5)
D=((xi)**2/((2*y)**2*t))    #Diffusion Constant

#Results
print("The value of Diffusion Constant for Boron =  %.2f cm^2/sec X 10^-13" %(D*10**13))

At distance equal to x=xi at which N = concentration n of doped silicon wafers , the net impurity density is zero. Thus xi is the distance at which junction  is formed
The concentration n = 0.96 cm^-3 x 10^16
The junction is formed when N = n
The value of Diffusion Constant for Boron =  5.23 cm^2/sec X 10^-13

Example 7.2, Page No 215

In [9]:
import math

#initialisation of variables
d=5.2*10**-13     #from previous example
depth=1.7*10**-4
t=2*3600.0
c=2.5*10**17     # boron concentration cm^3

#Calculations
y = depth/(2*(math.sqrt(d*t)))
q=(c*(math.sqrt(math.pi*4*10**-13*3420)))/(math.exp(-((depth**2)/(4*4*10**-13*3420))))


#Results
print("The value of Y is = %.2f  " %(y))
print("The value of Q is = %.2f  cm2 X 10^15 " %(q/10**15))

The value of Y is = 1.39  
The value of Q is = 3.22  cm2 X 10^15

Example 7.3, Page No 222

In [10]:
import math

#initialisation of variables
y=100.0*10**-4     #mm
h=500.0    #cm^2/V-s
p=10.0**16         #boron of concentration


#Calculations
Rs=1.0/(1.6*10**-19*h*p*y)

#Results
print("The value of Rs sheet resistance is = %.2f  ohm/sqare" %(Rs))

The value of Rs sheet resistance is = 125.00  ohm/sqare

Example 7.4, Page No 223

In [11]:
import math

#initialisation of variables
Rs=100.0    #ohm/square
l=50.0      #mm
w=10        #mm


#Calculations
R=Rs*(l/w)

#Results
print("The resistance of defused resistor is = %.2f  ohm" %(R))

The resistance of defused resistor is = 500.00  ohm

Example 7.5, Page No 225

In [12]:
import math

#initialisation of variables
A=100*10**-8       #mm^2
q=1.6*10**-19
Nd=10**16          #donor concentration /cm^3
e=11.9*8.85*10**-14
Vj=0.82      #v


#Calculations
C=A*math.sqrt((q*Nd*e)/(2*Vj))

#Results
print("The capacitance is = %.f  fF" %(C*10**15))

The capacitance is = 32  fF

Example 7.6, Page No 225

In [13]:
import math

#initialisation of variables
A=100*10*10**-8       #mm^2
q=1.6*10**-19
e=11.9*8.85*10**-14
Vj=0.98      #v
Mn=1300.0
pn=0.01



#Calculations
Nd=1/(q*Mn*pn)       #donor concentration /cm^3
C=A*math.sqrt((q*Nd*e)/(2*Vj))

#Results
print("The capacitance is = %.f  pF" %(C*10**12))

The capacitance is = 2  pF

Example 7.7, Page No 226

In [14]:
import math

#initialisation of variables
e=3.9*8.85*10**-14
d=20*10**-8


#Calculations
C=(e/d)*(10**9/10**8)

#Results
print("The capacitance per unit area is = %.2f   fF/mM^2" %(C*10**6))

The capacitance per unit area is = 17.26   fF/mM^2