# Chapter 6: MOSFET and Related Devices¶

## Example 6.1 Page 175¶

In [1]:
#initialisation of variable
from math import *
N=10**17;#concentration
n=9.65*10**9;#constant
Dp=11.9*8.85*10**-14;#dielectric permitivity
V=.026;#voltage
q=1.6*10**-19;#charge

#calculation
W=2*(Dp*V*log(N/n)/q/N)**.5#width

#result
print"maximum width is",round(W*10**4,1),"micro-m"

maximum width is 0.1 micro-m


## Example 6.2 Page 179¶

In [2]:
#initialisation of variable
from math import *
N=10**17;#concentration
d=5*10**-7;#mm
D=3.9;#dielectric constant
Dp=8.85*10**-14;#constant
W=10**-5;#width
n=9.65*10**9;

#calculation
C=D*Dp/d;#capacitance
w=2*.026*log(N/n);
Cmin=D*Dp/(d+(D/11.9)*W);#min. capacitance
P=Cmin*100/C;#%

#result
print"mininmum capacitance is",round(Cmin,9),"F/cm^2"

mininmum capacitance is 9.1e-08 F/cm^2
Cmin is about 13.0 % of Co


## Example 6.3 Page 184¶

In [11]:
#initialisation of variable
from math import *
N=10**17;#concentration
d=5;#nm
Co=6.9*10**-7;#capacitance
q=1.6*10**-19;#charge
Q=-.98;
Qf=5*10**11;#cm^-2

#calculation
V=Q-(q*Qf)/Co;#Voltage

#result
print"flat-band voltage is",round(V,2),"V"

flat-band voltage is -1.1 V


## Example 6.4 Page 184¶

In [6]:
#initialisation of variable
from math import *
import math
from scipy import integrate
t=20;#thickness
D1=0.00;
D2=2.00*10**-6;
q=1.6*10**-19;#charge
k=8.85*10**-14;#constant
Dc=3.9;#dielectric constant

#calculation
C=q/Dc/k;#constant
def integrand(x):
return x*(10**18-5*10**23*x)

#result
print"change in flat-band voltage is",round(C*V[0],2),"V"

change in flat-band voltage is 0.31 V


## Example 6.5 Page 192¶

In [12]:
#initialisation of variable
from math import *
N=10**17;#concentration
d=8*10**-7;#mm
Vg=3;#V
q=1.6*10**-19;#charge
Co=4.32*10**-7;#capacitance
E=11.9*8.85*10**-14;#constant
F=.42;#V

#calculation
K=(E*q*N)**.5/Co;
Vd=Vg-2*F+K**2*(1-(1+(2*Vg/K**2))**.5);#volatge

#result
print"VDsat is",round(Vd,2),"V"

VDsat is 1.51 V


## Example 6.6 Page 196¶

In [16]:
#initialisation of variable
from math import *
N=10**17;#concentration
Qf=5*10**11;
d=5;#
Vt=.6#terminal voltage
Co=6.9*10**-7;#capacitance
f=.42;#V
Vfb=-1.1;#Voltage forward biasisng
q=1.6*10**-19;#charge
E=11.9*8.85*10**-14;#constant

#calculation
VT=Vfb+2*f+(2*E*q*N*2*f)**.5/Co;#voltage
Fb=(Vt-VT)*Co/q;#flat-band shift

#result
print"VT for gate oxide is",round(VT,2),"V"
print"flat-band shift is",round(Fb,2),"cm^-2"

VT for gate oxide is -0.02 V
flat-band shift is 2.65717617948e+12 cm^-2


## Example 6.7 Page197¶

In [17]:
#initialisation of variable
from math import *
N=10**17;#concentration
Qf=5*10**11;#factor
q=1.6*10**-19;#charge
d=500;#nm
Co=6.9*10**-9;#capacitance
f=.42;#V
Vfb=-1.1;#voltage
E=11.9*8.85*10**-14;#constant

#calculation
Vt=Vfb+2*f+(2*E*q*N*2*f)**.5/Co;#voltage

#result
print"VT is",round(Vt,2),"V"

VT is 24.12 V


## Example 6.8 Page 198¶

In [18]:
#initialisation of variable
from math import *
N=10**17;#concentration
Qf=5*10**11;#factor
q=1.6*10**-19;#charge
d=500;#nm
Co=6.9*10**-7;#capacitance
f=.42;#V
Vbs=2;#Voltage
E=11.9*8.85*10**-14;#constant

#calculation
dVt=((2*E*q*N*2*f)**.5/Co)*((2*f+Vbs)**.5-(2*f)**.5);#change in threshold voltage

#result
print"change in threshold voltage is",round(dVt,1),"V"

change in threshold voltage is 0.2 V


## Example 6.9 Page 213¶

In [3]:
#initialisation of variable
from math import *
N=10**17;#concentration
Qf=5*10**11;#factor
q=1.6*10**-19;#charge
d=5;#nm
dsi=5*10**-6;#nm
Co=6.9*10**-7;#capacitance
f=.42;#V
Vfb=-1.1;#Voltage
E=11.9*8.85*10**-14;#constant

#calculation
Vt=Vfb+2*f+q*N*dsi/Co;#threshold voltage

#result
print"threshold voltage is",round(Vt,2),"V"

threshold voltage is -0.14 V