# Chapter 11: Fundamentals of the Metal-Oxide-Semiconductor Field-Effect Transistor¶

## Example 11.1, Page 456¶

In [1]:
import math

#Variable declaration
T=300#K
Na=10**16# cm^-3
ni=1.5*10**10 # cm^-3
epsilon0=8.85*10**-14# F/m
epsilons=11.7
e=1.6*10**-19# eV
Vt=0.0259 # V

#Calculations&Results
phifp=Vt*math.log(Na/ni)
print "the value of phisp is %.3f V"%phifp
xdT=(4*(epsilons*epsilon0)*phifp/(e*Na))**0.5
print "the value of xdT is %.e meter"%xdT

the value of phisp is 0.347 V
the value of xdT is 3e-05 meter


## Example 11.2, Page 459¶

In [2]:
import math

#Variable declaration
phim=3.20# v
x=3.25# v
Eg=1.11#eV
Na=10**14# cm^-3
k=1.3806*10**-23# JK^-1
T=300# K
ni=1.5*10**10# cm^-3
e=1.6*10**-19# eV

#Calculations&Results
phifp=(((k*T)/e)*math.log(Na/ni))
print "the value of phifp is %.3f V"%phifp
phims=phim-(x+(Eg/2)+phifp)
print "work function difference is %.2f V "%phims

the value of phifp is 0.228 V
work function difference is -0.83 V


## Example 11.3, Page 464¶

In [3]:
#Variable declaration
Nd=10**16# cm^-3
tox=500*10**-8# a=500A =500*10^-8 cm
Qss=10**11# electronic charge per cm
phims=-1.1# V
e=1.6*10**-19# eV
epsilonox=3.9
epsilon0=8.85*10**-14# F/m

#Calculations&Results
C=((epsilonox*epsilon0)/tox)
print "the value of C is %.1e F/cm^2"%C
Qss=10**11*e
print "the value of Qss is %.1e C/cm^2"%Qss
VFB=phims-(Qss/C)
print "the value of VFB is %.2f V "%VFB

the value of C is 6.9e-08 F/cm^2
the value of Qss is 1.6e-08 C/cm^2
the value of VFB is -1.33 V


## Example 11.4, Page 467¶

In [4]:
import math

#Variable declaration
T=300# K
k=1.3806*10**-23# JK^-1
Na=3*10**16# cm^-3
Qss=10**11# cm^-2
VTN=0.65# V
phims=-1.13# V
epsilon0=8.85*10**-14# F/m
epsilons=11.7
epsilonox=3.9
ni=1.5*10**10# cm^-3
e=1.6*10**-19# eV

#Calculations&Results
phifp=(((k*T)/e)*math.log(Na/ni))
print "the value of phifp is %.3f V"%phifp
xdT=(4*(epsilons*epsilon0)*phifp/(e*Na))**0.5
print "the value of xdT is %.2f micro-meter"%(xdT/10**-4)
QSD=e*Na*xdT    #[QSD(max)]=e*Na*xdT
print "the value of QSD is %.2e C.cm^2"%QSD
tox=((VTN-phims-2*phifp)*(epsilonox*epsilon0))/(QSD-(Qss*e))
print "tox is %.f A"%(tox/10**-7)

the value of phifp is 0.376 V
the value of xdT is 0.18 micro-meter
the value of QSD is 8.64e-08 C.cm^2
tox is 50 A


## Example 11.5, Page 468¶

In [5]:
import math

#Variable declaration
T=300# K
k=1.3806*10**-23# JK^-1
Na=10**14# cm^-3
Qss=10**10# cm^-2
tox=500*10**-8# a=500A =500*10**-8 cm
phims=-0.83# V
epsilon0=8.85*10**-14# F/m
epsilons=11.7
epsilonox=3.9
ni=1.5*10**10# cm^-3
e=1.6*10**-19# eV

#Calculations&Results
phifp=(((k*T)/e)*math.log(Na/ni))
print "the value of phifp is %.3f V"%phifp
xdT=(4*(epsilons*epsilon0)*phifp/(e*Na))**0.5
print "the value of xdT is %.3f milli-m"%(xdT/10**-3)
QSD=e*Na*xdT# [QSD(max)]=e*Na*xdT
print "the value of QSD is %.2e C/cm^2"%QSD
VTN=(QSD-(Qss*e))*(tox/(epsilonox*epsilon0))+phims+2*phifp# VTN=(QSD(max)-Qss)*(tox/epsilonox)+phims+2*phifp
print "the value of VTN is %.3f V"%VTN

the value of phifp is 0.228 V
the value of xdT is 0.243 milli-m
the value of QSD is 3.89e-09 C/cm^2
the value of VTN is -0.341 V


## Example 11.6, Page 470¶

In [6]:
import math

#Variable declaration
T=300# K
k=1.3806*10**-23# JK^-1
Qss=10**10# cm^-2
tox=650*10**-8# tox=650A =650*10**-8 cm
epsilon0=8.85*10**-14# F/m
epsilons=11.7
epsilonox=3.9
ni=1.5*10**10# cm^-3
e=1.6*10**-19# eV
Nd=2.5*10**14# cm^-3

#Calculations&Results
phifn=(((k*T)/e)*math.log(Nd/ni))#phifn=V1*log(Nd/ni)=((k*T)/e)*log(Nd/ni)
print "the value of phifn is %.3f V "%phifn
xdT=(4*(epsilons*epsilon0)*phifn/(e*Nd))**0.5
print "the value of xdT is %.2f milli-meter "%(xdT/10**-3)
QSD=e*Nd*xdT# [QSD(max)]=e*Na*xdT
print "the value of QSD is %.2e C/cm^2"%QSD
phims=-0.35# V
VTP=(-QSD-(Qss*e))*(tox/(epsilonox*epsilon0))+phims-(2*phifn)# VTP=(-QSD(max)-Qss)*(tox/epsilonox)+phims+2*phifn
print "the value of VTP is %.3f V"%VTP

the value of phifn is 0.252 V
the value of xdT is 0.16 milli-meter
the value of QSD is 6.46e-09 C/cm^2
the value of VTP is -1.005 V


## Example 11.7, Page 477¶

In [7]:
import math

#Variable declaration
T=300 #K
k=8.617*10**-5#eV/K
e=1.6*10**-19 #C
espox=3.9
esp0=8.85*10**-14
esp=11.7
tox=550*10**-8#550 Armstrong
Na=10**16#cm^-3
ni=1.5*10**10 #cm^-3

#Calculations&Results
Cox=(espox*esp0)/tox
print "oxide capacitance is %.2e F/cm^2 "%Cox

phi=(k*T)*math.log(Na/ni)
print "mini capacitance is %.3f V "%phi

xdt=math.sqrt((4*esp*esp0*phi)/(e*Na))
print "xdt is %.2e cm^-4 "%xdt

Cmin=(espox*esp0)/(tox+(espox/esp)*xdt)
print "Cmin is %.2e F/cm^2 "%Cmin

a=Cmin/Cox
print "ratio of Cmin to Cox is= %.3f"%a

Cfb=(espox*esp0)/(tox+(espox/esp)*math.sqrt((k*T*esp*esp0)/(e*Na)))
print "Cfb in F/cm^2 is= %.2e"%Cfb

b=Cfb/Cox
print "ratio of Cfb to Cox is = %.2f "%b

oxide capacitance is 6.28e-08 F/cm^2
mini capacitance is 0.347 V
xdt is 3.00e-05 cm^-4
Cmin is 2.23e-08 F/cm^2
ratio of Cmin to Cox is= 0.355
Cfb in F/cm^2 is= 5.03e-08
ratio of Cfb to Cox is = 0.80


## Example 11.8, Page 495¶

In [8]:
#Variable declaration
T=300 #K
k=8.617*10**-5#eV/K
e=1.6*10**-19 #C
Cox=6.9*10**-8#F/cm2
esp0=8.85*10**-14
Vtau=0.65#V
VGS=5#V
L=1.25*10**-4#cm
u=650#cm**2/Vs
IDsat=4*10**-3#A

#Calculations
W=(IDsat*2*L)/(u*Cox*(VGS-Vtau)**2)

#Result
print "W is %.1f micro-meter"%(W/10**-4)

W is 11.8 micro-meter


## Example 11.9, Page 496¶

In [9]:
#Variable declaration
T=300 #K
k=8.617*10**-5#eV/K
e=1.6*10**-19 #C
Cox=6.9*10**-8#F/cm2
esp0=8.85*10**-14
Vtau=0.65#V
VGS1=1.5#V
VGS2=2.5#V
VDS=0.10#V
L=2*10**-6#cm
u=650#cm**2/Vs
ID1=35*10**-6#A
ID2=75*10**-6#A
W=15*10**-6#m

#Calculations
un=(ID2-ID1)*L/(W*Cox*(VGS2-VGS1)*VDS)

#Result
print "un is %.f cm^2/Vs"%un

un is 773 cm^2/Vs


## Example 11.10, Page 500¶

In [10]:
import math

#Variable declaration
T=300# K
Na=3*10**16# cm^-3
tox=500*10**-8# tox=500A =500*10**-8 cm
k=1.3806*10**-23# JK^-1
VSB=1# V
epsilon0=8.85*10**-14# F/m
epsilons=11.7
epsilonox=3.9
ni=1.5*10**10# cm^-3
e=1.6*10**-19# eV

#Calculations&Results
phifp=(((k*T)/e)*math.log(Na/ni))# phifp=V1*log(Na/ni)=((k*T)/e)*log(Na/ni)
print "the value of phifp is %.3f V"%phifp
Cox=(epsilon0*epsilonox)/tox
print "the value of Cox is %.1e F/cm^2"%Cox
deltaVT=(math.sqrt(2*e*(epsilon0*epsilons)*Na))/Cox*((math.sqrt(2*phifp+VSB))-(math.sqrt(2*phifp)))
print "the value of deltaVT is %.2f V"%deltaVT

the value of phifp is 0.376 V
the value of Cox is 6.9e-08 F/cm^2
the value of deltaVT is 0.66 V


## Example 11.11, Page 506¶

In [11]:
import math

#Variable declaration
micron=400.# cm^2/V-s
L=4*10**-6# m
VT=1# V
VGS=3# V

#Calculations
ftau=(micron*(VGS-VT))/(2*math.pi*L*L)

#Result
print "the value of fr = %.f MHz"%(ftau/10**10)

the value of fr = 796 MHz