Chapter9:FIELD EFFECT TRANSISTORS:MOSFET

Ex9.1:pg-384

In [2]:
kbT = 0.026
apsilen = 11.9*8.85*10**-14
e = 1.6*10**-19
Na=10**16
ni = 1.5*10**10
phi_F= (-kbT*log(Na/ni))
print"The potential phi_F=","{:.2e}".format(phi_F),"V"
W = sqrt((4*apsilen*(-phi_F))/(e*Na))*10**4
print"The space charge width is ,W =","{:.1e}".format(W)," micro_meter"

The potential phi_F= -3.49e-01 V
The space charge width is ,W = 3.0e-01  micro_meter

Ex9.2:pg-385

In [3]:
kbT = 0.026
Eg = 1.11
e = 1.6*10**-19
Na=10**14
ni = 1.5*10**10
phi_m = 4.1
Es = 4.15
EF= ((Eg/2)+kbT*log(Na/ni))
print"The position of fermi level below conduction band is ,EF=","{:.2e}".format(EF),"eV"
Vfb = phi_m-(Es+EF)
print"The potential is ,Vfb =","{:.2e}".format(Vfb),"eV"

The position of fermi level below conduction band is ,EF= 7.84e-01 eV
The potential is ,Vfb = -8.34e-01 eV

Ex9.3:pg-385

In [5]:
kbT = 0.026
apsilen = 11.9*8.85*10**-14
e = 1.6*10**-19
Na=3*10**16
ni = 1.5*10**10
Vfb = -1.13
Eox = 3.9*8.85*10**-14
dox = 500*10**-8
Nt = 10**11
phi_F= (-kbT*log(Na/ni))
print"The potential phi_F=","{:.2e}".format(phi_F),"V"
Qs = sqrt((4*apsilen*(-phi_F))*(e*Na))
print"The maximum depletion width is ,Qs =","{:.2e}".format(Qs),"C cm**-2"
Vs = -(2*phi_F)
print"The surface potential is ,Vs =","{:.2e}".format(Vs)," V"
VT = Vfb+Vs+((Qs*dox)/Eox)
print"In the absence of any oxide charge, the threshold voltage is ,VT =","{:.2e}".format(VT)," V"
dVT = -((e*Nt*dox)/Eox)
print"when oxide has trap charges, the shift in threshold voltage is ,dVT =","{:.2e}".format(dVT)," V"
# Note : due to different precisions taken by me and the author ... my answer differ 

The potential phi_F= -3.77e-01 V
The maximum depletion width is ,Qs = 8.73e-08 C cm**-2
The surface potential is ,Vs = 7.54e-01  V
In the absence of any oxide charge, the threshold voltage is ,VT = 8.90e-01  V
when oxide has trap charges, the shift in threshold voltage is ,dVT = -2.32e-01  V

Ex9.4:pg-386

In [4]:
import math
mu_n=600
mu_p = 200
kbT = 0.026
apsilen = 11.9*8.85*10**-14
e = 1.6*10**-19
Na=5*10**16
ni = 1.5*10**10
Vfb = -0.5
Eox = 1.583*8.85*10**-14
dox = 200*10**-8
sigma_1= Na*e*mu_p
sigma_2= Na*e*mu_n
phi_F= (-kbT*log(Na/ni))
Qs = sqrt((4*apsilen*(-phi_F))*(e*Na))
print"The maximum depletion width is ,Qs = ","{:.2e}".format(Qs)," C cm**-2"
Vs = -(2*phi_F)
VT = Vfb+Vs+((Qs*dox)/Eox)
print"In the absence of any oxide charge, the threshold voltage is ,VT =","{:.2e}".format(VT)," V"
# Note : due to different precisions taken by me and the author ... my answer differ 

The maximum depletion width is ,Qs =  1.15e-07  C cm**-2
In the absence of any oxide charge, the threshold voltage is ,VT = 1.92e+00  V

Ex9.6:pg-393

In [5]:
kbT = 0.026
apsilen = 11.9*8.85*10**-14
e = 1.6*10**-19
Na=10**16
ni = 1.5*10**10
apsilen_ox = 3.9*8.85*10**-14
dox = 500*10**-8
Cox= apsilen_ox/dox
print"The oxide capacitance Cox=","{:.2e}".format(Cox),"F/cm**2"
phi_F =(-kbT*log(Na/ni))
print"The potential phi_F=","{:.2e}".format(phi_F)," V"
Wmax = sqrt((4*apsilen*(-phi_F))/(e*Na))
print"The maximum depletion width is ,Wmax =","{:.2e}".format(Wmax)," cm"
Cmin = (apsilen_ox/(dox+((apsilen_ox*Wmax)/apsilen)))
print"The minimum capicitance is ,Cmin =","{:.2e}".format(Cmin)," F/cm**2"
Cfb = (apsilen_ox/((dox)+((apsilen_ox/apsilen)*(sqrt((kbT*apsilen)/(e*Na))))))
print"The capicitance under flat band conditions is ,Cfb =","{:.2e}".format(Cfb)," F/cm**2"

The oxide capacitance Cox= 6.90e-08 F/cm**2
The potential phi_F= -3.49e-01  V
The maximum depletion width is ,Wmax = 3.03e-05  cm
The minimum capicitance is ,Cmin = 2.31e-08  F/cm**2
The capicitance under flat band conditions is ,Cfb = 5.43e-08  F/cm**2

Ex9.7:pg-400

In [1]:
mu_n=600
kbT = 0.026
apsilen = 11.9*8.85*10**-14
e = 1.6*10**-19
Na=10**16
ni = 1.5*10**10
apsilen_ox = 3.9*8.85*10**-14
dox = 500*10**-8
phi_ms = -1.13
Qss = 10**11
VGS = 5.0
Z=25*10**-6
L=1.5*10**-6
phi_F= (-kbT*log(Na/ni))
print"The potential phi_F=","{:.2e}".format(phi_F)," V"
Cox = apsilen_ox/dox
print"The oxide capicitance per unit area is ,Cox =","{:.2e}".format(Cox)," F/cm**-2"
Vfb = phi_ms-((Qss*e)/Cox)
print"The flat band potential is Vfb =","{:.2e}".format(Vfb),"V"
Vs = -(2*phi_F)
print"The surface potential is ,Vs =","{:.2e}".format(Vs)," V"
VT = Vfb+Vs+(sqrt(4*e*apsilen*Na*(-phi_F))/Cox)
print"In the absence of any oxide charge, the threshold voltage is ,VT =","{:.2e}".format(VT)," V"
ID = (Z*mu_n*Cox*(VGS-VT)**2)/(2*L)
print"The saturation current is ,ID = ","{:.2e}".format(ID)," A"

#NOTE: The value of Vfb in the text book is wrong for the above solution and thus the value of VT and saturation current is also wrong

The potential phi_F= -3.49e-01  V
The oxide capicitance per unit area is ,Cox = 6.90e-08  F/cm**-2
The flat band potential is Vfb = -1.36e+00 V
The surface potential is ,Vs = 6.97e-01  V
In the absence of any oxide charge, the threshold voltage is ,VT = 3.78e-02  V
The saturation current is ,ID =  8.50e-03  A

Ex9.8:pg-402

In [7]:
kbT = 0.026
Z = 10*10**-4
L = 1*10**-4
mu_n=700
apsilen = 11.9*8.85*10**-14
e = 1.6*10**-19
Na=4*10**14
ni = 1.5*10**10
apsilen_ox = 3.9*8.85*10**-14
dox = 200*10**-8
VGS = 5.0
Qs = sqrt(4*apsilen*(-phi_F)*e*Na)
print"The maximum depletion width is ,Qs =","{:.2e}".format(Qs)," cm**-2"
phi_F= (-kbT*log(Na/ni))
print"The potential phi_F=","{:.2e}".format(phi_F)," V"
Cox = apsilen_ox/dox
print"The oxide capicitance per unit area is ,Cox =""{:.2e}".format(Cox)," cm**-1"
Vs = -(2*phi_F)
print"The surface potential is ,Vs =","{:.2e}".format(Vs)," V"
VT = Vs+((Qs/Cox))
print"The threshold voltage is ,VT =","{:.2e}".format(VT)," V"
VDS = VGS-VT
print"The saturation voltage is ,VDS =","{:.2e}".format(VDS)," V"
ID = (Z*mu_n*Cox*(VDS)**2)/(2*L)
print"The saturation current is ,ID =","{:.2e}".format(ID)," A"
# Note : due to different precisions taken by me and the author ... my answer differ 

 The maximum depletion width is ,Qs = 9.70e-09  cm**-2
The potential phi_F= -2.65e-01  V
The oxide capicitance per unit area is ,Cox =1.73e-07  cm**-1
The surface potential is ,Vs = 5.30e-01  V
The threshold voltage is ,VT = 5.86e-01  V
The saturation voltage is ,VDS = 4.41e+00  V
The saturation current is ,ID = 1.18e-02  A

Ex9.9:pg-402

In [9]:
VDS = 0.1
Z = 10*10**-4
L = 2*10**-4
Cox=10**-7
ID1= 50.0
ID2= 80.0
VGS1 = 1.5
VGS2 = 2.5
mu_n = (((ID2-ID1)*10**(-6)*L)/(VDS*Z*Cox*(VGS2-VGS1)))
print"The mobility of electron in silicon is ,mu_n =",round(mu_n,2)," cm**2/Vs"

The mobility of electron in silicon is ,mu_n = 600.0  cm**2/Vs

Ex9.10:pg-403

In [10]:
kbT = 0.026
apsilen = 11.9*8.85*10**-14
e = 1.6*10**-19
Na=2*10**16
ni = 1.5*10**10
VSB = 1.0
apsilen_ox = 3.9*8.85*10**-14
dox = 500*10**-8
Cox = apsilen_ox/dox
print"The oxide capicitance per unit area is ,Cox =","{:.2e}".format(Cox)," F*cm**-2"
phi_F= (-kbT*log(Na/ni))
print"The potential phi_F=","{:.2e}".format(phi_F)," V"
dVT = ((sqrt(2*e*apsilen*Na)/Cox)*((sqrt((-2*phi_F)+VSB)-sqrt(-2*phi_F))))
print"The shift in threshold voltage is ,dVT =","{:.2e}".format(dVT)," V"

The oxide capicitance per unit area is ,Cox = 6.90e-08  F*cm**-2
The potential phi_F= -3.67e-01  V
The shift in threshold voltage is ,dVT = 5.47e-01  V

Ex9.11:pg-406

In [11]:
kbT = 0.026
apsilen = 11.9*8.85*10**-14
e = 1.6*10**-19
D = 10**-5
Na=10**14
dVT=.5
ni = 1.5*10**10
apsilen_ox = 3.9*8.85*10**-14
phi_F= (-kbT*log(Na/ni))
print"The potential phi_F=","{:.2e}".format(phi_F)," V"
dox = 5*10**-6
Cox = apsilen_ox/dox
print"The oxide capicitance per unit area is ,Cox =","{:.2e}".format(Cox)," cm**-1"
phi_ms = -0.83
VT = (phi_ms)-(2*phi_F)+((sqrt(4*e*apsilen*Na*(-phi_F)))/Cox)
print"the threshold voltage is ,VT =","{:.2e}".format(VT)," V"
Na = (dVT*Cox)/(e*D)
print"the dopant density is ,Na=","{:.2e}".format(Na)," cm**-3"
# Note : due to different precisions taken by me and the author ... my answer differ 

The potential phi_F= -2.29e-01  V
The oxide capicitance per unit area is ,Cox = 6.90e-08  cm**-1
the threshold voltage is ,VT = -3.15e-01  V
the dopant density is ,Na= 2.16e+16  cm**-3