Chapter6:MICROWAVE FIELD-EFFECT TRANSISTORS

Eg6.1.1:pg-229

In [1]:
#calculation of pinch-off voltage

a=0.1*(10**-6)           #channel height in m
Nd=8*(10**23)            #Electron Concetration in m-3
er=11.80                 #relative dielectric constant
es=8.854*(10**-12)*er    #permittivity of silicon in F/m
q=1.6*(10**-19)          #charge of electron in C
Vp=(q*Nd*(a**2))/(2*es)  #pinch-off voltage

print"Pinch-off volatge in(Volts)is=",round(Vp,2),"Volts" #answer is wrong in book 

Pinch-off volatge in(Volts)is= 6.13 Volts

Eg6.1.2:pg-233

In [41]:
import math
#(a)Calculate the pinch-off Voltage in Volts
a=0.2*(10**-4)            #channel height in cm
Nd=1*(10**17)             #Electron density in /cm3
er=11.80                  #relative dielectric constant
es=8.854*(10**-14)*er     #permittivity of silicon in F/cm
q=1.6*(10**-19)           #charge of electron in C
Vp=(q*Nd*(a**2))/(2*es)   #pinch-off voltage
print"The pinch-off volatge in(Volts)is=",round(Vp,2),"V"

#(b)Calculate the pinch-off current
un=800                    #electron mobility in cm2/V.s
L=8*(10**-4)              #channel length in cm
Z=50*(10**-4)             #channel width in cm
a=0.2*(10**-4)            #channel height in cm
Nd=1*(10**17)             #Electron density in /cm3
er=11.80                  #relative dielectrin constant
es=8.854*(10**-14)*er     #permittivity of silicon in F/cm
q=1.6*(10**-19)           #charge of electron in C
Ip=(un*(q**2)*(Nd**2)*Z*(a**3))/(L*es) #pinch-off voltage
Ip=Ip*1000                # in mA
print"The pinch-off current in(mA)is=",round (Ip,2),"mA"

#(c)Calculate the built-in voltage
Nd=1*(10**17)             #Electron density in /cm3
Na=1*(10**19)             #hole density in /cm3
w0=26*(10**-3)*math.log((Nd*Na)/((1.5*(10**10))**2))
print"Built-in voltage in(volts)is=",round(w0,3),"V"

#(d) Calculate the drain current
Vd=10                     #drain voltage in volt
Vg=-1.5                   #gate voltage in volt
Vg=-1*Vg                  #we take only magnitude
x=sqrt(((Vd+Vg+round(w0,3))/round(Vp,2))**3)
x=x*2/3
y=sqrt(((Vg+round(w0,3))/(round(Vp,2)))**3)
y=y*2/3
Id=(Vd/round(Vp,2))-x+y
Id=round(Ip,2)*Id
print"The drain current (mA)is=",round(Id,2),"mA"   #answer is wrong in book

#(e) Calculate the saturation drain current at Vg=0
Vg=-1.5                   #gate voltage in volt
Vg=-1*Vg                  #we take only magnitude
x=(Vg+round(w0,3))/(round(Vp,2))
y=sqrt(((Vg+round(w0,3))/(round(Vp,2)))**3)
y=y*2/3
Idsat=(1.0/3)-x+y
Idsat=round(Ip,2)*Idsat
print"The saturation drain current (mA)is=",round(Idsat,3),"mA" #answer is wrong in book

#(f) Calculate the cut-off frequency
fc=(2*un*q*Nd*(a**2))/(math.pi*es*(L**2));
fc=fc/(10**9)    #in GHz
print"The cut-off frequency(Ghz)=",round(fc,1),"GHz"

The pinch-off volatge in(Volts)is= 3.06 V
The pinch-off current in(mA)is= 9.8 mA
Built-in voltage in(volts)is= 0.937 V
The drain current (mA)is= -16.86 mA
The saturation drain current (mA)is= 0.105 mA
The cut-off frequency(Ghz)= 4.9 GHz

Eg6.2.1:pg-239

In [42]:
#calculate Pinch-Off Voltage Of a MESFET

a=0.1*(10**-6)        #channel height in meter
Nd=8*(10**23)         #Electron Concetration /m3
er=13.10              #relative dielectric constant
es=8.854*(10**-12)*er #permittivity of GaAs in F/m
q=1.6*(10**-19)       #electronic charge in C
Vp=(q*Nd*(a**2))/(2*es)#pinch-off voltage

print"Pinch-off volatge in(Volts)is=",round(Vp),"V"

Pinch-off volatge in(Volts)is= 6.0 V

Eg6.2.2:pg-244

In [44]:
#(a) Calculate the pinch-off voltage
a=0.1*(10**-6)           #channel height in meter
Nd=8*(10**23)            #Electron Concetration in /m3
er=13.1                  #relative dielectric constant
e=8.854*(10**-12)*er     #permittivity of GaAs in F/m
q=1.6*(10**-19)          #electronic charge in C
Vp=(q*Nd*(a**2))/(2*e)   #pinch-off voltage

print"Pinch-off volatge in(Volts)is=",round(Vp,2),"V"

#(b)Calculate the velocity ratio
un=0.08                 #electron mobility in m2/V.s
vs=2*(10**5)            #saturation drift velocity in m/s
L=14*(10**-6)           #channel length in meter   
n=(Vp*un)/(vs*L)
print"The velocity ratio is=",round(n,3)

#(c) Calculate the saturation current at Vg=0
L=14*(10**-6)         #channel length in meter
Z=36*(10**-6)         #channel width in meter
Ipsat=(q*Nd*un*a*Z*round(Vp,2))/(3*L)
Ipsat=Ipsat*1000       #in mA
print"The saturation current at Vg=0 is=",round(Ipsat,3),"mA"

#(d) Calculate the drain current

Vd=5                    #drain voltage
Vg=-2                   #gate voltage
Vg=-1*Vg
u=sqrt((Vd+Vg)/Vp)
p=sqrt((Vg)/Vp)
Id=(3*((u**2)-(p**2))-2*((u**3)-(p**3)))/(1+(n*((u**2)-(p**2))))
Id=Id*Ipsat
print"The drain current (mA)is=",round(Id,2),"mA"

Pinch-off volatge in(Volts)is= 5.52 V
The velocity ratio is= 0.158
The saturation current at Vg=0 is= 4.845 mA
The drain current (mA)is= 1.26 mA

Eg6.2.3:pg-247

In [46]:
import math
#(a) Calculate the cut-off frequency
gm=0.05         #device transconductance in mho     
Cgs=0.60*(10**-12) #gate source capacitance in Farad
fco=(gm)/(2*math.pi*Cgs) 
fco=fco/(10**9)   #in GHz
print"The cut-off frequency(in GHz)is=",round(fco,2),"GHz" 

#(b)Calculate the maximum operating frequency
Rd=450   #drain resistance in ohms
Rs=2.5   #source-gate resistance in ohms
Rg=3     #gate metallization resistance in ohms
Ri=2.5   #input resistance
fmax=(fco/2)*sqrt(Rd/(Rs+Rg+Ri)) 
print"The maximum operating frequency(in Ghz)is=",round(fmax,2),"GHz"

The cut-off frequency(in GHz)is= 13.26 GHz
The maximum operating frequency(in Ghz)is= 49.74 GHz

Eg6.3.1:pg-251

In [47]:
#Calculate the Drain Current
q=1.60*(10**-19)     #charge of electron in C
n=5.21*(10**15)      #two-dimensional electron gas density in /m2
W=150*(10**-6)       #gate width in meter
v=2*(10**5)          #electron velocity in m/sec
Ids=q*n*W*v 
Ids=1000*Ids         #in mA
print"The drain current in(mA) is=",int(Ids),"mA"

The drain current in(mA) is= 25 mA

Eg6.3.2:pg-253

In [48]:
#(a) Calculate the conduction band-edge difference between GaAs and AlGaAs
Ega=1.8           #AlGaAs bandgap in volt
Egg=1.43          #GaAs bandgap in volt
AEc=Ega-Egg 
print"The conduction band-edge difference(in Volt) is=",AEc,"V"

#(b) Calculate the sesitivity of the HEMT
q=1.6*(10**-19)    #charge of electron in C
Nd=2*(10**24)     #donar concentration /m3
wms=0.8           #metal-semiconductor schottky barrier potential in volt
Vth=0.13          #threshold voltage in volt
er=4.43           #AlGaAs dielectric constant
e=er*(8.854*(10**-12)) 
S=-sqrt((2*q*Nd*(wms-AEc-Vth))/(e)) #sesitivity of the HEMT
S=S/(10**6) 
S=-1*S
print"The sensitivity of the HEMT (mV/nm) is=",int(round(S)),"mV/nM"

The conduction band-edge difference(in Volt) is= 0.37 V
The sensitivity of the HEMT (mV/nm) is= 70 mV/nM

Eg6.4.1:pg-260

In [49]:
import math
#(a) Calculate the surface potential ws(inv) for strong inversion
kt=26*(10**-3) 
Na=3*(10**17)       #doping concentration in /cm3
Ni=1.5*(10**10) 
wsinv=2*kt*math.log(Na/Ni) 
print"The strong potential w(inv) for strong inversion(in volts) is=",round(wsinv,3),"V"

#(b)Calculate the insulator Capacitance
eir=4               #relative dielectric constant of SiO2
ei=8.854*(10**-12)*eir #permittivity of SiO2 in F/m
d=0.01*(10**-6)     #insulator depth in meter
Ci=ei/d 
Ci=Ci*(1000)  
print"The insulator Capacitance(in mF/m**2) is=",round(Ci,2),"mF/m2"

#(c) Calculate the threshold voltage
q=1.6*(10**-19) 
Na=3.0*(10**23) 
er=11.8 
e=8.854*(10**-12)*er  #permittivity of SiO2 in F/m
Vth=wsinv+((2/(Ci*(10**-3)))*sqrt(e*q*Na*(wsinv/2)))
print"The threshold voltage(in Volts) is=",round(Vth,2),"V"

The strong potential w(inv) for strong inversion(in volts) is= 0.874 V
The insulator Capacitance(in mF/m**2) is= 3.54 mF/m2
The threshold voltage(in Volts) is= 1.71 V

Eg6.4.2:pg-262

In [50]:
#(a)Calculate the insulator capacitance
eir=3.9                   #constant of SiO2
ei=8.854*(10**-12)*eir    #permittivity of SiO2 in F/m
d=0.05*(10**-6)           #insulator thickness in meter
Ci=ei/d 
print"The insulator capacitance(in F/m**2) is=","{:.2e}".format(Ci),"F/m2"

#(b)Calculate the saturation drain current
Z=12*(10**-6)       #channel depth in meter
Vg=5                #gate voltage in volt
Vth=0.10            #threshold voltage in volt
vs=1.70*(10**5)      #electron velocity in m/s
Idsat=Z*round(Ci,6)*(Vg-Vth)*vs
Idsat=Idsat*1000    #in mA
print"The saturation drain current(in mA) is=",round(Idsat,2),"mA"

#(c)Calculate the transconductance in the saturation region
Z=12*(10**-6)       #channel depth in meter
vs=1.70*(10**5)     #electron velocity in m/s
gmsat=Z*Ci*vs 
gmsat=gmsat*10**3
print"the transconductance in the saturation region(in millimhos) is=",round(gmsat,2),"millimhos" 

#(d)Calculate the maximum operating frequency in the saturation region
vs=1.70*(10**5)     
L=4*(10**-6)        #channel length in meter
fm=vs/(2*math.pi*L) 
fm=fm/(10**9)     #in GHz
print"The maximum operating frequency in the saturation region(in GHz) is=",round(fm,2),"GHz"

The insulator capacitance(in F/m**2) is= 6.91e-04 F/m2
The saturation drain current(in mA) is= 6.91 mA
the transconductance in the saturation region(in millimhos) is= 1.41 millimhos
The maximum operating frequency in the saturation region(in GHz) is= 6.76 GHz

Eg6.6.1:pg-278

In [51]:
# Calculate the power dissipation per bit
n=3          #number of phases  
f=10*(10**6) #clock frequency in Hertz
V=10         #applied voltage in volts
Qmax=0.04*(10**-12) #maximum stored charges in Coulomb
p=n*f*V*Qmax 
p=p*(10**6)  #in mW
print"The power dissipation per bit(micro watt)is=",int(p),"micro Watt"

The power dissipation per bit(micro watt)is= 12 micro Watt

Eg6.6.2:pg-279

In [58]:
#(a)Calculate  the  insulator  capacitance
eir=3.9  #insulator relative dielectric constant
ei=8.854*(10**-12)*eir  #permittivity of material in F/m
d=.15*(10**-6)    #insulator thickness in meter
Ci=ei/d 
Ci=Ci*(10**5) 
print"The  insulator  capacitance(in nF/cm**2) is =",int(round(Ci)),"nF/cm2" 

#(b)Calculate  the  maximum  stored  charges  per  well
Nmax=2*(10**12)  #electron density in /cm2
q=1.6*(10**-19)  #charge of electron in C
A=.5*(10**-4)     #insulator cross-section in cm2
Qmax=Nmax*A*q 
Qmax=Qmax*(10**12)  #in pC
print"The  maximum  stored  charges  per  well(picocoulombs)is=",int(Qmax),"pC"

#(c) Calculate  the  required  applied  gate  voltage
Nmax=2*(10**12) 
q=1.6*(10**-19) 
Vg=(Nmax*q)/(Ci*10**-9) 
print"The  required  applied  gate  voltage(in  Volts) is=",int(round(Vg)),"V"

#(d)Calculate  the  clock  frequency
P=.67*(10**-3)   #power dissipation allowable per bit in Watt
n=3 
f=P/(n*Vg*Qmax*(10**-12)) 
f=f/(10**6)      #in MHz
print"The  clock  frequency(in MHz) is=",int(f),"MHz" 

The  insulator  capacitance(in nF/cm**2) is = 23 nF/cm2
The  maximum  stored  charges  per  well(picocoulombs)is= 16 pC
The  required  applied  gate  voltage(in  Volts) is= 14 V
The  clock  frequency(in MHz) is= 1 MHz