# Chapter 6:Semiconductor Microwave Devices¶

## Example 1,Page No:292¶

In :
import math

# Variable Declaration
gs      = 0.0025;       # output conductance in mho
gl      = 0.0025;       # load conductance
r       = -250;         # negative resistance of microwave device

# calculations

#  P1  = Vl**2 *gl          # power that is transferred to load
#  P   = Vl**2 *gs          # source is matched to load
#  P   = [Is/(gl+gs)]**2 *gs
#      = ((Is**2)/(4*gs**2))*gs
#      = (Is**2)/(4*gl)
#  P2  = Vl**2 *gl          # Load power
#      = [Is/(gs+gl-g)]**2 *gl
#      = (Is**2 *gl)/(2gl - g)**2
# P2/P1 = ((Is**2 *gl)/(2gl - g)**2)*(4*gl)/(Is**2)
#       = (4*gl**2)/(2gl - g)**2;
#       = (4*gl**2)/(4gl**2 + g(g-4gl))
# For P2/P1 > 1 , 4gl > g so that denominator is less than numerator
g       = 1/float(r);
# let k = P2/P1
k       = (4*gl*gl)/((2*gs)+ g)**2

# Result
print'Power gain = %d'%k;

Power gain = 25


## Example 2,Page No:293¶

In :
import math

# Variable Declaration
Rl      = 500;      # load resistance

# Calculations
gl      = 1/float(Rl);     # load conductance
gmax    = 4*gl;     # max negative diff. conductance

# Result
print'gmax = %3.3f mho'%gmax;

gmax = 0.008 mho


## Example 3,Page No:293¶

In :
import math

# Variable Declaration
L       = 10*10**-6;     # width of N-region
Vs      = 10**5;          # saturated vel. of carriers

# Calculations
fo      = (3*Vs)/(4*L);     # oscillation frequency

# Result
print'Operational frequency = %3.1f Ghz\n'%(fo/float(10**9));
print'Note: In textbook it is wrongly printed as 6.5 Ghz';

Operational frequency = 7.5 Ghz

Note: In textbook it is wrongly printed as 6.5 Ghz


## Example 4,Page No:294¶

In :
import math

# Variable Declaration
L       = 10**-6;        # gate length
Vs      = 10**5;         # saturation velocity in m/s

# calculations
fT      = Vs/(2*math.pi*L); # cut-off freq.

# Result
print'Unity gain cut-off frequency = %3.0f Ghz'%(fT/float(10**9));

Unity gain cut-off frequency =  16 Ghz


## Example 5,Page no:294¶

In :
import math

# Variable Declaration
f       = 10*10**9;      # oscillating freq. of Gunn diode
Vs      = 10**5;          # saturation carrier velocity in m/s

# calculations
L       = Vs/float(f);         # length of active layer

# Result
print'Length of active layer = %3.0f µm'%(L/float(10**-6));

Length of active layer =  10 µm


## Example 6,Page No:294¶

In :
import math

# Variable Declaration
f       = 10*10**9;       # oscillating freq. of Gunn diode
Vs      = 10**5;          # saturation carrier velocity in m/s
er      = 13;             # relative permitivity
u       = 100*10**-4;     # mobility in m^2/V-s
eo      = 8.85*10**-12;  # permitivity in F/m
e       = 1.6*10**-19;   # charge of electron

# Calculations
L       = Vs/float(f);         # length of active layer
no      = (eo*er*Vs)/float((L*e*u));  # doping concentration

# Result
print'Doping Concentration no >> %3.2g /m**3'%no;

Doping Concentration no >> 7.2e+20 /m**3


## Example 7,Page No:295¶

In :
import math

# Given data
fo      = 40*10**9;     # oscillating freq. of Gunn diode
no      = 10**15;       # doping concentration
up      = 8000;         # mobility in positive conductance region
er      = 13;           # relative permitivity
um      = 100;          # mobility in m^2/V-s
eo      = 8.85*10**-14;  # permitivity in F/cm
e       = 1.6*10**-19;   # charge of electron

# Calculations
# (eo*er)/(e*up) << no/fo < (eo*er)/(e*um)  // condition to be satisfied
# let k = (eo*er)/(e*up) , l = (eo*er)/(e*um) , p = no/fo
p       = no/fo
k       = (eo*er)/(e*up)
l       = (eo*er)/(e*um)
if k<p:
if p<l:
print'Necessary Condition satisfied';


Necessary Condition satisfied


## Example 8,Page No:295¶

In :
import math

# Variable Declaration
n       = 10**15;        # doping concentration in /cm^3
u       = 8500;         # mobility in  m^2/V-s
er      = 13;           # relative permitivity
eo      = 8.85*10**-14;  # permitivity in F/cm
e       = 1.6*10**-19;   # charge of electron

# Calculations
Td      = (eo*er)/float((n*u*e));      # Dielectric relaxation time

# Output
print'Dielectric relaxation time = %3.3f ps'%(Td*10**12);

Dielectric relaxation time = 0.846 ps


## Example 9,Page No:296¶

In :
import math

# Variable Declaration
f       = 20*10**9;      # oscillating freq. of Gunn device
Vs      = 10**5;         # saturation carrier velocity in m/s

# Calculations
L       = Vs/float(f);          # length of device

# Result
print'length of device = %d µm'%(L*10**6);

length of device = 5 µm


## Example 10,Page No:296¶

In :
import math
# Given data from graph
up  = (2*10**7)/float(3000);                # mobility of diode in positive conductance region
un  = (2*10**7 - 10**7)/float(((10-3)*10**3)); # mobility of diode in negative conductance region

# Result
print'mobility of diode in positive conductance region = %d cm**2/(V-s)'%up;
print'mobility of diode in negative conductance region = %3.0f cm**2/(V-s)'%un;

mobility of diode in positive conductance region = 6666 cm**2/(V-s)
mobility of diode in negative conductance region = 1429 cm**2/(V-s)


## Example 11,Page No:297¶

In :
import math

# Variable Declaration
e       = 1.6*10**-19;   # charge of electron
Nd      = (10**15)*(10**6);    # mobility
L       = 10*10**-6;      # active layer of Barritt diode
er      = 12.5           # relative permitivity
eo      = 8.85*10**-12;   # permitivity in F/cm

# calculations
Ex      = (e*Nd*L)/float((2*eo*er)) # electric field for Va = Vpt and x = L/2
E       = Ex/float(10**2);           # electric field in v/cm
Vpt     = 10*10**-4*E

# Result
print'Electric field E(x) = %3.0d KV/cm\n'%(E/float(1000)),'Punch through voltage = %3.0f Volts'%Vpt;

Electric field E(x) =  72 KV/cm
Punch through voltage =  72 Volts


## Example 12,Page No:297¶

In :
import math

# Variable Declaration
fT      = 10;       # ft specification of BJT
f_a     = 2;        # operating freq in Ghz case a
f_b     = 10;       # operating freq in Ghz case b

# calculations
hFE_a   = fT/float(f_a);
hFE_b   = fT/float(f_b);

# Result
print'case a:\n  hFE = %d\n'%hFE_a,'case b:\n  hFE = %d\n'%hFE_b;


case a:
hFE = 5
case b:
hFE = 1



## Example 13,Page No:298¶

In :
import math

# Variable Declaration
n       = 10**15;        # doping concentration in /cm^3
er      = 15;            # relative permitivity
eo      = 8.85*10**-14;   # permitivity in F/cm
e       = 1.6*10**-19;    # charge of electron
sigma   = 133*10**-2;     # conductivity in ohm/cm

# calculations
Td      = (eo*er)/float(sigma);    # dielectric relaxation time constant
u       = sigma/float((n*e)) ;     # mobility

# Result
print'Dielectric relaxation time constant = %3.0f ps\n'%(Td*10**12),'Carrier Mobility = %d cm**2/V-s'%u;

Dielectric relaxation time constant =   1 ps
Carrier Mobility = 8312 cm**2/V-s


## Example 14,Page No:298¶

In :
import math

# Variable Declaration
gm      = 50*10**-3;       # conductance in mho
cgs     = 0.6*10**-12;     # gate to source capacitance
cgd     = 0.015*10**-12;   # gate to drain capacitance
Rg      = 3;               # gate resistance in ohm
Rs      = 2;               # source resistance in ohm
Ri      = 2.5;             # intrinsic channel resistance
Rds     = 400;             # drain to source resistance

# Calculations
fT      = gm/(2*math.pi*cgs);   # device's fT
t3      = 2*math.pi*Rg*cgd;
r1      = (Rg+Rs+Ri)/Rds;
fmax    = fT/(2*math.sqrt(r1 + (fT*t3)));    # max usable frequency
if fmax>40*10**9:
print'Operation at 40 GHz is Theoretically possible\n';

# utput
print' fT = %3.1f Ghz\n'%(fT/float(10**9)),' fmax = %3.1f'%(fmax/float(10**9));

Operation at 40 GHz is Theoretically possible

fT = 13.3 Ghz
fmax = 44.2


## Example 15,Page No:299¶

In :
import math

# Variable Declaration
f2      = 20;       # pump frequency in GHz
f1      = 2;        # signal frequency in GHz

# Calculations
Gp      = (f1+f2)/f1;       # power gain if parametric amp. operated as USB up-converter
Gp_dB   = 10*math.log10(Gp);     # power gain in dB
Gp_lsb  = (f2-f1)/f1;       # power gain if parametric amp. operated as LSB up-converter
Gp_db_lsb = 10*math.log10(Gp_lsb); # power gain in dB

# Result
print'Power gain of parametric amplifier when operated as USB up-converter = %3.1f dB\n'%Gp_dB ,'Power gain of parametric amplifier when operated as LSB up-converter = %3.2f dB'%Gp_db_lsb;

Power gain of parametric amplifier when operated as USB up-converter = 10.4 dB
Power gain of parametric amplifier when operated as LSB up-converter = 9.54 dB


## Example 16,Page No:300¶

In :
import math

# Variable Declaration
h       = 6.63*10**-34;     # planck's constant in Joule-sec
el      = 0.25;             # lower energy level in eV from energy level diag.
eh      = 1.5;              # higher energy level in eV from energy level diag.
e       = 1.6*10**-19;      # charge of electron
c       = 3*10**8;          # vel. of light in m/s

# calculations
hf      = (eh - el)*e;            # energy diff b/w two levels in J
f       = hf/float(h);                   # frequency
lamda   = c/float(f);                    # o/p laser wavelength in m

# Result
print'Output laser wavelength = %3.0e m '%(lamda),'or %3.0f µm '%(lamda*10**6);

Output laser wavelength = 1e-06 m  or   1 µm


## Example 17,Page No:312¶

In :
import math

# Variable Declaration
p   = 0.1*10**-2;        # resistivity in ohm-m
t   = 100*10**-6;        # thickness in m
AR  = 10/1;              # aspect ratio

# Calculations
ps  = p/float(t)
R   = ps*AR;             # Resistance in ohm

# Result
print'Resistance = %d Ω'%R;

Resistance = 100 Ω


## Example 18,Page No:312¶

In :
import math
# Given data from fig
R_a = 1000;      # resistance shown in fig a
W1  = 0.15*10**-3  # width of geometry fig 6.72a
L1  = 3*10**-3    # Length of geometry fig 6.72a
W2  = 75*10**-6   # width of geometry fig 6.72b
L2  = 1500*10**-6 # Length of geometry fig 6.72b
t1  = 10*10**-6   # thickness of geometry fig 6.72a
t2  = 20*10**-6   # thickness of geometry fig 6.72b

#R1  = ρs1*(L1/W1);  # resistor geometry of fig 6.72a
#ρs1 = (R1*W1)/L1;
ps1   = (R_a*W1)/L1;  # sheet resistivity of geometry of fig 6.72a
p     = ps1*t1;     # resistivity
ps2   = p/float(t2);       # sheet resistivity of geometry of fig 6.72b
R2    = ps2*(L2/W2); # resistance of geometry of fig 6.72b

# Result
print'For Geometry in Fig 6.72b\n','sheet resistivity = %3.0f Ω/□\n'%ps2,'Resistance = %d Ω'%R2;

For Geometry in Fig 6.72b
sheet resistivity =  25 Ω/□
Resistance = 500 Ω


## Example 19,Page No:313¶

In :
import math

# Variable Declaration
A       = 100*100*10**-12;       # Area of electrode
er      = 9.6;                  # relative permitivity
t       = 500*10**-6;            # substrate thickness
eo      = 8.85*10**-12;          # permitivity

# Calculations
C       = (eo*er*A)/float(t);            # capacitance in farad

# Result
print'Capacitance = %3.2e pF'%(C*10**12);

Capacitance = 1.70e-03 pF


## Example 20,Page No:314¶

In :
import math

# Variable Declaration
ps      = 100;      # sheet resistivity
L       = 1.04      # length
W       = 0.02      # width

# Calculations
NOS     = L/W        # number of squares
R       = ps * NOS   # resistance

# Result
print'Resistance = %3.1f KΩ' %(R/float(1000));


Resistance = 5.2 KΩ