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ECE 662
Microwave Devices
Microwave Materials,
Diodes and Transistors
February 3, 2005
Two-Terminal Negative
Resistance Devices
Varactor – small pn diodes that are operated as nonlinear capacitors
In the reverse bias region
Application of Negative Resistance Devices
Non  Reciprocal Multiport Device
The 2 - port has a positive real
characteri stic impedance R 0
Z L  Z0 R L  R 0
- R  R0
Reflection coefficien t, Γ 

when R L  R ,  
,
Z L  Z0 R L  R 0
- R  R0
If R  R 0 , then    so acts like an oscillator or amplifier with infinite gain.
Advantage  Simple, easy to fabricate (usually GaAs (larger bandgap voltage)
Disadvanta ge  Low power outputs, mW, low efficiency ( 2%), up as high as
100GHz demonstrat ed
Varactor
• Varactor = Variable reactor
• Use of voltage-variable properties (such as
capacitance) of reversed-biased p-n
junctions
• Reverse biased depletion capacitance is
given by Cj ~ (Vb + VR)-n or Cj ~ (VR)-n for
VR >> Vb, where n = ⅓ for a linearly graded
junction and n = ½ for an abrupt junction.
• Can further increase the voltage sensitivity
by using a hyperabrupt junction having an
exponent n greater than ½.
Charge Depletion Regions
 2V

d 2V

   2   In p - type material region (x  0)
2
dx

dx

eN a 2
d 2V - eN a
dV eN a
  -eNa



x

C

V

x  C1 x  C2
1
2
dx

dx

2
eN a
dV
boundary conditions : V(x  0)  0  C 2  0 &
 0  C1 
X1
dx x   X 1

repeat for n - type material with   eN d
also at x  -X1  V  -V1 and at x  X 2  V  V2
V1 
eN a 2
eN d 2
X 1 and V2 
X2
2
2
Charge Depletion Regions
e
Contact Potential VB  V1  V2 
(N a X 12  N d X 22 )
2
but N a X 1  N d X 2  (charge equality)


2VB
X1  

 eN a (1  N a / N d ) 
1/2


2VB
& X2  

 eN d (1  N d / N a ) 
kT  N a N d 
also VB 
ln  2 ; n i  1.45 1010 cm 3 
e  ni 
@ room temp for Si, charge separation  capacitanc e
1/ 2
dQ  eN a N d 
1/2
per unit area, C 

V
,

T
dV  2( N a  N d ) 
VT  VB  V, where V is negative for reverse bias.
1/2
Varactor
• Present applications mostly for harmonic
generation at millimeter and sub millimeter
wave frequencies and tuning elements in
various microwave applications.
• A common varactor is the reversed biased
Schottky diode.
• Advantages: low loss and low noise.
• Produces only odd harmonics when a
sinusoidal signal is applied, so a frequency
tripler can be realized without any second
harmonic.
Varactor
Dynamic Cutoff Frequency
( an important figure of merit) :
1 / Cmin  1 / Cmax
fc 
, where R s is the
2Rs
series resistance
Typical value of f c for a state of the art
varactor is 1 THz.
Varactor Frequency Multipliers
• Provide LO power to sensitive millimeter
and sub-millimeter wavelengths receivers.
• Schottky doublers can deliver 55 mW at
174 GHz
• Heterostructure Barrier Varactor Diodes
acting as triplers deliver about 9mW at 248
GHz.
Crossed Waveguide Frequency Multiplier
Ref. Golio
Varactor Devices
• Lower frequencies: reversed biased
semiconductor abrupt p+-n juction diodes
made from GaAs or Si.
• Higher frequencies: Schottky diodes (metalsemiconductor junction diodes
• High frequencies and power handling:
heterostructure barrier varactor – several
barriers stacked epitaxially
Tunnel Diode
• To achieve microwave capability
– Device dimensions must be reduced
– Parasitic capacitance and resistance must be minimized.
• Tunnel diode
– Associated with a quantum tunneling phenomenon
– Tunneling time is very short permitting its use well into the
millimeter region
– Used for low power microwave application
• Local oscillator, detectors, mixers, frequency locking circuit
• Low cost, light weight, high speed, low-power operation, low noise
Tunnel Diode
• In classical case, particle is reflected if E<
potential barrier height of V0
• In quantum case particle has a finite probability
to transmit or “tunnel” the potential barrier
• Single p-n junction which has both p & n sides
heavily dopeddepletion regions very narrow
and tunneling distance is small ~ 50 to 100 Å
– (1 Å =10-8 cm=10-4 m)
– High dopings cause Fermi levels within allowable
bands
p-n
junction
Tunnel Diode
- abrupt junctions of
heavily doped p & n
semiconductor
material p~n~1019
Tunnel Diode
• 1) For zero bias - electrons tunneled through
narrow barrier at equal rates in each
direction. Net current zero.
• 2) Small forward bias - electrons at bottom
of conductor band on n side are are raised to
energy levels corresponding to unoccupied
energy levels on the p side. Therefore,
tunneling current in forward direction with
increases with bias.
Tunnel Diode
• 3) For still larger bias, more and more
electrons are raised to levels lying opposite
the forbidden band on p side to which to
which no tunneling is possible therefore the
current reduces with increasing bias.
• 4) As bias increases further, the current
remains small until minority carrier
injection similar to conventional diodes
predominates.
Tunnel Diode
• 5) with reverse as an increasing number of
electrons on the p side find themselves
opposited allowed and empty levels in the
conduction band on the n side therefore
tunneling increases rapidly with increasing
bias.
Application of Negative Resistance Devices
Note negative resistance
Values of I p and I v determine the
magnitude of the negative resistance .
 I p /I v  figure of merit for tunnel
diode.
Empirical form for I - V characteri stic is given by
V 
 V 


I  Ip
exp 1    I 0
V 
 V 
p 
 p

1
 V
 Ip
 V 
 dI 
R
    1 exp 1  
 dV 
 V p  V p
 V p 
 low cost, light weig ht, high speed, low power operation,
low noise, high frequency (up to 100 GHz)
- very low output power (few mW)
1
Tunnel Diode
Note that small changes in VB result in large changes in i hence VRL
Negative Resistance Devices
I & V, 180 out of phase
I2R power absorbed, but if R  –R then power generated
Summary of Tunnel Diode
•
•
•
•
Quantum Tunneling Phenomena
Tunneling time short - mm waves
Low-power applications
n-p sides so heavily doped that the fermi levels
lie within the conduction and valence bands
• Good for extreme speed
• Rate of tunneling can change as fast as energy
levels can be shifted
• Devices such as transistors give more power,
but traditionally have suffered in speed due to
rate of diffusion of charge changing.
Solid-State
Device
Power
Output vs
Frequency
ref: Sze
and
modified
by Tian
Transistors
• Bipolar (Homojunction)
– Inexpensive, durable, integrative, relatively
high gain
• Bipolar (Heterojunction)
– High speed switching
• Field Effect Transistors
– Junction
– MESFET, MOSFET, High Electron Mobility
(HEMT)
– Av as well as Qc, better efficiency, lower noise
figure, higher speed, high input impedance
pnp transistor
with all leads
grounded
ref. Sze
pnp transistor in the
active mode of operation
ref. Sze
Various current components in a p-n-p transistor
under the active mode of operation. ref. Sze
Bipolar Transistor – Gain (f)
G( f ) 
G0
1/ 2
2

  G0   f  



1

   


k
f

    max  

4
, G0  low frequency gain
2
 f max 
 , k ~ 0.2 to 0.3
@high frequency G(f) ~ k 
 f 
2
  0 f 

f max  
 8rbCc 
 0  dc common
 derived in terms of emitter to



 collector signal delay tran sit time,  ec 
base current gain
f  1 /( 2ec ), rb  base spreading resistance
Cc  collector depletion layer capacitanc e
 ec   e   b   x   c
re  emitter resistance of forward - biased
Ce  depletion layer capacitanc e across base - emitter
Bipolar Transistor – Gain (f) – cont.
 b  W 2 /(3.5Deb )  Diffusion - limited transit t ime of carriers
b
through t he base width W b
Deb  diffusion constant of emitter injected electrons in the base
 x  Wc /( 2vs )  transit time of carriers through t he base - collector
depletion region.
Wc  width of base - collector depletion region
v s  saturation velocity of electrons ~ 8  10 6 cm/sec
 c  rc Cc  collector depletion layer charging time
rc  resistance associated with the undepleted region of the
collector
Cc  collector - base depletion layer capacitanc e
Bipolar Transistor – High Freq.
rb   b (W  s) /( wb )
 b  average resistivit y of undepleted part of base (width w b )
Cc  (W  s)C0 C0  collector capacitanc e/unit area
Bipolar Transistor – Gain (f)
1/ 2
2


0w b
wb
1

 , ec   b 
 f max 

4 (W  s )   ec  bC0 
nD eb
1
f max  1/ 2 , typically strip widths  1m; w b  0.15m,
wb
v
f
:;  for L  3m, f  3 GHz or
2L
for L  25m, f  400 MHz
Field-Effect Transistors
• Advantages
– 1) Voltage gain and current gain
(simultaneously)
– 2) Higher efficiency compared to bipolar
– 3) Lower Noise Figure
– 4) Higher fmax and consequently higher
operating frequency
– 5) High input resistance, up to several Meg
Field-Effect Transistors
V is changed by Vgs – to change channel size {reverse bias between
Source and gate to adjust channel forward bias between source and
Drain for current flow (majority carrier)}
d 2V

qN dV
qN
dV







(
y

a
)
b.c.
 0 at y  a
2
dy


dy

dy
2
qN
qNa 2
V 
( y  2ay ) b.c. V  0 at y  0 V  y  a   V p  
 pinch - off
2
2
voltage, where a  width of channel ~ 0.15m and N  doping of channel, Like
2
vs
1
 f max 
bipolar, G ~ k 

where,   L/v s  gate transit t ime,
 ; f max ~
2 2L
 f 
L  gate length, v s  saturation drift velo city ~ 2 107 @ E  3kV/cm, ( GaAs)
v s ~ 8 106 @ E  15 kV/cm (Si)
Field-Effect Transistors
32
For GaAs  f max 
L(Gate length in microns)
Key is larger saturation velocity for GaAs  f max ~ 60 GHz
GaAs FET
Bipolar Xtr.
Gain
20 – 40 dB
~10 dB
BW
Several GHz
Several 1/10 GHz
Power Out 0.5 to 5 W
20 W
fmax
~ 8 GHz
~ 3 GHz
Pfmax2
~ 3x1020 WHz2 ~ 2x1020 WHz2
Field-Effect Transistors
• To get larger output powers – use larger
gate widths
– ~ 1W / 1 mm gate width
• Single gate width ~ 250 to 500 m
• Use multiple gates (~12) to increase power
Technology Alternatives - 1
Ref: MPD, Nov 2002, Amcom Communications
• Material technologies (GaAs, Si, SiGe)
• Process technologies (Epitaxy, Implant)
• Device technologies (BJT, HBT, MESFET,
HEMT)
• Power levels less than 1 W
– BJT, HBT (use single polarity supply and offer
cost advantages at these power levels)
– GaAs, MESFET’s, pHEMT’s (better linearity
and efficiency)
Technology Alternatives - 2
Ref: MPD, Nov 2002, Amcom Communications
• High power levels above 10 W
– Si LDMOS (attractive at frequencies below 2
GHz)
– Wide band gap devices such as SiC,
MESFET’s, GaN, HEMT’s (higher power,
higher voltage and promising linearity
performance)
Terrestrial wireless systems
Ref: MPD,
Nov 2002, Amcom Communications
Broadband internet access – operate in the
frequency range of 1 – 6 GHz.
Low cost subscriber units: less than 1 W
transmit power: SiGe, GaAs HBT,
MESFET and pHEMT MMIC’s.
Higher power (2-10 W) GaAs FTE, pHEMT
(optimize RF power output and best
linearity performance over the specific band
of interest while keeping the cost low)