UNIT- IV

MICROWAVE SOLID STATE DEVICES

Introduction

Even though in the earlier stages of development of microwave technology, it was the
tubes that played a key role, in later stages it is the semiconductor or solid state
source that took the lead. The development of semiconductor technology in general
helped in fabricating low voltage operated and miniaturized solid state sources at a
low cost. With the advent of microwave solid state devices, the microwave
applications in the area of consumer electronics rapidly expanded.

The solid state sources are claimed of the advantages of longer life, requiring low
voltages, easy control of amplitude of the transmitted wave form, wider bandwidths,
low production costs and air cooling.

In this chapter, the basic principles of functioning of Gunn diodes are first explained.
Different modes of operation and theories explaining their behavior are then
discussed. IMPATT and TRAPATT diodes are used to design microwave amplifiers
and oscillators. Their function and design aspects are then explained. Tunnel diodes,
varactor diodes are introduced and the theory of their functioning is illustrated
parametric amplifies and tunnel diode amplifiers are then discussed. The chapter is
concluded with a discussion on detector diodes.

GUNN DIODES

Gunn oscillators and amplifiers are most important microwave devices that have
been extensively used as a local oscillators and power amplifiers covering the
frequency range of 1 to 100 GHz in which Gunn diode is a critical part. Gunn diode is
an n-type semi-conductor slab of one of the compounds, namely Ga As (Figure 7.1),
InP, InAs, InSb and CdTd. This diode exhibits dynamic negative resistances when it
is biased to a potential gradient more than a certain value known as threshold field
Eth due to the phenomenon known as Gunn Effect or Transferred Electron Effect
(TEE).

The importance of the Gunn diode lies in its dynamic negative resistance
characteristic [Figure 7.2]. In any n-type semiconductor, the following relations
govern current, field and drift velocity.

vd = μE d vd / dE = μ
and J = nq μE d J / dE = nqμ
∴

d/

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 Fig 7.1: Structure of Ga As Gunn diode

Fig 7.2: Variation of current density with electric field

Fig 7.3: Variation of drift velocity with electric field

In Gunn diodes, which are also n-type semiconductors,

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 When the field is less than the certain value, called threshold value Eth, increase
in the field intensity E causes the vd to increase resulting in the positive
mobility μ. Hence, an increase in the E causes / to increase resulting in
positive resistance.

 When the field is in between threshold value Eth and valley value Ev increase in
the field E causes the vd to decrease due to the onset of TEE resulting the
negative mobility μ. Hence an increase in the field the E causes J to decrease
resulting in the manifestation of differential negative resistance. When the field is
more than Ev increase in field E causes vd to increase resulting in the positive
mobility μ due to the disappearance of the TEE. Hence, an increase in
the E causes / to increase resulting in positive resistance.

 The threshold field values are GaAs-3.3 kV/cm, InP-10.53 kV/cm, InAs-1.63
kV/cm, lnSb-0.63 kV/cm, CdTd-13.03 kV/cm.

The TEE is actually ‘a field induced transfer of conduction band electrons from a
high mobility lower energy satellite valley to low mobility higher energy satellite
valley'. The salient features of this phenomenon are as follows:

 It is a bulk material property, i.e. it takes place at each and every point in the
body of the material.

 Due to this effect the mobility of the electrons in the diode exhibits negative
resistance property.
Certain important points pertaining to Gunn diodes worth noting are mentioned below.

 The electrons drift through the diode with velocities depending upon the field
intensity and it is maximum when the diode is biased to threshold value
[Figure 7.3].
 Peak drift velocities in various diodes are GaAs-2.2, InP-2.5, InAs-3.6,
InSb-5.0 and CdTd-1.5 times 107 cm/s.
 Noise in these diodes is of two types, one is AM noise normally small,
due to amplitude variations and the other one FM noise which is due to
frequency deviations.
 The upper frequency of the transferred electron devices (TEDs) is
limited to 150 GHz mainly due to the 'finite response time'.

The output power is inversely proportional to the square of the frequency, i.e.

1
pout  (7.1)
f2

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  Gunn oscillators and amplifiers are being widely used as local oscillators
and power amplifiers covering 1 to 100 GHz range.

Gunn Domains

The transfer to lower mobility valley starts with the electrons located in a small
region, where the field intensity is more due to lower carrier concentration. These
regions are called high field domains. The domains travel to anode shifting all the
electrons in their path to lower mobility valley. The velocity of domains is slightly more
than the drift velocity of electrons.

Salient features of gunn domains are:

 Domains start to form whenever the electric field in a region of the sample
increases above the threshold value and after formation they drift with the stream
through the device.

 If additional voltage is applied to the diode with a domain, the domain will
increase in size and absorb more voltage than was added and the current will
decrease.

 The domain disappears after reaching the anode or in the mid- way if the field
drops to a value less than sustain field value Ex.

 Decreasing the field slightly lower than the threshold value can prevent the
formation of new domain.

 The domain modulates the current through the device as the domain passes
the regions of different doping and cross sectional areas.

 The domain length is inversely proportional to the doping concentration.

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Two Valley Model Theory

Two valley model theory is one of the several theories put forth to explain the
manifestation of negative resistance in Gunn diodes. The salient features of this
theory are as follows:
• It has been proposed by Kroemer to explain the manifestation of negative
resistance in certain types of bulk semiconductor materials.
• In the conduction band of n-type GaAs, a high mobility lower valley is
separated from a low mobility upper valley by an energy difference of 0.36
eV.
• The effective mass and mobility of the electrons in lower valley are 0.068
and 8000 cm2/V s whereas these quantities are 1.2 and 180 cm 2/V s in the
upper valley of n-type GaAs (Table 7.1).
• Under equilibrium conditions the electron densities in both the valleys remain
same.
• When the applied field is lower than the field corresponding to the energies
of the electrons in the lower valley, then no transfer of electrons takes place
from one to other valley. The mobility of the carriers is positive.
• When the applied field is higher than the field corresponding to the
energies of the electrons in the lower valley and lower than the field
corresponding to the energies of the electrons in the upper valley, then
transfer of electrons takes place from high mobility lower to low mobility
upper valley. The mobility of the carriers becomes negative (Figure 7.4).
• When the applied field is higher than the field corresponding to the energies
of the electrons in the higher valley, then no transfer of electrons takes place
because by that time all the electrons of the lower valley must have been
transferred to the upper valley. The mobility of the carriers is positive.
TABLE 7.1 Data for two valley semiconductors
Semiconductor Gap Separation Threshold field Peak velocity
energy energy Eth(kV/cm) vp(107 cm/s)
(at 300 K) between two
valleys
Ez(eV) ∆E(eV)

Ge 0.80 0.18 2.3 1.4

GaAs 1.43 0.36 5.2 2.2

InP 1.33 0.60, 0.80 10.5 2.5

CdTe 1.44 0.51 13.0 1.5

InAs 0.33 1.28 1.60 5.6

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 InSb 0.16 0.41 0.6 5.0

Note: InP is a three valley semiconductor 0.60 eV is the separation energy between
the middle and lower valleys. 0.8 eV that between the upper and lower valleys

Fig7.4: Two valley model of n-type Ga As

RWH Theory
Ridley, Watkins and Hilsum (RWH) proposed this theory to explain the phenomenon
of Negative Differential Resistance (NDR) in certain bulk materials. Its salient features
are as follows:
 Bulk NDR devices are classified into two groups. One voltage controlled NDRs
and second current controlled NDRs.

 The characteristic relation between electric field E and the current density
J of voltage controlled NDRs is N shaped and that of the current controlled
NDRs is S shaped (Figure 7.5).

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 Fig 7.5:Diagram of negative resistance

 The electric field is multi-valued in the case of voltage controlled NDRs and
it is electric current that is multi-valued in case of current controlled NDRs.

 The differential resistivity increases with field in case of voltage controlled

NDRs and decreases in case of current controlled NDRs.

 A semiconductor exhibiting bulk NDR is inherently unstable because a

momentary space charge, which might have been created due to random
fluctuation in the carrier density, grows exponentially with time because the
relaxation time is negative.

 Because of NDR, the initially homogeneous semiconductor becomes

heterogeneous to achieve stability. It results in 'High field domains' in voltage
controlled NDRs and 'High current filaments' in current controlled NDRs
(Figure 7.6).

Fig 7.6: Diagrams of high field domain and high current filament

 The high field domain starts forming at a region, where the field intensity is
higher extending further perpendicular to the direction of current flow separating
two low field regions.

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  The high current filament starts forming at a region where the field intensity is
higher extending further along the direction of the current flow separating two low
current regions.

 The RWH theory explained the phenomenon of negative resistance and gave
the necessary conditions to be satisfied by the semiconductors with the help of
energy band theory. It said, for any semiconductor to exhibit negative
resistance

 The conduction electrons must exist in semiconductors at different energy

levels or valleys.

 The separation energy between the lower valley and the upper valley must be
several times larger than the thermal energy (about 0.026 eV) of the electrons at
room temperatures.

 The separation energy between the valleys must be smaller than forbidden
energy gap between the conduction band and valence band.

 Electrons in the lower valley must have high mobility, small effective mass and
low density of state whereas those in the upper valley must have low mobility,
large effective mass and high density of state.

 The semiconductors Si and Ge do not meet these criteria and hence they cannot
exhibit dynamic negative resistance.

Gunn modes of operation

Major factors that determine the modes of operation are the following:
1. Concentration and uniformity of the doping
2. Length of the active region
3. Operating bias voltage
4. Cathode contact property
5. Type of the external circuit used.
 The important criterion for classifying the modes of operation for the gunn
effect diodes is
 v
nL 
e | n |
For n-type GaAs εv/e|μn| ≈ 1012 cm-2.
Where

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 V = electron drift velocity
n = Negative electron mobility
ϵ = ϵo ϵr
Hence an important boundary separating the various modes of operation is
nL = 1012 cm-2.
 The TEDs with nL products less than 1012 cm-2 exhibit a stable field
distribution.( n= electron density, L = drift region length)

Ever since Gunn announced his observations of microwave oscillations in the n-

type GaAs and n-type InP diodes in 1963, various modes of operation have been
developed depending on the material parameters and operating conditions.
Copeland proposed four basic modes of operation in uniformly doped bulk diodes
with low resistance contacts, namely,
1. Gunn oscillation mode,
2. Limited space charge accumulation mode,
3. Stable amplification mode
4. Bias circuit oscillation mode.

1. Gunn oscillation mode:

 nL  1012cm 2 

 fL  2107 cm / s 


 

This mode is operated with the field more than the threshold value, i.e. E > Eth.
 The high field domain drifts along the specimen until it reaches anode or
low field value drops to below the sustaining field value, i.e. E < Esus.

 The frequency of oscillation is given by f = vdom/Leff, where vdom is the

velocity of the domain and Leff is the effective length the domain travels
before a new domain gets nucleated.

The gunn oscillation mode has three sub-modes namely.

a) Transit time domain mode,

b) Delayed domain mode and
c) Quenched domain mode.

The salient features of these modes are explained below.

(a) Transit-time domain mode: [ fL = 107 cm/s]
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  The high field domains are stable in the sense that they propagate with a
particular velocity but do not change in any way with time.
 When the high field domain reaches the anode, the current in the external
circuit increases.

The frequency of the current oscillations depends on among other things, the

velocity of the domain across the sample. If the velocity increases, the
frequency increases and vice versa. It also depends upon the bias voltage. The
shape of the domains in GaAs and InP TEDs is triangular. In this mode the
oscillation period is transit time. The efficiency is below 10%. It is
illustrated in Figure 7.7.

Fig 7.7: Transit Time domain mode

(b) Delayed domain mode: [106 cm/s < fL < 107 cm/s]

In this mode the domain is collected by the anode when E < Elh and the new
 domain formation gets delayed until the rise of the field to above threshold.

 The oscillation period is greater than the transit time as shown in Figure 7.8.

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 Fig 7.8: Delayed domain mode

 The oscillations occur at the frequency of the resonant circuit which is tuned
to a value below that of the gunn mode. The dipole domain will arrive at the
anode will in time but the formation of a new dipole domain will be delayed
until the oscillation voltage increases above the threshold value.

 The efficiency of this mode is about 20%.

(c) Quenched domain mode: [fL > 2 x 107 cm/s]
 While the domain is travelling, the bias field drops to a value less than Es.
Esus during negative half cycle quenching the domain. A new one cannot form
until the field again rises above the Eth.
 Oscillations occur at the frequency of the resonant circuit rather than the transit
time frequency. The resonant circuit is tuned to a value slightly above that of the TT
mode, the dipole domain will be quenched before it arrives at the above by the
negative swing of the oscillation voltage but the Gunn diode will operate mostly like
Gunn mode.
 The operating frequencies are higher than the transit time frequency as
shown in Figure 7.9.
 Formation of multiple high field layers takes place.
 The upper frequency limit for this mode is determined by the speed of
quenching.

 In this mode the efficiency is about 13%.

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 Fig 7.9: Quenched mode


2. Limited Space charge Accumulation LSA)  nL  10127cm2  mode:
 fL  2 10 cm / s 
 

 The coefficient of doping divided by frequency ( n l f) should be in between
2 x 104 and 2 x 105.

 This is the simplest mode of operation and it consists of uniformly doped

semiconductor without any internal space charge.

 As the frequency is high the domains do not get sufficient time to form as
shown in Figure 7.10.

 Most of the domains find themselves in the negative conduction state during a
large fraction of voltage cycle.

 A large portion of the device exhibits a uniform field resulting in efficient

power generation at the circuit controlled frequency.

 This mode is suitable to generate short pulses of high peak power. LSA mode
of operation can produced several watts of power with minimum efficiencies
of 20%. The power output decreases with frequency, viz 1 W at 10 GHz and
several mW at 100 GHz.

 Its maximum operating frequency is much lower than that of the TT devices.

 Its limitations are sensitivity to load conditions, temperature and doping

fluctuations.

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Fig 7.10: LSA mode

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  nL  1011 to 1012cm2   mode:
3. Stable amplification  
 fL  107 cm / s 
 

 In this mode the devices exhibit stable amplification at the transit time
frequency.

 Negative conductance is utilized to prevent the formation of the domains.

 There exists three regions of amplification depending on the product fL range

from 107 to 0.5 x 108.

4. Bias circuit oscillation  nL  1012cm2  mode:

 



 fLsmall 


 This mode occurs when there is either Gunn or LSA oscillation and fL is
small or less that about 10-12/cm2. The device exhibits amplification at the
transit time frequency rather than spontaneous oscillation. This situation
occurs because the negative conductance is utilized without domain
formation. Therefore amplification of signals near the transit time frequency
can be accomplished.
 When the diode is biased to threshold Gunn oscillation begin leading to
sudden decrease in the average current of the circuit driving it to oscillations.
Table 7.2

Mode nL fL

1. Gunn oscillation mode: nL  1012cm2 fL  2107 cm / s

[ fL = 107 cm/s]
(a) Transit-time domain mode:

[106 cm/s < fL < 107 cm/s]

(b) Delayed domain mode:

[fL > 2 x 107 cm/s]

(c) Quenched domain mode:

2. Limited Space charge nL  1012cm2 fL  2107 cm / s

Accumulation (LSA) mode:

3. Stable amplification mode: nL  1011 to 1012cm2 fL  107 cm / s

4. Bias circuit oscillation nL  1012cm2 fLsmall

mode:

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Fig 7.11: Comparision of waveforms in differenct gunn modes

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IMPATT DIODE

The IMPATT diode is now one of the most powerful solid state sources for the
generation of microwaves. It can generate higher CW power outputs in millimetre
wave frequencies, i.e. above 30 GHz of all solid state devices. These are compact,
inexpensive, moderately efficient and with improved device fabrication technology
these diodes also have become reliable under high temperature operation. The
salient features of this diode are as follows:
• IMPATT stands for TMPact ionization Avalanche Transit Time'.
• IMPATT diodes employ 'Impact ionization' and 'Transit time' properties ofsemi-
conductor structures to get negative resistance at microwave frequencies.
• Impact ionization or Avalanche multiplication: It is a process
related to semiconductors in which the generation and multiplication of hole-
electron pair takes place due to knocking off the valence electrons into
conduction band by the highly energetic carriers when the electric field is
increased above certain value'. The rate of pair production is a sensitive non-
linear function of field.
• The negative resistance occurs from the delay, which cause the current to lag
behind the voltage by half cycle time, have two components:

 One is avalanche time delay caused by 'finite buildup time of the

avalanche current.'
 Other is transit time delay by the finite time for the carriers to cross the
drift region.
• These diodes are made from GaAs, Ge, Si.
• Extremely high voltage gradient 400 kV/cm back biasing the diode is required
for its operation.
• In all the structures there exists two regions (Figure 7.13)
• Avalanche region: In this region avalanche multiplication takes, doping

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 concentration and field intensity are high.

• Drift region: In this region avalanche multiplication does not take place,
doping concentration and field levels are low.
Depletion region is Avalanche Region plus Drift Region.

Fig 7.13: Read diode

It can be shown that the maximum negative resistance occurs when the transit
angle θ = Π at which the operating frequency becomes f = vd / 2L. where vd is drift
velocity of the carriers and L length of the drift region. Its operation is
illustrated in Figure 7.14.

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 Fig 7.14: Field, voltage and currents in read diode.
IMPATT is the name of a diode family. Its basic members are
- Read diode p+ - n - i - n+ or its dual n+ - p - i - p+.

- Single drift diode p+ - n - p+.

- Double drift diode or RIMPATT diode p+ - p - n - n+.

- PiN diode p+ - i - n+.

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The noise measure in GaAs is low when compared to Si and for Ge it is in between
GaAs and Si. The main reason for the low noise behavior of GaAs is that for a
given field the electron and hole ionization rates are essentially same, whereas in
Si these are quite different.
The highest powers, frequency and efficiency are obtained from double drift diodes
that are also known as RIMPATTs. The power-frequency product is highest for these
diodes. The improved performance results mainly from the fact that holes and
electrons produced by the avalanche are allowed to give energy to RF signal while
traversing the drift region. In the case of single drift diodes only one type of carriers
is so utilized.
Comparison:
o When compared to Gunn diode these diodes have more efficiency around 30%,
more powerful around 15 W CW and their frequency can reach up to 200 GHz
whereas in the case of Gunn it is only 100 GHz.

o But when compared to Gunn diodes these are noisier.

o Below 40 GHz GaAs IMPATTs have higher powers and efficiency than do Si
IMPATTs.

o Between 40-60 GHz GaAs IMPATTs show higher power and efficiency whereas
Si IMPATTs give high reliability and yield.

Above 60 GHz Si IMPATTs outperform the GaAs IMPATTs. Around the frequency
• GHz, the efficiency is close to 40%.
10
Power output:

• At lower frequencies the power output is thermal-limited and is

inversely proportional to the frequency, i.e. varies as f -1.
• At higher frequencies (>50 MHz) the power is electronic limited and varies
as f 2
Drawbacks:

• The noise is high mainly because of the statistical nature of the

generation rates of electron hole pairs in the avalanche region.
• Highly sensitive to operational conditions.
• Large electronic-reactance, which can cause detuning or even burnout of
the device unless proper care is taken.
Applications:

IMPATT diodes are at present the most powerful CW solid state microwave power
sources. The diodes have been fabricated from germanium, silicon, and Ga As and can
probably be constructed from other semiconductors as well. IMPATT diodes provide

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potentially reliable, compact, inexpensive and moderately efficient microwave power
sources. They are generally used in

• microwave links, In CW radars

• In electronic counter measures

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