Microwave Engineering

ECE 327

Reference: Microwave Devices and

Circuits

Final: 80
Mid-term, Quiz, Attendance: 45
Total: 125
Negative resistance
• The common characteristic of all active two-terminal solid-state devices is their
negative resistance.
• The real part of their impedance is negative over a range of frequencies.

Passive devices Active devices

The current through the resistance and The current through the resistance and
the voltage across it are in phase. the voltage are out of phase by 180°.
The voltage drop across a positive The voltage drop across a negative
resistance is positive. resistance is negative.
Power of (𝐼 2 𝑅) is dissipated in the Power of (−𝐼 2 𝑅) is generated by the
positive resistance. power supply associated with the
negative resistance.
Positive resistances absorb power Negative resistances generate power
(passive devices). (active devices).
Transferred electron device (TED)

Microwave transistor Transferred electron device (TED)

Transistors operate with either junctions or TEDs are bulk devices having no
gates. junctions or gates.
Transistors operate with warm electrons whose TEDs operate with hot electrons
energy is not much greater than the thermal whose energy is very much greater
energy (0.026 eV at room temperature) of than the thermal energy.
electrons in the semiconductor.
Transistors are fabricated from elemental TEDs are fabricated from compound
semiconductors. semiconductors
1- Silicon 1- Gallium arsenide (GaAs)
2- Germanium 2- Indium phosphide (InP)
3- Cadmium telluride (CdTe)
Gunn diode
• J. B. Gunn discovered a periodic fluctuations of current passing through the n-type gallium
arsenide (GaAs) specimen when the applied voltage exceeded a certain critical value.
• Gunn-effect diodes are bulk devices in the sense that microwave amplification and
oscillation are derived from the bulk negative-resistance property of uniform
semiconductors rather than from the junction negative-resistance property between two
different semiconductors as in the tunnel diode.
• Gunn diode construction consists of three regions of n-type GaAs, two of them are heavily
doped on each terminal with a thin layer of lightly doped in between.
Background
• After inventing the transistor, Shockley suggested that two-terminal negative-
resistance devices using semiconductors may have advantages over transistors at
high frequencies.
• Ridley and Watkins described a new method for obtaining negative differential
mobility in semiconductors.
• The principle involved is to heat carriers in a light-mass, high-mobility subband
with an electric field so that the carriers can transfer to a heavy-mass, low-mobility,
higher-energy subband when they have a high enough temperature.
• Ridley and Watkins also mentioned that Ge-Si alloys and some III-V compounds
may have suitable subband structures in the conduction bands.
• Their theory based on achieving negative differential mobility in bulk
semiconductors by transferring electrons from high-mobility energy bands to low-
mobility energy bands.
Background
• Hilsum calculated the transferred electron effect in several III-V compounds.
• Hilsum was the first to use the terms transferred electron amplifier (TEA)
and oscillator (TEO).
• He predicted accurately that a TEA bar of semi-insulating GaAs would be
operated at 373°K at a field of 3200 V/cm.
• Hilsum attempts to verify his theory experimentally failed because the GaAs
diode available to him at that time was not of sufficiently high quality.
• J. B. Gunn discovered the Gunn effect in the n-type GaAs bulk diode.
Principle of operation of Gunn diode (Gunn effect)
• Gunn stated that above some critical voltage, corresponding to an electric field of
2000-4000 volts/cm, the current in every specimen became a fluctuating function of
time.
• In the GaAs specimens, this fluctuation took the form of a periodic oscillation
superimposed upon the pulse current.
• From Gunn's observation the carrier drift velocity is linearly increased from zero to
a maximum when the electric field is varied from zero to a threshold value.
• When the electric field is beyond the threshold
value of 3000 V/cm for the n-type GaAs,
the drift velocity is decreased, and the diode
exhibits negative resistance.
Gunn diode
• The frequency of oscillation was determined mainly by the specimen.
• The period of oscillation was usually inversely proportional to the specimen length
and closely equal to the transit time of electrons between the electrode calculated
from their estimated velocity.
• A schematic diagram of a uniform n-type GaAs
diode with ohmic contacts at the end surfaces.
Gunn diode
• Gunn found that the period of these oscillations was equal to the transit time of the
electrons through the specimen calculated from the threshold current.
Drift velocity = 𝑣𝑑 = 𝑓 𝑙
𝑙 : drift or specimen length.
𝑉
Threshold field = 𝐸𝑡ℎ =
𝑙
𝑉 : applied voltage.
• If electron densities in the lower and upper valleys are 𝑛𝑙 and 𝑛𝑢 , the conductivity
of the n-type GaAs is defined as:
𝜎 = 𝑒 (𝜇𝑙 𝑛𝑙 + 𝜇𝑢 𝑛𝑢 )
e : electron charge
𝜇: electron mobility
n = 𝑛𝑙 + 𝑛𝑢 is the electron density
 Ridley-Watkins-Hilsum (RWH) theory.
• The fundamental concept of the Ridley-Watkins-Hilsum (RWH) theory is the differential negative
resistance developed in a bulk solid-state III-V compound when either a voltage (or electric field) or a
current is applied to the terminals of the sample.
𝑑𝐼 𝑑𝐽
Negative resistance = NR = =
𝑑𝑉 𝑑𝐸

• There are two modes of negative-resistance devices: voltage-controlled and current-controlled modes.
• If an electric field 𝐸0 (or voltage 𝑉0 ) is applied to the sample, the current density 𝐽0 is generated.
• As the applied field (or voltage) is increased to 𝐸2 (or 𝑉2 ), the current density is decreased to 𝐽2 .
• When the field (or voltage) is decreased to 𝐸1 (or 𝑉1 ), the current density is increased to 𝐽1 .
Negative-resistance modes
Voltage-controlled mode Current-controlled mode
Current density can be multivalued Voltage can be multivalued

High-field domains are formed, separating two low- Splitting the sample results in high-current
field regions, and perpendicular to the current direction filaments running along the field direction
Two-valley model theory.
• Electron densities in the lower and upper valleys remain the same under an equilibrium condition.
• When the applied electric field is lower than the electric field of the lower valley (𝐸 < 𝐸𝑙 ), no
electrons will transfer to the upper valley
• When the applied electric field is higher than that of the lower valley and lower than that of the
upper valley (𝐸𝑙 < 𝐸 < 𝐸𝑢 ), electrons will begin to transfer to the upper valley.
• When the applied electric field is higher than that of the upper valley (𝐸𝑢 < 𝐸), all electrons will
transfer to the upper valley.
Criteria of the RWH theory
• On the basis of the Ridley-Watkins-Hilsum theory, the band structure of a
semiconductor must satisfy three criteria in order to exhibit negative resistance.

1- The separation energy between the bottom of the lower valley and the bottom of
the upper valley must be several times larger than the thermal energy (about
0.026 eV) at room temperature (∇E > 𝐾𝑇).
2- The separation energy between the valleys must be smaller than the gap energy
between the conduction and valence bands (∇E < 𝐸𝑔 ).
3- Electrons in the lower valley must have high mobility, small effective mass, and
a low density of state, whereas those in the upper valley must have low
mobility, large effective mass, and a high density of state.
Criteria of the RWH theory
• The two most useful semiconductors silicon and germanium do not meet
all these criteria.
• Some compound semiconductors, such as gallium arsenide (GaAs),
indium phosphide (InP), and cadmium telluride (CdTe) do satisfy these
criteria.
• Otherssuch as indium arsenide (InAs), gallium phosphide (Gap), and
indium antimonide (InSb) do not.
 Drift velocity versus electric field
• The magnitude of the current density in a semiconductor is given by:
𝐽=𝑞𝑛𝜐
q : electric charge
n: electron density
𝜐 : average electron v
• Differentiate with respect to electric field E yields:
𝑑𝐽 𝑑𝜐
=𝑞𝑛
𝑑𝐸 𝑑𝐸
• Condition for negative differential conductance is:
𝑑 𝜐𝑑
= 𝜇𝑛 < 0
𝑑𝐸
𝜇𝑛 : negative mobility