An introduction to

Gunn oscillator And electronics of TEDs

by Pejman Taslimi represented to Dr. Hassani

Microwave Lab 6th November 2005 – Shahed university of Tehran

Introduction The application of two-terminal semiconductor devices at microwave frequencies has

been increased usage during the past decades. The CW, average, and peak power outputs of these devices at higher microwave frequencies are much larger than those obtainable with the best power transistors.

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. In a positive resistance the current through the resistance and the voltage across it are in phase. The voltage drop across a positive resistance is positive and a power of (I2R) is dissipated in the resistance. In a negative resistance, however, the current and voltage are out of phase by 180°. The voltage drop across a negative resistance is negative and a power of (-I2R) is generated by the power supply associated with the negative resistance. In other words, positive resistances absorb power (passive devices), whereas negative resistances generate power (active devices).

The differences between microwave transistors and transferred electron devices (TEDs) are fundamental. Transistors operate with either junction or gates, but TEDs are bulk devices having no junctions or gates. The majority of transistors are fabricated from elemental semiconductors, such as silicon or germanium, whereas TEDs are fabricated from compound semiconductors, such as gallium arsenide (GaAs), indium phosphate (InP), or cadmium telluride (CdTe). Transistors operate with “warm” electrons whose energy is not much greater than the thermal energy (0.026 eV at room temperature) of electrons in the semiconductor, whereas TEDs operate with ‘hot” electrons whose energy is very much greater than the thermal energy. Because of these fundamental differences, the theory and technology of transistors cannot be applied to TEDs.

GUNN-EFFECT DIODES — GaAs DIODE Gunn-effect diodes are named after J. B. Gunn, who in 1963 discovered periodic

fluctuations of current passing through the n-type gallium arsenide (GaAs) specimen when the applied voltage exceeded a certain critical value. Two years later, in 1965, B. C. DeLoach, R. C. Johnston, and B. G. Cohen discovered the impact ionization avalanche transit-time (IMPATT) mechanism in silicon, which employs the avalanching and transit-time properties of the diode to generate microwave frequencies. In later years the limited space-charge-accumulation diode (LSA diode and the indium phosphate diode (lnP diode) were also successfully developed. These 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 Effect A schematic diagram of a uniform n-type GaAs diode with ohmic contacts at the end

surfaces is shown in the figure.

J. B. Gunn observed the Gunn Effect in the n-type GaAs bulk diode in 1963, an effect best exp1ained by Gunn himself, who published several papers about his observations. He stated in his first paper 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. . . . The frequency of oscillation is determined mainly by the specimen, and not by the external circuit ....The period of oscillation was usually inversely proportional to the specimen length and closely equal to the transit time of electrons between the electrodes, calculated from their estimated velocity of slightly over 107 cm/s. . . . The peak pulse microwave power delivered by the GaAs specimens to a matched load was measured. Value as high as 0.5 W at 1 Gc/s, and 0.15 W at 3 Gc/s, were found, corresponding to 1-2% of the pulse input power.

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 exhibit negative resistance. This situation is shown in the figure.

The current fluctuations are shown in

the following figures. The current waveform was produced by applying a voltage pulse of 16-V amplitude and 10-ns duration to a specimen of n-type GaAs 2.5 x 10-3 cm in length. The oscillation frequency was 4.5 GHz. The lower trace had 2ns/cm in the horizontal axis and 0.23 A/cm in the vertical axis. The upper trace was the expanded view of the lower trace. Gunn found that the period of these oscillations was equal to the transmit time of the electrons through the specimen calculated from the threshold current. Gunn also discovered

that the threshold electric field varied with the length and type of material. He developed an elaborate capacitive probe for plotting the electric field distribution within a specimen of n-type GaAs of length L = 210 µm and cross-sectional area 3.5 x 10-3 cm2: with a low-field resistance of 16 Ω. Current instabilities occurred at specimen voltages above 59 V. which

means that the threshold field is cmvoltsLVEth /2810

101021059

26 =××

== −

Modes of Operation: Since Gunn first announced his observation of microwave oscillation 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 operation conditions. The formation of a strong space-charge instability depends on the conditions that enough charge is available in the crystal and that the specimen is long enough so that the necessary amount of space charge can be built up within the transit time of the electrons. This requirement sets up a criterion for the various modes of operation of bulk negative-differential-resistance devices. Copeland proposed four basic modes of operation of uniformly doped bulk diodes with low-resistance contacts as shown in the figure below.

1. Gunn oscillation mode: this mode is defined in the region where the product of

frequency multiplied by length is about 107cm/s and the product of doping multiplied by length is greater than 1012 cm-2. In this region the device is unstable because of the cyclic formation of either the accumulation layer or the high-field domain. In a circuit with relatively low impedance the device operates in the high-field domain mode and the frequency of oscillation is near the intrinsic frequency. When the device is operated in a relatively high-Q cavity and coupled properly to the load, the domain is quenched or delayed (or both) before nucleating. In this case, the oscillation frequency is almost entirely determined by the resonance frequency of the cavity and has a value of several times the intrinsic frequency.

2. Stable amplification mode: This mode is defined in the region where the product of frequency times length is about 107 cm/s and the product of doping times length is between 1011 and 1012 cm-2.

3. LSA oscillation mode: This mode is defined in the region where the product of frequency times length is above 107 cm/s and the quotient of doping divided by frequency is between 2 x 104 and 2 x 105.

4. Bias-circuit oscillation mode: This mode occurs only when there is either Gunn or LSA oscillation, and it is usually at the region where the product of frequency times length is too small to appear in the figure. When a bulk diode is biased to threshold, the average current suddenly drops as Gunn oscillations begin. The drop in current at the threshold can lead to oscillations in the bias circuit that are typically 1 kHz to 100 MHz.

Gunn oscillation mechanism: Some bulk semiconductor materials such as

gallium arsenide (GaAs), indium phosphate (InP) and cadmium telluride (CdTe), have two closely spaced energy bands in the conduction band. A typical energy versus momentum band structure is shown in figure.

At low electric field strengths in the material,

most of the electrons will be located in the lower-energy band. At high electric field strengths, most of the electrons will be transferred into the high-energy band. In the high-energy band the effective electron mass is larger and hence the electron mobility is lower than what it is in the low-energy band. Since the conductivity is directly proportional to the mobility, there is an intermediate range of electric field strengths for which the fraction of electrons that are transferred into the high-energy low-mobility conduction band is such that the average mobility, and hence conductivity, decreases with an increase in electric field strength. Thus there is a range of applied voltages over which the current decreases with increasing voltage and a negative incremental resistance is displayed

by the device. A typical current-voltage characteristic for a Gunn device is shown in figure below.

A Gunn device is also called a transferred-electron device since the negative resistance arises from the transfer of electrons from the low to the high-energy band. The oscillations that occur in materials with the energy band structure noted above was discovered by J. B. Gunn. The possibility of obtaining negative differential resistance had been predicted earlier by Ridley and Watkins.

There are two principal modes of operation that result in oscillations for a Gunn device. When the applied voltage exceeds the threshold value, a dipole domain (a region of electron concentration and depletion) forms near the cathode end with most of the voltage drop appearing across the high-resistance part of the device. A short section of the input region is in the low-energy high-mobility state and electrons leave the cathode with a large velocity. At the point in the material that separates the high-mobility and low-mobility states, electrons accumulate on the left side and are depleted on the right side by virtue of the different motilities. This dipole arrangement of charge is shown pictorially in figure.

This dipole domain sweeps across the device and when it arrives at the anode, the

device is in a high-mobility state and a new dipole domain forms at the cathode end and moves toward the anode. This mechanism is self-repeating and represents an oscillation with a period equal to the transmit time. This mode of oscillation has a low efficiency (a few percent) of power generation and a frequency that cannot be controlled by the external circuit. This mode of oscillation is called the transit time mode or Gunn mode.

The second mode of oscillation is the limited-space-charge (LSA) mode. Operation of a Gunn oscillator in the LSA mode can produce several watts of power with efficiencies of around 20 percent or more. The power outputs that have been obtained decrease with

frequency and are below 1 W at frequencies greater than 10 GHz. Output power of several milliwatts can be obtained at 100 GHz. In the LSA mode the Gunn device is incorporated as part of a resonant circuit. The frequency of the resonant circuit is adjusted so that it is several times greater than that of the transit-time mode. As a consequence, dipole domains do not have sufficient time to form and the device operates essentially as a negative-resistance device. The dc bias is adjusted to a value somewhat greater than the threshold voltage. The RF voltage of the oscillations will build up to a peak-peak value approximately equal to the voltage increment over which the device resistance is negative as shown.

The resonator loading, represented by the resistor R, is adjusted to a value about 20 percent greater than the maximum negative resistance of the device. This will ensure that oscillations will start. The amplitude of the oscillations will build up until the average negative resistance of the Gunn device becomes equal to the resonator resistance R. If the resonator frequency is adjusted to a value slightly above that of the transit-time mode, the Gunn device will operate very much like the basic Gunn mode, but the dipole domain will be quenched before it arrives at the anode by the negative-going oscillation voltage. This type of operating mode is called a quenched-domain mode. Oscillations can also occur by adjusting the resonator frequency, so that it is lower than the frequency of the Gunn mode. In this case the dipole domains have sufficient time to sweep across the device and arrive at the anode. However, the initiation of a new dipole domain is delayed until the oscillation voltage rises above the threshold value. This mode of operation is called the inhibited or delayed mode.

Criterion for Classifying the Modes of Operation The Gunn-effect diodes are basically made from an n-type GaAs, with the

concentrations of free electrons ranging from 1014 to 1017 per cubic centimetre at room temperature. Its typical dimensions are 150 x 150 µm in cross section and 30 µm long. During the early stages of space-charge accumulation, the time rate of growth of the space-charge

layers is given by )exp()0,(),( dtvtXQtXQ τ−= , where n

d en µε

σετ

0

== is the magnitude of

the negative dielectric relaxation time, ε = semiconductor dielectric permittivity n0 = doping concentration µn = negative mobility e = electron charge σ = conductivity

Gunn Oscillation Modes (1012/cm2 < (n0L) < 1014/cm2) Most Gunn-effect diodes have the product of doping and length (n0L) greater than

1012/cm2. However, the mode that Gunn himself observed had a product (n0L) that was much less. When the product of (n0L) is greater than 1012/cm2 in GaAs, the space-charge perturbations in the specimen increase exponentially in space and time in accordance with Q(X,t). Thus a high-field domain is formed and moves from the cathode to the anode as

described earlier. The frequency of oscillation is given by the relationeff

dom

Lf

υ= , where υdom is

the domain velocity and Leff is the effective length that the domain travels from the time it is formed until the time that a new domain begins to form.

Gunn described the behaviour of Gunn oscillators under several circuit configurations. When the circuit is mainly resistive or the voltage across the diode is constant, the period of oscillation is the time required for the domain to drift from the cathode to the anode. This mode is not actually typical of microwave applications. Negative conductivity devices are usually operated in resonant circuits, such as high-Q resonant microwave cavities. When the diode is in a resonance circuit, the frequency can be tuned to a range of about an octave without loss of efficiency.

As described previously, the normal Gunn domain mode (or Gunn oscillation mode) is operated with the electric field greater than the threshold field (E > Eth). The high-field domain drifts along the specimen until it reaches the anode or until the low field value drops below the sustaining field ES required to maintain υs as shown in the figure. The sustaining drift velocity for GaAs is υs = 107 cm/s. Since the electron drift velocity υ varies with the electric field, there are three possible domain modes for the Gunn oscillation mode.

Transmit time domain mode (fL ≈ 107 cm/s): When the electron drift velocity is equal to the sustaining velocity υs, the high-field domain is stable. In other words, the electron drift velocity is given by υd = υs = fL ≈ 107 cm/s. Then the oscillation period is equal so the transit time--that is, τ0 = τt. This situation is shown in figure below (a). The efficiency is below 10% because the current is collected only when the domain arrives at the anode.

Delayed domain mode (106 cm/s < fL < 107 cm/s): When the transit time is chosen so that the domain is collected While E < Eth as shown in figure (b), a new domain cannot form until the field rises above threshold again. In this case, the oscillation period is greater than the transit time—that is, τ0 > τt. This delayed mode is also called inhibited mode. The efficiency of this mode is about 20%.

Quenched domain mode (fL > 2 x 107 cm/s): If the bias field drops below the sustaining field Es during the negative half-cycle as shown in figure (c), the domain collapses before it reaches the anode. Then the bias field swings back above threshold, a new domain is nucleated and the process repeats. Therefore the oscillations occur at the frequency of the resonant circuit rather than at the transit-time frequency. It has been found that the resonant frequency of the circuit is several times the transit-time frequency, since one dipole does not

have enough time to readjust and absorb the voltage of the other dipoles. Theoretically, the efficiency of quenched domain oscillators can reach 13%. A typical n-type GaAs Gunn diode has the following parameters:

Threshold field Eth = 200 V/cm Applied field E = 3200 V/cm Device length L = 10 µm Doping Concentration n0 = 2 x 1014

cm-3 Operating frequency f = 10 GHz Computed electron drift velocity vd = 107 cm/s Calculated current density J = q n v = 320 A/cm2 Estimated negative electron mobility µn = - vd /E = -3100 cm2/V s

Gunn Oscillator Circuits The equivalent circuit of a Gunn device operating in the LSA mode

is a negative resistance -Rd in parallel with a capacitance Cd as shown in figure. The negative resistance has a value that typically lies in the range 5

to -20 Ω. The required resistive loading from the cavity and the external load should be around 20 percent higher than the Gunn device resistance so that the parallel combination –R Rd/(R-Rd) will be negative. The cavity used for the resonator must generally have an impedance-transforming property in order to reduce the high impedance of the output waveguide to the appropriate low value required by the Gunn device. A simple cavity structure is shown in the following figure. The Gunn device is located under a post in a rectangular waveguide. The cavity is resonated at the desired frequency by adjusting the short-circuit position. The degree of coupling to the external waveguide is adjusted by changing the window opening in the inductive diaphragm located at the front of the cavity. The top of the post is insulated from the waveguide. The dc bias voltage (typically around 12 V) is applied to the post.

There is sufficient capacity between the post and the surrounding waveguide to

provide an adequate low-impedance RF bypass capacitance and thus RF currents do not flow through the bias voltage supply. Fine tuning of the cavity can be obtained by means of a tuning screw.

Also, another simple cavity arrangement for a Gunn oscillator is shown as well. In this cavity the high impedance of the waveguide is transformed into a low impedance path at the location of the Gunn device by means of quarter-wave transformers. The cavity resonant frequency can be adjusted by changing the location of the short circuit. A tuning screw can be used for fine tuning of the cavity.

The cavity first shown above is easily modified to have two posts, one for mounting the Gunn device and a second one for mounting a varactor diode. The capacitance of the varactor diode is a function of the control voltage V. By varying V, the resonant frequency of the cavity can be varied. If a saw-tooth sweep voltage is applied to the varactor diode, the Gunn oscillator will be frequency-modulated. The cross section of such cavity is shown.

The Gunn device can be operated as a pulsed oscillator by applying the dc bias voltage in the form of a pulse train of short rectangular pulses. If the duty cycle is low enough and very short bias pulses are used, the peak power output will be limited only by the peak current, since thermal heating of the device will be negligible during the short on time. For pulsed oscillator applications, the IMPATT diode, or variations of it, is preferred because of higher output power. The Gunn device can also be, and has been, used as a negative-resistance amplifier.

Summery As described earlier, if the applied field is less than

threshold the specimen is stable. While, however, the field is greater than threshold, the specimen is unstable and divides up into two domains of different conductivity and different electric field but the same drift velocity. The figure shows the stable and unstable regions.

At the initial formation of the accumulation layer,

the field behind the layer decreases and the field in front of it increase. This process continues as the layer travels from the cathode toward the anode. As the layer approaches the anode, the field behind it begins to increase again; and after the layer is collected by the anode, the field in the whole sample is higher than threshold. When the high-field domain disappears at the anode, a new dipole field starts forming again at the cathode and the process repeats itself. Since current density is proportional to the drift velocity of the electrons, a pulsed current output is obtained. The oscillation frequency of the pulsed current is given by f = vd/Leff, where vd is the velocity of the domain or approximately the drift velocity of the electrons and L is the effective length that the domain travels. Experiments have shown that the n-type GaAs diodes have yielded 200 W pulses at 3.05 GHz and 780-mW CW power at 8.7 GHz. Efficiencies of 29% have been obtained in pulsed operation at 3.05 GHz and 5.2% in CW operation at 24.8 GHz. Predictions have been made that 250-kW pulses from a single block of n-type GaAs are theoretically possible up to 100GHz.

The source generation of solid-state microwave devices has many advantages over the vacuum tube devices they are beginning to replace. However, at present they also have serious drawbacks that could prevent more widespread application. The most important disadvantages are:

1. Low efficiency at frequencies above 10 GHz 2. Small tuning range 3. Large dependence of frequency on temperature 4. High noise

These problems are common to both avalanche

diodes and transferred electron devices. The figure shows the latest state-of-the-art performance for GaAs and InP Gunn diodes. The numbers adjacent to the data points indicate efficiency in percent. Gunn diode oscillators have better noise performance than IMPATTS. They are used as local oscillators for receivers and as primary sources where CW powers of up to 100 mW are required. InP Gunn diodes have higher power and efficiency than GaAs Gunn diodes.

References:

• Microwave devices and circuits – Samuel Y. Liao – ISBN:0135812070 • Foundations for microwave engineering – Robert E. Collin – ISBN:0-07-011811-6