12 Transferred Electron Devices

Dr. Monika Tomar and Dr. Ayushi Paliwal

1. Introduction

A transferred electron device is a moderate power device which has low oscillator phase noise and it is a form of diode used at all microwave frequencies 300 MHz to 300 GHz. These devices are also called Gunn-devices or Gunn diode. These devices are bulk devices and do not contain any junction as we see in all other microwave semiconductor devices. In some semiconductors, namely GaAs, electron can exist in their normal low-mass high velocity state as well as in a high-mass low velocity state and under the application of steady electric field of sufficient strength, these electrons can be forced into the high mass state. In this state they form domains or clusters which cross the field at some constant rate which causes current to flow as a series of pulses. This is known as Gunn effect there is a special kind of diode which uses this effect consists of an epitaxial layer of n-type Gallium Arsenide (GaAs) grown on GaAs substrate. After the application of few volts of potential applied between the ohmic contacts to the substrate and n-layer produces the electric field which causes clusters. Current pulses so generated have some frequency and this frequency of current pulses is determined by the transit time through this n-layer and hence determined by thickness. When the diode is mounted on a tuned cavity resonator then current pulses causes oscillation generated by shock excitation and Radio Frequency (RF) power upto 1W at frequencies between 10 to 30 GHz can be obtained.

2. Historical background

The reason of alternative name of GUNN-devices is “transferred electron devices” is due to the fact that for their operation depends on transfer of electrons between two different valleys in the conduction band of the semiconductor. The experimental discovery was made by James Gunn (Gunn, 1963). Clearly, already in this rudimentary form of a GUNN device, sinusoidal oscillations resulted. GUNN was interested in what happened to the mobility of electrons in GaAs. at very high fields, and does not arrive at a satisfactory explanation of his observations in the original paper, although the previously mentioned papers were already published. Instead, Kroemer (1964) explained the oscillations observed by Gunn by using the results from Hilsum (1962) and Ridley and Watkins (1961). In following this explanation, we shall first discuss how electron transfer may lead to negative differential mobility (NDM), or equivalently negative differential resistivity (NDR).

3. Electron transfer and negative differential mobility

The detailed energy band diagram of GaAs is shown in figure 1 which is crucial to discuss electron transfer effects. As evident from figure 1, the top of the valence band and the bottom of the conduction band both occur at k = 0 indicating GaAs is a “direct bandgap” semiconductor. The bottom of the conduction band, the “lower valley”, is of course where most electrons reside at room temperature. The conduction band has two other types of minima, or “valleys”, however. One of these occurs in the <111> crystallographic direction, at the Brillouin zone boundary (the dotted vertical line in the figure), and has an energy which is 0.32 eV higher than the “lower valley” and let us refer to this minimum as the “upper valley”. The essence of the GUNN-effect is that as electrons are accelerated by a high electric field, they may gain sufficient energy in order to be able to transfer to the upper valley. Let us assume that electrons reside in either of these two valleys, characterized by their usual parameters for that valley. The effective mass of electrons is larger in the upper valley by a factor of about 8.2, while the mobility is smaller by an even larger ratio of about 53. Another important factor is the respective densities of states, which are proportional to the effective mass to the 3/2 power. The density of states in the upper valley must therefore be higher by about 23.5, times the number of valleys.

In the two-valley model we simply add the contributions to the current by the electrons in each valley, with their respective concentrations and mobilities:

4. Calculation of the Velocity versus Field Curve.

Electrons lose energy primarily by emitting optical phonons as they are accelerated through the crystal lattice. The average time between collisions which change the momentum (the “momentum relaxation time”) is of the order of 0.4 psec (derived from the low-field conductivity) while the average time between collisions in which energy is lost (the “energy relaxation time”) is about 1.0 psec, in GaAs. The effective time for transfer between valleys is estimated to be 1.5 psec as reported by Kroemer, 1978). Most of this time is actually expended for acceleration of the electron from the bottom of the band to – c ~ 0.31 eV, while the actual inter band transition is very fast once the electron has the required energy. Since there are frequent transitions between the two valleys in order to maintain the equilibrium, early theories of the GUNN-effect assumed that the electrons in the two valleys are in thermal equilibrium at some higher temperature, the electron temperature, T., corresponding to their increased energy. We are also assuming that the type of statistical distribution function (Maxwell-Boltzmann) of the electrons is un-changed, something which may not be true for all cases. The average thermal energy of the accelerated electrons is then 3/2 kB Te (kB is Boltzmann’s constant) and the excess energy, beyond the thermal energy at the ambient temperature, T, must be supplied by the electric field on the average as fast as it is being lost by relaxation (chazacterized by the energy relaxation time e), and we can write:

eEv = 3/2 kB (Te – T)/ e

Velocity/field curves based on a unique electron temperature, and the above simplified two-valley model, can now be calculated. In order to find Te, we approximate,

These equations thus enable us to estimate the electron temperature for electrons in GaAs at a given electric field and lattice temperature. One feature to note is that the electron temperature initially increases with the square of the electric field in this model. Also note that we regard the temperature of the crystal lattice (T) as a constant. We have just seen an example of the phenomenon called “hot electrons”, which is a concept to which we shall return in many other connections in this book. A better model uses one electron temperature for the lower valley, and another one for the upper valley. The electrons in the upper valley tend to be close to the lattice temperature, because the mobility is so low, and because the electrons arriving from the lower valley have little kinetic energy left after transfer.

5. Different modes of operation of Gunn Devices

5.1 Efficiency of a Solid State Device

The purpose of a typical solid state oscillator device is to convert DC power to microwave power. The efficiency will therefore be defined as the ratio of the output microwave power to the DC power supplied.

A hypothetical highly efficient GUNN device might be constructed such that it takes maximum advantage of the Negative Differential Mode (NDM) region by assuming that the electric field is uniform (although we know from the above discussion that this is impossible in practise), and by allowing the voltage to switch the current from the peak value to the minimum obtained for a higher electric field (if the field is uniform, then the current/voltage curve will have the same shape as the velocity/field curve). This is illustrated in Figure 3.

Figure 3: Current and electric field waveforms in an ideal GUNN device with uniform electric field, such that the I/E curve follows the v/E curve

α = Iv/Ip

β = V0/Vp

where V0 is the DC bias voltage, and all quantities are marked in Figure 3. The microwave power is obtained by finding the power for the fundamental

The maximum efficiency is obtained if the DC voltage is very high (large β) and if the peak-to-valley ratio (1/α) in the current (i.e. velocity) curve is a maximum. In GaAs, α = 0.43, and the hypothetical maximum efficiency is 32 % . Due to the fact that a uniform field-distribution through the device is impossible, and that waveforms of voltage and current are non-ideal, practical efficiencies are much lower. One useful feature of (2.22) is that it predicts the efficiency as a function of the valley-to-peak velocity ratio, α. This may be useful for a rough comparison of different materials for use in devices.

5.2 Dipole Domain Modes

Now that we have investigated the physics of the transferred electron effect in GaAs, we will look at how the effect is being put to use in a device. The device is typically packaged and inserted in a microwave resonant circuit. The schematic circuit will be as shown in Figure 4.

The bias supply biases the device to the NDM region, and is filtered with the inductances indicated which prevent microwave leakage. A by-pass capacitor is used to couple the microwave resonant circuit, represented by L, C, and GL. The resonant frequency of the microwave circuit (without the GUNN device) is fR and the corresponding period of oscillation is TR = 1/ fR. The active device will oscillate at a frequency which we will call fosc.The transit time of electrons across the full length of the device is t. There are three types of dipole domain modes which can typically occur:

(i) The Transit Time Mode: In this mode, TR = t. It is often also used in simple practical devices. The voltage and current wave-forms are shown in Figure 5. A domain starts at the cathode of the device when the voltage increases above the critical or “threshold” voltage, VT. A roughly constant current flows while the domain travels through the device. No major displacement current occurs in the contacts since the domain contains equal amounts of positive and negative charge.

(ii) The Delayed Domain Mode: In this mode, 2 t > TR > t. Figure 6 shows the voltage waveform, the moving domain charge, and the current waveform for this mode. Here, once the domain has been developed, a somewhat smaller voltage than VT (designated Vs) is sufficient to sustain the domain. The domain nucleates when the total circuit voltage passes the threshold voltage and then grows as it passes through the device. The domain decreases in size somewhat as the voltage again goes negative, but is sustained until it reaches the anode. The device current is given by the velocity of the carriers outside the domain. This current decreases as the domain develops. After the domain has reached the anode and disappeared, the average velocity will again increase, and the current will go up. The next domain nucleates when the voltage reaches VT and the current stays high until this happens. The current pulse therefore is somewhat broader than in case 1 above, resulting in higher efficiency, which could reach 20%. The frequency of oscillation becomes lower than l/Tt because of this delay. The delayed domain mode requires more careful tuning of the device than the transit-time mode.

(iii) The Quenched Domain/Limited Space-Charge Accumulation (LSA) Mode: The wave forms for the Quenched Domain Mode are shown in Figure 7.

Figure 7: Voltage waveform, high field domain propagation, and current waveform for a GUNN device in the quenched domain mode.

The condition for the occurrence of this mode is that

2 t > TR > s and fosc = 1/ t

Here, s is the time which it takes for a domain to be quenched. The voltage must swing below Vs in order for the domain to be quenched. The time s is roughly equal to the dielectric relaxation time (with positive differential mobility) which we mentioned earlier. The devices can be made longer since the transit time condition no longer applies. If they are very long, more than one domain may tend to form, although this may be handled if all domains can be quenched. The condition for the full LSA mode (domain never develops) requires that (1) the excess-charge must not grow to a full domain in one period of the oscillation and (2) the quenching (dielectric relaxation) time must be less than the period.

6. Summary

Transferred electron devices or Gunn devices :Electron transfer and negative differential mobility Velocity/Electric field curve for Gunn devices where the expression of electron temperature was calculated Different modes of operation of Gunn devices and in the domain transit mode its three types were discussed