The Gunn-diode: Fundamentals and Fabrication

Robert van Zyl, Willem Perold, Reinhardt Botha* Department of Electrical and Electronic Engineering, University of Stellenbosch, Stellenbosch, 7600

e-mail : rrvanzyl @ firga. sun .ac .za * Department of Physics, University of Port Elizabeth, Port Elizabeth, 6800

e-mail: phajrb@upe.ac.za

Abstrucf - A short tutorial on the Gunn-diode is presented. The principles underlying Gunn-oscillations are discussed briefly and illustrated by relevant simulations. The simulation of a typical Gum-diode in a cavity is also presented. In conclusion, the fabrication process of low power Gunn-diodes is discussed.

Keywords - Gunn-diode, Gunn-effect, transferred electron- effect, GaAs, energy band, Monte Carlo particle simulation.

I. INTRODUCTION

JB (Ian) Gunn discovered the Gunn-effect on 19 February 1962. He observed random noise-like oscillations when biasing n-type GaAs samples above a certain threshold. He also found that the resistance of the samples dropped at even higher biasing conditions, indicating a region of negative differential resistance. As will be explained later, this leads to small signal current oscillations.

In Figure 1 part of the famous page from one of Gunn's laboratory notebooks is shown with the entry "noisy" on the line for 704 volt. Describing it as the "most important single word" he ever wrote, it laid the foundation for what was to become a major mode of a.c. power generation.

Due to their relative simplicity and low cost, Gunn diodes remain popular to this day. It is, however, also true that

Fig. 1. made the discovery of the Gunneffect (taken from [l]).

A page from one of Gunn's laboratory notebooks on which he

relatively few electronic engineers understand clearly the principles behind the Gunn-effect. The aim of this paper is to give the reader an overview of the underlying theory of the Gunn-effect and how it is utilised in Gunn-diodes to produce a.c. power [2], [3]. Concepts which will be discussed include the negative differential mobility phenomenon in GaAs, Gunn-domain formation and the basic Gunn-diode structure. A typical simulation of a Gunn-diode in a cavity will also be presented.

The University of Stellenbosch, in conjunction with the University of Port Elizabeth, is currently fabricating GaAs Gunn-diodes for research purposes. The aim is to optimize Gunn-diodes for a.c. output at W-band frequencies. A review of this manufacturing process will be given.

The simulations in this paper have been performed by a Monte Carlo particle simulator developed at the University of Stellenbosch. A short review of the Monte Carlo simulation of semiconductors is given in [4].

11. THE GUNN-EFFECT IN THE STRICT SENSE

A. The Energy Band for GaAs

To understand the Gunn-effect it is necessary to have some insight into the behaviour of electrons in a crystal lattice, and most importantly, the allowed energy states electrons can occupy. These are dictated by the energy band structure of a semiconductor which relates an electron's energy to its wave vector k .

The band structure for GaAs is shown in Figure 2. Both the valence (negative electron energy) and conduction (positive electron energy) bands are shown. Only the conduction bands need to be considered for the study of electron dynamics, since electrons in the valence bands are stationary. Energy bands are very complex structures. It is, however, clear from Figure 2 that for realistic electron energies ( E

L A P A X WAVE VECTOR

Fig. 2. The full energy band structure of GaAs. Both valence (negative electron energy) and conduction (positive electron energy) bands are shown [3, p.41.

Conduction band structure T centralvalley satellite valley

r L wave vector k

Fig. 3. A simplified band structure of GaAs with the central (I3 and one satellite (L) valley shown. The energy gap (A) is the energy needed before an electron can undergo acentral to satellite transition.

The parabolic two-valley approximation is very simple to implement and proves sufficient for most moderate-field applications. A two-valley parabolic approximation to the energy band of GaAs is shown in Figure 3. In terms of this parabolic approximation, the energy of an electron in each valley is given by

h2k2 E =- 2 m

1: (1)

with k the magnitude of the wave vector, m* the effective mass of the electron associated with that valley and h the reduced Planck constant.

The effective mass of a free electron in a semiconductor differs from the mass of a free electron in a vacuum due to the interaction of the electrons with the atoms of the crystal. An electron in a semiconductor behaves dynamically as a classical particle with mass m'. It is important to note that the band structure of the central r- valley has a sharper curvature than that of the satellite L- valley. From (1) it follows that the effective mass associated with an electron in the central valley, m;, is much less than the effective mass associated with an electron in the L-valley, m;. (m;=5*m; for GAS) This

phenomenon is fundamental to the Gunn-effect as will be explained later. The energy gap A shown in Figure 3 is the energy that an electron in the r-valley will have to acquire before it could undergo a transition to the L-valley. For GaAs A=0.36eV.

B. The transferred electro,n mechanism

When no bias is applied to a semiconductor, almost all the electrons occupy the r-valley since their respective thermal energies are usually much less than the energy gap A. If the sample is biased, the electrons are accelerated by the applied electric field and may gain sufficient energy to be transferred to the satellite valley. This phenomenon is verified by Monte Carlo simulations and illustrated by the graphs in Figure 4.

It is clear from the graphs in Figure 4 that the mean electron energy increases :For increasing biasing fields. This results in an ever increasing number of electrons gaining enough energy (0.36eV for GaAs) to be bridge the gap between the I?- and L-vidleys and be transferred from the lower I'-valley to the upper L-valley. Significant population of the L-valley takes place for biasing exceeding 0.4 MVm-'.

E b s = 0. I MV/m 0.6

0.5 I

@ 0.4

; 0.1 0.3

5 0.2

0 0 100 200 300 400 m

Electron samples

Satellite valley

E hu = 0.4 MV/m 0.6

2 0.5 Satelliie I

- _ i3 0.4 g 0.3 5 0.2 m t r a l ; 0.1

0 0 100 200 300 400 5Ml

Electron samples

E h = l.OMV/m 0.6 I I I I I

SateHie

. - -

antral valley

0 100 200 300 400 500 Electron mmples

Fig.4 Valley occupation of electrons in bulk GaAs for three applied electrical fields, namely O.lMVm", D.4MVm" and 1MVm.l respectively. As expected, the mean energy of the ensemble of electrons increase with stronger applied fields. Significant population of the satellite L-valley takes place at fields exceeding 0.4MVm-'.

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The electrons that have been transferred from the I-valley to the L-valley will immediately move slower due to the increase in their effective mass. The average drift velocity of the electrons, and consequently the current, will therefore decrease with an increase in the applied field. This manifests a region of negative differential resistance (NDR) for applied fields exceeding 0.4 MVm-I, as shown in Figure 5.

Fig. 5 The simulated steady-state average drift velocity of electrons in bulk GaAs as a function of the applied electnc field at 300K. The regon of NDR is indicated.

C. The formation of Gunn-domains

The question of exactly how the NDR phenomenon in GaAs results in Gunn-oscillations can now be answered with the aid of Figure 6.

A sample of uniformly doped n-type GaAs of length L is biased with a constant voltage source V,. The electric field is therefore constant and its magnitude given by E, = V& From the bottom graph in Figure 6 it is clear that the electrons flow from cathode to anode with constant velocity vs.

It is now assumed that a small local perturbation in the net charge arises at t = to. This is indicated by the solid curve in Figure 6. This non-uniformity can, for example, be the result of local thermal drift of electrons. The resulting electric field distribution is also shown (solid curve).

The electrons at point A, experiencing an electric field E,, , will now travel to the anode with velocity v,. The electrons at point B are subjected to an electric field EH,. They will therefore drift towards the anode with velocity v2, which is smaller than v,. Consequently, a pile-up of electrons will occur between A and B, increasing the net negative charge in that region. The region immediately to the right of B will become progressively more depleted of electrons, due to their higher drift velocity towards the anode than those at B.

The initial charge perturbation will therefore grow into a dipole domain, commonly known as Gunn-domains. Gunn-domains will grow while propagating towards the anode until a stable domain has been formed. A stable domain is shown at a time instance t > to, indicated by the dashed curve. At this point in time, the domain has grown

sufficiently to ensure that electrons at both points C and D move at the same velocity, v, , as is clear from the bottom graph in Figure 6.

I I ! I

&2 416 4n 4e Becbicfield

Fig. 6. A graphical illustration of the formation of Gum-domains.

It is important to note that the sample had to be biased in the NDR region (see Figure 5) to produce a Gunn-domain. Once a domain has formed, the electric field in the rest of the sample falls below the NDR region and will therefore inhibit the formation of a second Gunn-domain.

As soon as the domain is absorbed by the anode contact region, the average electric field in the sample rises and domain formation can again take place. The successive formation and drift of Gunn-domains through the sample lead to a.c. current oscillations observed at the contacts. In this mode of operation, called the Gunn-mode, the frequency of the oscillations is dictated primarily by the

annihilated at the anode. This is roughly the length of the active region of the sample, L. The value of the d.c. bias will of course also affect the drift velocity of the domain, and consequently the frequency.

distance the domains have to travel before being

The process of domain growth, drift and absorption at the anode is verified by the simulation results for a 5 pn GaAs sample shown in Figures 7 and 8. The sample is uniformly doped with concentration l O ~ m ~ and biased at 5V. The frequency of oscillation is roughly 25GHz.

409

t=QOps 15 I I

10 I

I

I i

0 1 2 3 4 5

10

5

- 0

c c - .5 i i

0 0 1 2 3 4 5 T -

1 2 3 4 5

t=150ps 15

10

5

0

5 0 1 2 3 4 5

Distance froni cathode (pti i) Fig. 7 The simulated net charge concentration in a 5pm GaAs sample biased at 5V. The distributions are shown at four successive time instances to illustrate the formation, drift and absorption at the anode of a dipole domain in a Gunn- diode.

111. SIMULATION OF A MILLIMETER-WAVE G U N N - E ~ C T OSCILLATOR

A typical application of a Gunn-diode in a cavity will now be discussed. A high frequency oscillator (70 GHz) has been chosen since it reveals an important aspect in the understanding of the high frequency limit inherent to Gunn-oscillators.

The doping profile of the Gunn-diode is shown in Figure 9. An active region is sandwiched between highly doped anode and cathode regions. These highly doped regions ensure good ohmic contact with the external circuit. A 50% notch in the doping is included to provide an initial high electric field near the cathode. The reason for the notch will be explained later. The cavity is modeled as a parallel resonant circuit shown in Figure 10.

The simulated voltage and current waveforms are given in Figure 11. From these graphs it is evident that the oscillator generates in the order of 140mW at 7OGHz with an efficiency of 2.4%. These values are typical of Gunn-

0 t=QOps

1

2

-3

-4

5

0 1 2 3 4 5

I E O 1 2 3 4 5 >

0 t = l 3 0 s ~! r 7 J - (I, -l .- + U L I I U

.-

j i ; = - w - 4 I I " .5 0 1 2 3 4 5

0 1 2 3 4 5

Distance ft-om cathode (pi l i ) Fig. 8 The simulated field distribution for the dipole distributions in Figure 7. Nore the growth in the peak value and the subsequent drop in the field throughoutthe rest of the sample to below the NDR region shown in Figure 5.

diode oscillators operating at these frequencies.

The formation and drift of the dipole domains are illustrated with the sequeiice of field distributions in Figure 12. A "dead zone", where no dipoles form, is clearly evident near the cathode. Electrons injected at the cathode are initially confined to the central valley of the conduction band. They do not immediately gain enough energy to be transferred to the upper L-valley. This results in a delayed domain formation and a consequent dead zone in the region of the cathode.

The presence of a dead zone in the diode impacts negatively on the efficiency of the oscillator, because the length of the active region in which the domain can grow, decreases. Smaller domaim translate into smaller output power. The existence of' a dead zone affects high frequency (> 30 GHz) Gunn-oscillators the most, since the physical lengths of these diodes are of the order a few micron, roughly the same as the dead zone. Optimizing Gunn-diodes invariably involves decreasing the dead zone by encouraging domain nucleation as near to the cathode as possible.

410

7 , I

Distance from cathode [microns]

U 5x10" cm-' 1x10" cm-'

0 1.2Sx10"cmJ

Fig. 9. The doping profile of the simulated Gunn-diode.The active region is sandwiched between the highly doped anode and cathode regions. A notch in the doping appear at the cathode.

Fig. 10. The circuit schematic for the simulated Gunn-diode in a cavity. The diode is biased with a 3V d.c. power supply. The oscillator feeds into a 23Q load.

0 5 10 15 20 25 30 Time [ps]

Fig. 11. The simulated voltage v(t) and current i(t) waveforms for the Gunn-oscillator desribed in the text. v(t) and i(t) are defined in Figure 10.

The doping-notch is one way of reducing the dead zone, since it forces a high electric field at the notch. This stronger field will accelerate the electrons faster than would otherwise be the case. The electrons will therefore gain enough energy for transfer to the L-valley in a shorter time and distance.

Another, more successful, method is the injection of "hot" or energetic electrons directly into the cathode region. This is accomplished by inserting a heterojunction between the cathode contact and the active region of the diode 161. A detailed discussion on hot electron injection is not within the scope of this tutorial. In essence, when an electron traverses a heterojunction of the correct type, it gains almost immediately a certain amount of energy dictated by the heterojunction. If this energy exceeds the gap, A, transfer to the L-valley, and consequently Gum-domain

. . . . . . . . . . . . . . . . .

. . . . . . . . : . . . . . . . . .

. . . . . . . - 2 . . . . . . . . . . w

0104 . : I 0 0.5 1 1.5 2

-10-4 ' : ' : ' : : I 0 0.5 1 1.5 2

0 0.5 1 1.5 2

- l o ! ' : . : I 0 0.5 1 1.5 2

Distance from cathode [microns] Fig. 12. The simulated sequence of fields for the Gunn-oscillator described in the text clearly shows a dead zone at the cathode.

formation, is possible. Heterojunctions are typically 50nm in length, implying a drastic reduction in the dead zone and a subsequent improvement in efficiency.

IV. FABRICATION OF GaAs GUNN-DIODES

The authors are currently in the process of manufacturing 10 GHz Gunn-diodes for research purposes. The aim is to apply the experience gained in this process to the development of efficient Gunn-diodes operating at frequencies in excess of 100 GHz. A chronological outline of the fabrication process is discussed below with a graphical representation of the process given in Figure 13.

A. Growth of diode structure

The diode layers have been grown at the Department of Physics, University of Port Elizabeth, by a process known as Metalorganic Vapor Phase Epitaxy (MOVPE). Growth was performed in a horizontal, laboratory scale quartz reactor, capable of accepting a 2x2cm2 piece of substrate. The diode structures were grown on a 250pm GaAs:Si substrate with doping density n=1.3x10L8 cmA3. This was

411

followed by a 0 . 6 ~ buffer layer (n=1.4~10'* ~ m - ~ ) , a 0 . 3 ~ undoped injection layer ( n = l . l ~ l O ' ~ cm-3 ) which serves as doping-notch, a l o p undoped active region layer (n=2.5x101' ~ m - ~ ) and a 0 . 6 ~ Si-doped contact layer (n=1.4x101* ~ m - ~ ) .

The GaAs substrate was placed on a molybdenum susceptor, which was heated to 670C before growth. Trimethylgallium and arsine (10% in H2), diluted in a H, carrier gas, were used as source materials. n-Type doping of the contact layers was achieved by introducing SiH, gas into the reactor. Growth rate is approximately lOA per second.

The doping levels were determined from electrochemical capacitance-voltage profiling of the grown structures and Hall measurements on calibration layers. CV-profiling also provided an independent measurement of layer thicknesses.

Metal contacts were thermally evaporated onto both sides of the structure to provide good electrical contact with the external circuitry. These metal contacts consist of three layers, namely a 80nm layer of AuGe sandwiched between two lOnm layers of Ni. It was found that these contacts disintegrate at currents exceeding 20mA, because they are so extremely thin. Additional AuGe had to be evaporated onto the existing contacts to a depth of 0 . 7 ~ .

B. Etching and scribing of individual diodes

Individual diodes are defined on the grown structures by a standard photolithographic procedure. A mask defines the desired metal contacts at the anode (top) side of the structures. Contacts with a lOOpm diameter have been etched. The unwanted AuGe metal was etched away using a mixture of iodine crystals, potassium-iodide and water. The unwanted GaAs was etched away using a mixture of methanol, phosphoric acid, and H,O,. The GaAs had to be etched to a depth of at least 1Opm to ensure that the active region is of the same dimensions as the metal contacts. The individual diodes can now be cut out using a diamond edge scriber. Each diode is roughly 4 0 0 p in diameter.

C. Packaging ,

The diodes are mounted in containers of suitable size. The packaging of an individual diode is shown in Figure 14. The diode is bonded to the gold plated copper base of the bottom external metal contact using a highly conducting epoxy. The two external contacts are separated by a ceramic spacer. 25pn gold bonding wires connect the top diode contact with the top lid. The wire is bonded onto the diode contact with the same conducting epoxy.

D. Experimental results

Experimental results will be presented at the conference.

V. CONCLUSIONS

The Gunn-effect in bulk GaAs and how this phenomenon

~

412

Growth of diode structure

+ r e m - b y r M(r b y r

Define individual contacts by etching

Define individual diodes by etching

c - - - - d -- Fig. 12. Step-by-step fabrication of low power Gunn- diodes

c.thcdE

Fig. 13. Packaged low power Gunn-diode.

is harnessed in the generation of ax. power have been discussed. The fabrication olf low power Gum-diodes has been dealt with briefly. It is the desire of the authors that this tutorial will have brought home an appreciation for these devices which have served us so well over the past three decades.

REFERENCES

[l] John Voelcker, "The Gunneffect", IEEE Spectrum, p.24, July 1989. [2] BG Bosch, RWH Engelmann), Gunn-eflecr Electronics, Pitman

Publishing, London, 1975. [3] JE Carroll, Hot Electron Microwave Generators, Edward Arnold

Publishers, London, 1970. [4] RR van Zyl, WJ Perold, " n e Application of the Monte Carlo Method

to BermconducIor Sirnutanon'., 77ans. S A I , pp. 58-64, June 1996. [SI K Tomizawa, Numerical Simuiration of Submicron Semiconductor

Devices, Artech House, London, 1993. [6] 2 Greenwald et al. "The Effect o f a High Energy Injection on the

Performance of mm Wave Gunn Oscillators", Solid-State Electronics, Vol. 31,N0.7,pp. 1211-1214, 1988.