CORRESPONDENCE 29 1

V

0

I ,-TRUE WAVEFORM

C U R R E N T WAVEFORM WITH MODIFIED I-V

illustrated by the solid line in Fig. 2. On the other hand, as A is in- creased in value, the characteristic becomes one like the dotted line shown in Fig. 2, and more like the velocity-field characteristic of GaAs. Taking A=0.9, 6=0.5, a=0.5, ,6=3.5, and K=2.75, I found after carrying out the necessary computation that 71 = 14.7 percent, with a normalized value of Rt = 13.63, and essentially infinite positive impedance at the second harmonic, Le., no power into the second harmonic. I have obtained similar but not better results with other choices of A. With lower values of A the efficiency tends to be lower. I did not try higher values of A as these computations were merely intended to illustrate a trend. These results are, of course, like those of Copeland, who used a similar characteristic in his computations [3].

Thus it is apparent that although the original analysis was incor- rect, it should be possible, as has been shown experimentally, to improve the efficiency of a Gunn diode by using a properly chosen second-harmonic tuning as well as tuning at the fundamental. Hys- teresis, of course, should change the results yet again. However, the computations I have carried out show that putting in a phase dif- ference between the second harmonic and the fundamental, using the original I- V characteristic, does not help.

REFERENCES 111 V. S. Andreyev and V. I. Popov, private communication to IEEE Trans. Elec-

[Z] W. Frey, 'Influence sf a second harmonic voltage component on the operation tron Devices.

of a Gunn oscillator, Proc. 8th In2. C o d . Microwaves and Optical Genevation and Anzplificatioql Kluwer-Deventer. The Netherlands; 1970, pp. 2-38-2-42.

3) J. A. Copeland, LSA waveforms for high efficiency, Pvoc. IEEE (Corresp.), vol. 57, pp. 1666-1667, Sept. 1969.

0 7l

T

Fig. 1. A schematic of the voltage and current waveforms. The solid line current waveform is an approximation to the true theoretical waveform.

271

GaAs IMPATT Diodes for Microstrip Circuit Applications

v/ VT

Fig. 2. The V-I characteristic used in the original theory (solid line) and a modified V-I characteristic (dashed line).

The second harmonic power which I calculated is of the right magni- tude but has the wrong sign.

In reexamining this problem I have found it convenient to con- sider the current waveform to be like that shown by the solid line in Fig. 1, which is a rough approximation to the actual current waveform also illustrated. With this approximation it can be shown analytically and by drawing out the harmonic components, as is done in Fig. 1, that if the time for which the current is a t threshold is less than the time for which it is at the valley value, the power output into the second harmonic is negative, as stated by Andreyev and Popov. By using a simple analysis based on this waveform, I came out with

W. R. WISSEMAN, H. Q. TSERNG, D. W. SHAW, AND D. N. McQUIDDY

Abstract-GaAs IMPATT diodes with plated heat sinks are shown to be particularly well suited for microstrip circuit applications. De- tails of materials growth and device fabrication procedures are given, and experimental results are presented for a GaAs IMPATT micro- strip oscillator operating at X band.

INTRODUCTION Kim and Arrnstrong [ l ] have shown that GaAs Schottky barrier

IMPATT diodes are high-efficiency sources of microwave power at X- band frequencies. Published work on these diodes has involved their operation in coaxial or waveguide circuits. There are requirements for oscillators and amplifiers mounted in microstrip circuits that will operate a t X band and higher frequencies, and GaAs IMPATT diodes have the required properties for these applications. The procedures used to fabricate GaAs IMPATT diodes with plated heat sinks [2] are reported in this correspondence. The fact that the diode and its heat sink form an integral unit is particularly convenient for microstrip circuit applications. This was demonstrated by mounting these diodes in microstrip circuits that were designed for X-band operation and comparing their performance as X-band oscillators with the per- formance of similar diodes mounted in waveguide circuits.

MATERIALS AND DEVICE FABIIICATION

I = C Y + - - - - 1 + (V - 1)/A

I v > l 6 Manuscript received September 1, 1971; revised October 1. 1971. This work was

where 6 and A are arbitrarily chosen constants. If a + 6 = 1, as A+O, Space Flight Center, Huntsville. Ala. supported in part by the National Aeronautics and Space Administration. Marshall

the characteristic approaches the one originally used in the paper and ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ , ~ ~ ~ . ~ ~ ~ p ~ ~ ~ ~ ~ Research and Texas Instrurnentsv

292 IEEE TRANSACTIONS ON ELECTRON DEVICES, FEBRUARY 1972

T 1 DC BIAS

B I A S P A D

HIGH I M P E D A N C E B I A S L I N E

A L U M I N A S U B S T R A T E

Fig. 1. Microstrip circu .t for X-band IMPATT diode oscillator.

Fig. 2. Scanning electron r~icrograph showing diode placement (X40).

formity from run to run. Two epitaxial layers are grown in sv~ies. The initial epitaxial layer is heavily doped (-5 X 1017 cm-*) so I hat its resistivity does not differ greatly from the substrate. On t ~ ) p of this intermediate n+ layer, the active n layer is grown. This xch- nique removes the depletion region from the immediate vicini :y of the substrate-epitaxial interface and results in improved perform ince.

The first step in the fabrication of the diode is the electropl lting of a platinum Schottky barrier contact onto the cleaned and etclled n layer of the GaAs slice. Schottky barriers formed in this manner have very sharp reverse I-V characteristics, and the platinum has exc8,'llent adherence to the GaAs. A 0.010-in-thick copper or silver heat s rrk is plated next. With the slice supported by the heat sink, the GaA sub- strate is thinned to 25 pm by lapping and etching. (Note tha-. this procedure allows removal of the entire subztrate if the intermcciiate n + layer is thick enough. I t would make it possible to use high q . ality undoped substrates which should result in superior epitaxial la ms.) After evaporation of a Auo.sGeo.lIno.1 film, the mesas are etched csing standard photolithographic procedures. The AuGeIn metallizai Lon is then alloyed at -350°C to form an ohmic contact. The mesa d ame- ters are typically 5 mil, giving an active area of about lop4 cm2 The final fabrication step involves sawing the heat sink into 25-mil+ luare dies with centered mesas.

CIRCUIT DESIGN In order to design an optimum circuit for a microstrip II'WATT

oscillator, a n accurate characterization of the microwave impe lance of the diode must be obtained. The true junction parameter'? of a packaged diode were measured by using a modified form of tht: pro- cedure described by Gewartowski and Morris [4]. The modifi:.;ttion consists of comparing the changes in the imaginary part of the 1 7icro- wave impedance (rather than the real part) with the changes :dcu- lated from low-frequency C-V data. The comparison is mad, at a number of bias voltages ranging from zero to breakdown. A min..mum mean-square error criterion is used to provide the best fit betwet:11 the measured and calculated data, The ideal transformer turns ri, t io N

and network reactance X thus obtained are used in a manner similar to that of Gewartowski and Morris to obtain the diode wafer im- pedance as a function of current density, frequency, and RF drive level. Series negative resistances ranging from 3-10 s2 with a cor- responding capacitive reactance range of 20-40 D were measured for X-band GaAs IMPATT diodes. The diodes had breakdown voltages between 50 and 60 V and were biased at a current density of approxi- mately 500 A/cm2.

A microstrip oscillator circuit that has proven successful for ob- taining near optimum device performance (power, efficiency) is shown in Fig. 1. The oscillator circuit consists of a quarter-wave trans- former with a 5 0 4 output transmission line. A short length of 5 0 4 line is included between the active device and the quarter-wave trans- former. The dc bias is introduced through a bias pad to the lowest impedance point of the circuit. The device with its integral heat sink is soldered directly to a Au-plated copper block that also acts as a carrier plate for the microstrip substrate. The unencapsulated device mounted in this manner results in a minimum thermal impedance, while allowing a maximum degree of flexibility in the control of para- sitic elements associated with the device-circuit connection.

is shown in Fig. 2. The total height of the mesa plus the plated heat A scanning electron micrograph of the device-circuit connection

sink is about 11 mil. A 10-mil-thick alumina substrate with an evaporated Cr-Au film is used for the microstrip circuit. A 5-mil-wide A u strap is used to bond the device to the circuit. A width-to-height ratio of 5 will produce a characteristic impedance of 50 s2 for an air dielectric microstrip line.

EXPERIMENTAL RESULTS

Using the microstrip circuit described in the preceding section, a number of GaAs IMPATT oscillators operating in X band were con- structed that had CW output powers ranging from 700-900 mW with a 10-11 percent efficiency. Fig. 3(a) shows the microwave perfor- mance of a 1-W, 14 percent efficiency X-band packaged diode tested

CORRESPONDENCE 293

0.2

0.8 { ‘ O r

t i 00 -o INPUT POWER (Wl

( a >

0 a

,/*

0 E F F i C l E N C Y

‘ P O W E R O U T P U T

1

i

Fig. 3. Comparison of the RF performance of GaAs IMP ATT diodes from the same

increasing input power the waveguide oscillator frequency varied from 9.0-9.1 slice mounted in (a) microwave package in waveguid e and (b) microstrip. For

GHz and the microstrip oscillator frequency varied from 10.0-10.15 GHz.

in a waveguide circuit. The RF performance of a similar diode (same fabrication batch) in the microstrip circuit is shown in Fig. 3(b). A slight difference in the areas of the two diodes shown in Fig. 3(a) and (b) accounts for the difference in the optimum operatingfrequencies of the two oscillators.

SUMMARY The procedures for fabricating GaAs IMPATT diodes with integral

plated heat sinks were described. These procedures allow fabrication of large numbers of devices having nearly equal dimensions and elec- trical properties. The relatively large heat sink aids in handling and makes it possible to repeatedly mount diodes with low thermal re- sistances in the desired close proximity to the microstrip circuit.

ACKNOWLEDGMENT The authors wish to thank J. L. Woods and M. C. Banks for the

epitaxial GaAs; R. L. Ragsdale, B. W. Caldwell, and R. W. Cantrall for device and microstrip circuit fabrication; and Dr. T. E. Hasty and Dr. T. G. Blocker for valuable discussions of this work.

REFERENCES [ I ] C. K. Kim and L D Armstrong “GaAs Schottky barrier avalanche diodes,”

121 R. A. Zettler and A. M.’C&vley, ‘;Batch fabrication of integral-heat-sink %lid-State Electron., ;ol. 13 pp 5&56 1970

IMPATT diodes.” EEccfvon. Lett.. Val. 5. pp. 693-694, 1969; N. J. Tolar. private communication.

[3] D. W. Shaw, “Kinetics of transport and epitaxial growth of GaAs with a Ga-

I41 J. W. Gewartowski and J. E. Morris, “Active IMPATT diode parameters ob- ASCII system,’ J . Crystal Growfh, vol. 8, pp. 117-128, 1971.

tained by computer reduction of experimental data,” I E E E Trans. Macrowave Theory Tech., vol. MTT-IS. pp. 157-161, Mar. 1970.

. ~. ~,

A Discussion on the Feasibility of u Transmission-Line Analog for Crossed-Field Nonuniform Drifting Electron Beams

S. G. LELE

Abstract-It is shown that, under certain assumptions, a lossless transmission-line analog does not exist for the case of a drifting, nonuniform, crossed-field beam.

I. INTRODUCTION A major contribution to the noise available at the output of a

traveling-wave tube amplifier and a crossed-field amplifier comes from the noise transported by the electron beam that interacts with the signal on the slow-wave circuit to produce amplification of the signal. Noise reduction schemes like the use of velocity jumps in a drifting electron beam are based on the study of wave propagation on drifting electron beams. One important technique for such a study is to develop a transmission-line analog for the electron beam sup- porting these waves. Bloom and Peter [l ] have shown that for the 0-type uniform velocity beam, the analog transmission line is lossless and uniform, whereas for the nonuniform velocity beam, the analog turns out to be lossless but nonuniform. For the constant velocity M-type beams, Rowe and Wadhwa [2] have shown that a transmis- sion-line analog exists and the analog line is lossless and uniform. In this correspondence it is shown that, under certain assumptions, it is not possible t o obtain a lossless transmission-line analog that repre- sents a thin, one-dimensional crossed-field beam moving undeviated with a prescribed velocity variation.

11. ELECTRON-BEAM MODEL AND PERTINENT ASSUMPTIONS The dc magnetic field is x-directed and the dc electric field is so

adjusted that the electron beam extending infinitely in the x direction and very thin in the y direction moves along the z direction with a prescribed variation in velocity. The assumptions made in this an- alysis are as follows.

1) Nonrelativistic mechanics is used. Thus, R F magnetic fields may be neglected in the Lorentz force equation.

2) Variations in a given quantity are assumed small relative to its average value. This results in neglecting terms of second order in smallness.

3) Quantities vary in time as d o t and they do not vary in the x and y directions. Y component of the ac electric field is assumed zero.

4) Space-charge effects are neglected.

111. ANALYSIS The Lorentz force equation gives the following equations of mo-

tion for an electron moving in the field configuration mentioned earlier.

and

where 1) is the absolute charge-to-mass ratio of an electron and the dot denotes derivative with respect to time. Writing velocity and field components as the sums of the ac and dc parts, the ac parts of (1) and (2) are given by

Manuscript received July 16, 1971‘ revised September 8, 1971. The author is with the College o! Engineering, Tennessee Technolonical Uni-

versity, Cookeville, Tenn. 38501.