THEORETICAL STUDY OF 100 GHz GaAs TRANSFERRED-ELECTRON DEVICES

HAL Id: jpa-00221655

https://hal.archives-ouvertes.fr/jpa-00221655

Submitted on 1 Jan 1981

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

THEORETICAL STUDY OF 100 GHz GaAs TRANSFERRED-ELECTRON DEVICES

P. Rolland, M. Friscourt, G. Salmer, E. Constant

To cite this version:

P. Rolland, M. Friscourt, G. Salmer, E. Constant. THEORETICAL STUDY OF 100 GHz GaAs

TRANSFERRED-ELECTRON DEVICES. Journal de Physique Colloques, 1981, 42 (C7), pp.C7-171-

C7-176. �10.1051/jphyscol:1981719�. �jpa-00221655�

M THEORETICAL STUDY OF 100 GHz GaAs TRANSFERRED-ELECTRON DEVICES

P.A. Rolland, M.R. Friscourt, G. Salmer and E. Constant

Centre Hyperfrequenoes et Semieonducteurs, Laboratoire Associe au C.N.R.S.

n°287, Batiment P43 Universite des Sciences et Techniques de Lille 1, 59655 Villeneuve d'Ascq Cedex, France

Résumé. - Des simulations numériques du comportement de dispositifs à trans- fert électronique â l'AsGa ont été effectuées grâce à un modèle prenant en compte les effets de dynamique électronique non stationnaire ainsi que les phénomènes de diffusion. Des résultats concernant les diodes Gunn fonction- nant à 100 GHz sont donnés et commentés.

Abstract. - Computer simulations of GaAs Transferred Electron Devices have been performed using a model which includes relaxation effects as well as spatial dependence. Some results are presented and discussed for 100 GHz GaAs short Gunn diodes.

Introduction. - In the centimeter wave range TED's classically depend upon the bulk properties of the compound, mainly the negative differential mobility. According to several authors [1] [2] [3] this fundamental small signal negative mobility vanishes near 70 GHz or below in GaAs because of relaxation effects. In a previous paper we have shown that a substantially higher cut-off frequency could be obtained under large signal operation [4], However it may be asked how do 100 GHz GaAs TED's work.

For a better understanding of the relaxation effects involved, we have derived a one dimensionnal model which should lead to optimum design of such devices.

The model. - An analytical formulation was preferred to a Monte Carlo technique because it provides a better accuracy for shorter computing times (especially for phase shift determination).

This model is based on the integration of the Boltzmann's transport equation over the k-space. A first integration is performed, valley by valley and 3 equations can be derived which express the conservation of particles, momentum and energy [5].

The formulations obtained are quite similar to those given by Blotekjaer [5] and Bosch [3].

One of the original features of our model is that, in order to save computing times, all the relevant quantities are then averaged over the three valleys of the conduction band. After some rearrangement and within some assumptions [6] [7], the conservation equations may be written in the following form :

3 3

• # +

4^= 0

x This work was supported by the D.R.E.T. under contract n° 79/357.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981719

JOURNAL DE PHYSIQUE

where : n is the particle density E is the electric field

T is the average electron temperature E is the average energy

%is the thermal equilibrium energy v is the average drift velocity mX(&) is the average effective mass Lm(&) is the momentum relaxation time

r ; € ( ~ )

The effective mass mX(E), the momentum and energy relaxation times <,(E) and LE(Ej respectively are taken as functions of the average energy. Following Shur [81 these functions were obtained by using the results of !lonte Carlo simulations under uniform field and static operations.

In a similar manner the average electron temperature is expressed as a func- tion of the average energy using the relation :

where E is the potential energy of carriers located in the satellite Land X valleys.

P

It can be seen thus that the main assumption of our model is that the effec- tive mass and electron temperature are taken as functions of the instantaneous average energy while neglecting the particles relaxation times.

This model was checked by comparison with 'lonte Carlo simulations assuming spatial uniformity of the electric field in the case of GaAs at 100 GHz and InP at 200 GHz [ 4 ] . In addition results obtained in more realistic cases are in good agree- ment with experimental findings.

Main results.

-

Fig. 1 (a,b,c,d) shows, at various times during a 100 GHz cycle, the spatial evolution of the electric field, carrier density, energy and drift velocity for a N+NN+ Gunn diode with a 1.55 um thick active layer and a flat doping profile of about

1016/cm3. It can be seen that this diode can operate in a fundamental transit time mode although the small signal differential mobility is positive at this frequency as it has been previously shown [ 4 ] . These transit time oscillations occur only in a portion of the diode adjacent to the anode, the region adjacent to the cathode

Fig. 1 : Spatial evolution of the characteristic electrical quantities in a GaAs Gunn diode at various times &iring a 100 GHz cycle.

a

-

-

-

d

-

JOURNAL DE PHYSIQUE

being an inactive heating zone. This heating zone corresponds to the distance neces- sary for the electrons to acquire a kinectic energy at least equal to the energy of the satellite valleys in the band structure, which for GaAs is close to .33 eV.

The fact that transit time oscillation can start may be understood as follows.

In the dead zone where the energy is lower than the . 3 3 eV threshold energy, elec- trons are drifting under non stationnary conditions and reach high overshoot velocity because of the relaxation effects. At the end of the dead zone electrons have

acquired near threshold energy and then their drift velocity quickly decreases to a value close to their saturated drift velocity. In that region electrons are

strongly slown down which results in a space charge accumulation. Thus this behaviour can be described by a local V(E) characteristic, the classical threshold field Eth being changed into a threshold energy ~ ~ Since the energy strongly depends on the h . electric field, the position where this accumulation layer occurs in the active zone is modulated by the instantaneous electric field.

Typical results obtained with optimum flat doping profile (# 1016/cm3) are shown in Figure 2 as a function of the RF swing. 2.2 % efficiency is achievable with such a fundamental transit time mode. This value is in close agreement with experi- mental findings.

The length of the dead zone depends on the field strengththus on the bias voltage. It was found to range from .6 to 1.4pm with a value close to 1.2 p~ for optimum operation. The overshoot velocity and the existence of the dead zone have been previously pointed out and our findings fall between those of Bosch C31 and

those given by Jones and Rees which are somewhat greater (1-2 um). This dead zone explains the increasing Nd . L product while keeping stability behaviour. This point has been already discussed [ 2 ] [ 3 ] .

But one of the most important effect due to the existence of this dead zone is a frequency limitation.Indeed as the frequency gets higher the transit time active zone gets shorter so that the influence of this inactive zone increases.

This is illustrated in the case of 140 GHz operation. Figure 3 shows that a transit time mode is yet possible at I40 GHz but the inactive region strongly lowers the output negative resistance as shown in Figure 4. The upper frequency limit of this mode of operation thus depends on the minimum matchable impedance. With present technology we found that this limit falls near 150 GHz.

One way to increase this frequency limit is to reduce the inactive zone length, by using cathode contacts other than N+ on N . An ideal contact might be a reverse-biased shottky barrier with a low height (AE 0 . 3 eV). Unfortunately up to now such a cathode barrier is not conceivable from a technological point of view.

So we have investigated notched doping profile in order to improve the field increa- se with distance. The best result obtained is shown in Figure 5 where it can be seen that a slight increase in the efficiency is achieved at the price of a lower output power and resistance (see fig. 4). Thus notched profiles do not seem to be of

swing. ( S i s t h e d i o d e c r o s s s e c t i o n ) .

F i g . 3 : S p a t i a l e v o l u t i o n d u r i n g a 140 GHz F i g . 4 : E v o l u t i o n o f t h e optimum o u t - c y c l e of t h e c a r r i e r d e n s i t y . p u t power v s t h e o u t p u t d i o d e r e s i s t a n -

c e .

C7-176 JOURNAL DE PHYSIQUE

great interest for m.m. wave Gunn. The problem of mm. Gunn diode cathode contact is still opened to investigation.

Conclusion.

-

However fundamental transit time operating modes are possible up to 150 GHz, but the increasing influence of the dead zone strongly limitstheir performances in the case of ohmic cathode contacts. The theoretical results obtained are in quantitative agreement with experimental findings which shows that the model used is a realistic one.

References. -

[I] H.D. REES, I B Y J. Xes. Develop. 13, 537 (1969) [2] D. JONES and H.D. REES, Electron. Lett. 8, 363 (1972)

D. JONES and H.D. REES, Electron. Lett. 8, 566 (1972) D. J O m S and H.D. REES, Electron. Lett. 9, 105 (1973) D. JONES and H.D. REES, J. Phys. C6, 1781 (1973)

[31 R. BOSCH, H.W. THI!4, IEEE Trans. El. Dev., vol ED-21, No 1, January 1974, pp. 16-25

[4] P.A. ROLLAND, E. CONSTANT, G. SALW,R, R. FAU?UEMBEXGUE, Electron. Lett., 1979, Vol. 15, No 13, pp. 373-374.

[51 K. BLOTEKJAER, IEEE Trans. El. Dev. vol ED-17, no 1, January 1970, pp. 38-47.

t61 A. CAPPY, 3rd cycle Thesis, Lille, June 1981.

[71 J.P. NOUGIER et al, J. Appl. Phys. 52 (2), pp. 825-832, February 1981.

[81 ?4. SHUR, Electron. Lett., vol. 12, pp. 615-616, 1976.