Pergamon Solid-State Electronics Vol. 39, No. 4, pp. 523-527, 1996 Copyright© 1996Elsevier ScienceLtd 0038-1101(95)00180-8 Printed in Great Britain.All rights reserved 0038-1101/96 $15.00 + 0.00 NUMERICAL MODELLING OF ABRUPT InP/InGaAs HBTs JUAN M. LOPEZ-GONZALEZ and LLUIS PRAT Departament d'Enginyeria Electr6nica, Campus Nord, c/Gran Capiui s/n, Universitat Politrcnica de Catalunya, 08034 Barcelona, Spain (Received 5 April 1995; in revised form 27 July 1995) Abstract--High performance heterojunction transistors are expected from a InP/InGaAs system owing to the electrical properties of these materials. In order to understand the physical mechanisms which control the behaviour of this kind of transistor, a numerical device model has been developed. This model combines drift-diffusion transport in the bulk regions with tunnelling and thermionic emission at the base-emitter interface. The electrical characteristics of the above HBT are analysed using this model. The collector current is dominated by tunnelling transmission through the spike appearing in the conduction band. The base current is dominated by recombination in the base bulk region, but tunnelling transport has an additional effect on this current. The maximum unity-grain frequency is limited by the base transit time. !. INTRODUCTION Heterojunction bipolar transistors realised in InP/InGaAs are presently a research topic of great interest. High performance transistors are expected owing to the electrical properties of these materials. The high electron mobility of InGaAs can improve the frequency response. The band gap difference between base and emitter allows a higher efficiency emitter. The base current can be reduced by the smaller surface recombination velocity and conse- quently the current gain can be increased. Finally, the energy band structure leads to forward VeE values comparable to silicon bipolar devices. In spite of the small amount of work carried out on these devices, spectacular experimental results have already been reached. In the late 80s, fr trans- ition frequencies as high as 165 GHz were achieved for InP/InGaAs HBTs fabricated by Cben et al.[1] using molecular beam epitaxy (MBE) technology. Recently values of 186 GHz forfT and 180 GHz for fmax have been reported[2,3]. Because of the recent developments of these devices, there are some electrical material parameters and transport mechanisms which are not well established yet[4]. The number of analytical models reported for this device is still small[5-9]. The energy band structure presents spikes preventing the use of conventional models. It is well known that the drift-diffusion transport model is not valid, when there are discontinuities in the energy bands larger than kT in a length shorter than the mean free path[10]. This is the case for abrupt InP/InGaAs HBTs. Transport through the base emitter interface, where discontinuities in energy levels occur, is controlled by thermionic emission and tunnelling transmission through the spike[l 1]. 523 As the numerical modelling of HBTs can help to understand the physical behaviour of the device and optimize its design, it has a great deal of interest. However, most of the numerical models published in the literature[12-15] are based on drift--diffusion transport and apply only to structures with smooth changes in composition. Recently, Horio and Yanai[16] proposed a numerical model which com- bines thermionic emission at the base-emitter inter- face and drift-diffusion in the bulk of the device. This model was extended by Yang et aL[17] to include tunnelling transmission through the energy barrier present at that interface. Their model was applied to analyse abrupt AIGaAs/GaAs HBTs[18]. In this work, a numerical model for InP/InGaAs abrupt HBTs is presented. This model solves the Poisson and the electron and hole continuity equations, merging the drift--diffusion transport model in the bulk regions and tunnelling and thermionic emission across the base--emitter inter- face. This model is described in Section 2. The electrical parameters used for the material are dis- cussed in Section 3. Results obtained by applying this model to InP/InGaAs HBTs are discussed in Section 4. 2. NUMERICAL MODEL The numerical model solves simultaneously the Poisson and the hole and electron continuity equations: div(EVqQ = -q[p -n + N~ -N~], (1) div(Jp) = -qR, (2) div(Jn) = qR, (3)