An Analytical Heterojunction Bipolar Transistor Model Including Thermal and High-Current Effects

Abstract

The down scaling of AIGaAslGaAs heterojunction bipolar transistor (HBT) structure has increased the collector current density to the range of lo5 to lo6 A/cm2 under normal bias conditions. This high-current handling capability makes HBTs very attractive to high-power, high-frequency microwave amplifier applications. Recently, output power up to 12.5 W cw have been demonstrated from a monolithic, 2-stage HBT power amplifier 111. Such a high power level, together with the poor thermal conductivity of GaAs, can inevitably generate a large amount of heat in the HBT and therefore result in a much higher temperature in the HBT than that of the ambient. Since all the physical properties of the HBT are strongly influenced by the lattice temperature T, the performance of HBTs used in power amplifiers will be affected significantly by the thermal effect. Ob iective: This paper presents a physics-based, analytical HBT model including high-current and thermal effects. The model can predict three figures of merit commonly used in analyzing the performance of an HBT the d.c. current gain, cutoff frequency, and maximum frequency. The required parameters are the device configuration and material parameters. Compared to the numerical counterpart [2], the analytical model developed is more suitable for circuit simulation because of its simplicity and flexibility in implementation. Furthermore, the inclusion of thermal effect in device simulation often suffers numerical divergence, and such a problem can be easily averted in analytical solutions. Consider an N/p+/n A1,,G%i7As/GaAs single HBT (Fig. 1). The heat P, (W) generated in the HBT is P, = J,V,,A,, where J, is the collector current density, A, is the emitter area, and VCE is the collector-emitter voltage. The heat generated in the HBT is primarily dissipated through the S.I. GaAs substrate. Thus P, is related to the thermal resistance R+ of the substrate as T - To = P,Rth, where To = 300 K is the ambient temperature and R,, is a functlon of the lateral diffusion angle 6 (Fig. 1) as well as the temperature-dependent thermal conductivity K, in GaAs [3]. Some Results: Fig. 2 shows the lattice temperature versus the collector density calculated frod the present model, calculated from the isothermal model, and simuiated from a numerical program [2] which solves the Poisson and continuity equations coupled with the heat transfer mechanism, as well as takes into account the nonuniform spatia1 temperature and band distribution and carrier degeneracy. The corresponding base and collector current densities versus the base-emitter applied voltage are plotted in Fig. 3. The details of the model, as well as the simulation results, will be presented in the Symposium.