Physical modelling of HBTs for microwave power applications

Abstract

This paper presents a one-dimensional HBT physical model which can accurately simulate the characteristics of microwave power transistors. The structure of the model is briefly discussed, and simulation results for a three layer device are presented and compared with analytical results. Measured and modelled DC characteristics for a power HBT are also presented, and these show good agreement over several decades of base and collector current. HBT Physical ModelHBTs are becoming increasingly popular for use in power amplifiers due to a combination of high gain, linearity and high output power [1,2], The successhl design of circuits using HBTs often requires accurate device models and many equivalent circuit and physics-based equivalent circuit models have been published [3,4,5]. These models are suitable for circuit and device simulation, but require extensive characterisation, often using sophisticated test equipment, before they can be used successfully. Physical models do not suffer from this drawback since they allow the characterisation of intrinsic device performance from the physical structure of the transistor and its doping profile. HBT physical models have been reported which have been used to study device behaviour [6,7], and more recently circuit performance [8], demonstrating the flexibility of physical models The HBT model presented in this paper solves the de-coupled set of drift-diffusion semiconductor equations and Poisson's equation. Boltnann statistics are assumed and the basic equations have been modified by the inclusion of band parameters to allow the modelling of heterojunctions [9]. The modified one-dimensional simulation equations are shown in (2.1) -(2.5) and the band parameters expressions are shown in (2.6) and (2.7). 0-7803-4135-X/ 97/ $5.00 01997 IEEE 211 -=--d2ip 4 (N,-n+p-N,)----1 dq,.cr dip dx2 EO Er E& dx dx where n and p are the carrier densities, 9 is potential, J is the current density, Nc and NV are the density of states in the conduction and valence bands, NA and N o are the impurity concentrations, GR is the generation recombination rate, E is the permittivity and x is the electron affinity. The transport equations and Poisson's equation are solved using a finitedifference approach and a modified Newton scheme w i t h successive-under relaxation. Important effects such as doping and field-dependent mobility, and band-gap narrowing [ 103, are included. The software can model both graded and abrupt devices with arbitrary layer structures, doping profiles and bias conditions. Simulation ResultsThe DC simulation results for two different HBTs are presented. The first device simulated was a simple 3-layer structure with an abrupt heterojunction, which allows the validation of the model's performance. The structure used is summarised in Table 1. Figure 1 shows the energy band diagram for this device at thermal equilibrium, which has been calculated from the simulated carrier densities, shown in Figure 2. Figure 1 clearly shows the typical spike and notch discontinuity associated w...