Simulation of Band-structure Dependent Transport and Impact Ionization in Semiconductor P-n Junctions Using an Improved Multivalley Hydrodynamic Model

An improved multivalley hydrodynamic model (HDM) including realistic band structure effects and impact ionization is developed. Unlike the recently-proposed HDM by Thoma et al [1] for nonparabolic band structures, our model minimizes the number of relaxation times and includes impact ionization. Furthermore, the intervalley transitions of hot carriers are considered. Also, the momentum relaxation times are finally eliminated from the set of hydrodynamic equations (HDE's). Instead, the carrier mobility is selfconsistently derived from the HDE's themselves. On the basis of this model, the HDE's are solved in the pi-n diode over a large scale of reverse bias voltages (up to the avalanche breakdown). The results of simulation are compared with those we previously presented [2] using the classical HDE's with constant carrier effective mass. It's shown that the inclusion of the realistic band structure results in smaller, and hence more realistic, breakdown voltages. IINTRODUCTION It is well known that the concept of the effective mass breaks down at high carrier energies when the external forces are strong enough to preclude interband transitions. So far, the impact ionization mechanism, which naturally encounters interband transitions, was either neglected [1] or considered with a constant carrier effective mass [3]-[4] in the HDM. According to the Monte-Carlo simulation results of Tang and Hess [5], the inclusion of the second conduction band of Si and the L-minimum of the first one is necessary for an accurate simulation of the high-field transport and impact ionization phenomena in silicon devices. In fact, even with the inclusion of a nonparabolicity factor in the E(k) relation, the dynamics of energy exchange between valleys is not properly taken into account when using a singlevalley description [6]. On the other hand, the simultaneous presence of many groups of charge carriers (i.e. many valleys) with significantly unequal carrier energies needs to a large number of relaxation times particularly if the band structure of each valley is considered. In addition, we must admit that the validity of the relaxation time approximation becomes questionable near avalanche breakdown zone where the deviation from the equilibrium is more pronounced. In order to reduce the complexity of the HDM while maintaining its ability to rigorously simulate high-field transport phenomena, we try to minimize the number of the relaxation times. We do so by suppressing the least significant intervalley relaxation times and expressing some of the intravalley relaxation times selfconsistently as functions of the average carrier energy. We also redefine the carrier temperature tensor in such the manner that it satisfies the themodynamic definition and keeps the number of relaxation times as minimum as possible.