Memory Efficient Scattering Matrix Device Simulation By Decomposing The Effect Of Carrier Scattering And Field Acceleration

Abstract

Solving the Boltzmann equation (BE) has typically been a trade-off between memory and speed. Monte Carlo simulation is generally slow but memory efficient, while deterministic techniques are faster but significantly more memory intensive. The Scattering Matrix Approach (SMA) [l-31 belongs to this latter class of BE solutions and thus has also suffered from extensive memory requirements. These requirements, however, have now been substantially reduced by introducing a new technique to decompose the effects of and the electric on carrier transport. This reduction makes even detailed multi-band and 2-D device simulation feasible on today's modestly equipped workstations. The technique of separating carrier from acceleration, which can be mathematically justified for a thin slab, is shown in Fig. 1. In the SMA, the device is divided into thin slabs which are each represented by a matrix. Previously, each matrix characterized both the effects of and the electric on carriers in discretized momentum space. Many matrices had to be stored because, for a realistic device, the electric differs for each slab. In the new technique, the acceleration and the processes are treated by separate matrices. Despite the added number of matrices, the memory requirements are now drastically reduced because only a few symmetrical scattering process matrices need to be st0re.d for the entire device and the field matrices, which are still needed for every position, are extremely sparse (see Fig. 2). For example, storing all the matrices for a 100 slab device in highly discretized momentum space requires almost 500 MB using the old method, but less'than 20 MB after using the decomposition technique. This new technique has been implemented in matrix simulators for both Si and GaAs devices. As shown in Fig. 3, the new method reproduces the bulk velocity-field characteristic for single valley electron transport in Si and for three-valley transport in GaAs. Figure 4 shows results for a Si device structure, demonstrating that the decomposition method, which resolves velocity overshoot at the boundary, is applicable to devices. In our presentation we will discuss recent results such as bipolar and heterostructure device simulation, both of which have been made much more efficient by the decomposition technique. In conclusion, we have developed a technique that substantially reduces the memory requirements of the Scattering Matrix Approach, a direct solution method to the Boltzmann equation. Using this technique, we will demonstrate memory/computation efficient device simulation involving bipolar and heterostructure transport. An important ramification of this technique is that fullbandstructure and 2D and 3D simulation, previously thought memory prohibitive for direct solutions to the BE, should be feasible even for the capacity of today's workstations.