Efficient memory management for cellular Monte Carlo algorithm

The Cellular Monte Carlo (CMC) method according to M. Saraniti and S. M. Goodnick (2000) was introduced as a faster alternative to the traditional Ensemble Monte Carlo (EMC) according to M. V. Fischetti and S. E. Laux (1988) approach for the full band simulation of charge transport in semiconductors. Within the CMC formalism, all possible transitions between cells of the discretized momentum space are precomputed and stored in large look-up tables. The selection of the new momentum of a charge carrier after scattering is then reduced to the generation of a random number according to M. Saraniti and S. M. Goodnick (2000), greatly reducing the computational burden of the EMC final state selection scheme. However, the CMC energy resolution is strictly related to the coarseness of the discretization grid, and, since the size of the look-up table grows as the square of the number of grid points in momentum space, the requirement for fast access storage (RAM) quickly reaches the 3 GByte limit of 32-bit processors. To overcome this issue, the authors have developed several techniques to reduce the memory requirements of the CMC without sacrificing accuracy.