Next: 2.4.1 Multiple Refresh Up: 2. Carrier Transport Previous: 2.3 Drift-Diffusion Transport Model
As mentioned above, one of the most popular computational methods to solve the BTE is the Monte-Carlo method, because it is flexible and allows for the incorporation of many features such as real band structure, various scattering mechanisms, and other physical models [154]. In the MC approach, carrier trajectories are traced at the microscopic level in a given device structure. As a consequence, carriers are subjected to the impact of the electric field, the device topology, and scattering mechanisms. Carrier flight and scattering are stochastically treated in accordance with probabilities describing the physical processes. A self-consistent MC solution (as DD and HD schemes) also considers the Poisson equation. At the same time, due to its stochastic nature, the method requires substantial computational resources and is very time-consuming. This disadvantage manifests itself while modeling processes determined by small populations, e.g. small currents or high-energy tails of the DF, and hence a trade-off between the computational efficiency and noise reduction must be considered. The latter problem becomes essential in the context of HCD modeling because, in many regimes, the bond-breakage process is triggered by particles characterized by high energies and low probabilities. In other worlds, due to the stochastic nature of the MC approach, the number of carriers to be simulated must be sufficiently high to obtain reliable statistics. Various statistical enhancement and iteration schemes employed in MC simulations result in additional varying degrees of simulation noise. Moreover, statistical enhancement aims at the reduction of the simulation time which is necessary for the desired device characteristics computation. Enhancement algorithms are quite useful when the system behavior is caused by rare events in the transport process, which is appropriate in the case for HC effects simulation. Most MC approaches employing statistical enhancement use population control techniques [154,157]. They are based on the special splitting procedure of the particles entering a given phase space region of interest.