A simple and efficient method for the calculation of carrier-carrier scattering in Monte-Carlo simulations

The analysis of the carrier-carrier scattering is getting more important and it can be done by the particle-particle-particle-mesh (P³M) algorithm. A problematic part of the algorithm is to avoid double-counting of the pair forces in short-range. Here, we solve the problem by introducing an efficient numerical method to the algorithm. The improvements in accuracy and applicability are confirmed with various test cases. In addition, the modified P³M method is integrated with a 3D ensemble Monte Carlo (EMC) simulator and applied to the device simulations. The results are compared with those of the PM (particle-mesh)-EMC approach, which reveals the limitations of the scattering rate based methods and the importance of the P³M method to treat carrier interactions.