A novel parallel approach for quantum effect simulation in semiconductor devices

A new parallel implementation of quantum confinement effects simulation for semiconductor devices is presented. In this simulation, a set of self-consistent Schrödinger and Poisson equations is solved iteratively with the parallel divide and conquer algorithm and the monotone iterative (MI) method on a Linux-cluster with the message-passing interface library. To solve the Schrödinger equation, instead of using the conventional large-scale approach for the matrix eigenvalue problem, we apply a novel parallel divide and conquer algorithm to compute all the corresponding wave functions and energy levels (i.e., eigenvectors and eigenvalues). Moreover, the nonlinear Poisson equation is solved with the MI method instead of the Newton's iterative method. Based on this simulation approach, the parallel implementation shows that a well-designed simulation can significantly reduce the execution time up to many orders of magnitude. For a realistic thin oxide metal-oxide-semiconductor device, we compare (1) our simulated result, (2) the fabricated and measured capacitance-voltage data, and (3) the so-called classical result obtained by considering only the solution of the Poisson equation to demonstrate the accuracy and efficiency of the method.