Self-Consistent Solution of the Schrodinger and Poisson Equations Applied to Quantum Well Heterostructures

A novel numerical approach to solving Schr odinger's equation as applied to quantum well heterostructures is described. The quantum mechanical energy subbands, wave functions and charge density are calculated based on a two-directional fourthorder Runge-Kutta (RK4) algorithm. The algorithm is applied to well-de ned quantum well structures. Results are compared with analytic solutions to ensure numerical accuracy. The approach is then extended to a self-consistent solution of the Schrodinger and Poisson equations applied to a Si/Si1 xGex/Si heterostructure. The advantages of this method are compared to other solution techniques.