Broyden method for the self-consistent solution of Schrodinger and Poisson equations

With scaling down of semiconductor devices, it´s more important to simulate their characteristics by solving the Schrodinger and Poisson equations self-consistently. It is necessary to introduce new method to accelerate the convergence of nonlinear equations system. In this paper, the Broyden method, which has been used in nonlinear systems, is described. We solved 1D semiconductor quantum line self-consistently and got the result of electron density and electric potential, separately using the Broyden method and the SOR method (Newton method). Compared with SOR method, the Broyden method can get the right result and use less iteration steps