In this paper, a hybrid solution method is implemented for solving the semiconductor transport equations. The hybrid “local Newton” method consists of a combination of the fixedpoint iteration (FPI) and Newton’s methods. The FPI technique is nearly ideally suited to solving large, 3-D systems of semiconductor equations on machines of limited computer memory ; however, it has certain limitations. This motivates the local Newton method, which coordinates the use of both the FPI and Newton’s methods, for convergence faster than either method alone.