This paper is concerned with the numerical solution of the Boltzmann semiconductor equation. Our main objective is the development of a fast deterministic solution procedure for the numerical computation of the steady state solutions. The discretization strategy is based on an upwind finite difference approximation of the gradient terms and on a deterministic conservative calculation of the integral operators. The resulting algebraic system is then solved by a least squares methodology which reduces the system to a quadratic minimization problem to be solved by a standard conjugate gradient algorithm.