Effect Of Doping Profile On Transonic Steady-state Solution Of Hydrodynamic Model For Semiconductor

In this paper,we study the steady-state solution of the hydrodynamic model for one-dimensional one-pole semiconductor.We mainly consider the effects on subsonic and supersonic solutions of hydrodynamic model without the vacuum condition with a supersonic doping and the doping profile function being piecewise function.The n-E phase plane of the system is obtained by using the phase orbital analy-sis.On this basis,we prove the existence and uniqueness of the steady-state solution through calculating the monotonicity of the length of the corresponding x with respect to some parameters with some mathematical analysis method.Under condition with-out semiconductor effect,that is the pure euler poisson equation(τ→∞),the existence and uniqueness of subsonic and transonic solutions can be proved under the influence of doping profile.It also analyzes some cases of no solution.This study lays a foundation for further investigation on the case of doping profile non-constant function.