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(???),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.