The Analysis Of Drift-diffusion And Hydrodynamic Models For Semiconductors

The hydrodynamic and the drift-diffusion models are the most widely used models to describe semiconductor devices today.No sooner the drift-diffusion equations were set forth and formulated in the early fifties of last century than they became the most popular model for the simulation of semiconductors. With the miniaturization of semiconductors, the drift-diffusion model is brought into its limit of validity since electrons are no longer at the lattice temperature.The developments of microelectronics technology made it necessary to search for more accurate description of carrier transport in semiconductor. As one of the several models to improve the drift-diffusion model, the hydrodynamic model plays an increasingly important role in simulating the behavior of the charge carrier in sub-micron semiconductor devices because it can exhibit velocity overshoot and ballistic effects for which are not accounted the classical drift-diffusion model.There are two main topics in this dissertation. At first, we mainly investigate the quasineutral limit of the 1-dimension bipolar standard drift-diffusion equations modelling insulated semiconductor devices with p-n junctions, i.e.,The convergence of standard drift-diffusion equations to quasineutral models is presented for a class of special initial data. It reads as follows: Theorem 2.2 Let (nλ,pλ, Eλ) be the classical solutions of the problem (1.1)-(1.4). Also, assume that D(x) € C'l,Dx(x = 0,1) = Dxxx(x= 0,1) = 0, and that there exist a constant M and an a > 0 such that, forany λ > 0Then there exists an λ0 : 0 < λ0 <1, depending upon T, such that, for any A : 0 < λ < λ0,for any δ∈(0, min{a, 2}) and some constant M independent of A.The main method used in solving this problem is energy method. The key techniques are the introductions of a typical function transformation and A-weighted norm, which yield the uniform estimate with respect to the scaled Debye length.Secondly, we study the asymptotic behavior of the global spherically symmetric smooth solutions to the initial boundary value problem for the multidimensional model for semiconductors in the exterior domain, i.e.,We prove that the solution of the problem converges to a stationary solution time asymptotically exponentially fast. This result was published in the Journal of Henan University (Natural Science,4(2003)).