Introduction Of Research Advance In Semiconductor Equations

This paper is a review of the article, a brief introduction to the nearly 10 years of semiconductorequations of progress. Semiconductor equations mainly research that the model of the transport of the carriers in a semiconductor device.At present,generally,we use drift-diffusion model.It can be described in a parabolic-elliptic coupled system. The unknown qualities coupled strongly in the model,with the complicated mixed boundary value prob-lem.It is a challenging thing for us to do the fixed solution problem of the model.There are five parties in this paper.As follows:First part:Introducing the semiconductor equation has a great influenced on the field of the mathematic and the practical worth.Second part:Introducing the character of the semiconductor equation,mainly introduce the research advance of the global existence and uniqueness of the weak solution,and so on.The equation is as follows:-△ψ= f + p-n, (1.1)n_t-(?)·?_n = -R{n,p), (1.2)p_t-(?)·?_p = -R{n,p). (1.3)Third part:Introducing the character of the semiconductor equation with avalanche term,mainly introduce the research advance of the stationary solution and nonstationary solution,and so on.The equation is as follows:-△ψ= f + p-n, (1.4) n_t-(?)·?_n = -R{n,p)+g, (1.5)p_t-(?)·?_p = -R{n,p)+g. (1-6)here the g =α₁((?)ψ)|J₁| +α₂((?)ψ)|J₂| is the avalanche term.Fourth part:Introducing the character of the semiconductor equation without temperatureeffect,mainly introduce the research advance of the existence of the weak solution,and so on.The equation is as follows:-△ψ= f + p-n, (1.7)n_t-(?)·?_n= R(n,p) + g(x,n,p, (?)n, (?)p, (?)ψ), (1.8)p_t-(?)·?_p = R(n, p) + g(x, n, p, (?)n, (?)p, (?)ψ). (1.9)here the g is the laser density in the device.Fifth part:Introducing the character of the semiconductor equation with temperature effect,mainly introduce the research advance of the stationary solution and nonstationary solution,and so on.The equation is as follows:-(?)·(σ(θ)·(?)ψ) = f + p-n, (1.10)n_t - (?)·J_n = R{n·p) + g{x,n,p,(?)n,(?)p,(?)ψ), (1.11)n_p-(?)·J_p=R(n·p) + g(x, n,p, ?)n,(?)p,(?)ψ), (1.12)θ_t-(?)(k(θ)·(?)θ) = H. (1.13)The equation involved the meaning of symbols can be found in the body of the paper.