PN junction Simulation with Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg74123] PN junction Simulation with Mathematica*From*: "e-touch\ at libero\.it" <e-touch at libero.it>*Date*: Mon, 12 Mar 2007 04:33:33 -0500 (EST)

Dear MathGroup I'm a student and I'm trying to simulate the bahaviour of a p-n junction = by solving the continuity equations for charge carriers and the poisson e= quation. It is a system of coupled PDEs 1)d/dt P[x,t]=-k*P[x,t]*d/dx El[x,t] -k*El[x,t]*d/dx P[x,t] +k2 dd/dx2 P[x,t]; 2)d/dt N[x,t]=+k*N[x,t]*d/dx El[x,t] +k*El[x,t]*d/dx N[x,t] +k2 dd/dx2 N[x,t]; 3)d/dx El[x,t]=P[x,t]-N[x,t]+Nd[x]-Na[x] Where I want to find P[x,t],N[x,t] and El[x,t]. Nd[x] and Na[x] are functions wich define the distribution of fixed charg= es(and the initial conditions for P and N) The first two equations without the terms with El[x,t] are just simply di= ffusion equations and I have no problems to solve them...but when I try t= o couple them with the Electric field I get only error messages: "NDSolve::pdord: Some of the functions have zero differential order so th= e \ equations will be solved as a system of differential-algebraic equations.= " "NDSolve::bcart: Warning: An insufficient number of boundary conditions h= ave \ been specified for the direction of independent variable x. Artificial \ boundary effects may be present in the solution." "LinearSolve::sing: Matrix SparseArray[<180030>,<<1>>] is singular." "NDSolve::icfail: Unable to find initial conditions which satisfy the res= idual \ function within specified tolerances. Try giving initial conditions for = both \ values and derivatives of the functions." I insert in NDSolve all the initials conditions wich have physically sens= e... -P[x,0]=UnitStep[-x] -P[100,t]=0 -P[-100,t]=1 -N[x,0]=UnitStep[x] -N[100,t]=1 -N[-100,t]=0 -El[x,0]=0 -El[100,t]=0 should be not necessary -El[-100,t]=0 should be not necessary I saw in the archive that somebody already tried to solve his kind of pro= blem, but it didn't get help from those posts... I'm prety new of Mathematica, so, if someone could help me or tell if the= re is another way to solve this problem it would be really helpful. Thank you Matteo=0A=0A=0A------------------------------------------------------=0AP= assa a Infostrada. ADSL e Telefono senza limiti e senza canone Telecom=0A= http://click.libero.it/infostrada=0A