HW2
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EE 735 HW#2: Carrier Transport – Diffusion Submission deadline: 11.55pm, 18/08/2015 1. Fick’s laws of diffusion and continuity equation: State the Fick’s laws of diffusion and derive the continuity equation for carriers in the presence of diffusive transport. Assume constant generation rates and SRH based recombination (refer to the book “ Semiconductor Device Fundamentals” by Robert Pierret). 2. Numerical solution of steady state continuity equation: For each of the cases listed below, provide analytical solutions and compare with numerical results, if possible. Assume D=30cm 2 /s, unless otherwise stated. a. Consider diffusive transport of particles from point A to point B and the separation between these points being 100m. The concentration of particles at A is n=10 12 cm -3 , and at B is n=0cm -3 . Assume = ∞ . Find the particle profile from A to B. What is the particle flux from A to B? b. Solve (a) with = 10 −7 and other conditions remaining the same. Compare with the solution obtained in part (a). c. For the configuration in part (a), assume that the boundary condition at B is such that = , where is the particle flux (outgoing), = 10 3 /, and is the particle density. Assume = ∞ . Find the particle profile from A to B and the particle flux at B. Explore the implications of the change in boundary conditions at B. d. Solve (c) with = 10 −7 and other conditions remaining the same. Can you comment on the conservation of particles for the whole system? e. For the configuration in part (a), assume that a particle flux is introduced at x=30m at the rate of 10 12 cm -2 /s. Assume that the particle density at A and B are held constant at n=0 and = ∞ . Find the particle profile from A to B, and the flux at A and B. f. Solve (e) with the boundary condition at A and B being = , where is the particle flux (outgoing), = 10 3 /, and is the particle density.
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EE 735 HW#2: Carrier Transport Diffusion Submission deadline: 11.55pm, 18/08/2015 1.Ficks laws of diffusion and continuity equation: State the Ficks laws of diffusion and derive the continuity equation for carriers in the presence of diffusive transport. Assume constantgenerationratesandSRHbasedrecombination(refertothebook Semiconductor Device Fundamentals by Robert Pierret). 2.Numericalsolutionofsteadystatecontinuityequation:Foreachofthecaseslisted below,provideanalyticalsolutionsandcomparewithnumericalresults,ifpossible. Assume D=30cm2/s, unless otherwise stated. a.ConsiderdiffusivetransportofparticlesfrompointAtopointBandthe separation between these points being 100m. The concentration of particles at A isn=1012cm-3,andatBisn=0cm-3.Assume = .Findtheparticleprofile from A to B. What is the particle flux from A to B? b.Solve(a)with =107 andotherconditionsremainingthesame.Compare with the solution obtained in part (a). c.For the configuration in part (a), assume that the boundary condition at B is such that = ,whereistheparticleflux(outgoing), = 103/,andisthe particledensity.Assume = .FindtheparticleprofilefromAtoBandthe particle flux at B. Explore the implications of the change in boundaryconditions at B. d.Solve(c)with =107 andotherconditionsremainingthesame.Canyou comment on the conservation of particles for the whole system? e.Fortheconfigurationinpart(a),assumethataparticlefluxisintroducedat x=30m at the rate of 1012cm-2/s. Assume that the particle density at A and B are heldconstantatn=0and = .FindtheparticleprofilefromAtoB,andthe flux at A and B. f.Solve(e)withtheboundaryconditionatAandBbeing = ,whereisthe particle flux (outgoing), = 103/, and is the particle density.
