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I'm trying to solve for electron and hole distribution function using Boltzmann equation with various scattering mechanisms. Since I land up with an integro-differential equation, analytical solution is very difficult. So, I am looking for general advice on where to start, and on how this problem could be solved using numerical methods?

If you suggest some references with illustrative examples that would be really useful.

Thanks!

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A fantastic introductory book (final year undergraduate to graduate level) for simulation of electron and holes in semiconductor is, Fundamentals of Carrier Transport by M. Lundstrom.

Fundamentals of Carrier Transport front cover

The book covers difference techniques of solving the Boltzmann transport equation and it has a chapter on Monte-Carlo. It should provide you with an overview of the relevant techniques, hopefully this will get you started or provide you with references where you need more information.

Prof. Lundstrom's lectures are also published on nanohub.org, I would recommend viewing the ECE 656 lecture series.

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