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Boltzmann diffusive transport including relaxation time and mobility ingraphene limited by ionized impurity scattering is investigated. The relaxationtime is evaluated with two different methods, first one directly use Boltzmanntransport equation via scattering matrix, second one is based on scatteringcross-section. Two methods yield the same relaxation time results for graphene.Assume linear Thomas-Fermi screening and a reasonable electron carrier density,relaxation time and mobility can be calculated and plotted, which demonstratesgraphene is a very promising high mobility material for ultra fast electronicdevice applications.

Two distinct methods to evaluate graphene relaxation time and mobility  in Boltzmann diffusive transport, considering ionized impurity scattering and  Thomas-Fermi screening