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Knowing the influence of the substrate type on the diffusion coefficient andthe momentum relaxation in graphene is of great importance for the developmentof new device models specifically adapted to the peculiarities of thismaterial. In this work, the influence of surface polar phonons at low and highelectric fields is evaluated by means of ensemble Monte Carlo simulations forseveral types of substrates. The results show that at low fields surface polarphonons have a major role on reducing the scattering time, breaking thecorrelation of velocity fluctuations and degrading the diffusion coefficient.At high fields the differences with regard to suspended samples in terms ofdiffusivity and momentum relaxation tend to reduce, providing at the same timelarger saturation velocities, particularly for h-BN.

Influence of the substrate on the diffusion coefficient and the momentum relaxation in graphene: the role of surface polar phonons