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