We developed a full-band Monte Carlo simulator to investigate electron transport in a single layer of graphite (graphene). The electron and phonon dispersion curves of graphene are first obtained by applying the tight-binding method to the two inequivalent atoms of the graphene unit cell, considering their nearest four neighbors. The electron-phonon scattering rates for interactions that conserve momentum and energy are then determined using Fermi’s golden rule and the deformation potential approximation. Average electron velocities due to external fields applied in different directions are calculated using these electron-phonon scattering rates and a semiclassical electron and electric field interaction. Graphene transport simulations at room temperature indicate large low-field graphene electron mobilities of approximately 4.0×104, 6.0×104, and 8.0×104 cm2/Vs along the ky (kx=0), kx=ky, and kx (ky=0) momentum directions, respectively. These low-field electron mobilities further suggest graphene field-effect mobilities of 1.3−2.6×104 cm2/Vs, which agree with experiments. Also, a large peak electron velocity of roughly 4.6×107 cm2/Vs at high fields is obtained.

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We present a device performance modeling methodology that self-consistently resolves device operation at cryogenic temperatures (T > 30 K) in conjunction with incomplete ionization effects that take into account the change in dopant activation energies as a function of doping. Using this methodology, we developed a device simulator that predicts n-channel MOSFET (NMOSFET) device characteristics for a wide range of temperatures by solving semiconductor equations, along with the Poisson equation. Comparison of our calculated results with measurements shows that proper inclusion of variations in activation energy as a function of doping level is necessary for accurately monitoring device operation at cryogenic temperatures. Using dopant activation energies that are independent of doping levels leads to current rolloff and eventually device turn-off at low-temperature simulations. However, activation energy models that give lower activation energies for higher doping levels result in improved NMOSFET performance at colder temperatures, which agrees with experiments. Furthermore, calculations indicate that different incomplete ionization models affect the NMOSFET characteristics mainly through changes in the resistances of the heavily doped source and drain regions, and the substrate.