Kinetic effects on the transport properties of nanostructured devices investigated by deterministic solutions of the Boltzmann-Poisson system

High-field transport and optical phonon scattering in graphene

“…Nevertheless, we find occupation numbers g η 1 for all optical phonon modes. Bulk calculations show much lower excitations, 5,17 even if exactly the same scattering processes are considered. 17 This highlights the importance of a space-dependent treatment of the transport equations for systems close to the ballistic regime.…”

“…These results required a space-dependent simulation, as these effects are not accessible by numerical studies of bulk materials. 5,17,33 Our kinetic model describes these phenomena in an efficient and detailed manner.…”

“…We use the same angular discretization for the wave vectors of the electrons and optical phonons, which is not absolutely necessary, but greatly simplifies the implementation. Following this scheme, the modulus of optical phonon wave vectors q is discretized by q In this discretized coordinate system, the electron-phonon collision operator (4) takes the form (17) with the discretized electron distribution functions f i klm = f i (x k ,k(ε l ,ϕ m ),t) and f j kl±t η n = f i (x k ,k(ε l ±hω η ,ϕ n ),t) and the scattering element…”

“…13 This cannot be assured for phonon distribution functions g η (q). In the discrete collision term (17), g η± klmn = g η (x k ,q η± klmn ) has to be evaluated at (19) which in general is not a grid point for optical phonons. This necessitates an interpolation to obtain a value for g η± klmn in terms of the values of the surrounding grid points.…”