B\"uttiker probes and the Recursive Green's Function; an efficient approach to include dissipation in general configurations

An efficient and compact approach to the inclusion of dissipative effects in Non-Equilibrium Green's Function (NEGF) simulations of electronic systems is introduced. The algorithm is based on two well known methods in the literature, firstly that of the so-called Recursive Green's Function (RGF) and secondly that of B\"uttiker probes. Numerical methods for exact evaluation of the Jacobian are presented by a direct extension to RGF which can be modularly included in any codebase that uses it presently. Then using both physical observations and numerical methods, the computation time of the B\"uttiker probe Jacobian is improved significantly. An improvement to existing phonon models within B\"uttiker probes is then demonstrated in the simulation of fully atomistic graphene nanoribbon based field effect transistors in n-i-n and p-i-n operation.