Quantum calculations of the carrier mobility in thin films: Methodology, Matthiessen's rule and comparison with semi-classical approaches

We discuss the calculation of the carrier mobility in silicon films within the quantum Non-Equilibrium Green's Functions (NEGF) framework. We introduce a new method for the extraction of the carrier mobility that is free from contact resistance contamination, and provides accurate mobilities at a reasonable cost, with minimal needs for ensemble averages. We then introduce a new paradigm for the definition of the partial mobility $μ_{M}$ associated with a given elastic scattering mechanism "M", taking phonons (PH) as a reference ($μ_{M}^{-1}=μ_{PH+M}^{-1}-μ_{PH}^{-1}$). We argue that this definition makes better sense in a quantum transport framework as it is free from long range interference effects that can appear in purely ballistic calculations. As a matter of fact, these mobilities satisfy Matthiessen's rule for three mechanisms [surface roughness (SR), remote Coulomb scattering (RCS) and phonons] much better than the usual, single mechanism calculations. We also discuss the problems raised by the long range spatial correlations in the RCS disorder. Finally, we compare semi-classical Kubo-Greenwood (KG) and quantum NEGF calculations. We show that KG and NEGF are in reasonable agreement for phonon and RCS, yet not for SR. We point to possible deficiencies in the treatment of SR scattering in KG, opening the way for further improvements.