New approaches for first-principles modelling of inelastic transport in nanoscale semiconductor devices with thousands of atoms

We present two different methods which both enable large-scale first-principles device simulations including electron-phonon coupling (EPC). The methods are based on Density Functional Theory and Nonequilibrium Greens Functions (DFT- NEGF) calculations of electron transport. The inelastic current is in both methods calculated in a post-processing step to a self consistent DFT calculation. The first method is based on first order perturbation theory in the EPC self-energy within the Lowest Order Expansion (LOE) approximation. The method requires calculation of the first-principles EPC in the device region and it includes the effect of each phonon mode on the current perturbatively. This approach is made practical by calculating the EPC of the device region using a smaller periodic reference system. In addition, the phonon modes are assembled into a small number of energy intervals in which phonon modes are described collectively. The second method involves calculating the electron transmission for a single configuration where the atoms are displaced according to the phonon temperature of the system. Thus, this method has a computational cost equivalent to conventional elastic transport calculations. Both methods have been implemented in the Atomistix ToolKit (ATK) and we apply the methods for calculating the inelastic current in a silicon n-i-n junction and for calculation of phonon limited mobilities of silicon nanowires.