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The nonequilibrium Green's function (NEGF) method is often used to predicttransport in atomistically resolved nanodevices and yields an immense numericalload when inelastic scattering on phonons is included. To ease this load, thiswork extends the atomistic mode space approach of Ref. [1] to include inelasticscattering on optical and acoustic phonons in silicon nanowires. This work alsoincludes the exact calculation of the real part of retarded scatteringself-energies in the reduced basis representation using the Kramers-Kronigrelations. The inclusion of the Kramers-Kronig relation for the real part ofthe retarded scattering self-energy increases the impact of scattering.Virtually perfect agreement with results of the original representation isachieved with matrix rank reductions of more than 97%. Time-to-solutionimprovements of more than 200$\times$ and peak memory reductions of more than7$\times$ are shown. This allows for the solution of electron transportscattered on phonons in atomically resolved nanowires with cross-sectionslarger than 5 nm $\times$ 5 nm.

Mode-space-compatible inelastic scattering in atomistic nonequilibrium Green's function implementations