Application of cumulant expansion to the modeling of non-local effects in semiconductor devices

The cumulant expansion method is proposed to solve the Boltzmann transport equation (BTE) in semiconductors. This method involves deriving a set of partial differential equations for the expansion coefficients from a Fourier transformation of the BTE. The collision terms for phonon emission and absorption scattering are obtained directly from quantum computed scattering transition rates, without invoking the relaxation time approximation. Unlike the moment expansion method used in hydrodynamic models, the cumulant expansion converges much faster when the distribution function is close to a drifted maxwellian because, for this case, only the first three cumulants are non-zero. This method also provides a way to construct an arbitrary distribution function from the computed cumulants, without being limited to a shifted maxwellian.