Electron–phonon interactions in silicon: Mean free paths, related distributions and transport characteristics

The mean free path (MFP) for electron–phonon interactions in pure silicon is an important characteristic needed both for low energy electron transport calculations using Boltzmann transport equation, and for Monte Carlo simulations. Full band calculations present a basic (though complicated) approach to the solution of the problem. Simpler approaches based on analytical presentation of the scattering rates have also been used; however they are valid for a restricted range of electron energies, below 2 eV. In this paper we introduce a hybrid method that utilizes the density of energy states calculated from the full band calculations for electron energies larger than 2 eV, allowing to extend the analytical approach for energies up to 5 eV, where the impact ionization becomes the dominant mechanism of electron interactions within bulk silicon. The resulting MFPs as function of electron energy and lattice temperature, together with the integral probability distribution for given energy losses by phonon emission (or energy gain by absorption of phonons) form the database for Monte Carlo calculations. Using this method, we calculate the electron diffusivity and mobility as function of the electron and lattice temperatures. These parameters are important for solution of the two temperature model, used for calculations of the track structure created by swift ions and nanosecond laser beams.