Simulation of hot carriers in semiconductor devices

Two approaches to calculate the population of hot carriers in semiconductor devices are studied in this thesis. Hot carriers are of interest because they have an energy significantly higher than the mean carrier energy and can thus cause device degradation by injection into the oxide and by interface state generation. In the first approach the hydrodynamic model was used to calculate the first three moments of the carrier distribution using the Boltzmann transport equation. The calculated mean electron energy was then used to estimate the hot carrier population and the substrate current for MOSFET's. The drain current obtained from the hydrodynamic model was accurate for all biases and channel lengths down to 0.16 /m, but the calculated substrate current had a large error when compared with experimental data, near the threshold voltage of the MOSFET. The error is attributable to the use of an ensemble average, the temperature, to describe the details of the distribution, which is quite anisotropic at this bias condition. To overcome this error which is inherent in a moments method, the second part of the thesis studies a method that solves the Boltzmann equation directly by expanding the distribution function in surface spherical harmonics in momentum space. Using the spherical harmonic expansion in momentum space and a standard finite difference discretization in real space, the Boltzmann equation is solved after incorporating the relevant scattering mechanisms and an appropriate band structure. The novelty of this thesis lies in the use of a Galerkin method which allows the spherical harmonic formulation for arbitrary order expansions. Results are presented for expansions up to third order in both one and two real space dimensions. It is shown that the higher order harmonics are significant at high fields. In two dimensions a rotated coordinate system approach was proposed and demonstrated. This method minimizes the number of harmonics that are needed for a given level of accuracy by always aligning the polar direction of expansion with the electric field direction. Important details regarding the the discretization of the spherical harmonic coefficients as well as computational efficiency issues are also addressed. Thesis Supervisor: Jacob White Title: Associate Professor