| An efficient and physically accurate method, based on directly solving the Boltzmann transport equation, for modeling 2-dimensional submicron semiconductor devices has been developed. This method gives the distribution function for the entire device, does not rely on mobility models, and can therefore be applied for deep submicron devices where the concept of average mobility may not be applicable. Also, with the distribution function, hot electron reliability effects, including oxide degradation, can be more accurately determined.;Initial studies focused on numerically solving the multi-band homogeneous Boltzmann transport equations in silicon, while incorporating the effects of acoustic, optical intervalley, and optical interband phonon scattering. To account for the multi-band model, a Boltzmann transport equation is formulated for each of the four energy bands. First-order and generalized Legendre polynomial expansion approaches are used to formulate the Boltzmann equation, and numerical methods are then applied to solve for the distribution function. Average energy, average velocity, and the electron concentration in each energy band are calculated and compared with the results of the Monte Carlo method.;Once the distribution function is known, it can be used to calculate the impact ionization coefficients in bulk silicon. Using first-order perturbation theory and a random-k approximation, the impact ionization rate is determined to reflect the multi-band density of states in silicon. Calculated values for the impact ionization coefficients are in excellent agreement with experiments.;For simulation of two-dimensional devices, a spherical harmonics expansion method is used to formulate the Boltzmann equation. Upon introducing a change of variables, the Boltzmann equation is transformed into a closely self-adjoint form. This form is ideally solved using a fixed point SOR iterative technique, and avoids direct solution of large matrix equations. It is also inherently parallel, which can easily be implemented on parallel computers. Example calculations have been performed on a 0.5... |
