Physics of Semiconductor Transport under High Field Conditions

Semiconductor transport equations are typically derived and justified by taking moments of the microscopic Boltzmann equation.  This procedure generates an infinite hierarchy of equations which must then be truncated by imposing an ad hoc closure condition in order to arrive at a useful macroscopic description.  This truncation is generally done after the second (momentum) or third (energy) moment, and the resulting theories are widely used despite many questions.  Among the insufficiently explored issues are: (i) when does it become necessary to include an explicit energy balance law, (ii) how important are history dependences in the description of scattering, and (iii) is electron viscosity ever a relevant concept.  The present work is a progress report on our research on these foundational issues.  Our effort is built on a careful examination of the underlying constitutive theory and employs a combination of hydrodynamic and Monte Carlo modeling.  For the former we utilize the well-known flux-corrected transport algorithm to obtain stable time-domain solutions in 1D and 2D that include any or all of the complicating factors under study.  The corresponding microscopic modeling is used for calibration purposes and is carried out with the public-domain code Archimedes.