ABSTRACT
Semiconductor device transport is, in general, a tough problem from both the mathematical and the physical points of view. In fact, the Boltzmann transport equation (BTE), assumed to be the fundamental description of carrier transport, does not
8.1 Introduction ................................................................................................... 165 8.2 Boltzmann Transport Equation ..................................................................... 166 8.3 Ensemble Monte Carlo Charge Transport Simulation .................................. 167
8.3.1 EMC Flow Chart ............................................................................... 167 8.3.1.1 Free Flight .......................................................................... 168 8.3.1.2 Scattering Event ................................................................. 170 8.3.1.3 Carrier Energy.................................................................... 171
8.3.2 Scattering .......................................................................................... 172 8.4 Device Applications ...................................................................................... 173
8.4.1 Hot-Electron Effects in n-Type Structures ........................................ 174 8.4.1.1 Computational Details ....................................................... 174 8.4.1.2 Alloy Scattering ................................................................. 174 8.4.1.3 Results ................................................................................ 175
8.4.2 AlGaN Solar-Blind Avalanche Photodiodes ..................................... 177 8.4.2.1 Computational Details ....................................................... 177 8.4.2.2 Results ................................................................................ 177
8.4.3 Gunn Oscillations in GaN Channels ................................................. 182 8.4.3.1 Basics ................................................................................. 182 8.4.3.2 Motivation .......................................................................... 183 8.4.3.3 Computational Details ....................................................... 184 8.4.3.4 Results ................................................................................ 184
8.5 Concluding Remarks ..................................................................................... 189 References .............................................................................................................. 190
offer simple analytical solutions due to the carrier density evolving in time and space according to a complicated nonlinear integro-differential equation. Furthermore, numerical solution techniques, such as iterative, path integral, and orthogonal polynomial expansion methods, usually are not applicable to real device systems. Another alternative method that has been widely used in studies of the physics of hot-carrier transport, allows simulation of the trajectories of individual carriers as they move through a device under the applied ”elds and experience various scattering or collision events. In order to implement such a model we need to directly incorporate a statistical method of at least the scattering processes, and this is done by the use of Monte Carlo (MC) techniques.
