### Instructor: Alessandra MichelettiElementary electronic devices (such as MOS transistors) have been continuously shrinked in size since many years. State-of-the-art transistors have typical dimensions of a few tens of nm, therefore only a few dopant atoms are present in the active region. Since the dopants number and position are random variables, the electrical characteristics differ stochastically from one device instance to another.
In particular electron transport depends on the coulombian interaction with such dopant atoms. Since this interaction decrease strongly with the electron-dopant distance, the resulting local mobility (ratio between velocity and electric field) varies across the device depending on the local dopant arrangement.
The problem we want to solve is to find a suitable analytical model (to be used in a Drift-Diffusion framework) describing the local mobility as a function of the discrete dopants number and position.
Given a statistical set of doping arrangements and of the corresponding local mobility data (provided by Montecarlo simulations, assumed as a reference) first of all the most appropriate functional form has to be found, then its parameters have to be optimized to provide the best overall agreement with the mobility data.
__Preferred mathematical background:__ Multivariate statistics, mathematical physics for semiconductors,
Montecarlo simulation |