Modelling the impact of discretized donor distribution for ultra-small scale transistors

When devices are scaled down into the ultra-submicron regime, the thermal de Broglie wavelength for electrons in semiconductors is of the order of the device dimensions. In such cases the semiconductor transport approaches the category of quantum transport. Such quantum transport theory may be based on the density matrix or on equivalent approaches such as the Wigner distribution function. Another way is to include quantum mechanical corrections to classical transport in ultra-submicron dimensions. Such an approach is used in this case: a set of quantum moment equations is developed from the Wigner function equation-of-motion, which preserves explicit quantum corrections as well as the classical hydrodynamic model features. We have applied this technique to an AlGaAs/GaAs HEMT, using discrete charge distribution and the equivalent uniform doping distribution, in a uniform grid with a mesh spacing equal to 2 nm.