2.4.3.3 Quantum Device Simulation

Recently, strong efforts have been undertaken to couple the most accurate classical device simulation approach, the technique, with quantum-mechanical formulations. These approaches are termed quantum techniques [87,88,89].

One possibility is to use an effective potential instead of the solution of POISSON's equation [90,91] in the simulation. That can be achieved by convoluting the electrostatic potential with a GAUSS^2.11 function which leads to a smoothing of the original potential.

A more rigorous approach is to solve the WIGNER transport equation (2.20) by means of techniques. Unlike classical distribution functions, however, the WIGNER function (2.18) permits positive and negative values. Therefore, it cannot be interpreted as a probability distribution function, what is known as the negative sign problem. Instead, the WIGNER function can be modeled as the difference of two positive functions which describe in-scattering and out-scattering of particles [89]. This approach has the advantage that it allows for a seamless transition between classical and quantum-mechanical regions in a device.

A. Gehring: Simulation of Tunneling in Semiconductor Devices