Theoretical foundations of the quantum drift-diffusion and density-gradient models

In this paper we examine the theoretical foundations of the quantum drift-diffusion and density-gradient transport models for the simulation of fully-depleted silicon-on-insulator and silicon-nanowire FETs. In doing so, we highlight the strengths and limitations of both approaches. In the former case, the harmonization of the classical and quantum-mechanical perspectives is pursued by means of Bohm's theory of quantum potential and by solving, in addition to the coupled Schroedinger-Poisson equations, as many drift-diffusion equations as the number of populated subbands. The latter approach is affected instead by more serious conceptual problems, as it basically replaces the Schroedinger equation with a simplified non-linear equation in the electron-charge concentration, by which energy quantization, multiple subbands, and multiple effective masses are neglected. Despite these limitations, the density gradient model turns out to be remarkably successful in predicting the device I-V characteristics. Simulation examples are discussed and the model predictions are compared. In our implementation, the simulation efficiency of the QDD is superior to that of the DG model.