Multi-dimensional tunneling in density-gradient theory

For engineering-oriented simulations of quantum confinement effects, density-gradient (DG) theory has come into wide use including in multi-dimensions. It is therefore somewhat curious that the DG description of tunneling (Ancona, 1990) has not been similarly applied to practical device simulation. The two most important explanations would seem to be: (i) questions of principle; and (ii) that the existing DG theory is restricted to one-dimensional tunneling for which quantum mechanics (e.g., NEGF) often provides a realistic alternative. In the present work our primary focus is on how tunneling problems can be treated in multi-dimensions in DG theory.