Density-gradient theory of tunneling: Physics and verification in one dimension

The application of an engineering-oriented continuum description of electron transport known as density-gradient theory to quantum mechanical tunneling is investigated, and its legitimacy, physical fidelity, and limitations are assessed using detailed comparisons with nonequilibrium Green's function simulations in one dimension. These comparisons demonstrate that despite the apparent contradiction, quantum tunneling can often be well represented by the classical field theory with the electron inertia term of Newton's second law playing a significant role. Moreover, the density-gradient approach is found to be quite accurate with the main source of error not being the description of the tunneling itself, but rather the representation of the carriers at high density inside the electrodes. A physical understanding of the ad hoc tunneling boundary conditions used in previous work is also provided. (c) 2008 American Institute of Physics. [DOI: 10.1063/1.2990065]