Sub-band States in a Nanometer Width Silicon Accumulation Layer/ Vacuum Structure Obtained from Self-Consistent Solution of the Coupled Schrödinger-Poisson Equation

Abstract

A vacuum microelectronic device based on an n-type Si(100)-vacuum structure was theoretically studied. A nanometer width accumulation layer in the Si(100) region is created when a negative voltage is applied to the Si(100). The potential profile of the structure was obtained from solving self-consistently the coupled Schrödinger-Poisson equation with inclusion of the space charge and quantum effects. The finite difference method was employed in the self-consistent solution. It was found that the quantum well in the Si(100) region is deep and narrow with a small bump, which could cause resonant tunneling phenomena in the vacuum device. Three lowest sub-band states, which are composed of two states in the lower valley and one in the higher valley, exist in the quantum well. The sub-band energy levels increase with increasing the external electric field. The lowest energy level of each valley become lower than the Fermi energy as the electric field is higher than 50 MV/cm. Most electrons occupy the lowest state of each valley. The occupancy of the lowest state of the lower valley is lower than that of the lowest state of the higher valley because the degeneracy and density of states mass of the state of the higher valley are higher than those of the state of the lower valley. The lifetimes of all states decrease exponentially as the external electric field is increased. As the electric field becomes higher than 30 MV/cm, the lifetime is less than 100 s. Therefore, electrons have probability of escaping the vacuum barrier via tunneling process.