Simulation of time-dependent quantum transport in field emission from semiconductors: Complications due to scattering, surface density, and temperature

Abstract

The prediction of electron emission characteristics from semiconductors is difficult due to the extreme conditions (e.g., band-bending effects, high field, etc.) under which field emitting arrays (FEAs) operate in vacuum microelectronics applications. A fundamental quantum transport theory that incorporates semiconductor properties is needed for understanding of limitations of semiconductor FEA device performance, as the assumptions inherent in the low-field transmission-coefficient based approach are not adequate. Here, the Wigner distribution function (WDF) approach to quantum transport has been used to successfully determine the self-consistent potential, density, and current characteristics in a time-dependent simulation. The self-consistent potential is affected by the temperature- and electron density-dependent scattering operator. The field in vacuum was determined solely by the boundary conditions, and was not fixed a priori. The behavior of the WDF is shown to be compatible with the needs of a hybrid scheme in which the supply function in a transmission coefficient-based approach is supplied by the WDF, thereby allowing for a computationally tractable and robust method for estimating emission behavior from semiconductors.