Analytic model of electron transport through and over non-linear barriers

Abstract

Tunneling barriers are an essential component of electron sources, sensors, detectors, and vacuum nanoelectronics and a pivotal factor in their performance, but the barriers themselves routinely depart from the analytic models used to model their behavior. A new formalism is developed to analytically and accurately model emission through and over barriers associated with depletion layers, nanotip barriers, and metal–insulator–metal (MIM) structures. The transmission probability for depletion layers and MIM and metal–oxide–semiconductor (MOS) barriers is accurately modeled as the electron energy exceeds the barrier height using approaches designed for rapid implementation demanded by simulation codes and extensible to general barriers. The models supersede conventional thermal and field models in depletion and MIM/MOS barrier studies. Thermal-field methods are used to treat the transmission probability and shape factor methods to treat the tunneling factor. Analytic formulas for current density are obtained. The methods ease device simulation and characterization of current–voltage relations for emerging technologically interesting barriers with better accuracy.