Voltage and oxide thickness dependent tunneling current density and tunnel resistivity model: Application to high-k material HfO2 based MOS devices

In this paper presents a straightforward efficient investigation of tunneling current density for ultra thin oxide layer based metal-oxide-semiconductor (MOS) devices to realization the gate current as a function of applied potential and oxide thickness. Solutions to the Schrödinger's wave equation are evolved for the different potential energy regions of the MOS device considering appropriate effective mass for each region. For finding approximate mathematical solutions to linear differential equations using spatially changeable coefficients the Wentzel-Kramers-Brillouin (WKB) approximation technique is considered. A p-substrate based n-channel MOS device has been analyzed consisting of SiO2 material as the oxide dielectric along with high-k material HfO2. The tunnel resistivity is correspondingly assessed employing this tunneling current density model. Synopsys Technology Computer Aided Design (TCAD) tool results are employed to validate the analytical model. Tremendous agreements among the results are observed.