Tunneling Current Calculation Using the Linear‐Bound Potential Model

A model of the tunneling current through an ultrathin insulating barrier coming from carriers in an inversion layer using a simple linear potential model is presented. This model provides analytical expressions for the wavefunctions of these carriers and simple equations to obtain numerically their corresponding eigenvalues. These expressions can be inserted in the tunneling current equation allowing a more simple understanding of the physics involved in this tunneling problem. As an example, one can fit the experimental results for the leakage current obtained by different authors in planar metal oxide semiconductor field effect transistors and also in a LaAlO 3 /SrTiO 3 and a HfO 2 /Ge bilayer. The modification of the tunneling current when the dielectric constant is increased, a subject of interest in device applications, is explored.