Kronig‐Penney‐Type Calculations for Electron Tunneling through Thin Dielectric Films

Using a Kronig‐Penney model and matrix methods the probability D = exp ( − 2 χ a) of an electron tunneling through a thin dielectric film can be calculated exactly for an arbitrary value of the thickness a. The relation between the damping constant χ and the electron energy E in the band gap of the dielectric depends on the thickness a. For thick films containing more than 10 to 15 crystal planes the E(χ2)‐curves approximate to the usual ones obtained from band theory. However, the simple model involving potential walls without any potential wells is the limiting case for very thin films. Nevertheless, the departure of the complex band structure of the dielectric from the free electron‐approximation usually used in tunneling calculations should be observable qualitatively even for very thin films.