Influence of non-uniform thickness of dielectric layers on capacitance and tunnel currents

Abstract The paper deals with the influence of non-uniform thickness of dielectric films both on capacitance and tunnel currents of thin film elements with a MIM structure. For the dielectric film thickness the relation s = nq is assumed, where q is a constant and n is an integer with Poisson distribution. It is shown that a systematic difference s −s c ≈ q exists between the thickness s c determined from the capacitance measurement, and the mean thickness s . Furthermore, the paper studies in some details the influence of non-uniform thickness on the tunnel current and points out that especially under favourable conditions the ratio ( s T s ) vs. s may be constant ( s T is the thickness determined from the tunnel current). It may be shown as well that under quite reasonable assumptions for q , in the case of AlAl 2 O 3 Al sandwiches, s T ≈ 1 2 s c , as has been found experimentally. Some proofs of important relations, needed for the understanding of the behaviour of capacitance in systems with non-uniform thickness, are given in the Appendix.