Analysis of current crowding in thin film contacts from exact field solution

The paper presents a systematic evaluation of current crowding and spreading resistance in thin film contacts, based on the exact field solution that contains very large contrasts in dimensions and resistivity. It is found that current crowding becomes more severe as the interface specific contact resistivity decreases, the resistivity ratio of the contact electrode to the thin film decreases, or the thickness of either the contact or the thin film decreases. The current transfer length from our exact field solution is compared to that of transmission line model (TLM), , where is the interface specific contact resistivity, and ρsh is the sheet resistance of the thin film under contact. It is found that, if is small, is bounded by the smaller of the two dimensions—thin film thickness and contact size. As increases, increases, but saturates at a constant value, determined by the smaller of the two dimensions—contact size and . The total contact resistance is decomposed into three components: the interface resistance due to , the spreading resistance due to current crowding, and the resistance due to the contact electrode. Unambiguously identified, each component is explicitly evaluated and compared in detail.