Error analysis leading to design criteria for transmission line model characterization of ohmic contacts

Abstract

The transmission line model (TLM) is a standard method for planar specific contact resistance measurement. Although widely used, the accuracy of a measurement is typically not stated. In addition to contributions from random errors, there can be substantial contributions from systematic errors in typical TLM measurements. In this paper, we develop an analytical model for the experimental uncertainty from the fundamental TLM expressions in order to understand and calculate the uncertainty associated with the specific contact resistance and sheet resistance derived by the TLM method. The experimental uncertainties in measured resistances, together with the pad width and pad spacing, are the dominant contributions to the total uncertainty. Analytical expressions for relative random and systematic uncertainties in contact resistance and sheet resistance are developed in terms of the error contributions and the parameters of the TLM geometry. Expressions for minimum uncertainty, with associated optimum widths and sheet resistances, serve as a basis for the design of TLM structures with minimum uncertainty. The model quantifies the increase in relative uncertainty associated with decreasing contact resistance. Simulations of uncertainty under various sheet resistance, contact resistance, and pad width are implemented and uncertainties are calculated for realistic data sets.