The effect of substrate curvature on capacitance and current–voltage characteristics in thin-film transistors on flexible substrates

Abstract

Mechanically flexible electronics are devices designed to operate under significant physical deformations such as bending, twisting, and stretching. While the materials systems and devices compatible with flexible substrates have been extensively studied, the mathematical framework for analysis remains identical to that of traditional planar silicon-based electronics. However, the non-planar and dynamic form factors desired from flexible electronics invalidate assumptions made in these models. For electronic devices to be predictable and ultimately commercially viable, they must be understood in any physical form. Here we employ the method of moments to calculate the capacitance between two electrical conductors of arbitrary shape. Combined with a model for source–drain current in thin-film transistors (TFTs) on the surface of a cylinder, we are able to calculate the current–voltage characteristics in curved TFTs as a function of bending angle. We demonstrate how deformations to device geometry are expected to lead to non-negligible changes in current–voltage characteristics. This work represents the first step towards a new framework for understanding and characterizing electronics with any physical form factor, ultimately bringing flexible electronics closer to commercial viability.