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.

机械柔性电子设备是设计用于在明显的物理变形（例如弯曲，扭曲和拉伸）下运行的设备。尽管已经广泛研究了与柔性基板兼容的材料系统和设备，但是用于分析的数学框架仍然与传统的平面硅基电子产品相同。但是，柔性电子设备所需的非平面和动态形状因数会使这些模型中的假设无效。为了使电子设备可预测并最终在商业上可行，必须以任何物理形式理解它们。在这里，我们采用矩量法来计算任意形状的两个电导体之间的电容。结合圆柱表面上薄膜晶体管（TFT）的源极-漏极电流模型，我们能够计算弯曲TFT中的电流-电压特性随弯曲角度的变化。我们证明了器件几何形状的变形如何导致电流-电压特性的不可忽略的变化。这项工作代表了迈向新框架的第一步，该框架旨在理解和表征具有任何物理形状因素的电子产品，最终使柔性电子产品更接近于商业可行性。