The effect of substrate curvature on capacitance and transfer characteristics for thin film transistors on the surface of spheres

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Conformable, flexible, and stretchable thin film transistors hold promise for ubiquitous and low-cost electronics. As part of the research endeavor toward this goal, the challenges associated with compatible materials and growth processes have been intensely studied. What is seldom considered, however, is how device electrostatics change as the physical form of devices change. In this report, we study how one would expect the current–voltage characteristics of thin film transistors to change as they are deformed on the surface of a sphere. We derive analogous equations to those derived in the gradual channel approximation to relate current to applied voltage for various spherical geometries. Combined with a finite-difference strategy to evaluate geometric capacitance, example current–voltage characteristics are calculated. The results demonstrate for certain deformations in this geometry, the behavior deviates from what one would expect using just the gradual channel approximation. For flexible electronics to be commercially viable, it must be predictable in any physical form. These results represent some of the first steps in a broader effort to quantify the relationship between device geometry and electrical behavior.