Anomalous Scaling Exponents of Capacitance-Voltage Characteristics

Capacitance-Voltage (CV) measurements along with the Mott-Schottky (MS) analysis are widely used for characterization of material and device parameters. Using a simple analytical model, supported by detailed numerical simulations, here we predict that the capacitance of thin film devices scale as V^-2 (V is the applied potential), instead of the often used V^-0.5 dependence of MS analysis- with significant implications towards extraction of parameters like doping density, built-in voltage, etc. Surprisingly, we find that the predicted trends are already hidden in multiple instances of existing literature. As such, our results constitute a fundamental contribution to semiconductor device physics and are directly applicable and immediately relevant to a broad range of optoelectronic devices like organic solar cells, perovskite-based solar cells, and LEDs, thin film a-Si devices, etc.