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Electron accumulation in transparent conductive oxides (TCOs), when driven by a gate voltage, is capable of inducing extremely strong electro-optic absorption at the telecommunication wavelength window due to the epsilon-near-zero (ENZ) effect and various waveguide modulators have been proposed in recent years. This paper conducts a comparative analysis of TCO modulators by reviewing several representative designs based on the uniform concentration accumulated carrier model and the classical continuous carrier distribution model. We also apply the quantum moment model to analyze the free carrier distribution of the TCO based metal-oxide-semiconductor (MOS) capacitor for the first time, and reveal significantly different device physics compared with previous simulation models. The quantum moment model predicts a much higher driving voltage in order to turn the TCO materials into ENZ and a stronger modulation strength compared with the classical model. Especially, the requirement of the higher gate voltage brings a great challenge to the insulator layer as the electric field in the insulator is exceeding the breakdown strength, which raises the concern of reliability. In order to evaluate the accuracy of different models, we compare the simulation results with two of the most recent experimental papers and show that the quantum model has a better match in terms of the electro-absorption rate and the differential driving voltage. However, the quantum moment model still cannot explain some other experimental results, which may be induced by different modulation mechanisms.
Gao et al. (2018) studied this question.