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Signal-to-noise ratio (SNR) is a valuable figure of merit in determining the operating scope of infrared detectors. Antenna-couple metal-oxide-metal diodes have been shown to detect infrared radiation without cooling or applied bias, but so far have been hampered by their SNR. This paper details a comprehensive study of the fabrication parameters that control the formation of the tunneling oxide barrier to optimize the performance of these detectors. Since the tunneling barrier affects both current-voltage and infrared detection characteristics, fabrication parameters can be optimized to improve device performance. The current-voltage characteristics of the devices are detailed in this paper; resistance, nonlinearity, and curvature coefficient are parameterized on fabrication procedures. Infrared detection characteristics are detailed and SNR is studied as a function of device nonlinearity and biasing conditions.