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Alternative types of artificial cooling techniques are of large interest for multiple applications. Here, we develop a framework for studying the role of electro-optical coupling in the analysis of solid-state refrigerators based on electroluminescent cooling (ELC) by combining device measurements with optical simulations. The studied device consists of a light-emitting diode (LED) epitaxially connected to a photodetector (PD) in a double-diode structure (DDS). Previous results of the DDS have indicated that the LED side already operates at conditions corresponding to ELC, but Ohmic losses and imperfect photodetection of the LED light in the PD have prevented observing the effect directly. Here, to break down the detection losses of the DDS, we report on the electro-optical response of the LED and the PD in detail, as well as the role of the spectral coupling from the LED to the PD. We present a detailed framework for combining measurements and simulations of the DDS to gain quantitative insight of the electro-optical response of the LED and PD, as well as the coupling between them, including the analysis of effects that are not directly accessible by standard measurements. The developed approach allows identifying the different photodetection loss mechanisms from the current-voltage and electroluminescence measurements and thereby gives guidance for designs toward a direct demonstration of ELC at practically relevant cooling powers. Somewhat surprisingly, the results show that an imperfect spectral absorption efficiency of the PD, in addition to its below unity quantum efficiency, are together required to explain the previously observed low photodetection efficiency of the DDS even for several microns thick PD structures. In comparison, the LED top mirror introduces only a minuscule drop in photodetection efficiency. Put in plain numbers, our analysis reveals that in the current DDS designs, there is headroom by 14% in the spectral matching between the LED and the PD, 5% in the charge collection efficiency of the PD, and 4% in the efficiency at which photons emitted from the LED reach the PD.
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