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Phenomenological models for the internal quantum efficiency of Schottky barrier photodetectors suitable for the detection of optical radiation below the bandgap energy of the semiconductor are presented and discussed. The detection mechanism is internal photoemission from the metal film into the semiconductor substrate. Three detector configurations are considered: the first consists of a thick metal film on a semiconductor substrate forming a single Schottky barrier; the second consists of a thin metal film on a semiconductor substrate also forming a single Schottky barrier; and the third consists of a thin metal film buried in semiconductor and forming two Schottky barriers (one along each metal-semiconductor interface). In the three cases, illumination through the semiconductor substrate is assumed. The two thin-film configurations provide enhanced internal quantum efficiencies due to multiple hot carrier reflections within the metal film, with the double-barrier case providing the greatest enhancement due to emission over two barriers. The models proposed are based on assessing the emission probability of hot carriers as a function of their energy, taking into account multiple reflections within the metal film and energy losses due to internal scattering (e.g., with phonons and cold carriers). The thin-film single-barrier model was tested via comparisons with responsivity measurements reported in the literature for PtSi/p-Si and Pd2Si/p-Si detectors.