We report on the surprisingly strong, broadband emission of coherent terahertz pulses from ultrathin layers of semiconductors such as amorphous silicon, germanium and polycrystalline cuprous oxide deposited on gold, upon illumination with femtosecond laser pulses. The strength of the emission is surprising because the materials are considered to be bad (amorphous silicon and polycrystalline cuprous oxide) or fair (amorphous germanium) terahertz emitters at best. We show that the strength of the emission is partly explained by cavity-enhanced optical absorption. This forces most of the light to be absorbed in the depletion region of the semiconductor/metal interface where terahertz generation occurs. For an excitation wavelength of 800 nm, the strongest terahertz emission is found for a 25 nm thick layer of amorphous germanium, a 40 nm thick layer of amorphous silicon and a 420 nm thick layer of cuprous oxide, all on gold. The emission from cuprous oxide is similar in strength to that obtained with optical rectification from a 300 μm thick gallium phosphide crystal. As an application of our findings we demonstrate how such thin films can be used to turn standard optical components, such as paraboloidal mirrors, into self-focusing terahertz emitters.