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Applied physics letters 120, 104102 (2022). doi:10.1063/5.0078927, Electron photoinjectors provide high-brightness electron beams to numerous research applications in physics, chemistry, material, and life sciences. Semiconductor photocathodes are widely used here, as they enable the production of low-emittance beams with variable charge at high repetition rates. One of the key figures of merit of photocathodes is the minimum achievable bunch length. In semiconductor cathodes, this is dominated by scattering effects and varying penetration depths of the extracting photons, which leads to a characteristic electron emission function. We present a method to determine this cathode time response with resolution on the tens of femtoseconds level, breaking the resolution barrier encountered in previous studies. The method is demonstrated with cesium-telluride (Cs$_2$Te) and gold cathodes, revealing response times of (184 �� 41) fs up to (253 �� 58) fs for the semiconductor and an upper limit of (93 �� 17) fs for the metal. Monte Carlo simulations of Cs$_2$Te emission benchmarked to these results give detailed information about the cathode material., Published by American Inst. of Physics, Melville, NY