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In state of the art photoemission electron sources, the transverse emittance of the electron beam is approaching its intrinsic value from the cathode. To reduce the intrinsic emittance, it is straightforward to tune the photon energy of the drive laser toward the photocathode emission threshold. This paper aims at constructing an improved model which takes into account an intermediate energy level to better explain the near threshold photoemission for semiconductors. A dynamic model is alsodoi:10.1103/physrevaccelbeams.22.123403 fatcat:fvzkoakkova6fa2motrajxpvmy