We present the relationship between surface roughness and dark current measured for avalanche photodiodes with InGaAs absorbers and thin InAlAs multiplication layers fabricated from material grown lattice-matched to InP by molecular beam epitaxy. In particular, the leakage current at unity gain measured for sets of 125 mum diameter devices was found to have an exponential dependence upon the peak-to-peak surface roughness of the material, and was characterized by an order of magnitude increase for every 15 nm of roughness. We also present the results of an atomic force microscope study of surface morphology and growth conditions, interpreting the results in the context of diffusional versus convective growth modes. The best material was obtained at a substrate temperature of 500degreesC and an arsenic beam pressure of 8 x 10(-6) Torr; the smooth growth window was bounded on the high-arsenic/low-temperature side by roughness resulting from low adatom surface mobility, and on the low-arsenic/high-temperature side by nonstoichiometric arsenic deficient growth. (C) 2004 Elsevier B.V. All rights reserved.