We report on the growth of GaN with a zinc‐blende, wurtzite, or a mixed phase structure on (001)GaP and (001)GaAs substrates by a low‐temperature modified molecular beam epitaxy technique. By systematically varying the incident arsenic overpressure, films grown at a moderate substrate temperature of ≊620 °C show predominately wurtzite &agr;‐GaN, zinc‐blende &bgr;‐GaN, or a mixed phase of the two. Films containing only the metastable phase &bgr;‐GaN were achieved by using a relatively high growth temperature of ≊700 °C and with an arsenic overpressure of ≊2.4×10−5Torr. X‐ray diffraction measurements indicate an improved crystalline quality for the layers grown at ≊700 °C compared to those grown at ≊620 °C as evident by a narrower full width at half‐maximum of 35 min for &bgr;‐GaN, which is among the narrowest reported to date. ©1995 American Institute of Physics.