We report on the growth and doping of InAs by atomic layer epitaxy (ALE). The InAs layers were grown using ALE cycles in a metal organic chemical vapor deposition reactor, and Si doping of the films was studied for different SiH4 flow sequences. When SiH4 was added to trimethylindium during the group-III step, the silicon concentration in the film was above 5 × 1019 cm-3. When SiH4 was added to tertiarybutylarsine during the group-V step, much lower incorporation of Si was observed. Conformal Si doped InAs layers were selectively grown by ALE on In0.47Ga0.53As patterned layers made on silicon substrates, demonstrating the suitability of the growth method for III-V device technology on silicon.