We investigate the morphology of epitaxial Si layers grown on clean and on hydrogen terminated Si(0 0 1) to explore the growth strategy for the fabrication of a Si-based quantum computer. We use molecular beam epitaxy to deposit 5 monolayers of silicon at a temperature of 250 degreesC and scanning tunnelling microscopy to image the surface at room temperature after growth and after various rapid annealing steps in the temperature range of 350-600 degreesC. The epitaxial layer grown on the hydrogenated surface shows a significantly higher surface roughness due to a lower mobility of silicon surface atoms in the presence of hydrogen. Annealing at temperatures greater than or equal to550 degreesC reduces the roughness of both epitaxial layers to the value of a clean silicon surface. However, the missing dimer defect density of the epitaxial layer grown on the hydrogenated surface remains higher by a factor of two compared to the layer grown on clean Si(0 0 1). Our results suggest a quantum computer growth strategy in which the hydrogen resist layer is desorbed before the epitaxial silicon layer is grown at low temperature to encapsulate phosphorus quantum bits. (C) 2003 Elsevier Science B.V. All rights reserved.