An epitaxial reactor enabling simultaneous deposition of thin films on a multiplicity of wafers is disclosed. During deposition, a number of wafers are contained within a wafer sleeve comprising a number of wafer carrier plates spaced closely apart to minimize the process volume. Process gases flow preferentially into the interior volume of the wafer sleeve, which is heated by one or more lamp modules. Purge gases flow outside the wafer sleeve within a reactor chamber to minimize wall deposition. In addition, sequencing of the illumination of the individual lamps in the lamp module may further improve the linearity of variation in deposition rates within the wafer sleeve. To improve uniformity, the direction of process gas flow may be varied in a cross-flow configuration. Combining lamp sequencing with cross-flow processing in a multiple reactor system enables high throughput deposition with good film uniformities and efficient use of process gases.