The method of the invention involves depositing a plurality of thin layers of film, each layer having a thickness ranging from about 500Å to about 2000Å. Low Pressure Chemical Vapor Deposition or other techniques known in the art maybe used to deposit each thin layer of film. The film is polysilicon or silicon-germanium, where the germanium content ranges from about 4% by weight to about 20% by weight germanium. A Rapid Thermal Anneal (“RTA”) is performed on a deposited thin film layer to relieve residual film stress in at least that film layer. The use of RTA rather than furnace annealing permits much shorter annealing times. Optionally, but advantageously, hydrogen may be present during RTA to permit the use of lower processing temperatures, typically about 20% lower relative to a customary anneal. A series of film deposition/rapid thermal anneal cycles is used to produce the desired, nominal total thickness polysilicon film. This method is generally useful for producing polysilicon films in the range of from about 2 microns to about 20 microns.