A novel method to solve the thermal mismatch problems in a heteroepi-taxial structure is presented, in which an amorphous film deposited on a single crystalline substrate is crystallized in solid phase by annealing under ultra high pressure and both temperature and pressure are decreased proportionally. Under a specific relation between the temperature and pressure, it is expected that the effective thermal expansion coefficients, the expansion coefficients modified by elastic strain, of the film and substrate are equal and that neither defects nor strain is generated in the film during the cooling process. Theoretical consideration and experimental results for Ge films on Si(100) substrates are presented.