Strain Relaxation in Heteroepitaxial Ge/Si Structures by Annealing Under Ultra High Pressure
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STRAIN RELAXATION IN HETEROEPITAXIAL Ge/SI STRUCTURES BY ANNEALING UNDER ULTRA HIGH PRESSURE HIROSHI ISHIWARA*, TAKAYOSHI SATO*, AND AKIRA SAWAOKA** *Precision and Intelligence Laboratory, Tokyo Institute of Technology. 4259 Nagatsuda, Midoriku, Yokohama 227 Japan "**Laboratory for Engineering Materials, Tokyo Institute of Technology ABSTRACT A novel method to solve the thermal mismatch problems In a heteroepitaxial 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(lO0) substrates are presented. INTRODUCTION Heteroepitaxial growth of dissimilar materials is considered to be a useful method to fabricate novel electronic and optical devices. Therefore, various studies to grow semiconductor heterostructures have been reported In recent years. In these structures, however, crystalline quality of the films is not necessarily good because of the lattice and thermal mismatch between the films and substrates, and the defects often prevent practical uses of the heterostructure devices. A typical example is laser diodes fabricated in GaAs-on-Si structures, whose lifetime is as short as several hours due to dislocations generated In the GaAs films by the thermal mismatch between Si and GaAs. In this paper, we propose a novel method to solve the thermal mismatch problem, in which amorphous films deposited on single crystalline substrates are grown by solid phase epitaxy under UHP. Annealing under UHP is considered to also be effective to improve crystalline quality of heteroepitaxial films which have been grown by MBE (molecular beam epitaxy) or CVD (chemical vapor deposition). THEORETICAL CONSIDERATION It is generally known that a soft material has a relatively large thermal expansion coefficient a . Therefore, it is expected in a heteroepitaxial structure that the difference of the thermal expansion coefficient between the film and substrate can be compensated by that of elastic strain e which is produced by hydrostatic pressure applying to the sample. That is, if the effective thermal expansion coefficient a ', which is defined by a - e /6 T, is the same between the film and substrate, the thermal mismatch problem will be solved, where 5 T is the temperature difference. Under hydrostatic pressure, the relation between e and the pressure p Is given by Eq.(1) In a cubic crystal 1 ). Thus, a ' is expressed by Eq.(2). e= p/(c 1 1 +2c 1 2 ) (1) a
= a
- p/(cll +2c 1 2 )6 T
(2)
where, cij is the elastic stiffness constant. Under an assumption that the temperature dependences of
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