Abstract:
Based on the energy approach, the energy change in generating a misfit dislocation is analyzed and a closed formula to determine the critical thickness is derived from the dislocation-elasticity study. It is easier to form a misfit dislocation at the interface between the epilayer and the substrate if the substrate is softer than the epilayer, and consequently the critical thickness is smaller. The dislocation-dislocation interaction yields work hardening when generating a fresh dislocation as pre-existing dislocations being in the interface. The harder the epilayer than the substrate, the higher the work hardening occurs. Grading composition of the epilayer changes the mismatch stress field and makes dislocation emission more difficulty. As a result, the aspect ratio of threading dislocation density to mismatch dislocation density is lower in a compositionally-graded epilayer than that in a compositionally-uniform epilayer.
Based on the dislocation mechanism of twinning, an analytical solution is given to determine the critical thickness of misfit twinning. For a given epilayer thickness and lattice mismatch strain, the twin formation energy should reach its minimum to determine the twin width and a minimum formation energy of zero determines the critical thickness for misfit twinning. A misfit-twin-and-perfect-dislocation predominance chart is constructed to predict the predominant regions of misfit twinning and perfect misfit dislocation in the domain of mismatch strain versus specific twin boundary energy.
Explicit formulas for period arrays of misfit twins with the same orientation and with alternating orientations are derived by superposition of the solutions for a single misfit twin. The equilibrium morphology for a periodic array of misfit twins is characterized by the twin width and spacing. The effects of elastic mismatches between the epilayer and the substrate on the equilibrium morphology of twins are also studied comprehensively. The theoretical predictions agree with experimental observations.
* This work was fully supported by a Central Allocation Research Grant, HKUST15/CRF/08 and PolyU7/CRF/08, from the Research Grants Council of the Hong Kong Special Administrative Region, China.
Chair Professor Tong-Yi Zhang, PhD
Education:
1985, PhD [University of Science and Technology Beijing, China (USTB)]
1982, Master (USTB)
Academic positions:
2008-present, Chair Professor, 2002-2008, Professor, 1995-2001, Associate Professor, 1993-1995, Lecturer (Hong Kong University of Science and Technology); 1990-1993, Associate Research Scientist (Yale University, USA); 1988-1990, Postdoctoral Fellow (University of Rochester, USA); 1986-1988, Research Fellow of the Alexander von Humboldt Foundation (Universität Göttingen, Germany); 1985-1986, Lecturer (USTB)
Research areas:
Mechanical properties of materials, Micro/nanomechanics, Surface stress of solids, Fracture of piezoelectric materials, Thin films, Microbridge tests
Honours:
2011, Academician of the Chinese Academy of Sciences
2010, Visiting Professor at Kyoto University supported by the Fellowship Award (Short-Term), Japan Society for the Promotion of Science (JSPS), Japan
2009, Plenary Lecture “Fracture of Piezoelectric Ceramics” at the 12th International Congress on Fracture, Ottawa, Canada
2007, Second Prize of 2007 State Natural Science Award, China
2003, Croucher Senior Research Fellowship Award, Hong Kong
2001, Fellow Award from ASM International, USA
1988, National Award for Young Scientists, China
1987, Second Prize of 1987 State Natural Science Award, China |
