Lattice Dynamics Study On Thermal Properties Of Crystal Film In MEMS

Because of the size and surface effects, the thermal properties of MEMS components are different from those of the corresponding bulk crystals. The study on thermal properties of MEMS components is very important for designing MEMS correctly and applying it reliably. Nowadays, the usual approach to study the thermal properties of MEMS components on atomic or molecular level is molecular dynamics(MD) simulation. Because of the limitations in size scale and computation time, MD can hardly be used to simulate the components that contain more than 105 atoms within limited time except with high performance computer. A new approach to simulate all the thermal properties of MEMS components based on lattice dynamics is put forward in this dissertation, and is applied to study the thermal properties of silicon films and argon films. This approach enable us to simulate the thermal properties including specific heat capacity, melting temperature, thermal expansion coefficient and thermal conductivity of film containing more than 105 atoms easily with ordinary microcomputer. The followings are main research contents and corresponding results.1. Lattice dynamics of crystal filmsThe lattice dynamics matrixes and lattice dynamics equations of crystal films are derived in the hybrid representation which includes the wave representation in the in-plane direction and the lattice representation in the cross-plane direction simultaneously, and then the formulas for atomic displacements, moments, Hamiltonians and phonon Green's functions of harmonic crystal films in phonon's number representation are derived with the eigenvalues and eigenvectors of the lattice dynamics equations. The formulars for the anharmonic potentials of the crystal films are derived with the formula for atomic displacements, and then the formulas for Green's function and linewidth of phonon in the anharmonic crystal films are obtained with the anharmonic potentials treated as perturbations. The numerical calculation results show that there are no propagation waves but only standing waves with no ideal sine waveform in the cross-plane direction, the phonon energy bands of crystal films split into a series of sub-bands, and the mean phonon linewidth of crystal film increases but the mean phonon lifetime decreases with decreasing film thickness.2. Melting proerties of crystal filmsThe formulas for atomic mean square displacements (MSD) in crystal films are derived with the lattice dynamics of crystal film and the fluctuation-dissipation theorem, and then numerical calculations are carried out. With these results and Lindemann melting criterion, the melting properties of crystal film are analyzed, and the relationships between melting points and thicknesses of films are obtained. The results show that the MSDs of surface atoms are bigger than those of inner atoms in crystal films, and the thinner film has larger MSDs. Therefore film starts melting from surface, the thinner film has a lower melting temperature and is easier to melt.3. Specific heat capacities of crystal filmsThe formulas for specific heat capacities of crystal films are derived with lattice dynamics of crystal film. The numerical calculation results show that thinner film has a larger specific heat capacity; and the specific heat capacity of film decreases and approaches to that of corresponding bulk crystal when its thickness increases.4. Thermal expansion properties of crystal filmsThe formulas for thermal expansions and thermal expansion coefficients of crystal films are derived on the basis of the lattice dynamics of crystal film, the stationary perturbation theory and the quantum statistics. The numerical calculation results show that the thermal expansion coefficients of Ar films and Si films in the in-plane direction are larger than those in the cross-plane direction respectively; the thinner Ar film has a larger thermal expansion coefficient in the in-plane direction and has a smaller one in the cross-plane direction; the thinner Si film has larger thermal expansion coefficients in the in-plane direction and in the cross-plane direction; the thermal expansion coefficients of film in the in-plane direction and in the cross-plane direction approach the thermal expansion coefficient of corresponding bulk crystal when its thickness increases.5. Thermal conductivity properties of crystal filmsThe formulas for energy fluxes of Argon film and Silicon film are derived with the help of the lattice dynamics of crystal film and Hardy formula for energy flux, then the formulas for thermal conductivities of crystal films are derived with the aid of the Kubo formula. The numerical calculation results show that the thermal conductivities of films in the in-plane direction are larger than those in the cross-plane direction; the thinner film has smaller thermal conductivities in the in-plane direction and cross-plane direction than thicker film; the thermal conductivities of film in the in-plane direction and cross-plane direction approach the thermal conductivity of corresponding bulk crystal when its thickness increases.