Numerical methods for simulating radiation, propagation, and scattering of waves in microscopic structures such as film bulk acoustic resonator (FBAR), surface acoustic wave (SAW) devices, open resonators, and a photoresist in lithography are developed and various second-order effects which degrade the performance of the devices are investigated. The methods are based on the finite element method (FEM) and the concept of the artificial absorber to gain generality and accuracy. Application of the piezoelectric FEM to FBAR shows that the quality of the resonator is very sensitive to the surface conditions such as surface parallelism. The validity of the method is also checked by comparing the results with those made by the Mason equivalent circuit model. In SAW filters,bulk acoustic waves reflected at the bottom side degrades the stop band rejection performance and the electrostatic coupling between transmitting and receiving transducers overrides the acoustic coupling when the grounds of both transducers are connected. These imply that the packaging process where the acoustic absorber and metal shield are attached to the device is important. The substructure technique is developed to deal with real devices which is very large relative to the wavelength scale and it is applied to compute the frequency characteristics of a SAW filter with 40 electrode finger pairs.
In simulation of the light scattering in a photoresist on stepped substrates,the proposed method that employs the perfectly matched layer (PML) absorbing boundary condition does not depend on a specific configuration of imaging system. The validity of the method is examined by comparing the results with those made by the vertical propagation model or previous two-dimensional models. When the method is applied to the eigenmode analysis problem, accurate value of resonant frequency and quality factor of open resonators are obtained. The results of numerical error analysis for a Fabry-Perot resonator suggest that the PML thickness of λ_0 /2 (λ_0 is the wavelength of the eigenmode) and nodal density of 24 with quadratic elements are optimal for the efficient computation.
