Rigorous Diffraction Model Research Articles

Agarose-Gel Based Guided-Mode Resonance Humidity Sensor

A photonic relative-humidity (RH) sensor employing the guided-mode resonance effect is designed, fabricated, and characterized. An agarose-gel transduction layer is integrated with a periodic silicon-nitride film to form a sensitive optical resonance structure. As the agarose-gel humidifies, the resonance wavelength shifts. Comparison with rigorous diffraction models allows quantification of the gel's refractive index and the attendant relative humidity. For the example sensor structure treated, the resonance wavelength shifts by ~9 nm on relative-humidity change from 20% RH to 80% RH

On the phase of plasmons excited by slits in a metal film

The excitation of surface plasmons by subwavelength slits in metal films is studied using a rigorous diffraction model. It is shown that the plasmon is launched by a slit in antiphase with the incident magnetic field. This is true independent of slit width and of the metal used. Using this phase information, maxima and minima in transmission are explained in the case of two and more slits.

Diameter estimation of cylinders by the rigorous diffraction model

The Fraunhofer diffraction formula is commonly used for estimating the diameter of thin cylinders by far field diffractometry. However, an experimental systematic overestimation of the value of the cylinder diameter by this diffraction model and other three-dimensional models has been reported when this estimation is compared with those obtained from interferometric techniques. In this work, a rigorous electromagnetic diffraction model is analyzed to determine the cylinder diameter by using the envelope minima of the far field diffraction pattern. The results of this rigorous model are compared with those from the Fraunhofer diffraction formula. The overestimation by the Fraunhofer model is predicted theoretically, presenting a dependence on the wavelength, the polarization state of the incident wave, and the cylinder diameter. The discrepancies are shown to be due to the three-dimensional geometry.

Resist footing variation and compensation over nonplanar wafer

We report a problem regarding DUV lithography on topographical substrates and a solution for obtaining desired CD control and resist pattern shape. In our experiment, large footings for a 250-nm resist pattern are observed when the resist pattern is transferred over a polysilicon step pattern of 175 nm in height. This pattern error is not negligible regarding device performance. The exposure tool used is a KrF scanner of NA 0.6. The resist is 500 nm thick with no antireflective coating (ARC). Computer simulation is used to demonstrate the amount of the footing. A nonrigorous diffraction model did not recreate the footing appearance at the poly-Si step. However, a rigorous diffraction model of incident light in a cone recreated the footing amount at the poly-Si step faithfully. In this simulation, optical distribution in the resist over the nonplanar wafer is solved by the finite-difference time-domain (FDTD) method. Optical intensity at the sidewalls of the step differs between the two models. Experimental results as well as simulation results show that larger coherency results in larger footing. In the case of a large coherency, the illumination rays come from various directions to the wafer, and a large shadow area is likely to appear behind the steep step. We also propose a shadow model for simple footing simulation. As a consequence, optical behavior in the vicinity at the steep step has a strong impact on the resist footing.

Efficient optimization of diffractive optical elements based on rigorous diffraction models.

An efficient optimization strategy for the design of diffractive optical elements that is based on rigorous diffraction theory is described. The optimization algorithm combines diffraction models of different degrees of accuracy and computational complexity. A fast design algorithm for diffractive optical elements is used to yield estimates of the optimum surface profile based on paraxial diffraction theory. These estimates are subsequently evaluated with a rigorous diffraction model. This scheme allows one to minimize the need to compute diffraction effects rigorously, while providing accurate design. We discuss potential applications of this scheme as well as details of an implementation based on a modified Gerchberg-Saxton algorithm and the finite-difference time-domain method. Illustrative examples are provided in which we use the algorithm to design Fourier array illuminators.