Hirokimi Shirasaki

Design charts by waveguide model and mode-matching techniques of microstrip line taper shapes for satellite broadcast planar antenna

The optimum shapes in which the reflected wave decreases at a specific frequency for a satellite broadcast reception were considered with the Klopfenstein (1956) and Hecken (1990) tapers. The tapered parts were divided like a flight of stairs. The scattering coefficients of each step were combined by using both the mode-matching and generalized scattering methods. The /spl lambda//4 transformer changes to the Klopfenstein taper shapes, and the exponential taper changes to the Hecken taper shapes, when a longer length is used in the wide passband frequency. By choosing the parameters adequately, it becomes possible to choose the appropriate proportioned necessary bandwidth. This paper shows that practical designs for optimum shapes were obtained using the Klopfenstein and Hecken tapers when the reflected wave decreases at a specific frequency for the satellite broadcast reception.The author discusses the waveguide model followed by the single step and multistep connection. In numerical calculations the impedance shapes of the tapers and the reflection properties are discussed.

Linewidth measurement simulations for semiconductor circuits by scatterometry using FDTD and time shortening calculation method

This paper shows the basic numerical calculation methods for measuring linewidths between 45-80nm using normal and oblique incident lightwaves to control the resist and silicon linewidths for the next-generation semiconductor circuits. The shape measurement method by nondestruction and noncontact, using the light wave scattering method is called Scatterometry. While using the scatterometry with the actual manufacturing process, it is necessary to compare the characteristics in proportion to the trench shape with the measured values in the real-time. In this paper, we use the finite-difference time-domain (FDTD) method as the numerical analysis method. FDTD method takes a lot of time to analyze with the Maxwell equation in the time domain until the electromagnetic fields are stabilized. Then, the examinations on the methods for shortening the FDTD calculation times are carried out by using the periodicity and the sub-grids. By using the periodicity and the incident plane waves, we only calculate the electromagnetic fields in the half pitched region of the grooves. Next, FDTD divides the analytic region into main- and sub-grids. We only allocate the silicon substrates and air parts to the main-cells. The sub-grids are created by dividing in the main-grids in the resist parts, because the resist parts have to be exmained with the minute groove changes. The oblique incidence analysis is important for ellipsometry and many other applications. It is ascertained for silicon that the amplitude reflectance calculated by using FDTD agreed well with Fresnels law for TE and TM modes to the largest angle. Then, the oblique incidence amplitude reflectance for the resist grooves on silicon is calculated. Finally, we confirm the FDTD analysis is effective to obtain the reflected light characteristics close to the real photolithographic models.

Arbitrary 3D linewidth form measurement simulations for the next-generation semiconductor circuits by scatterometry using the FDTD method

This paper shows basic numerical data for measuring the double periodic linewidths in the complicated LSI circuits using lightwaves. The double periodic areas, containing contact holes, memory arrays, and the mazy and arbitrary line structures are hard to analyze by the RCWA (rigorous coupled wave analysis). Therefore we analyze them using the finite-difference time-domain (FDTD) method. The 3D FDTD analysis is explained in this paper. The refleced electromagnetic waves in the near fields are obtained by the vertical plane wave incidences. The far field solutions are calculated using the numerical integration of the near field currents and the magnetic currents. Then, the scatterometry characteristics can be calculated as a far field by superimposing the scattering electromagnetic fields in a periodic reference surface (a square or rectangular region). Finally, we confirm the FDTD analysis is effective to obtain the reflected light characteristics close to the complicated real photolithographic models.

3D isolated and periodic grooves measurement simulations for the semiconductor circuits by scatterometry using the FDTD methods and the time shortening calculation method

First, we establish numerical calculation techniques for the three-dimensional arbitrary cross section measurement equipment production using oblique incident light waves. In the 3D analysis, the enormous calculation times are problematic to analyze arbitrary cross sections using the FDTD (Finite Difference Time Domain) methods. Then, the sub-grids are used for the time shortening analysis. The sub-grid methods are carried out by the adoption to change the cell dimensions in some specific regions. The multilayer thin film parts are necessary to use the small lattice because we had to deal with the small shape changes. Second, the Gaussian beam incidence analysis for non periodic and isolated grooves is examined. The spot beams are needed for the analysis of the 3D isolation grooves. The scattering characteristics are examined using the spot size of 0.2-1.0 microns. Third, the cell size in the FDTD method must be small enough ( SPIE Advanced Lithography AL 51 2006-02-19|2006-02-24 SPIE 31st International Symposium on Advanced Lithography ML06 648736 San Jose, California, United States Metrology, Inspection, and Process Control for Microlithography XX 6152 Posters Session 16

Scatterometry simulator using GPU and evolutionary algorithm

In this paper, we show scatterometry simulation software which has the spectroscopy calculation and optimization algorithm systems. The calculation is sped up by parallel computing using the GPU (Graphics Processor Unit). Here, we use the programming language CUDA (Compute Unified Device Architecture) and CULA (CULApack) for the NVIDIA GPU. We calculate the spectroscopy using the rigorous coupled wave analysis (RCWA) which provides a method for calculating the diffraction of electromagnetic waves by periodic grating. An evolutionary algorithm (EA) and a conjugate gradient (CG) method are used as the technique to automatically search the data which resembles the given spectrum. Then, the results using this simulator are provided.

3D semiconductor grooves measurement simulations (scatterometry) using nonstandard FDTD methods

In this paper, we analyze the nonstandard finite-difference time-domain (NS-FDTD) method for the rectangular prismatic and cylindrical medium mounts that are put on the substrate periodically. FDTD is useful for analyzing the light scattering from arbitrary shape grooves and mounts. Using the NS-FDTD algorithms, we can get the deep null in the dispersion error at the design frequency and the error is nearly sixth power of grid size with a same computational cost. First, the 3D NS-FDTD formulation is obtained from Maxwell equation for the conducting medium. We analyze structures of rectangular prismatic and cylindrical mounts on the substrate. We show the propagation characteristic calculated by NS-FDTD. Next, the standard (S) FDTD and NS-FDTD reflectance convergences are checked for the grid size h (=Δx=Δy=Δz) changes. The reflectance is compared with the RCWA results. For the case that the layer lattice and the substrate were the same silicon and had some extinction coefficient, the NS-FDTD reflectance convergences are better than the S-FDTD convergences. Finally, we calculate the reflectance from the cubic and cylindrical periodic mounts put on the silicon substrate.

Approximate step analysis of linear and raised cosine tapered microstrip lines by using a waveguide model

Based on a waveguide analysis model for discontinuity in microstrip line circuits, the model-matching method and the generalized scattering matrix method were used. The effective dielectric constant and effective width of linear and raised cosine tapers were considered by approximate step analysis, and the return loss was calculated. Our results indicate that the characteristic is much better for a linear taper when the length of taper exceeds a certain value. Shape evaluation was performed with the characteristic defined by a property chart. The return loss of a circuit with the same taper in the input and output was analyzed.

Oblique incidence scatterometry for 2D/3D isolation mounts with RCWA and PML

In this paper, we examine the sensitivity of scatterometry for the 2D and 3D isolation mounts on the substrate by applying the PML in the RCWA method. We analyze the reflectance from the silicon and resist single mount on the silicon substrates by changing the incident beam angles. First, we show the propagation properties of the electromagnetic fields propagating for the isolation mounts on the silicon substrates. Second, we examine the oblique incident reflectances for the TE and TM waves by changing the beam sizes and wavelengths. We show the reflectance properties by changing the mount length, width and height on the Si substrates. Finally, we examine the reflectances calculated by changing the wavelength for the oblique incident beams. Then, we understand that the scatterometry observation is possible for isolation mounts.

3D isolation mounts scatterometry with RCWA and PML

In this paper, we examine the sensitivity of scatterometry for the isolation mounts on the substrate by applying PML in RCWA. We analyze the reflectance from the silicon and resist single mount and the silicon double mounts on the silicon substrate. First, we investigate the mode convergences and the beam width dependences of reflectance. Second, we show the propagation properties of the electromagnetic fields propagating for the isolation mounts on the silicon substrate. Finally, we examine the wavelength properties of reflectance calculated by changing the beam width, the mount width and the mount height for single mount and the silicon mount positions for the double silicon mounts. Then, we understand that the scatterometry observation is possible in several decade microns beam width.

Scatterometry simulator development with GPU, real-coded GA and RCWA

In this paper, we show the 2D and 3D scatterometry simulation software which has spectroscopy calculation and optimization algorithm systems. The scatterometry analysis for 3D-structure requires a lot of memory and along calculation time. The calculation is sped up by parallel computing using the GPU (Graphics Processor Unit). Here, we use the programming language CUDA (Compute Unified Device Architecture) and CULA (CULApack) for the NVIDIA GPU. Then, we use the real-coded GA (RCGA) to increase the population, to make a more sensitive solution and to get better fitting groove figures. The scatterometry characteristic is examined by choosing the n-th power cosine type period groove.