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.
In this paper, we examine the sensitivity of scatterometry for the 3D 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 beam width dependences of reflectance. Second, we show the propagation properties of the electromagnetic fields propagating for the isolation mounts on the silicon substrate. Third, we show the reflectance properties by changing the mount length and width on the Si substrate. Finally, we examine the wavelength properties of reflectance calculated by changing the mount length, width and height for single mount and the silicon mount positions for the double silicon mounts. Then, we understand the scatterometry observation is possible in several microns beam width.
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.
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.
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.
In this paper, we show Scatterometry simulation software which has the spectroscopy calculation and optimization
algorithm systems. We analyze the spectral Scatterometry using the wavelength range of 400nm to around 800nm. The
calculation is sped up by parallel computing using a multicore CPU. Threading Building Blocks (TBB) techniques are
used in the parallel computing. 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. A conjugate
gradient (CG) method is used to automatically search the data which resembles the given spectrum. In this simulation, we can check the sensitivity for profile measurements. And we provide the results using this simulator.
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.
In this paper, we analyze the finite-difference time-domain (FDTD) method for the anisotropic medium mounts that are
put on the silicon substrate periodically. FDTD is useful for analyzing the light scattering from arbitrary shape
anisotropic grooves and mounts. We consider anisotropic conductive films which have a uniaxial anisotropy, a biaxial
anisotropy and off-diagonal dielectric constants tensor components. First, the FDTD formulation is obtained from
Maxwell equation for the anisotropic medium. Next, we show light propagation aspects and reflection coefficients in the
structure of anisotropic flat layer put on the silicon substrate. The electric field polarized in the y direction is
perpendicularly emitted to the x-y plane. In this case, only the Ey scattered components appear in the isotropic
medium, the uniaxial anisotropy and the biaxial anisotropy. However, we show that the Ex components also slightly
appear in the off-diagonal anisotropic case, since there are off-diagonal dielectric components. The reflection
coefficients are compared with the RCWA results calculated by approximating that the refractive indices are isotropy.
Then, we confirmed that the anisotropy calculation is right. Finally, we calculated the reflection coefficients from the
anisotropic periodic mounts put on the silicon substrate.
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 (
This paper shows the basic numerical calculation methods for measuring line widths and shapes between 45-80nm using normal and oblique incident light waves to control the resist and silicon line widths for the next-generation semiconductor circuits. The shape measurement method by no destruction and no contact, using the light wave scattering method is called "Scatterometry". While using 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 calculate the scattering characteristic from the resist trenches that are put on the silicon substrate. Arbitrary shape groove regions are divided into multilayers using step approximations. The electromagnetic field in each layer can be expanded into eigenmodes of Maxwell's equations. Then, the scattering matrices are obtained. Here, we use the generalized scattering matrix method for the multi-step connection and propose the time shortening method for seeking the groove shapes. Next, the 3D rectangular and arbitrary shape grooves analysis is carried out by considering the oblique incidence using RCWA and FDTD, respectively.
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.
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 Fresnel's 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.
This paper obtains basic numerical data fro measuring linewidths using light waves to contorl the sub-100nm resist and silicon linewidth. We use the finite-difference time-domain (FDTD) method as the numerical analysis method, becuase the method can consider the losses of permittivity of the resist and the silicon substrate. The linewidths are 2D on the assumption that they are uniformed in the same direction and the 2D Gaussian beams are irradiated. The TM modes with only electric fields and the TE modes with magnetic field polarized parallel to the trench are irradiated. Then, we examine the differences of complex amplitude reflectance by changing the groove widths and thickness of the resist and silicon. Since the TM modes have the cutoff property and the TE modes do not, the amplitude and the phase changes of TM modes are different from the TE modes. Especially, the phases change in linear and in proportion to the groove widths and depths. The amplitude relfectance characteristics of the reflected waves are also examined in changing the incidence angles and the wavelengths of the Gaussian beam. Finally, we confrim teh FDTD analysis is effective to obtain the reflected light characteristics close to the real photolithographic models.
The scattering properties made by the irradiated two dimensional plane wave beams in the square trench are analyzed by the boundary element method (BEM) and the finite-difference time-domain (FDTD) method. We calculate the scattering patterns by using the wavelength dispersion because the silicon substrate is thought to be a dispersive and the dielectric has energy loss in the visible light range. Then, we investigate the scattering patterns by changing the depth and the width of the trench, the trench array number, and the polarization and the angles of incidence of the 2D beams. The patterns change well when the channel width is under the examined cutoff wavelength of light. Also, the radiation beam phases change well using the groove width from the range of 0.07 to 0.2 micron meters. Then, the trench depth was examined by the continuous wavelet analysis with the interference spectrum data. In the wavelet analysis, the horizontal axis (the x axis) shows the frequency and the vertical axis (the y axis) is converted into scales (1/times) and the signal strength is shown in the z axis. The vertical axis scales correspond to the reciprocal of time and it is possible to obtain the depth by multiplying time and light velocity continuously in the wavelet analysis. So the tapered trenches are analyzed using the wavelet analysis.
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