Thomas V. Pistor

Laser intensification by spherical inclusions embedded within multilayer coatings

The initiation of laser damage within optical coatings can be better understood by electric-field modeling of coating defects. The result of this modeling shows that light intensification as large as 24x can occur owing to these coating defects. Light intensification tends to increase with inclusion diameter. Defects irradiated over a range of incident angles from 0 to 60 deg tend to have a higher light intensification at a 45 deg incidence. Irradiation wavelength has a significant effect on light intensification within the defect and the multilayer. Finally, shallow, or in the case of 45 deg irradiation, deeply embedded inclusions tend to have the highest light intensification.

Light intensification modeling of coating inclusions irradiated at 351 and 1053 nm

Electric-field modeling provides insight into the laser damage resistance potential of nodular defects. The laser-induced damage threshold for high-reflector coatings is 13x lower at the third harmonic (351 nm) than at the first harmonic (1053 nm) wavelength. Linear and multiphoton absorption increases with decreasing wavelength, leading to a lower-third harmonic laser resistance. Electric-field effects can also be a contributing mechanism to the lower laser resistance with decreasing wavelength. For suitably large inclusions, the nodule behaves as a microlens. The diffraction-limited spot size decreases with wavelength, resulting in an increase in intensity. Comparison of electric-field finite-element simulations illustrates a 3x to 16x greater light intensification at the shorter wavelength.

Searching for optimal mitigation geometries for laser-resistant multilayer high-reflector coatings

Growing laser damage sites on multilayer high-reflector coatings can limit mirror performance. One of the strategies to improve laser damage resistance is to replace the growing damage sites with predesigned benign mitigation structures. By mitigating the weakest site on the optic, the large-aperture mirror will have a laser resistance comparable to the intrinsic value of the multilayer coating. To determine the optimal mitigation geometry, the finite-difference time-domain method was used to quantify the electric-field intensification within the multilayer, at the presence of different conical pits. We find that the field intensification induced by the mitigation pit is strongly dependent on the polarization and the angle of incidence (AOI) of the incoming wave. Therefore, the optimal mitigation conical pit geometry is application specific. Furthermore, our simulation also illustrates an alternative means to achieve an optimal mitigation structure by matching the cone angle of the structure with the AOI of the incoming wave, except for the p-polarized wave at a range of incident angles between 30° and 45°.

Electric-field enhancement by nodular defects in multilayer coatings irradiated at normal and 45° incidence

The standing-wave electric-field profile within multilayer coatings is significantly perturbated by a nodular defect. The intensity, which is proportional to the electric field squared, is increased in the high index material by ≥3x at normal incidence and ≥12x at 45 degrees incidence angle. Therefore is it not surprising that nodular defects are initiation sites of laser-induced damage. In this study, the impact of reflectance-band centering and incident angle are explored for a 1 μm diameter nodular defect seed overcoated with a 24 layer high-reflector constructed of quarter-wave thick alternating layers of hafnia and silica. The modeling was performed using a three-dimensional finite-element analysis code.

Rigorous simulation of mask corner effects in extreme ultraviolet lithography

A windowing and multilayer acceleration methodology for rigorous electromagnetic analysis of extreme ultraviolet masks in three dimension is introduced and used to explore strong feature asymmetries associated with off-axis illumination. Specifically synthesizing large features from smaller simulation domains and replacement of the multilayer substrate by upward radiating equivalent sources are used and allow mask corner effects to be analyzed in about 10 h on a 200 MHz workstation. Windowing synthesizes the fields for a large mask feature from simulation of smaller domains such as corners. With off-axis illumination at angles of even a few degrees, hot spots in the near field occur at edges of the mask which face the illumination. This effect is associated with diffraction of the upward reflected light and its propagation in the presence of the side wall of the mask edge profile.

Rigorous electromagnetic simulation applied to alignment systems

Rigorous electromagnetic simulation with TEMPEST is used to provide benchmark data and understanding of key parameters in the design of topographical features of alignment marks. Periodic large silicon trenches are analyzed as a function of wavelength (530-800 nm), duty cycle, depth, slope and angle of incidence. The signals are well behaved except when the trench width becomes about 1 micrometers or smaller. Segmentation of the trenches to form 3D marks shows that a segmentation period of 2-5 wavelengths makes the diffraction in the (1,1) direction about 1/3 to 1/2 of that in the main first order (1,0). Transmission alignment marks nanoimprint lithography using the difference between the +1 and -1 reflected orders showed a sensitivity of the difference signal to misalignment of 0.7%/nm for rigorous simulation and 0.5%/nm for simple ray-tracing. The sensitivity to a slanted substrate indentation was 10 nm off-set per degree of tilt from horizontal.

Modeling of light intensification by conical pits within multilayer high reflector coatings

Removal of laser-induced damage sites provides a possible mitigation pathway to improve damage resistance of coated multilayer dielectric mirrors. In an effort to determine the optimal mitigation geometry which will not generate secondary damage precursors, the electric field distribution within the coating layers for a variety of mitigation shapes under different irradiation angles has been estimated using the finite difference time domain (FDTD) method. The coating consists of twenty-four alternating layers of hafnia and silica with a quarter-wave reflector design. A conical geometrical shape with different cone angles is investigated in the present study. Beam incident angles range from 0° to 60° at 5° increments. We find that light intensification (square of electric field, |E|2) within the multilayers depends strongly on the beam incident direction and the cone angle. By comparing the field intensification for each cone angle under all angles of incidence, we find that a 30° conical pit generates the least field intensification within the multilayer film. Our results suggest that conical pits with shallow cone angles (≤ 30°) can be used as potential optimal mitigation structures.

Effects of shifter edge topography on through focus performance

We have investigated the effects of the topography of the phase-shifting mask on the aerial image characteristics in DUV lithography. The calculation of near fields is carried out through simulation of the mask with TEMPEST and linking the resultant near fields to EM-Aerial for imaging. It is shown that the Fourier spectrum for an alternating phase-shifting mask can be decomposed into Fourier spectra for single openings. The amplitude and phase of the diffraction orders for the single opening are utilized for the systematic analysis of the shifter edge topography. The analysis framework developed in this paper clearly identifies the effects of the wall of the phase shifter, the residual transmittance through the chromium area, and the cross-talk between adjacent features. This analysis framework also allows these effects be merged in design. The near field profile in the vicinity of the shifter wall is also investigated for different feature sizes, and the optimum design for different feature sizes is discussed. The effect of the wall angle profile is shown to be acceptable.

Rigorous electromagnetic simulation of stepper alignment

A model for ASMLs ATHENA alignment system based on electromagnetic simulation of scattering from the alignment mark structure is presented. The seven lowest scattered order pairs are calculated for various mark topographies. The scattered order pairs are analyzed to determine both the signal strengths and alignment errors. Both a rigorous and a scalar model for calculating scattered orders are presented and compared. The models are then used to investigate the importance of topographical variations such resist thickness and surface shape, and mark asymmetry caused by CMP. The clipping of one side of the chop marks was seen to introduced alignment error of equal magnitude in all several order pairs. Resists variations were also found to be very important affecting both signal strength and alignment accuracy. Simulation is found to be a useful tool in understanding stepper alignment engineer develop strategies for improving alignment.

Analysis of sub-wavelength sized OPC features

Abstract Rigorous 3-D electromagnetic analysis is used to examine the actual near field characteristics and assess the resulting effects on imaging of light passing through serifs and hammer head line-ends in optical proximity correction (OPC) of photomasks. The simulation is carried out using the finite-difference time-domain simulator TEMPEST using up to 5 million nodes and 150M of memory. OPC features which are contiguous and share sides with open features transmit very effectively, whereas OPC features which are isolated by chrome stringers or are cut-off by nearly touching chrome corners are much less effective and require rigorous electromagnetic analysis.