We present a simple technique which uses a random phase object for single-shot characterization of an optical system's phase transfer function. Existing methods for aberration measurement typically involve holography, requiring complicated wavefront sensing optics or through-focus measurements with known test objects (e.g. pinholes, fluorescent beads) for pupil recovery from the measured wavefront. Here, it is demonstrated that a weak diffuser can be used to recover the pupil of an imaging system in a single measurement, without exact knowledge of the diffuser's surface. Due to its stochastic nature, the diffuser scatters light to a wide range of spatial frequencies, thus probing the entire pupil plane. A linear theory based on the weak object approximations predicts the spectrum of the measured speckle intensity to depend directly on the pupil function. Numerical simulations of diffusers with varying strength confirm the validity of the theory and indicate sufficient conditions under which diffusers act as weak phase objects. Using index matching oils to modulate diffuser strength, experiments are shown to successfully recover aberrations from an optical system using coherent illumination. Additionally, this technique is applied to the recovery of defocus in images of a weak phase object obtained through a commercial microscope under partially coherent illumination.
Mask topography contributes to phase at the wafer plane, even for OMOG binary masks currently in use at
the 22nm node in deep UV (193nm) lithography. Here, numerical experiments with rigorous FDTD simulation
are used to study the impact of mask 3D effects on aerial imaging, by varying the height of the absorber stack
and its sidewall angle. Using a thin mask boundary layer model to fit to rigorous simulations it is seen that
increasing the absorber thickness, and hence the phase through the middle of a feature (bulk phase) monotonically
changes the wafer-plane phase. Absorber height also influences best focus, revealed by an up/down shift in the
Bossung plot (linewidth vs. defocus). Bossung plot tilt, however, responsible for process window variability
at the wafer, is insensitive to changes in the absorber height (and hence also the bulk phase). It is seen to
depend instead on EM edge diffraction from the thick mask edge (edge phase), but stays constant for variations
in mask thickness within a 10% range. Both bulk phase and edge phase are also independent of sidewall angle
fluctuation, which is seen to linearly affect the CD at the wafer, but does not alter wafer phase or the defocus
process window. Notably, as mask topography varies, the effect of edge phase can be replicated by a thin mask
model with 8nm wide boundary layers, irrespective of absorber height or sidewall angle. The conclusions are
validated with measurements on phase shifting masks having different topographic parameters, confirming the
strong dependence of phase variations at the wafer on bulk phase of the mask absorber.
Mask topography contributes diffraction-induced phase near edges, affecting the through-focus intensity variation and hence the process window at the wafer. We analyze the impact of edge diffraction on projection printing directly with experiments on an aerial image measurement system (AIMS). We show here that topographic effects change with illumination angle and can be quantified using through-focus intensity measurements. Off- axis incidence influences not just defocus image behavior (as for normal incidence), but also the at-focus intensity at wafer. Moreover, with oblique illumination, mask diffraction varies for left-facing and right-facing sidewalls, the nature of the asymmetry being polarization dependent. The image degradation due the polarization parallel to the sidewall (TE) is seen to be stronger, owing to the interplay of mask topography and pupil filtering in the imaging system. This translates to a CD variation of 2% between the two polarizations, even at focus. A simple thin-mask boundary layer model that treats each sidewall independently is shown to be able to approximate mask topography induced diffraction for both polarizations with 5-10nm wide boundary layers.
The Transport of Intensity equation (TIE) solves for the complex field at a plane of interest using intensity measurements at multiple defocus planes. Patterning the illumination enables multiplexing at the source instead of the detector, enabling quantitative phase without any moving parts. A general theory is formulated here to describe the defocus coupling of the illumination and object fields, providing a joint framework for analyzing grating interferometry and defocus based phase imaging methods. We use the theory to devise a measurement scheme that isolates object phase gradients by combining defocus images for different illumination patterns, using sinusoidal illumination as an example. Since the phase image recovered corresponds to a first derivative of phase, it is expected to have better low frequency noise resilience than the traditional TIE, which measures the second derivative of phase. The method is validated in simulations, and subsequently in experiments using a spatial light modulator.
Photomasks are expected to have phase effects near edges due to their 3D topography, which can be modeled
as imaginary boundary layers in thin mask simulations. We apply a modified transport of intensity (TIE) phase
imaging technique to through-focus aerial images of photomasks in order to recover polarization-dependent edge
effects. We use AIMS measurements with 193nm light to study the dependence of recovered phase on mask type
and geometry. The TIE is an intensity conservation equation that quantitatively relates phase in the wafer plane
to intensity through-focus. Here, we develop a modified version of the TIE for strongly absorbing objects, and
apply it to recover wafer plane phase of attenuating masks. The projection printer blurs the fields at the wafer
plane by its point spread function, hence an effective deconvolution is used to predict the boundary layers at
the mask that best approximate the measured thick mask edge effects. Computation required for the inverse
problem is fast and independent of mask geometry, unlike FDTD computations.
Thick mask electromagnetic edge effects in attenuating phase-shift masks (ATT-PSM) are analyzed by extracting optical phase at the wafer plane from a series of through focus aerial images with 193nm light. The thick edges of an ATT-PSM can lead to phase distortions, creating asymmetric intensity contrast on either side of focus. Here we use through focus intensity images from an AIMS tool to quantitatively recover phase via the Transport of Intensity Equation (TIE). The TIE can recover the effective phase across the mask due to edge effects by analyzing the through focus image stack. We verify a previously proposed model for edge effects by adding quadrature phase boundary layers at the edges during simulation and compare the simulated through focus images with experimental data. After tuning the real and imaginary part of the boundary layer and the angle of the substrate, the simulated through focus behavior agrees with experiment, giving a measure of the edge effects. This leads to comparable quantitative phase profiles recovered at the wafer plane for simulation and experiment with the ATT-PSM. We expect that the method is applicable for the approximation of topographical effects in other types of thick masks as well.