Aamod Shanker

Low-noise phase imaging by hybrid uniform and structured illumination transport of intensity equation

We demonstrate a new approach to the transport of intensity equation (TIE) phase retrieval method which uses structured illumination to improve low-frequency noise performance. In the hybrid scheme, two phase images are acquired: one with uniform and one with sinusoidal grating illumination intensity. The former preserves the high spatial frequency features of the phase best, whereas the latter dramatically increase the response at low spatial frequencies (where traditional TIE notoriously suffers). We then theoretically prove the design of a spectral filter that optimally combines the two phase results while suppressing noise. The combination of uniformly and structured illuminated TIE (hybrid TIE) phase imaging is experimentally demonstrated optically with a calibrated pure phase object.

Transport of intensity phase imaging in the presence of curl effects induced by strongly absorbing photomasks

We report theoretical and experimental results for imaging of electromagnetic phase edge effects in lithography photomasks. Our method starts from the transport of intensity equation (TIE), which solves for phase from through-focus intensity images. Traditional TIE algorithms make an implicit assumption that the underlying in-plane power flow is curl-free. Motivated by our current study, we describe a practical situation in which this assumption breaks down. Strong absorption gradients in mask features interact with phase edges to contribute a curl to the in-plane Poynting vector, causing severe artifacts in the phase recovered. We derive how curl effects are coupled into intensity measurements and propose an iterative algorithm that not only corrects the artifacts, but also recovers missing curl components.

Critical assessment of the transport of intensity equation as a phase recovery technique in optical lithography

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.

Defocus-based quantitative phase imaging by coded illumination

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.

Speckle metrology for extreme ultra-violet lithography

Stochastic effects in extreme ultraviolet lithography are contributed by the EUV optical speckle and diffusion chemistry of the photoresist. These cause line edge roughness (LER) in the etched features, shrinking the process window at the sub-20nm lithography node. We explore possibilities of utilizing the speckle for optical metrology and resist characterization by measuring the latent image of the EUV light on photoresist. The latent image on a standard photoresist measured using atomic force microscopy is shown to linearly depend on the aerial image intensity within a specific dose range, hence serving as an in-situ imaging modality to measure the EUV aerial image without a camera. Potential applications include EUV wavefront measurement, resist characterization, and LER engineering.

Special Section Guest Editorial: UC Berkeley Sculpted Light in the Brain 2017 debates future technologies to communicate with the brain

This article summarizes presentations at Sculpted Light in the Brain 2017.

Optical transfer function characterization using a weak diffuser

We present a simple technique which uses a random phase object for single-shot characterization of an optical systems 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 diffusers 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.

Recovering Curl Using an Iterative Solver for the Transport of Intensity Equation

The Transport of Intensity Equation solves for optical phase from through-focus intensity when the in-plane power flow is curl-free, giving artifacts in presence of curl. An iterative solver is shown to correct artifacts and recover power flow curl.

Absorber topography dependence of phase edge effects

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.

Characterizing the dependence of thick-mask edge effects on illumination angle using AIMS images

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.