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

Abstract

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.

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

“…Note that although the TIE equation is based on the paraxial approximation, it is justified for the mask-side NA of 0.3375 in the experiments here. More details on the experimental setup can be found in [23]. Images of the experimentally recovered phase are shown in Fig.…”

“…We then propose an iterative wrapper for the traditional TIE solver that corrects such errors to produce a more accurate phase result. This method was first described in [23,24] and later appeared in [25]. We further derive how the curl component is coupled into the intensity measurements, and show that our proposed method also recovers part of the missing curl.…”

“…5 likely indicate that OMOG is similar to attenuating phase shift mask (ATT-PSM), in that the diffraction at the primary edge reduces with the rotation of the polarization and the phase drops in magnitude by about a factor of 5. A detailed analysis can be found in [23].…”

“…This work is motivated by our studies of electromagnetic phase edges in optical lithography masks [23,24]. Unlike many other applications, photomasks are designed specifically to have strong absorption.…”

Absorber topography dependence of phase edge effects

“…In previous work, 3 using experimental images of an OMOG absorber taken with AIMS T M (Aerial Imaging Measurement System 4 ), the wafer phase across a feature was obtained from a through-focus intensity stack by solving the Transport of Intensity Equation (TIE) . 5,6 It was observed that significant phase modulation does exist across the absorber, especially when illumination polarization is perpendicular to the feature edge (TM), seen in Fig.…”