Development of a tomographic Mueller-matrix scatterometer for nanostructure metrology

Abstract

In this paper, we describe the development of a novel instrument, tentatively called tomographic Mueller-matrix scatterometer (TMS), which enables illuminating sequentially a sample by a plane wave with varying illumination directions and recording, for each illumination, the polarized scattered field along various directions of observation in the form of scattering Mueller matrices. The incidence angle is varied from 0° to 65.6° with the rotation of a flat mirror that changes the position of the focal point of a light beam on the back focal plane of a high numerical aperture objective lens. The scattering Mueller matrices are collected over a wide range of scattering angles (0°-67°) and azimuthal angles (0°-360°). The developed instrument was then applied for the measurement of nanostructures in combination with an inverse scattering problem solving technique. The experiment performed on a periodic nanostructure preliminarily demonstrates the performance of TMS as well as its potential in nanostructure metrology. It is expected that the TMS would be a powerful tool for characterizing the polarized scattered-field distributions and measuring nanostructures in nanomanufacturing.

Metrology of Nanostructures by Tomographic Mueller-Matrix Scatterometry

“…Details about the calibration of P 0 , A 0 , C 10 , C 20 , δ 1 and δ 2 , as well as M BS r , M BS t , M OB f and M OB b can be found in Ref. [21] and are omitted here for the sake of brevity. information that one can extract from a linear polarization scattering process, the full polarization properties of the scattered field are thus achieved.…”

“…Details about the calibration of P0, A0, C10, C20, δ1 and δ2, as well as M can be found in Ref. [21] and are omitted here for the sake of brevity.…”

“…To address the challenges or limitations in conventional optical scatterometry, several designs have been presented with the idea of trying to collect the scattering information about the nanostructure under test conditions as much as possible, such as with the goniometric optical scatter instrument [12][13][14], through-focus scanning optical microscopy [15], scatterfield microscopy [16], tomographic diffractive microscopy [17,18], and Fourier scatterometry [19,20]. Recently, we have also developed a novel instrument called the tomographic Mueller-matrix scatterometer (TMS) [21]. The TMS illuminates a sample sequentially by a plane wave with varying illumination directions (incidence angles 0 •~6 5.6 • and azimuthal angles 0 •~3 60 • ) and records.…”

“…For each illumination direction, the polarized scattered filed along various directions of observation (scattering angles 0 •~6 7 • and azimuthal angles 0 •~3 60 • ) can be seen in form of scattering Mueller matrices. The experiments performed on a Si grating had preliminarily demonstrated the potential of a TMS in nanostructure metrology [21].Due to the strong correlation between pitch and other structural parameters, it is a common practice to predetermine grating pitch by another metrology tool such as AFM, or directly fix grating pitch to its nominal value in the solution of the inverse problem in optical scatterometry. In this work, we present the application of a TMS for the accurate reconstruction of lithographic patterns.…”

“…For each illumination direction, the polarized scattered filed along various directions of observation (scattering angles 0 •~6 7 • and azimuthal angles 0 •~3 60 • ) can be seen in form of scattering Mueller matrices. The experiments performed on a Si grating had preliminarily demonstrated the potential of a TMS in nanostructure metrology [21].…”