A review of selected current and new Maxwell equation solve algorithms used in critical dimension metrology is
presented. We show that the standard RCWA can have serious issues under certain conditions, even in some typical
scatterometry applications. We present some results showing that some of the newer algorithms we developed can
significantly outperform the RCWA. The strengths and weakness of algorithms are illustrated.
Spectra of contact hole arrays with target diameters ranging from 106 to 131 nm and pattern pitch ranging from 220 to 300 nm are taken from an off-axis (65°) rotating compensator spectroscopic ellipsometry (RCSE).[1] 3-dimensional finite difference (FD3D) model developed by H. Chu,[2] is applied in the studies. To ensure accuracy of optical dispersion of each film, the simultaneous use of angle resolved beam profile reflectometry (BPR), broadband spectroscopic reflectometry (BB), and SE of an Opti-Probe 7341 are used for characterizing of the resist and BARC films. In particular, The extracted n&k dispersions are used to model the contact hole SE data using Therma-Wave's proprietary 3-dimensional RT/CD technology.[3,4] The performance of stability of both static and dynamic repeatability, uniformity, and correlation to other independent technology (i.e., SEM) will be presented in this paper.
In real-time optical CD applications of shallow trench isolation (STI), shallow trench removal (STR), deep trench isolation (DTI), and deep trench removal (DTR), a single recipe is required for each type of application to accommodate wide ranges of process windows by monitoring parameters such as bottom CD (BCD), middle CD (MCD), top CD (TCD) and side wall angle (SWA). The modeling of the grating profiles of silicon trenches with nitride caps requires a large number of slices (> 10) to generate smooth shapes for top rounding of the nitride, curvature of the silicon trench waist, and the silicon trench footing or undercut. The number of orders for Fourier expansion is also high (larger than 13 in the best case). With these requirements we found that the rigorous coupled wave analysis (RCWA) algorithm is generally too slow to calculate the CD profiles from the raw scatterometry spectra. In this paper we present a finite difference (FD) algorithm and its applications to real-time CD scatterometry. The mathematical analysis of the FD algorithm was published elsewhere. We demonstrate that the FD algorithm has an advantage over RCWA in terms of calculation speed (up to a factor of 10 improvement), better capture of profile shapes in comparison with cross sectional SEM (X-SEM) and more robust in terms of numerical stability. Details of comparisons between FD and RCWA will be shown for the applications of STR and DTR.
This paper presents measurement results of the 3-D contact hole profiles using RT/CD technology for various diameter-to-space (D/S) ratios and film stacks. The key controlling parameters (hole depth, diameter, sidewall angle, and hole openness, etc.) for lithography processing of contacts and vias were studied in terms of measurement sensitivity on samples with different pitches and D/S ratios and film stacks. Good correlation (R2 ~ 0.99) between CD-SEM and RT/CD was obtained for the sample structures. The static and dynamic measurement stability of contact diameter and contact depth was better than 1 nm using simple profile modeling.
Fast and efficient finite difference scheme in the vertical direction for optical scattering of gratings is presented. A second order central difference with boundary corrections or a pseudo fourth order operator splitting method is used. A stable recursion formula for the impedance matrix can be obtained. Matrix diagonalizations can be used for rectangular grating profiles when many discretization points are required. The recurrence relation is equivalent to a UL decomposition of block tridiagonal matrix. It is numerically stable compared to existing finite difference methods for gratings and many times faster than the popular rigorous coupled wave analysis method.
We have developed fast numerical solutions to the diffraction of light from a periodic array of contact holes (CH) in microelectronic structures. We present results for contact holes in oxide and in 193 nm and 248 nm photoresists. We also show detectability limits of the CH and observed variations across wafers processed with state-of-the-art lithography.
We have developed fast numerical solutions to the diffraction of light from periodic array structures that allow real-time regression fitting to optical data. In contrast to previous publications, the solutions we have developed are easily applied to focused beams with arbitrary angles of incidence on periodic structures with complex shapes and multiple layers both within and below the structure. The adaptive nature of the shape definition makes it relatively easy to characterize typical microelectronic patterning effects, including undercut, rounding, footing and encroachment in a robust manner on poly-gate, STI, Damascene and resist structures. This real-time approach is not limited by a priori knowledge or assumptions about the range of variation of the CD parameters, and is therefore able to deal with large excursions in process parameters. It is also not limited by parameter discretization effects. The program itself is easily configured for any type of optical measurement (ellipsometry, reflectometry, etc). Data will be presented for several categories of microelectronic CD structures that have been measured with this approach.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.