Generalized ellipsometry of artificially designed line width roughness
Introduction
Line width roughness (LWR) represents one of the challenges of today's semiconductor technology process control [1]. With constantly decreasing pitch, the importance of LWR increases as the ratio between LWR and mean line width also increases. Optical characterization tools, proven invaluable for fast and non-destructive inline process control, require new methods and models in order to achieve the efficiency needed for the real-time quality measurement of the LWR [2]. There has been previous demonstration of an optical method for LWR assessment using reflectometer operating in the Fourier space [3]. More recent theoretical work on the sensitivity of angularly resolved data to LWR [4], [5] demonstrated the significance of the problem and explored limits of effective medium approximations for the purpose of LWR modeling.
It is becoming even more challenging with new applications requiring measurements to be done in very small (usually less than 100 μm) targets. Such measurements using spectral ellipsometer techniques require significant focusing of the light beam (with few degrees wide incidence angles range) in order to access small targets and achieve sufficient light intensity. The numerical aperture of the incident light beam puts more demands on the optical modeling and requires reevaluation of the sensitivity of the optical methods to the LWR. The effects of the finite numerical aperture include non-coherent averaging over incidence and azimuthal angles that result in a “washing out” of the spectral features [6]. This may decrease the sensitivity of the data to imperfections in line shapes, namely to LWR.
In order to investigate the sensitivity of the Mueller matrix ellipsometry technique to the LWR, a sample with artificially designed periodic perturbation of the lines was manufactured using e-beam lithography. The periodicity does not exactly resemble the random nature of typical LWR, but it allows the origin of the change in the spectral optical response to be positively confirmed. The purpose of this work is to present an approach consisting of finding the proper parametric model for the unperturbed grating and determining the magnitude of the change in mean square error (MSE) due to the line perturbation. The periodic LWR can be modeled using a generalized biperiodic rigorous model [7]. This approach provides necessary certainty in order to confirm that the differences in the optical response are due to the line perturbation and are not due to some other imperfection or omitted feature(s) in the line grating model.
In Section 2 the basic experimental background is given, together with a description of the multi-azimuth Mueller matrix ellipsometric method. Special emphasis is put on the modeling of depolarization effects caused by the significant numerical aperture of the instrument. Section 3 summarizes results showing clear distinction between the quality of fits for the unperturbed and perturbed line gratings. Differences are explained using a rigorous model for biperiodic gratings which leads to a comparable quality of the fit for both gratings. Results are summarized in Section 3.
Section snippets
Experimental details and modeling methods
The sample studied in this work was manufactured at the University of North Carolina, Charlotte, using e-beam lithography to etch a 736 nm pitch line grating into the silicon wafer. Nominal heights of gratings are 400 nm with nominal middle widths are 300 nm. Samples with different levels of perturbation are situated into different 100 μm × 100 μm targets. A scanning electron microscope image taken from the top of the unperturbed sample is shown in Fig. 1(a). A second sample has its artificial LWR
Results and discussions
In this work, we evaluate sensitivity of advanced ellipsometric methods to LWR represented by periodic perturbation of lines. The main goal is to confirm that observed differences between measured data obtained with and without LWR are solely due to the line width perturbation and not some other imperfection in the model or another physical difference between two samples. In order to do that, we have established a reasonably accurate and stable optical model of the unperturbed grating based on
Conclusions
In this work we have presented an advanced ellipsometric method applied to the study of line-width roughness. Measurements and RCWA modeling were performed on the reference etched silicon line grating and the grating with artificially designed periodic line-width roughness. The multi-azimuth, Mueller matrix method used in this work allowed for a conclusive decision on the correctness of the proposed grating profile and helped to identify the overhang on the top of the grating line, which had a
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Cited by (11)
Nondestructive analysis of lithographic patterns with natural line edge roughness from Mueller matrix ellipsometric data
2016, Applied Surface ScienceCitation Excerpt :Due to the rich information provided by the Mueller matrices, MME-based scatterometry has been demonstrated to achieve better measurement sensitivity and accuracy than conventional ellipsometric scatterometry [12–14]. Although the characterization of line roughness using MME has been reported [15], they only demonstrated the potential to confirm origins of differences between the optical responses with and without significant line width roughness (LWR). Moreover, the investigated LWR in Ref. [15] was artificially designed with periodic variations, just as was done in most of the previously experimental studies on LER metrology [6–8], and is nevertheless representative of real situations.
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