Two-Dimensional Simulation and Modeling in Scanning Electron Microscope Imaging and Metrology Research

Transcription

1 SCANNING VOL. 24, (2002) Received: October 30, 2001 FAMS, Inc. Accepted with revision: February 15, 2002 Two-Dimensional Simulation and Modeling in Scanning Electron Microscope Imaging and Metrology Research MICHAEL T. POSTEK,ANDRÁS E. VLADÁR,JEREMIAH R. LOWNEY,WILLIAM J. KEERY National Institute of Standards and Technology, 1 Gaithersburg, Maryland, USA Summary: Traditional Monte Carlo modeling of the electron beam specimen interactions in a scanning electron microscope (SEM) produces information about electron beam penetration and output signal generation at either a single beam-landing location, or multiple landing positions. If the multiple landings lie on a line, the results can be graphed in a line scan-like format. Monte Carlo results formatted as line scans have proven useful in providing one-dimensional information about the sample (e.g., linewidth). When used this way, this process is called forward line scan modeling. In the present work, the concept of image simulation (or the first step in the inverse modeling of images) is introduced where the forward-modeled line scan data are carried one step further to construct theoretical two-dimensional (2-D) micrographs (i.e., theoretical SEM images) for comparison with similar experimentally obtained micrographs. This provides an ability to mimic and closely match theory and experiment using SEM images. Calculated and/or measured libraries of simulated images can be developed with this technique. The library concept will prove to be very useful in the determination of dimensional and other properties of simple structures, such as integrated circuit parts, where the shape of the features is preferably measured from a single top-down image or a line scan. This paper presents one approach to the generation of 2-D simulated images and presents some suggestions as to their application to critical dimension metrology. Key words: modeling, Monte Carlo, metrology, scanning electron microscope, linewidth, critical dimension PACS: 61.16Bg, Bp, s, n, Fr, Fk 1 Contribution of the National Institute of Standards and Technology, not subject to copyright. Address for reprints: Michael T. Postek Precision Engineering Division Technical A-347 National Institute of Standards and Technology Gaithersburg, MD 20899, USA postek@nist.gov Introduction Electron beam interaction modeling in the scanning electron microscope (SEM) is traditionally done by using Monte Carlo techniques. Monte Carlo models have been used to provide information regarding beam penetration and SEM signal generation at a single-beam landing location, or at multiple-beam landing locations. Early Monte Carlo models for metrology were based on the pioneering work of Drs. David Joy, Dale Newbury, Robert Myklebust, and others (reviewed by Joy 1995). More recently, a series of Monte Carlo computer codes named MONSEL (MONte Carlo for Secondary ELectrons), specifically designed for critical dimension (CD) metrology, have been developed at NIST 2 (Lowney 1996a, Lowney et al. 1994) and are undergoing continual development and improvements. Other electron beam interaction models, such as CASINO exist ( These models have been specifically designed and used for x-ray microanalysis, as well. Modeling with zero-dimension (0-D) is equal to a point analysis; modeling a line-scan signal on a flat sample with regions of different composition is a one-dimensional (1- D) analysis; two-dimensional (2-D) analysis works across a plane, for example, on integrated circuit lines described with their widths, heights, angles, and so forth, on a different material substrate, and the three-dimensional (3-D) analysis deals with a fully 3-D sample and reports 3-D signals. Monte Carlo simulation along a line that agrees with the corresponding experimental line scans is useful in providing dimensional information about the sample, such as the width, wall angle, and even height of the line (Davidson and Vladar 1999). In the case in which multiple beam landing locations are modeled, the signal-generation that results along a line can be graphed to simulate observed secondary or backscattered electron line scans experimentally. Monte Carlo line scans that agree with the corresponding experimental line scans are useful in providing 1-Dimensional information about the sample (e.g., linewidth). When used in this way, this process is called forward line scan modeling. Inverse- 2 Copies of the MONSEL program can be obtained by contacting Dr. Jerry Lowney at jlowney@erols.com.

2 180 Scanning Vol. 24, 4 (2002) modeling of SEM line scans matches a modeled line scan to an experimental line scan and adjusts the input parameters to the Monte Carlo modeling to obtain a good match (Fig. 1). Using the MONSEL model in a patterned silicon target, the location of an edge has been determined to an error below 6 nm from comparisons between computed and experimentally measured backscattered and secondary electron signals in an SEM (Lowney et al. 1995). The MON- SEL series of Monte Carlo computer codes are based on first-principles physics (Lowney 1996a). The code simulates the backscattered, secondary, and transmitted electron signals (where appropriate) from complex targets in the SEM. The calculations in MONSEL are fully 3-D, but only MONSEL III has been designed to deal with the modeling of actual 3-D targets (Lowney 1996b). The 3-D target is a two-by-two array of short lines with trapezoidal faces and ends. They can be of any length or width, but all four are identical. Measurements have been made on a special target composed of a 1 µm step in a silicon substrate in a high-resolution SEM (Postek et al. 1995). By overlaying the measured data with the simulation (which predicts the expected signal for a given target geometry), it is possible to determine the position of a measured feature in the target to a low level of uncertainty (Lowney et al. 1995). This work proved that it is possible to obtain agreement between theoretical models and controlled experiments. In the work described here, the concept of image construction using the simulation (for the inverse modeling of images) is introduced where the Monte Carlo line scan results are carried one step further to construct simulated SEM images (i.e., theoretical SEM micrographs). The MONSEL method follows the electrons in 3-D, and MON- SEL-III can provide information regarding edges and other 3-D structures. Therefore, it is possible to computer construct a theoretically derived image in two dimensions. Clearly, it is possible to just compare single lines of data (line scans) to a single Monte Carlo line scan. However, SEM users are more comfortable viewing and comparing Unknown real IC structure Library of waveforms Measured waveform Fully adjusted waveforms Raw modeled waveforms Best match FIG. 1 Measurement and inverse modeling through modeled library to find the best match. IC = integrated circuit. n+1 n n 1 Known modeled structures images. The resultant image is also very useful in blind analysis and testing of algorithms currently found in SEMs used for metrology. This technique also provides a graphic if not educational capability to show the effects of changes in instrument parameters introduced to the instrument. These simulated images in which all the parameters are well known can be directly and visually compared with experimentally observed images. This approach is the first step in an inverse modeling process in which an image generated from a forward-modeled line scan is optimized to agree with an actual SEM image. This demonstration of the generation of SEM images from Monte Carlo line scans provides the ability to simulate and compare 2-D SEM images. For the work represented here, the examples for the simulations were semiconductor lines where the importance of the development of accurate linewidth metrology resides. The interesting and economically important location for the linewidth measurement is far from the tip or tips of the lines, thus those are the ones that were modeled and reconstructed. The ability to generate Monte Carlo SEM images that agree with the experiment is very important for comparing instruments and measurement algorithms and for analyzing the images of a given instrument. Monte Carlo images can be used as a reference image for instrument-comparison purposes or as a standard image for monitoring the performance of a given instrument over time. In addition, the agreement between modeled and real images is one way to obtain confidence that the details of the real image are being interpreted correctly. As modeled images get closer and closer to real images, it becomes possible to deal with, and better account for, the minute details of SEM image generation. This is becoming increasingly more important as the semiconductor industry approaches measurements with uncertainties at atomic dimensions. Materials and Methods Modeling In the present work, the NIST-developed MONSEL Monte Carlo program (Lowney 1996b) was used to compute the electron beam interactions and the resulting SEM output signals. The specimen modeled by MONSEL consisted of parallel APEX E photoresist lines on a silicon substrate, palladium lines on silicon, and silicon lines on silicon (Shipley Company, LLC, Marlborough, Mass., USA). The photoresist lines were µm wide on top with a 2 wall slope, and 1 mm high with a pitch of µm. The direction perpendicular to the axis of these lines was designated as the X-direction. The emitted secondary and backscattered electron distributions were computed for 20,000 incident beam electrons at each of one thousand locations along this X-direction. The electron collection is considered to be polar, thus approximating an instrument with an in-lens electron detector similar to the current lab-

3 M. T. Postek et al.: 2-D simulation and modeling in SEM 181 oratory instrument. Other electron collection schemes could be implemented, but have not been at this time. MONSEL was run on a CRAY 90 Computer 3, (Cray Inc., Seattle, Wash., USA) and the computation time was about 24 h. MONSEL has also been installed and tested on a 200 MHz desktop personal computer (PC) running FORTRAN 77 (Salford Software Ltd., Manchester, UK). The computation times on the desktop computer were found to be about the same as for the CRAY 90, since the central processing unit (CPU) time is shared with other users with the CRAY 90, and the PC CPU is used totally to run the MON- SEL code. The buildup of a positive or negative charge on a not fully conductive specimen remains a problem for SEM metrology. Therefore, conditions were chosen in the experimental examples in which charge build-up was not present or negligible. Charging can affect the electron beam and thus the measurements (Postek 1984). Accurate metrology in the SEM requires that an accurate charging model also be developed or that charging be avoided. Currently, MONSEL does not incorporate a charging model algorithm; therefore, the work here was restricted to noncharging conditions. Ko and Chung (1998) and Ko et al. (1998) have quantitatively investigated the effects of charging utilizing Monte Carlo modeling. Such modeling will be incorporated into MON- SEL in the future; however, specimen and instrumentation variations make charging difficult to reproduce and thus remain difficult to study in the quantitative manner necessary for accurate metrology at this time. Magnification Since pixel size in the experimental SEM image to be compared with the MONSEL image was an important parameter, the X direction (i.e., scan direction) magnification of the experimental SEM image was calibrated with the NIST magnification standard SRM 484 (NIST, Gaithersburg, Md., USA). Beam Diameter The input parameters to MONSEL included line and substrate material, line geometry (including wall angle), separation of neighboring lines, and so forth. MONSEL then provided signal output data for a multi-point line scan with known positions in the X-direction for the beam/specimen interaction of an infinitely small electron beam diameter. The output for such a calculation for a 3-line photoresist structure is shown in a line scan format in Figure 2. These data were then transferred to an auxiliary computer 3 Certain commercial equipment is identified in this report to describe the experimental procedure adequately. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the equipment identified is necessarily the best available for the purpose. SE intensity 0 Pixels 1000 FIG. 2 Monte Carlo modeled line scan of the secondary electron (SE) signal of photoresist. program to account for the finite electron beam at each X location (Lowney 1996b). An electron beam that had induced astigmatism could be modeled but has not been implemented at this time. Residual, hence sufficiently small astigmatism can be dealt with using proper convoluting parameters. Amplitude Scaling The next step in the process was to scale the amplitude of the line-scan data produced by MONSEL. The intensity of the SEM output signal produced by MONSEL was in arbitrary units and needs to be scaled to lie within the range of 0 to 255 (the typical range of the stored digitized image in the SEM) for comparison with experiment. This is done by the same auxiliary program, which normalizes the maximum computed amplitude to 255. Formation of an Image After amplitude scaling, the line-scan data points were then turned into an image by multiple replication of the line-scan results in a direction parallel to the axis of the lines (Y direction), as shown in Figure 3. Various image-processing steps similar to those commonly used in the SEM were then applied to the resulting Monte Carlo image in order to obtain a match closer to the actual images. This was done by using Adobe Photoshop 3 software tools (Adobe Systems, Inc., San Jose, Calif., USA) starting with the modeled image of Figure 3. The following operations were performed: (1) addition of noise, (2) adjustment of contrast and brightness, and (3) application of filter operations to account for blur effects in the real image. The final result is shown in Figure 4. Photoshop was used because it provides a convenient and effective way for making very fine changes to an image. It must also be noted that the processing functions chosen in this work were carefully checked to make sure that no alteration in pixel position (in either X or Y) was made inadvertently (which would invalidate any dimensional measurements using the processed modeled image to interpret geometry information about the specimen). The technique described here demonstrates the ability of matching modeled and measured images to the level of ex-

4 182 Scanning Vol. 24, 4 (2002) cellent similarity. Artificial or modeled images, with known parameters (i.e., the amount and type of noise, nonlinearity, etc.) that otherwise closely resemble measured images, can be used for such purposes as metrology algorithm comparisons. In general, there are several ways of comparing and finding the best fits for 1-D (line scans) and 2- D distributions (images). This was shown on line scans obtained from top-down CD-SEM images of photoresist lines (Davidson and Vladar 1999) and is the subject of ongoing research. Final Touches Relative position values corresponding to the SEM image were then added to the Monte Carlo image, as shown in Figure 4. Alphanumeric characters could also be added to the image to make it more convincing. In addition, using other digital imaging techniques, additional noise, and sample edge roughness or other sources of imprecision were introduced into the image to provide an image that closely matches the standard SEM image shown in Figure 5. Discussion FIG. 3 Raw Monte Carlo-simulated lines with a known beam diameter convoluted into the data and reproduced in the Y-direction to form an image. Images formed from Monte Carlo line scans have many uses if, in fact, they agree with the corresponding experimentally measured images by some reasonable criteria. For example, Figure 6 shows the effect of different Gaussian beam diameters upon the quality of the edge and its location. Notice how the image becomes softer and the edge becomes less defined as the beam diameter is increased. Figure 7 demonstrates the difference between collected secondary and backscattered electrons on the expected image. These figures should agree with the experimental results. If they do not agree, then something is wrong either with the Monte Carlo model, its input parameters, or the experiment itself. One reason for a discrepancy could be that the model may not take into account all of the significant features of the signal generation for the SEM and/or the specimen in question. In addition, the assumed properties of the SEM itself or of the specimen may not be correct or appropriate. For example, in a study of x-ray mask metrology (Postek et al. 1993), the model predicts FIG. 4 Monte Carlo-modeled lines after several processing steps, as described in the text. FIG. 5 Actual scanning electron microscope (SEM) image of measured photoresist lines taken in a critical-dimension SEM as a comparison with the modeled image shown in Figure 4.

5 M. T. Postek et al.: 2-D simulation and modeling in SEM 183 that a characteristic notch or ledge should be present on the modeled profiles. This notch was predicted to occur when the electron beam was incident on the sloping edge of the line and the size of the notch relates directly to the slope. The size of the notch was predicted to be about 8 10 nm for a wall having 4 of slope. This notch was not observed in initial SEM experimental data because the thermionic emission cathode SEM used was not resolving that particular detail. Recognizing and looking for this detail as a characteristic that should be present in the experimental data required higher instrument resolution. Utilizing a field-emission instrument to view the sample resolved the discrepancy between the modeled and experimental data. Clearly, recognizing and correcting the causes of disagreement between Monte Carlo-generated images and the corresponding experimental images can lead to a more complete understanding of the particular specimen used and/or the SEM itself. (a) (b) FIG. 6 Monte Carlo modeled image of palladium lines on silicon with a known Gaussian beam diameter convoluted into the data; (a) 60nm beam diameter, (b) 150 nm beam diameter. (a) FIG. 7 Monte Carlo modeled image of palladium lines on silicon; (a) secondary electron image, (b) backscattered electron image. (b)

6 184 Scanning Vol. 24, 4 (2002) Comparison of measurement algorithms is another excellent application of this simulation work. The various edge-detection criteria in present SEM linewidth measurements are somewhat arbitrary and, at best, are usually not on a firm theoretical foundation. Table I shows the results of the application of several common algorithms to the measurement of a simulated palladium on a silicon-line image such as those described above. A simulated image is extremely valuable in this measurement because all the input parameters to the simulated image are known. Hence, the pitch, linewidth, and space width are accurately known. A similar discrepancy among width measurements was demonstrated in the SEM Interlaboratory Study using experimental data (Postek et al. 1993). For accurate determination of where the measurement of width should be made on the intensity profile, an accurate model is required. The images and line scans taken with the CD-SEM contain much more information than is generally being used. Modeling the possible cases can be helpful in drawing correct conclusions and makes it possible to use more accurate, customized measurement algorithms. In principle, the accuracy of the measured linewidth can be determined, as well as its robustness to such perturbing factors as edge roughness, edge non-verticality, proximity effects, signalto-noise ratio, focus, astigmatism, and so forth. Unfortunately, the results of such studies will be specimen and SEM specific and are not generally applicable to all the cases encountered in practice. However, if the model were sufficiently fast and user friendly it would be conceivable to generate all the necessary images. Monte Carlo-generated images of suitably designed test specimens can be useful for evaluating the properties of the SEM itself. Indeed, the Monte Carlo input parameters required to obtain an acceptable agreement between theory and experiment has the potential for revealing a significant amount of information about the properties and behavior of an SEM. Once an acceptable level of agreement is obtained for an SEM, the Monte Carlo image can be used as a standard of comparison to monitor the future performance of that SEM. The advantage of the Monte Carlo image over its corresponding real image is that any changes in the SEM over time can be analyzed by repeating the modeling on the changed image and noting the change in the input parameters required. If an acceptable level of agreement between theoretical and experimental images of a test (or standard) specimen TABLE I Comparison of measurement algorithms applied to a modeled image Algorithm Space width (nm) Linewidth (nm) Peak Threshold Regression Sigmoid Actual has been demonstrated, then the corresponding input parameters to the Monte Carlo modeling can be used to characterize that SEM for comparison purposes. The recently proposed SEM Monitor Fourier-transform method of providing a figure of merit for monitoring any degradation in SEM performance over time used a single figure of merit of that particular SEM when optimized (or when new) as a standard of comparison (Postek and Vladár 1998, Vladár et al. 1998). The use of Monte Carlo-generated images of a suitable specimen could provide more meaningful and more easily understood characterization parameters for this purpose. Monte Carlo modeling in the absence of the necessary information about the specimen and/or about the SEM itself can be a frustrating, expensive, and time-consuming job. However, once the input parameters pertinent to the SEM have been characterized by using an appropriate standard specimen, only the current specimen parameters remain in question, and the work required to get agreement between theory and experiment is considerably easier. Indeed, the specimen parameters thus obtained should be useful for understanding the behavior of the specimen in the SEM, for understanding its SEM image, and for making more accurate dimensional measurements on the specimen. Conclusion There have been several recommendations on how to characterize and/or monitor the performance of an SEM. However, in the final analysis, it is the quality of the image (or micrograph) that is usually of prime importance. A single figure of merit may have the advantage of simplicity to implement, but has the disadvantage of providing only limited information. The alternative, discussed in this paper, is to evaluate the input parameters of a Monte Carlo model necessary to obtain a satisfactory agreement between the modeled and the real image of some well-selected standard specimen. This alternative has the advantage of providing more and more easily understood information about the microscope, but has the disadvantage of being more difficult to implement. However, it has the further advantage that, once implemented, the necessary input parameters to obtain a satisfactory agreement for unknown specimens can yield important information about those specimens (e.g., line width). Clearly, it is possible just to compare single lines of data (line scans) to obtain similar results. However, SEM users are more comfortable with images and this provides a graphic if not educational capability to show the effects of changes in instrument parameters introduced to the instrument. Acknowledgments The authors would like to thank and acknowledge the support provided by International SEMATECH and the Of-

7 M. T. Postek et al.: 2-D simulation and modeling in SEM 185 fice of Microelectronics Programs at NIST for partially funding this work. References Joy DC: Monte Carlo Modeling for Electron Microscopy and Microanalysis. Oxford University Press, N.Y. (1995) Davidson MP and Vladar AE: An inverse scattering approach to SEM line width measurements. Proc SPIE 3677, (1999) Ko Y-U and Chung M-S: Monte Carlo simulation of charging effects in linewidth metrology (II) on insulator substrate. Scanning 20, (1998) Ko Y-U, Kim SW, Chung M-S: Monte Carlo simulation of charging effects during observation of trench structures by scanning electron microscope. Scanning 20, (1998) Lowney JR: Application of Monte Carlo simulations to critical dimension metrology in a scanning electron microscope. Scan Microsc 10, (1996a) Lowney JR: Monte Carlo simulation of scanning electron microscope signals for lithographic metrology. Scanning 18, (1996b) Lowney JR, Postek MT, Vladár AE: A Monte Carlo model for SEM linewidth metrology. Proc SPIE 2196, (1994) Lowney JR, Postek MT, Vladár AE: Workshop report 3: Edge positions from scanning electron microscope signals by comparing models with measurements. MAS Proceedings (Ed. Etz E), (1995) Postek MT: Low accelerating voltage inspection and linewidth measurement in the scanning electron microscope. SEM/1984/III, SEM, Inc., (1984) Postek MT and Vladár AE: Image sharpness measurement in scanning electron microscopy, Part 1. Scanning 20, 1 9 (1998) Postek MT, Lowney JR, Vladar AE, Keery WJ, Marx E, Larrabee RD: X-ray lithography mask metrology: Use of transmitted electrons in an SEM for linewidth measurement. J Res Natl Inst Stand Technol 98, (1993) Postek MT, Vladár AE, Banke GW, Reilly TW: Workshop report 1: Scanning electron microscope metrology as related to a defined edge structure. MAS Proceedings (Ed. Etz E), (1995) Postek MT, Vladár AE, Jones S, Keery WJ: Interlaboratory study on the lithographically produced scanning electron microscope magnification standard prototype. NIST J Res 98, (1993) Vladár AE, Postek MT, Davidson MP: Image sharpness measurement in scanning electron microscopy, Part 2. Scanning 20, (1998)