Simulation of Backscattering Images in the FE-SEM
RAYNALDGAUVIN
Département de génie mécanique, Université de Sherbrooke, Sherbrooke, Québec, Canada
Since the famous picture of Ogura1, it is known that high resolution, at the nanometer level, backscattered electron (BSE) images can be obtained in a field emission scanning electron microscope (FE-SEM). Since then, there has been some new ideas about the contrast and resolution mecha-nisms of BSE images in the FE-SEM2. Even if thousans of high resolution BSE pictures have been taken in the FE-SEM since then, there is still a need of explaining the con-trast and resolution of BSE images in the FE-SEM. In order to do so, a new Monte Carlo program has been
devel-oped to simulate BSE images in multilayered structures. A line scan was simulated for an AlAs layer of 1 nm thick embedded in GaAs for an 1 keV incident electron beam.
For each run, 5000 electrons trajectories were simulated.
The beam size was set to 2.5 nm. Such line scan is shown in Figure [1]. From this line scan, a contrast of 6 % is com-puted. Figure [2] shows a line scans simulated for the same condition as in Figure [1], but with energy filtration of the BSE. Only the BSE which have loss less than 2 % of their initial energy have been used in the computation of this line scan. A contrast of 6.5 % is computed. It is clear that there is no advantage to use energy filtration of BSE at 1 keV for such a small feature since the small gain in contrast is off-set by the strong decrease in signal, which is about 30 times smaller.
References
1. K. Ogura, A. Ono, S. Franchi, P.G. Merli and A. Migliori (1990), Observation of GaAs/AlAs Superlattice Structures in both Sec-ondary and Backscattered Electron Imaging Modes with an Ultrahigh Resolution Scanning Electron Microscope, Proc. of XII th Int. Cong. Elect. Microsc., Vol. 1, p. 404.
2. P.G. Merli, A. Migliori, M. Nacucchi, D. Govoni, G. Mattei (1995), Ultramicroscopy, 60, pp. 229–239.
Applications of SEM Monte Carlo Modeling to Geometry Determination in Single-Crystal Silicon Test Patterns
J. S. VILLARRUBIA, A. E. VLADÁR, J. R. LOWNEY, S. JONES, ANDM. T. POSTEK
National Institute of Standards and Technology,*
Gaithersburg, MD, USA
Width measurements pose a particularly problematic calibration problem. The measurement entails determining the distance between inherently dissimilar edges. Even in the simplest imaginable case, an ideal line of rectangular cross section, the left and right edges are not identical but are, rather, mirror images of one another. Any error, ∆x, in the assignment of one edge is mirrored (-∆x) on the other edge, resulting in twice the error when the positions are sub-tracted to determine the width. In the scanning electron microscope (SEM), this makes modeling of the instru-ment response, for example by using Monte Carlo tracing of electron trajectories, critical to an accurate measurement.
As part of a project to test the accuracy of NIST’s MON-SEL1Monte Carlo model, we have performed measure-ments on the (110) face of single–crystal Si test structures fabricated in SIMOX and BESOI.2–4These are two tech-nologies for producing a 200 nm to 1000 nm layer of crys-talline Si on top of an insulating oxide of similar thickness.
Structures containing lines in the [1–
12] and [11–
2] directions were etched into this material. Along these directions the (110) top surface of the line is intersected at 90° by {111}
sidewalls that are slow–etch planes for the KOH etchant.
FIG. 1 Simulated backscattered coefficient as a function of beam position for a 1 nm AlAs vertical layer embedded in GaAs for a 1 keV electron beam. The scale is in A (1 A = 0,1 nm) and the AlAs layer is between –5 and 5 A.
FIG. 2 Line scan simulated with the same condition of Figure [1], but with energy filtration of the BSE. Only the BSE which have loss less than 2% of their initial energy were used in the computation of this line scan.
BSE, 2% Energy filtered
0.014 0.012 0.010 0.008 0.006 0.004 0.002 –60 –50 –40 0
Beam position (A)
–30 –20 –10 0
Back coeff.
0.34 0.335 0.33 0.325 0.32 0.315 0.31 0.305 0.3 0.295 0.29
–60 –50 –40
Beam position (A)
–30 –20 –10 0
Because of preferential etching, the structures are expected to have low edge and wall roughness and nearly vertical sidewalls.
We collected several series of SEM images of these structures and compared the profiles to the MONSEL result for Si lines of rectangular cross section. For SIMOX struc-tures, the agreement was good. The SEM profiles on BESOI differed from those predicted in these significant respects: 1) The observed profiles were often asymmetri-cal, with one edge brighter than the other. 2) The extent of the asymmetry varied with position on the sample. 3) Even in locations where there was left–right symmetry, the observed edges were brighter than predicted. These dif-ferences necessitated revisiting the geometrical assump-tions. By allowing the line to have a skewed trapezoidal cross section, with the extent of skew varying with posi-tion, we were better able to fit the observed intensities.
The extent of deviations from the expected 90° that pro-duces the best fit to the observations is quite small, typi-cally 0.2° of trapezoidal splay skewed to left or right by amounts ranging from –0.2° to 0.2°. Even though these are small angles, Monte Carlo results indicate very high sen-sitivity of the SEM profiles to angular changes of this magnitude. This high sensitivity is confirmed experimen-tally by tilting the sample by comparable amounts.
* Contribution of the National Institute of Standards and Technology;
not subject to copyright in the United States.
References
1. J. R. Lowney, A. E. Vladár, and M. T. Postek, “High-accuracy critical-dimension metrology using a scanning electron micro-scope,” Proc. SPIE 2725, pp. 515-526, (1996); J. R. Lowney,
“Application of Monte Carlo simulations to critical-dimension metrology in a scanning electron microscope,” Scanning Micro-scopy 10, pp. 667-678, (1996).
2. M. W. Cresswell, J. J. Sniegowski, R. N. Ghoshtagore, R. A.
Allen, L. W. Linholm, and J. S. Villarrubia, “Electrical Test Structures Replicated in Silicon-on-Insulator Material,” Proc.
SPIE 2725, p. 659, (1996).
3. J. S. Villarrubia, R. Dixson, S. Jones, J. R. Lowney, M. T.
Postek, R. A. Allen, and M. W. Cresswell, “Intercomparison of SEM, AFM, and Electrical Linewidths,” Proc. SPIE Vol. 3677, pp. 587-598 (1999).
4. J. S. Villarrubia, A. E. Vladár, J. R. Lowney, M. T. Postek, R.
A. Allen, M. W. Cresswell, and R. N. Ghoshtagore, “Linewidth Measurement Intercomparison on a BESOI Sample,” Proc. SPIE Vol. 3998 (2000) in press.
Regularization Methods for Beam Broadening Corrections
BERTW. RUST
National Institute of Standards and Technology, Gaithersburg, MD, USA
SEM scans suffer a loss of resolution because the inci-dent beam is broadened around the focal point. This
broad-ening is modelled by a convolution of the signal with a Gaussian kernel. Discretizing the integral equations for the convolution gives an underdetermined linear regression model. Additional assumptions about the signal must be imposed in order to specify a unique least squares solution, but even then that solution is pathologically sensitive to measurement errors in the observed signal.
At Scanning 97, Rust and Lowney presented a method for stabilizing the problem by truncating the singular value decomposition in a way which discards signal components that are dominated by the measurement errors, when those errors are uncorrelated (Rust and Lowney, 1997). At Scan-ning 98 they extended the method to the more difficult case, which sometimes occurs at high scan rates, where errors in adjacent pixels are correlated (Rust and Lowney, 1998).
The methods described in the present paper use a dif-ferent approach, called regularization, which incorporates additional information about the desired solution in order to stabilize the problem. This is done by appending a sys-tem of linear constraints to the regression model and weighting them with a free parameter whose magnitude determines the relative importance assigned to the mea-surements and to the a priori constraints. The paper addresses three important concerns in using such methods:
(1) choosing the proper a priori constraints, (2) picking the optimal value of the regularization parameter, and (3) using the residuals as diagnostics for assessing the quality of the resulting estimate.
References
Rust, B.W. and Lowney, J.R., “Correcting for the Effect of Electron Beam Broadening in Critical Dimension Metrology in Scanning Electron Microscopy”, Scanning, vol. 19, 1997, pp. 222-223 Rust, B.W. and Lowney, J.R., “Correcting for Beam Broadening in
Critical Dimension Metrology”, Scanning, vol. 20, 1998, p.
220
Application of 3D Monte Carlo Simulation of Auger Line-Scanning in Analyzing Field Emission Device
HUANYAN* ANDLICHEN†
*IKON Image Systems Solutions, Inc., Toronto, Ontario, CANADA; †Ceravision Ltd., Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, UK
3D Monte Carlo simulation1is applied into Auger line-scanning and imaging contrast of various field emission devices2,3(FED). The current reported device is silicon-based Si-SiO2-Cr sandwich-like structure, the spindle sil-icon tip has either diamond-like carbon coated layer or SiO2 layer. Following phenomena have been observed in the simulation:
1.Clear O[KLL] signal from insulator layer of SiO2 is recorded from detectors with relative large polar angle. The SiO2is distributed underneath the gate.
2. Recognizable Cr[LMM] Auger signal is recorded at scanning positions of the emission tip apex. It is observed regardless of the detector angle configura-tion, while its shape is sensitive to the angles.
Possible mechanism for the phenomena has been inves-tigated. In which, the tip introduces the primary electron and back-scattered electron into the hidden part of cave of the FED. These energetic electrons within that part of the cave have higher probabilities to hit the cave-wall. The component of the wall includes not only surface of the sub-strate (i.e., Si) but also that of insulator layer (SiO2) and internal-facets of gate although they are not in radiation region of primary electron beam when it scans at the apex area of the tip. This eventually leads to detectable Auger signal from these hidden facets. Such effect may be called Cave-Probing.
The first phenomenon has an agreement with reported experimental work.2The second one is waiting to be exam-ined by experimental observations and further studies.
References
1. Yan H, El-Gomati MM, Prutton M, Wilkinson DK, Chu DP, Dowsett MG: Mc3D: A three-dimensional Monte Carlo system simulating image contrast in surface analytical scanning elec-tron microscopy I—Object-oriented software design and tests.
Scanning 20, 465–484 (1998)
2. Wei Y, Chalamala BR, Smith BG, Penn CW: Surface chemical changes on field emitter arrays due to device aging. J. Vac. Sci.
Techno. B 17(1), 233–236 (1999).
3. Chen L, El-Gomati MM: Fabrication of Tungsten-Coated Sili-con-based gated emitters. J. Vac. Sci. Techno. B 17(2), 638–641 (1999).
Studies of Samples Having Shallow Surface Topography by the Low-loss Electron (LLE) Method in the Scanning Electron Microscope (SEM)
OLIVERC. WELLS,* MAURICEMCGLASHEN-POWELL,*
MICHAELT. POSTEK† ANDANDRASE. VLADAR†
*IBM Research Division, Yorktown Heights, NY;
†NIST, Gaithersburg, MD
The low-loss electron (LLE) image in the scanning elec-tron microscope (SEM) is being applied to samples that are at right angles to the beam with a view to applications in the semiconductor metrology, inspection and review areas.
The LLE image is obtained by collecting electrons from a (usually tilted) specimen in the forward direction with 100 to 500 eV energy loss. This has been done in two ways.
First, with a retarding-field energy filter and an external-focus magnetic lens. Second, by magnetic energy filtering with an immersion lens.
Advantages of the LLE method include the following:
1. It is insensitive to charge potentials on a poorly con-ducting specimen.
2. It gives strong topographic contrasts from a nearly flat surface.
3. The information depth can be as shallow as tens of nanometers even when the beam energy is as high as 10 or 20 keV.
4. Penetration effects at sharp edges are greatly reduced.
5. Morin et al. (1979) have demonstrated the direct imaging of crystal defects by the high voltage LLE method.
6. However, the sample must not be too rough.
As a result of this technique, imaging of shallow topo-graphy is improved, and penetration fringes at sharp edges are reduced.
References
Morin,P., Pitaval,M., Vicario,E., and Fontaine,G., (1979). Scanning electron microscope observation of single defects in solid crys-talline materials, Scanning, vol.2, 217–224
SMART—Routines to Measure SEM Resolution and Performance
DAVIDC. JOY
EM Facility, University of Tennessee, Knoxville, TN The imaging resolution of a scanning electron micro-scope (SEM) is usually the parameter of most interest to a user of the instrument. It is, however, a quantity that has been found difficult to measure reliably and as a result most users have to take the specifications and quoted perfor-mance of current instruments on trust because they are inca-pable of testing and verifying the values for themselves.
The basis of an objective and reliable method for the measurement of resolution is the power spectrum (2-dimen-sional Fourier transform) of the image1. This displays the intensity distribution of different spatial frequencies in the image, with the frequency increasing along the radius from the center of the transform. At some frequency the signal becomes submerged in the random noise of the system.
This frequency then defines the information limit of the SEM and hence the achieved spatial resolution. An elegant commercial system which can perform this measurement in real time is now available2. Unfortunately this approach also has two fundamental problems: first, the technique assumes that the sample being examined contains infor-mation at spatial frequencies beyond the resolution limit of the microscope. Samples which satisfy this condition for present high resolution machines are notably rare although
recent work by Postek et al.3may provide a suitable test specimen. Second, it is impossible to distinguish signal from noise on a pixel by pixel basis, so the boundary between signal and noise cannot be accurately determined and hence the resolution figure remains elusive. It is that difficulty which is considered here.
Two approaches which can alleviate this problem are available. The first uses the procedure of cross-correlation4 which compares two overlapping regions of the same micrograph and plots the cross-correlation function (CCF) between them. The width of the CCF is a direct measure of the resolution, and the peak to background ratio of the CCF is an estimate of the signal-to-noise ratio of the image.
By sampling the image twice and looking for correlated features this method avoids the problem of distinguishing signal from noise since noise is always uncorrelated. For successful application, however, the image needs to be homogeneous and free from extremes in signal level. An interesting application of this approach is a rapid tech-nique for the measurement of SEM spot size. Using a sim-ple STEM adapter, the bright field image of a thin carbon film is obtained and the CCF method used to deduce the resolution. Since beam broadening is negligible under these conditions, the resolution is equivalent to the probe size.
A second approach4uses two micrographs of the same area, the images being recorded sequentially. These images are superimposed, but with a small linear offset, and the power spectrum is obtained as before. Intensity from cor-related detail in the images is now modulated by parallel fringes while random noise remains unmodulated. The boundary representing the resolution cut-off is now clearly identified as the extremity of the fringe pattern permitting an accurate measurement to be obtained.
Code implementing each of these procedures has been written in the form of a macro for use with the NIH Image, or SCION Image, image processing programs. This code, called SMART (Scanning Microscope Analysis and Res-olution Testing) works identically in either program, car-ries out the analysis without operator intervention on any of the digital image formats recognized by the programs, and produces a result within a second or two. SMART can be downloaded from http://web.utk.edu/~srcutk
References
1. TA Dodson and DC Joy (1990), Fast Fourier transform technique for measuring SEM resolution, Proc. 12th ICEM, 406–407.
2. Micrologia from SPECTEL Research. See AE Vladar, MT Postek and MP Davidson (1998), Image sharpness measurement in scanning electron microscopy—Part II, SCANNING 20, 24–34.
3. Youn HK and Egerton RF, (1997), Resolution measurement of SEM using CCF, Proc. Micros.Soc. Canada 24, 62–63.
4. Erasmus S J and Smith KCA (1980), On-line computations of diffractograms for the analysis of SEM images, Inst. Phys.
Conf. Ser. 52, 73–77.
LISPIX: Image Processing and Data Visualization Tool for the PC and Macintosh*
DAVIDS. BRIGHT
Surface and Microanalysis Science Div., National Inst. of Standards and Technology, Gaithersburg, MD
Lispix is a public domain scientific image processing and analysis program maintained by the Microanalysis Group at NIST. It is a general purpose program with additional special purpose tools with enough utility to be of general interest. Lispix is an update of MacLispix,1a public domain image processing system for the Macintosh,*with tools for a variety of image processing problems such as: analysis of diffraction spots,2 uniform display of x-ray maps,3 deter-mination of fractal dimension of particle outlines,4 and analysis of image stacks or data cubes.5Due to interest from the PC community, the software now also runs on both Windows*and the Mac*, is public domain, and available along with source, instructions, and sample images.6
Lispix accommodates TIFF files and raw image files (no header), both with pixel types of signed and unsigned 8, 16 and 32 bit integers, 4 and 8 byte IEEE standard floating point numbers, and 3x8 bit RGB color. Lispix has a vari-ety of standard image processing operations, such as thresh-olding, edge finding (gradient), filtering, Linear Hough Transform, and particle measurement. Lispix also reads JPEG files, and a few other image formats.
Lispix has a variety of scaling and enhancement features.
For example, clipped scaling (trimming outliers) is espe-cially useful for display of x-ray maps, and images with noise or very bright or very dark artifacts. Scaling enhances visibility of features, and is done using a copy of the image, so that the original is available for measurements, such as intensity mean, min, max, variance, etc. Once an image is scaled, manipulation of the palette, or color look up table can further enhance visibility, or mark intensity ranges of interest. Lispix has these adjustable color scales: gray level, thermal, thresholding, color bars, and gamma correction.
There is also a logarithmic banded color scale3that, with-out adjustment, is useful for visualization of images with up to three decades of dynamic range.
Lispix now accommodates large images by means of a navigator window, similar to Photoshop*. Lispix also accommodates groups; i.e., images in the group can be zoomed and scrolled, arranged on the screen and processed all together.
Lispix has a periodic table designed for selecting ele-ments for various analyses, but is useful by itself. Click-ing on an element displays a list of its properties and iso-topes. The table can be colored according to any of the numerical properties in the list.
To facilitate examination of groups of registered images displaying different signals such as chemical composition or spectrum interval, Lispix can make RGB color overlays and XY or XYZ scatter diagrams. For more than three
images, the data cube facility is useful, and includes Prin-cipal Component Analysis. A selection of the component images often represents the original data. Visually check-ing the component images and examincheck-ing a reconstruction of the original data out of the components, both indicate whether or not the data is well represented.
* Certain commercial equipment or software are identified in this report. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the equipment or software identified are nec-essarily the best available for the purpose.
* Certain commercial equipment or software are identified in this report. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the equipment or software identified are nec-essarily the best available for the purpose.