Deconvolution of Scanning Electron Microscopy Images

Transcription

1 SCANNING Vol. 15, (1993) OFAMS, Inc. Received November 3, 1992 Deconvolution of Scanning Electron Microscopy Images FUMIKO YANO AND SETSUO NOMURA* Central Research Laboratory, Hitachi Ltd., Tokyo, Instrument Division, Hitachi Ltd.. Ibaraki. Japan Summary: This paper describes a method of removing blurs in scanning electron microscopy (SEM) images caused by the existence of a finite beam size. Although the resolution of electron microscopy images has been dramatically improved by the use of high-brightness electron guns and low-aberration electron lenses, it is still limited by lens aberration and electron diffraction. Both are inevitable in practical electron optics. Therefore, a further reduction in resolution by improving SEM hardware seems difficult. In order to overcome this difficulty, computer deconvolution has been proposed for SEM images. In the present work, the SEM image is deconvoluted using the electron beam profile estimated from beam optics calculation. The results show that the resolution of the deconvoluted image is improved to one half of the resolution of the original SEM image. Key words: SEM, STEM, deconvolution, electron beam profile, image processing Introduction Endless miniaturization of large scale integration devices and magnetic materials for files has required high spatial resolutions for observation and analysis. To reduce the resolution of the scanning electron microscope (SEM), electron guns and electron lenses have been improved for decades (Crewe et al. 1968, Komoda and Saito 1972). Because of these efforts, the resolution of several has been achieved (Kuroda et al. 1987). However, the inevitable electron-lens aberration and electron-wave diffraction have recently become the primary limiting fac- tors determining the resolution of the SEM. Further reduction of the resolution by improving hardware seems to be very difficult. Although the transmission electron microscope (TEM) and scanning tunnelling microscope (STM) provide much higher resolutions of less than la, reducing the SEM resolution is still essential in many real sample characterizations, because the SEM has the advantages of simple sample preparation, simple observation, and direct information of surface configuration. The purpose of this study is to remove the blur from SEM images caused by the electron-beam sizc and to overcome the hardware limitations of the SEM. Our approach is to numerically reconstruct the information of high spatial frequency, which is lost because of the finite size of the electron beam. This technique is applied only to SEM and scanning transmission electron microscopy (STEM) in this study; however, we think it is also useful for auger electron spectroscopy (AES), secondary ion mass spectroscopy (SIMS), and all other material-analysis techniques in which the beam size determines the instrumental resolution. First. the deconvolution method is shown. then calculations of an electron-beam profile and experiments are discussed. Finally, the results of deconvolutions are shown. Method of Deconvolution An SEM image is an image formed with secondary electrons excited by a scanning electron beam. If the beam is focused to a zero-extent spot on the sample surface and the range of interaction between the electron beam and the sample is negligibly small, the SEM image reflects the surface configuration exactly. In practice, an electron beam cannot be focused to a zero-extent spot because of lens aberration and electron diffraction. Therefore. the SEM image Y(X) is blurred and is generally expressed by a convolution form, Address for reprints: Fumiko Yano Central Research Laboratory, Hitachi Ltd., Higashi-Koigakubo. Kokubunji Tokyo 185, Japan where Yo(X) represents a true sample profile and Io(X) is an electron-beam profile on the sample surface. The Fourier transformation of Eq. (1) is written as

2 20 Scanning Vol I. where F( Y } denotes the Fourier transformation of Y(X). SEM and STEM observation (Hitachi S-900) (proto-type STEM) SEM optical parameters & The absolute ulue of the Fourier transformation F( Y] is a power spectrum of an SEM image in the spatial frequency space. Eq. ( 2) shows that the Fourier transformation of the blurred image F(Y] is the result of the true image F( Yo} perturbed by the electron beam profile F( 1 ~ ). If the electron beam is ideally focused to a zero-extent spot. F( I()] is constant over the whole frequency range. then F{Y] is equal to F(YI)) without creating the blur. However. F( 10) is decreasing with spatial frequency when an electron-beam spot has a finite size. Therefore. F( Y] also decreases at high frequency. and missing the information at high spatial frequency leads to the blurred SEM images (Kubota 1978). From Eq. (3). the Fourier transformation of a true image YdX) is written as The inverse Fourier transformation of Eq. (4) gives the true image Yo(X) as This shows that we can reconstruct the true image Yo(X) (5) from the SEM image Y(X). if the electron beam profile IdX) is known. In the present work. we calculate the electron beani profile I(X) from the optical parameters of the utilized machine and the observation conditions, and we use I(X) in the deconvolution instead of the true electron beam profile IdX). The deconvolution process mentioned above is shown in Figure I Calculation of an Electron-Beam Profile Precise assigntiient of an electron beam profile I(X) is thc key to succedul deconvolution. When I(X) is close enough to the truc electron profile Io(X). the deconvolution successfully improves the resolution. On the other hand. the deconvoluted image might include serious artifacts when an unsuitable beam protile is used. In this section. the calculation of an electron beam profile is described. When an electron wave goes through a Iem. its phase is shifted. The shift x (~r.p) is written (Spence 1981) as Ftc. I Transfer and digitizing SEM image Y(x,y), (TV camera-image processor) Calculate electron beam profile + + Calculate Fourier transformation of deconvoluted image, Yo F(Y0} = F(Y} / F(I} Inverse Fourier transform Reconstruction SEM image Yo Yo = F-1 (F{'f'} / F(I}} Deconvolution process. electron beam on the sample can be written as Here. QAx) is a wave amplitude of the electron beam on the electron source at x = (x,y); u = (a/h,p/h) is a position on the lens plane: and X = (X,Y) is a position on the sample surface. Integrated region (m,fi~) is expressed by the maximum incident angle limited by an aperture and M is the magnification of the lens. Then. the beam profile I(X) can be written as LXE7 Objective plan (Electron source) Lens I I \ x=(x!y) VMl \ (6) where w. and p are angles between the lens axis and an electron wave (Fig. 7).?i is the electron wavelength and C, and C,, are the spherical aberration coefficient and astigmatism. respectixly. Dr. is defocus adjusted to obtain the best image b! the operator. Then. the wave amplitude of an Image (Sample surface) FIG. 2 Electron optics x = (X, Y)

3 F. Yano and S. Noniura: Deconvolution of SEM images 21 Here, I(X) is defined for a certain electron energy V (or wavelength A). For a practical electron beam, chromatic aberration effects should be included because of energy dispersion. When the energy dispersion function of the electron beam is assumed as cp(v>, I(X) can be written as KX) = 1 I cp(x,v) I* HV) dv, where h and Df are corrected as h(v) = J V( ( ~10-~V) (9) (10) Figure 4, respectively. The calculated electron beam profiles employed for these deconvolutions are also shown in Figure 4. Figure 4a shows one of the successful results. An improvement in the spatial resolution can be recognized. In this figure, particles of 1 nm can be distinguished in the deconvoluted image, while only particles larger than 2 nm can be distinguished in the SEM image of Figure 3b. In this deconvolution, the defocus Df is chosen to be 0.14 pn. Figure 4b is a deconvoluted image with Df of pm. Calculations show that this condition provides the electron where C, is the chromatic aberration coefficient and Vo is the mean value of the electron energy dispersion. Because the diameter of the electron source is demagnified to less than 0.1 nm in the field emission SEMs employed in the present work, we assume a zero-size spot configuration for the electron source image. Energy dispersion function cp(v) is approximated to be a rectangle of 0.3 ev width, which is appropriate for the field emission electron beam. Experiments SEM observations were made with Hitachi s S-900 SEM (Nagatani 1987). We employed a gold-microparticles specimen, evaporated on a carbon substrate. SEM images were recorded as photographs. The photographs were read by a video camera and digitized to 256 X 256 pixels of 64 gray scales. Deconvolution was performed by a mainframe computer (Hitachi M-680H). SEM optical parameters and observation conditions are listed in Table I. Results and Discussion SEM images of AU microparticles on a carbon substrate and their deconvoluted images are shown in Figure 3 and FIG. 3 SEM images of Au microparticles. (a) Wide view of -0.4 pn fize area, (b) image used for deconvolution experiment. TABLE 1 SEM optical parameters and observation conditions employed for deconvoluting SEM images Fig. 3 Fig. 5 SEM optical parameters Spherical aberration coefficient cs 1.9 mm 1.5 mm Astigmatism Ca 0 0 Chromatic aberration coefficient cc 2.5 min 2.0 mm Energy dispersion dv 0.3 ev 0 ev Observation conditions Aperture size a 10 mrad 10 mrad Defocus Df p p 1 Acceleration voltage V 20 kv SO kv

4 Scanning Vol ( 1993) o Distance (nrn) o Distance (nm) 1.5.o Distance (nm) FIG. 4 Decon\olutiun results and electron beam profiles used in the deconvolution. (a) Df = 0. Idpm. (b) Df = pm. (c) Di = -0.20pm. beam w.ith the circle of least confusion at the sample surface position. The operator must have adjusted the SEM optics to this condition to obtain SEM images with the best rewhition. Nevertheless. the spatial resolution has not been improved by the deconvolution with this beam profile. Figure 4c is a deconvoluted image with D, of p. Noisy artifacts at higher spatial frequencies appear in the deconvoluted image. We can see a clear improvement in spatial resolution in Figure 4a, but not in Figure 4b, in spite of its conditions, which are regarded as suitable for practical SEM observation. We speculate that the reason is one or more of the following: The range of interaction between an electron beam and a sample cannot be neglected (Koshikawa and Shimizu

5 F. Yano and S. Nomura: Deconvolution of SEM images 23 FIG. 5 (a) STEM image, (b) deconvolution result. 1974). The blurring function cannot be expressed with only a beam profile. The calculated beam profile I(X) is not exactly equal to the true profile Io(X). For example, we assume a zero-size spot configuration for the electron source image. The linearity of signal intensity versus secondary electron intensity is lost when the SEM images are converted into photographs, read by a video camera, and digitized. The dynamic range of 64 gray scales is insufficient. We apply this method to a STEM image, where the range of interaction between an electron beam and a sample is negligibly small because a very thin film is employed as a sample. In Figure 5a, we show an STEM dark-field image taken by a dedicated field emission STEM developed in our laboratory (Nomura et al and Todokoro ef a/. 1976). The sample is lumps of thorium atoms supported by a carbon film. The sample was prepared by placing a droplet of lop5 N thorium nitride on a film of about 3 nm thickness. The STEM provides a high resolution of 0.3 nm and produces single atom images of Th when the atoms are separately placed (Todokoro et al. 1976). The STEM image in Figure 5a was deconvoluted under the conditions listed in Table I. The result is shown in Figure 5b. We can see arrangements of small particles in the lumps. The particles could not be distinguished in the original STEM image (Fig. 5a). The particles are regarded as single Th atoms. The interesting point is that the particles are arranged as if they form a two-dimensional lattice with a separation of about 0.5 nm. This STEM result shows that this deconvolution is very effective when the range of interaction between an electron beam and a sample can be neglected. In the present work, we applied calculated electronbeam profiles to deconvolution. We believe that by using the measured electron- beam profiles, we may be able to improve the reliability of deconvolution. The deconvolution process enhances signals with higher spatial frequencies rather than with lower frequencies. Therefore, the result of deconvolution is highly affected by the signal- to-noise ratio and gray scales of the original images. Reading SEM images directly into a computer (without taking photographs) may also be very important and effective in avoiding the degradations in the dynamic range and imagesignal linearity. Conclusion This study demonstrates numerical deconvolution so as to remove the electron-beam blurs from SEM images. The deconvoluted images show improvement in the spatial resolution for both SEM and STEM images. The results suggest that this method can be usefully applied to other analytical methods, such as electron probe micro analysis (EPMA), AES, and SIMS, where the probing beam size limits the analytical resolution. Recently, many SEM applications have developed for insulator materials such as resists. A lower-energy electron beam (for instance, 1kV) is applied to avoid the charging up of these samples. In this case, observation with a high resolution is difficult because of a larger chromatic aberration in the lower-energy electron beam. On the other hand, the lower-energy beam produces fewer cascades and creates secondary electrons in a shallower and smaller region, that is, the range of interaction can be ignored. Then, the beam profile should become the main cause of the blur in SEM images, and the prerequisites set for the present deconvolution hold. Therefore, this method is considered to be more effective for high resolution SEM observation with a low-energy electron beam for insulator specimens. Acknowledgments The authors wish to thank Dr. Akira Fukuhara for his useful discussions. They also are greatly indebted to Mr. Yasushi Nakaizumi for providing useful information about

6 24 Scanning Vol. 15, 1 (1993) SEM instrumentation and to Mr. Shingo Nakagawa for the SEM observations. References Crewe AV, Eggenbeger DN, Wall J, Welter LM: Electron gun using a field emission source. Rev Sci Instrum 39, (1968) Komoda T, Saito S: Experimental resolution limit in the secondary electron mode for a field source scanning electron microscope. Scanning Electr Microsc (1972) Koshikawa T, Shimizu R: A Monte Carlo calculation of low-energy secondary electron emission from metals. J Phys D: Appl Phys 7, (1974) Kubota H: Ouyou Kougaku. Iwanami Zensyo (1959) Kuroda K, Hosolu S, Komoda T Observation of tungsten field emitter tips with an ultra-high resolution field emission scanning electron microscope. Scan Microsc 1, (1987) Nagatani T, Saito S, Sato M, Yamada M: Development of an ultrahigh resolution scanning electron microscope by means of a field emission source and in-lens system. Scan Microsc 1, (1987) Nomura S, Todokoro H, Komoda T Development of a field emission STEM and its application to element analysis. 34th Ann Proc Electron Microsc Soc Am, Miami Beach, Florida, (1976) Spence JCH: Experimental High-Resolution Electron Microscopy. Clarendon Press, Oxford (1981) Todokoro H, Nomura S, Komoda T Observation of atom images by means of field emission STEM. 34th Ann P roc Electron Microsc Soc Am, Miami Beach. Florida, (1976)