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Measurement of 100-nm polystyrene sphere by transmission electron microscope
Powder Technology 126 (2002) 255 – 265 www.elsevier.com/locate/powtec
Measurement of 100-nm polystyrene sphere by transmission electron microscope K.Y. Jung a, B.C. Park b,*, W.Y. Song a, B.-H. O a, T.B. Eom b a
College of Electrical and Computer Engineering, Inha University, Inchon 402-751, South Korea Length Group, Korea Research Institute of Standards and Science, P.O. Box 102, Yusong, Taejon 305-600, South Korea
b
Received 23 August 2001; accepted 4 March 2002
Abstract The mean diameter of the 100-nm polystyrene sphere was measured with the transmission electron microscope (TEM) with a view to the development of the accurate and visual sizing technique for nm scale particles. To minimize the sizing error due to the inaccurate instrumentstated magnification and the edge location uncertainty, the 300-nm spheres were mixed with 100-nm spheres to provide an internal calibrator, whose diameter is accurately known. The diameters of 100-nm spheres were determined by comparing with that of 300-nm spheres in the same negatives (TEM pictures). For the correction of the electron beam-induced shrinkage effect, the dependence of the shrinkage on the accelerating voltage, beam intensity, and the exposure time was examined and analyzed. Based on such an investigation, and with the several data manipulation routines, the mean diameter was determined with the expanded uncertainty of approximately 2% at the 95% confidence level. The measured value is consistent with those obtained by other laboratories using different techniques for the same spheres. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Standard particle; Polystyrene sphere; Internal calibrator; TEM; Acceleration voltage; Intensity; Shrinkage
1. Introduction Accurate particle size standard is important for the semiconductor industry since the particle counters and scanning surface inspection systems, which are routinely used for the detection of the small contaminants throughout the wafer as well as the integrated circuit manufacturing process, is very sensitive to the particle size when it is smaller than the wavelength of the probe beam. In particular, the accurate assessment of 100-nm polystyrene spheres has been a recent issue since 100 nm is the current size limit for most of such state-of the-art instruments. Several independent measurements of the 100-nm sphere have been made by various methods. These include transmission electron microscopy [1 – 3], differential mobility analysis (DMA), also called an electrostatic classification [4], quasi-Millikan method [5,6], and light-scattering method [7,8]. DMA method is the only method so far whose uncertainty budget is fully investigated and then reported. Quasi-Millikan and light scattering method has
*
Corresponding author. E-mail address: [email protected] (B.C. Park).
its own unique characteristics, but, those deals with a group of particles rather than an individual particle. TEM has the advantage over other methods in that it can provide information about the shape of individual particles in addition to their size. The usual TEM method, however, has a couple of problems that make it unsuitable for measurement of the 100-nm particle size standard [1]. The instrument-stated magnification is not so credible. It is difficult to calibrate high magnifications with the grating replica. The actual magnification can vary between photos at the same magnification in the same instrument. Even if the magnification is perfectly calibrated, reliable particle diameter cannot be obtained by measuring the particle image itself because of the following reasons. First, the distortion of polystyrene spheres under the strong electron beam contributes an unknown amount to the under-estimation and the measurement uncertainty of the particle size. Secondly, the sphere edges are difficult to locate since the microscopic image is not sharp at the edges when viewed at high magnification. The ‘internal standard method’ for reducing those errors involved with the conventional TEM method has been reported. In this study, 100-nm spheres were photographed together with 300-nm spheres, and certified diameter was
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K.Y. Jung et al. / Powder Technology 126 (2002) 255–265
provided as an internal calibrant [1]. In the method, the distortion of the two different kinds of spheres was assumed similar since they are made out of the same material and are subjected to the same condition. This assumption, however, was not experimentally checked. If distorted differently, the initial diameters should have been measured and then compared with each other before they were exposed to damage by means of an electron beam. Furthermore, the determination of the diameter by inserting the particle image into two parallel lines with known distance is always influenced by the edge location uncertainty. The work reported here is directed toward a more thorough examination of TEM method for particle size measurement. The distortion of the spheres was studied under a range of beam conditions—acceleration voltage, beam intensity and exposure time. The diameter is obtained from the calculated area of the separated particle image on the negative rather than the spacing of the two parallel lines holding the image inside, to reduce the statistical error coming from the inaccurate edge location as well as imperfect roundness. The modified TEM method was applied to the calibration of the 100-nm standard sphere. The detailed processes and data treatments are described in Section 2. The results are presented and discussed in Section 3, followed by the conclusion in Section 4.
2. Measurement procedure The entire measurement procedure is summarized in Fig. 1a. The sample is a mixture of 100- and 300-nm particles deposited on the TEM grid. The TEM picture is taken so that as many separated particles as possible are included in a shot. To eliminate errors due to the magnification, the particles are measured directly from the negatives. The negatives are scanned and then converted into the image files. The images of the particle is then digitally processed by means of the image analysis program, to get the mean diameter and size distribution of the 100-nm particles.
times, and then the specimens were dried in the air (temperature = 20 jC, relative humidity = 50%) for 18– 20 h.
2.1. Preparation of the TEM specimen
2.2. TEM measurement
Deionized water filtered with 0.1-Am filter was used for diluting the original solution of polystyrene latex as well as for cleaning the bottles for the preparation of the samples. The 100- and 300-nm particle solutions were diluted to make about 0.1% and 0.05% in weight concentration, respectively, and then added by the same amount of each solution. The 100-nm particle solution is JSR SC-011-S, and 300-nm particle solution is NIST SRM 1691. A drop of the mixed solution was put on a TEM specimen, which is a carbon –metal film supported by 200-mesh copper grids. The drop was elongated and torn with both ends of the forceps prior to putting in order to prevent the agglomeration of the spheres. The same procedure was repeated 10
TEM (EM912 omega, Carl Zeiss) was used for measurement, which records the image on the negative of the size 80 80 mm. The magnification used throughout the study was 50,000, where ten or so 100-nm particle images could appear on a negative, together with one or two 300-nm particle images. It was considered that the area of the particle image should be sufficiently large to reduce the quantization error coming from the pixel size when the image is converted into digital form. Before the photograph was taken, the specimen was overviewed at a low magnification of 8000 to find a relatively large area of isolated particles. To decrease the possible particle shrinkage, the beam intensities was adjusted as low as possible to produce
Fig. 1. The measurement procedure of 100-nm sphere with TEM (a) for different exposure times (bold type numbers) (b).
K.Y. Jung et al. / Powder Technology 126 (2002) 255–265
viewing screen illumination just visible in total darkness by the dark-adjusted eye. Only particles in the same negative were compared in order to avoid any variation of magnification depending on the different batches of shot. For a selected group of mixed particles on a negative, eight pictures were taken with eight different exposure times. The exposure times chosen are 20, 30, 40, 50, 60, 70, 80 and 200 s. Those include, as seen in Fig. 1b, the unavoidable exposure required before the first shot, the 3 s for taking a picture, and the intentional exposure. In order to investigate
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the effect of the beam condition on the particle shrinkage, a set of negatives with different exposure time, were obtained for a range of beam conditions. The set of conditions is comprised of one of the accelerating voltages of 80, 100 and 120 kV, and currents of either 300 or 720 pA. At the acceleration voltage of 60 kV, the image becomes unstable, thus the corresponding experiment was not performed. All of the negatives were scanned by a commercial scanner (HP 4c), and converted into digital files. The scanner has a resolution of 1200 DPI (1200 pixels per inch),
Fig. 2. Image processing being performed to calculate the size of 100- and 300-nm particles, respectively.
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Fig. 3. The change of particle lines (circular) as the grayscale threshold increases. The lines at the threshold of 49 and 63 are not good. The other circles between them are good, although they look almost the same at the bandwidth of the threshold between 52 and 58. Then the center value, 55 is chosen for the radius determination, and the bandwidth of 6 (from 52 to 58) produces the corresponding uncertainties.
Fig. 4. Comparison of intensity profiles of 100- and 300-nm particles. The intensity profiles of 300 nm are scaled down.
K.Y. Jung et al. / Powder Technology 126 (2002) 255–265
and 256 gray levels. For processing of the scanned image, the commercial image analysis program (GLOBAL LAB) was used. The program uses grayscale threshold values to separate the pixels in an image into particle and background, and from the number of pixels inside, the particle diameter is determined in terms of pixels. The edge of the particle image on a negative is not sharp; rather, it has a distributed intensity profile. The best circle, which might represent the actual peripheral edge of the particle image, should be found before determining the diameter from the circle area. Fig. 2 shows how the image analysis is performed for 100- and 300-nm particles, respectively. The area of the region enveloped by yellow line is shown at the top and left. The best circle is chosen when the circle is judged as the clearest while increasing the ‘threshold’. The process is well illustrated in Fig. 3. The lines at the threshold of 49 and less, or 63 and greater are not good. The other circles at the threshold between 52 and 58 look best. Then the center value, 55 is chosen for the radius determination, and the bandwidth of 6 (from 52 to 58) becomes the interval of the corresponding error. This method is applied the same way to both particles, 100 and 300 nm, since their intensity profiles are nearly the same except the scale as can be seen in Fig. 4. As the boundary of the particle is fixed, then the interior area is calculated in the unit of pixels to convert into the diameter for the circle of the same area. For optimal accelerating voltage (80 kV) and beam current (300 pA), which were chosen after comparing the results of aforementioned experiments, photographs were taken of mixtures of 100 and 300 nm, and finally 17 negatives, including eighty-two 100-nm particles in total, were obtained for analysis as shown in Table 1. The numbers in ‘300 nm’ and ‘100 nm’ columns of Table 1
Table 1 The list of TEM negatives used for the study Negative no.
Number of 300-nm particle
Number of 100-nm particle
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Total
2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 20
3 3 2 4 4 4 6 3 3 6 4 7 6 7 9 6 5 82
The numbers in ‘300 nm’ and ‘100 nm’ columns represent the number of particles existing in the corresponding negatives.
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represent the numbers of particles existing in the corresponding negatives. Unfortunately, the sample preparation technique did not allow a sufficient number of both particles to be obtained in a negative. Development of the efficient deposition technique on the TEM specimen will save much time, and make this sizing method more powerful. The 300-nm particle diameter, or the average if there are two, on each photograph has been used as the calibration diameter for the measurement of 100-nm particle diameters on the photograph. Then the individual 100-nm particle diameters thus obtained are used to calculate the mean and standard deviation.
3. Results and discussion Figs. 5 and 6 show the exposure time versus measured particle size curves. The diameters for zero exposure time in each graph are not the measured values. They are extrapolated from the measured sizes with different exposure times, which was varied from 20 to 200 s. Fig. 5 shows the size change obtained for four specimens with two electron beam currents of 300 and 700 pA at the accelerating voltage of 120 kV. Pictures of two of the specimens (Fig. 5a and b) were taken with the beam current of 300 pA, while the others (Fig. 5c) were taken with 700 pA. There is a case (b) where the increase in size happened with 300 pA, while the remaining three cases where the usual shrinkage happened as expected. It is not certain to the authors whether such an increase came from an unusual contamination or from an unknown effect due to high acceleration voltage. Such a behavior, however, was not observed for other acceleration voltages, 100 and 80 kV, throughout the study. The results in Fig. 5 are further summarized in Fig. 6a and b, where each dot represents an averaged size over the particles in a negative corresponding to a specific exposure. In other words, each curve represents a change of the averaged particle size in a negative as the exposure varies. Fig. 6c,d and e,f shows the equivalent results for the accelerating voltages of 100 and 80 kV, respectively. In all cases, the sizes decrease monotonically with increasing exposure time, as expected. The rate of shrinkage is different from specimen to specimen even under similar conditions, so that the difference in the mean diameter significantly changes as the exposure increases in Fig. 6. Although the shrinkage does not show any noticeable dependence on the voltage and current, the shrinkages at 80 kV and 300 pA looks more consistent that under at any other condition. Therefore, the condition of 80 kV and 300 pA has been chosen to measure the diameter of 100-nm standard sphere. The choice also rests upon the idea that lower voltage and current will bring less damage to the particles, and our measurement results will be affected less from the beam conditions. Even for spheres of the same material and undergoing the same beam conditions, it is observed that the shrinkage ratio can differ slightly from particle to particle, and from
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Fig. 5. The exposure time versus particle size curves at the accelerating voltage of 120 kV. Each graph corresponds to each negative, and each dot in the graph represents the size of the individual particle.
specimen to specimen. Fig. 7 shows the shrinkage for the spheres on three specimens ing exposure time, respectively. The 300spheres seem to have the same shrinkage
examples of with increasand 100-nm behavior. A
shrinkage of 3 –10% is observed after an exposure of 1– 4 min, which is consistent with the result of Ref. [9]. It should be noted that the additional shrinkage occurs if the specimen is exposed further. That means the measured
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Fig. 6. The exposure time versus averaged particle size curves at the accelerating voltage of 120 kV (a, b); 100 kV (c, d); 80 kV (e, f). Two graphs at each voltage are with different beam currents.
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Fig. 7. The exposure time versus shrinkage ratio shown for the three samples out of 17 samples in total. The shrinkage at the zero exposure (extrapolated) is set to zero.
K.Y. Jung et al. / Powder Technology 126 (2002) 255–265
particle diameter is affected by the measurement time, which means that the extrapolation to zero exposure time diameter is needed. As another evidence of the finding that shrinkage rates are similar, the mean shrinkage rates, over the first 20 s, are computed for each set of 100- and 300nm particles, respectively. Then the ratios of the mean shrinkages for each photograph are obtained and plotted in Fig. 8. The difference in shrinkage rates does not exceed 0.3% in standard deviation, which can be given as the standard uncertainty due to any slight difference in the shrinkage rates. In order to measure the mean and the standard deviation of the 100-nm standard sphere, 17 negatives were obtained where 100- and 300-nm spheres appear together for comparison. On average, one to two 300-nm particles, and three to seven 100-nm particles are included in each negative. In total, twenty 300 nm-spheres, as internal calibrators for the photograph where they are found, and eighty-two 100-nm spheres were taken, and are listed in Table 1. Fig. 9 is a histogram of the obtained diameters of eighty-two 100-nm spheres. The measured mean and the standard deviation of 100-nm particle are 109.2 and 3.2 nm, respectively. There was no outlier when the criterion of 4r (r: standard deviation) is used—that is, no particles deviated from their mean by more than 4r. Measurement uncertainties are summarized in Table 2. The uncertainties can be categorized into two evaluations, type ‘A’ and ‘B’. While type A evaluation is calculated from series of the repeated observations, type B evaluation uses available knowledge [11]. Type A uncertainty comes from the finite number of spheres taken to determine the mean diameter. The corresponding standard uncertainty is then given by the standard deviation of the 100-nm sphere, divided by the square root of the number of particles. The apparent standard deviation 3.2 nm obtained as described above, however, is broadened because of the breadth of the size distribution of the 300-nm particles. The apparent
Fig. 9. Size distribution of the measured diameters of 100-nm sphere.
relative standard deviation, 3.2 nm/109.2 nm will be therefore given by the square root of the sum of the squares of the relative standard deviations for the 300- and 100-nm spheres. The standard deviation of the 300-nm particles is 6 nm, according to TEM measurement results [10], and the standard deviation of the 100 sphere is computed as 2.1 nm (1.9%). Type B uncertainties have six sources. (1) Magnificationassociated uncertainty in the transfer of the particle image from a negative to a digital file. The image can be distorted due to the spatial inhomogeneity of the scanner magnification, the thermal bending of the negative, and different magnification along the horizontal and vertical direction. To estimate the uncertainty, one particle image was scanned
Table 2 Summary of the TEM measurement uncertainties of 100-nm standard sphere Uncertainty type
Source of uncertainty
Standard uncertainty (nm)
Type A
Finite sample size (N = 82; rD = 2.1) Scanner magnification Edge location of the particle image Uncertainties of the certified values of the reference sphere (300 nm) Finite sample of 300-nm particles Difference in shrinkage rates for 100- and 300-nm spheres Pixel size uc=(u21 + u22 + . . .)1/2
0.2
Type B
Fig. 8. The ratios of 300- to 100-nm particle shrinkage rates for the first 20-s exposure.
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Combined standard uncertainty Expanded uncertainty
U = 2uc
0.4 0.2 1.0
0.5 0.3
0.002 1.3 2.6
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in five different positions; center, up, bottom, left and right. The measured radii in the unit of pixel are 309.37, 308.39, 309.39, 309.66, 309.03 (mean = 309.2; 1r = 0.5, 0.2%) for the 300-nm particle, and 122.44, 121.44, 121.93, 121.85, 121.51 (mean = 121.8; 1r = 0.4, 0.3%) for the 100-nm particle. The positions of both particles (300 and 100 nm) in a negative affect the results through the inter-comparison. The corresponding standard uncertainty for the magnification is calculated as [(0.5/309 109)2+(0.4/122 109)2]1/2 = 0.4 nm for 109 nm. (2) Edge location uncertainty in the process of determining the threshold for the best circle as described previously. The maximum uncertainty due to this error was estimated for the case of the largest bandwidth, which is illustrated in Fig. 3. The shape of the circle is maintained best as the intensity of the threshold changes from 52 to 57. The corresponding areas enclosed by the ‘best’ circle are 43,358, 43,191, 43,065, 42,977, 42,891 and 42,815 pixels. The average area is 43,050 and the standard deviation is 200 or 0.47% of the average area. Considering that the relative error of diameter is given by a half of that of the area, the corresponding uncertainty is 0.2 nm for 109 nm. (3) Uncertainty of the certified diameter of the 300-nm particle. The 300-nm particle used for internal calibrator is originally certified as 269 F 7 nm by TEM, and 275 F 7 nm by QELS [10]. The uncertainty cited here approximately corresponds to the expanded uncertainty at the confidence level of 95%, although the total uncertainty is taken as the linear sum, instead of the square sums recommended by ISO [11,12]. For the vial used for the experiment, the mean diameter was re-measured as 273 nm by QELS at KRISS [13], with the combined standard uncertainty (1r) is 3 nm, which is used to give the equivalently standard uncertainty of 1 nm for the diameter of 109 nm. (4) Uncertainty due to the finite number of the 300-nm particle as internal calibrators, The uncertainty of the mean value for a set of n particles is expressed by the standard deviation of the size distribution divided by the square root of n. It is calculated to be 1.34 nm since twenty 300-nm particles in total are used, and the standard deviation is 6 nm [10], which then gives the corresponding standard uncertainty of 0.5 nm to the obtained mean diameter of 100-nm particles. (5) Uncertainty associated with the different shrinkage rates between 300- and 100-nm particles. The standard uncertainty is 0.3 nm or 0.3% of the diameter as given above. (6) Quantization-associated uncertainty due to the finite pixel size. Since the particle area is obtained in terms of the number of finite pixel area d2, there is a corresponding quantization error in the obtained diameter, whose standard uncertainty is given by pixel size divided by the circumference, which can be easily derived. The particle area is expressed as A = pD2/ 4 = Nd2, where A, D, d2 and N are the particle area, particle diameter, pixel area, and the number of pixels inside the particle threshold, respectively. The standard deviationpof ffiffiffi the area due to the ‘resolution’ is rA ¼ pDrD =2 ¼ d2 =2 3. The standard uncertainty, therefore, pffiffiffi is given by the standard deviation in diameter rD ¼ d2 = 3pD, which is 0.002 nm
for D = 109 nm, and 0.0008 nm for D = 309 nm with d = 1.2 nm. This uncertainty is obtained twice since both particles, 300 and 100 nm, are involved, and the resultant uncertainty is [(0.0008/309 109)2 + 0.0022]1/2 = 0.002 nm for 109 nm. It is negligible compared with the other uncertainties. The values of uncertainties are listed in Table 2, in terms of standard uncertainty from corresponding source, standard combined uncertainty, and finally the expanded uncertainty with the coverage factor of 2, which nearly represents the confidence interval at the confidence level of 95%.
4. Conclusion The diameters of 100-nm polystyrene sphere have been measured with the improved TEM method. The mean and the combined standard deviation are 109.2 and 2.1 nm, respectively over the 82 participant particles. The expanded uncertainty of the mean diameter is 2.6 nm at the confidence level of 95%. The measured mean diameter is 9% greater than the value reported by the manufacturer. This coincides well with the values obtained by DMA method at NIST [4] and quasiMillikan method at NRLM [5], which are also 10% and 9% larger, respectively. In conclusion, TEM can be used to calibrate the diameter of around the 100-nm polystyrene sphere, through the comparison with a larger particle whose diameter is already accurately known. The method described here, however, is very time-consuming at its current stage. It will be a very efficient way of calibrating 100-nm or less polystyrene spheres if we can deposit particles more densely and more uniformly on the TEM specimen. By then, the process could be easily automated because the analysis deals with the separated particle. Further improvements has yet to be done. Although the same material particles are treated in the present study, this method, in principle, can be applied to the comparison of different material particles. The extrapolated zero exposure size, which is used for direct comparison, is supposed to be the initial size before the shrinkage, and material-independent. Therefore, the method described here will potentially extend the use of TEM in the precise particle size measurement.
Acknowledgements We sincerely thank Dr. Youn Joong Kim and Young Boo Lee at Korea Basic Science Institute for lots of TEM measurement and discussion.
References [1] S.D. Duke, E.B. Layendecker, Internal standard method for size calibration of sub-micrometer spherical particles by electron microscope, Presented at the Fine Particle Society Meeting, 1988; Copyright 1992 Duke Scientific Corporation.
K.Y. Jung et al. / Powder Technology 126 (2002) 255–265 [2] Y. Yamada, K. Miyamoto, A. Koizumi, Size determination of latex particles by electron microscopy, Aerosol Sci. Technol. 4 (1985) 227 – 232. [3] T. Katsuta, T. Shiibashi, S. Aotani, Particle size measurement of polystyrene particles by transmission electron microscope, Aerosol Res. 2 (1987) 134 – 139. [4] G.W. Mullholland, N.P. Bryner, C. Croakin, Measurement of the 100 nm NIST SRM 1963 by differential mobility analysis, Aerosol Sci. Technol. 31 (1999) 35 – 39. [5] K. Ehara, Electro-gravitational aerosol balance and its application to the development of particle size standard, National Research Laboratory of Metrology, Seminar at KRISS, 1997. [6] K. Ehara, C. Hagwood, K.J. Coakley, Novel method to classify aerosol particles according to their mass-to-charge ratio-aerosol particle mass analyzer, J. Aerosol Sci. 27 (2) (1996) 217 – 234. [7] S.D. Duke, R.E. Brown, E.B. Layendecker, Calibration of spherical particles by light scattering using photon correlation spectroscopy, Part. Sci. Technol. 7 (1989) 223 – 228.
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[8] Y. Yamada, K. Miyamoto, A. Koizumi, Size measurements of latex particles by laser aerosol spectrometer, Aerosol Sci. Technol. 5 (1986) 377 – 384. [9] G.C. Claver, W.H. Farnham, Polymer particle damage in the electron microscope—a practical problem, Powder Technol. 6 (1972) 313 – 316. [10] T.R. Lettieri, G.G. Hembree, Certification of NBS SRM 1691: 0.3um-diameter polystyrene spheres, NBSIR 88-3730 (1988) 1 – 27. [11] Guide to the Expression of Uncertainty in Measurement, 1st edn., ISO, Geneva, 1993. [12] B.N. Taylor, C.E. Kuyatt, Guidelines for evaluating and expressing the Uncertainty of NIST measurement results, NIST Tech. Note 1297, 1994 Edition. [13] B.C. Park, M.S. Chung, Uncertainty improvement in measurement of mean diameter of 0.3-Am-diameter polystyrene sphere by using quasielastic light scattering, J. Opt. Soc. Korea 9 (4) August 1998.
Measurement of 100-nm polystyrene sphere by transmission electron microscope K.Y. Jung a, B.C. Park b,*, W.Y. Song a, B.-H. O a, T.B. Eom b a
College of Electrical and Computer Engineering, Inha University, Inchon 402-751, South Korea Length Group, Korea Research Institute of Standards and Science, P.O. Box 102, Yusong, Taejon 305-600, South Korea
b
Received 23 August 2001; accepted 4 March 2002
Abstract The mean diameter of the 100-nm polystyrene sphere was measured with the transmission electron microscope (TEM) with a view to the development of the accurate and visual sizing technique for nm scale particles. To minimize the sizing error due to the inaccurate instrumentstated magnification and the edge location uncertainty, the 300-nm spheres were mixed with 100-nm spheres to provide an internal calibrator, whose diameter is accurately known. The diameters of 100-nm spheres were determined by comparing with that of 300-nm spheres in the same negatives (TEM pictures). For the correction of the electron beam-induced shrinkage effect, the dependence of the shrinkage on the accelerating voltage, beam intensity, and the exposure time was examined and analyzed. Based on such an investigation, and with the several data manipulation routines, the mean diameter was determined with the expanded uncertainty of approximately 2% at the 95% confidence level. The measured value is consistent with those obtained by other laboratories using different techniques for the same spheres. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Standard particle; Polystyrene sphere; Internal calibrator; TEM; Acceleration voltage; Intensity; Shrinkage
1. Introduction Accurate particle size standard is important for the semiconductor industry since the particle counters and scanning surface inspection systems, which are routinely used for the detection of the small contaminants throughout the wafer as well as the integrated circuit manufacturing process, is very sensitive to the particle size when it is smaller than the wavelength of the probe beam. In particular, the accurate assessment of 100-nm polystyrene spheres has been a recent issue since 100 nm is the current size limit for most of such state-of the-art instruments. Several independent measurements of the 100-nm sphere have been made by various methods. These include transmission electron microscopy [1 – 3], differential mobility analysis (DMA), also called an electrostatic classification [4], quasi-Millikan method [5,6], and light-scattering method [7,8]. DMA method is the only method so far whose uncertainty budget is fully investigated and then reported. Quasi-Millikan and light scattering method has
*
Corresponding author. E-mail address: [email protected] (B.C. Park).
its own unique characteristics, but, those deals with a group of particles rather than an individual particle. TEM has the advantage over other methods in that it can provide information about the shape of individual particles in addition to their size. The usual TEM method, however, has a couple of problems that make it unsuitable for measurement of the 100-nm particle size standard [1]. The instrument-stated magnification is not so credible. It is difficult to calibrate high magnifications with the grating replica. The actual magnification can vary between photos at the same magnification in the same instrument. Even if the magnification is perfectly calibrated, reliable particle diameter cannot be obtained by measuring the particle image itself because of the following reasons. First, the distortion of polystyrene spheres under the strong electron beam contributes an unknown amount to the under-estimation and the measurement uncertainty of the particle size. Secondly, the sphere edges are difficult to locate since the microscopic image is not sharp at the edges when viewed at high magnification. The ‘internal standard method’ for reducing those errors involved with the conventional TEM method has been reported. In this study, 100-nm spheres were photographed together with 300-nm spheres, and certified diameter was
0032-5910/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 ( 0 2 ) 0 0 0 6 2 - 1
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K.Y. Jung et al. / Powder Technology 126 (2002) 255–265
provided as an internal calibrant [1]. In the method, the distortion of the two different kinds of spheres was assumed similar since they are made out of the same material and are subjected to the same condition. This assumption, however, was not experimentally checked. If distorted differently, the initial diameters should have been measured and then compared with each other before they were exposed to damage by means of an electron beam. Furthermore, the determination of the diameter by inserting the particle image into two parallel lines with known distance is always influenced by the edge location uncertainty. The work reported here is directed toward a more thorough examination of TEM method for particle size measurement. The distortion of the spheres was studied under a range of beam conditions—acceleration voltage, beam intensity and exposure time. The diameter is obtained from the calculated area of the separated particle image on the negative rather than the spacing of the two parallel lines holding the image inside, to reduce the statistical error coming from the inaccurate edge location as well as imperfect roundness. The modified TEM method was applied to the calibration of the 100-nm standard sphere. The detailed processes and data treatments are described in Section 2. The results are presented and discussed in Section 3, followed by the conclusion in Section 4.
2. Measurement procedure The entire measurement procedure is summarized in Fig. 1a. The sample is a mixture of 100- and 300-nm particles deposited on the TEM grid. The TEM picture is taken so that as many separated particles as possible are included in a shot. To eliminate errors due to the magnification, the particles are measured directly from the negatives. The negatives are scanned and then converted into the image files. The images of the particle is then digitally processed by means of the image analysis program, to get the mean diameter and size distribution of the 100-nm particles.
times, and then the specimens were dried in the air (temperature = 20 jC, relative humidity = 50%) for 18– 20 h.
2.1. Preparation of the TEM specimen
2.2. TEM measurement
Deionized water filtered with 0.1-Am filter was used for diluting the original solution of polystyrene latex as well as for cleaning the bottles for the preparation of the samples. The 100- and 300-nm particle solutions were diluted to make about 0.1% and 0.05% in weight concentration, respectively, and then added by the same amount of each solution. The 100-nm particle solution is JSR SC-011-S, and 300-nm particle solution is NIST SRM 1691. A drop of the mixed solution was put on a TEM specimen, which is a carbon –metal film supported by 200-mesh copper grids. The drop was elongated and torn with both ends of the forceps prior to putting in order to prevent the agglomeration of the spheres. The same procedure was repeated 10
TEM (EM912 omega, Carl Zeiss) was used for measurement, which records the image on the negative of the size 80 80 mm. The magnification used throughout the study was 50,000, where ten or so 100-nm particle images could appear on a negative, together with one or two 300-nm particle images. It was considered that the area of the particle image should be sufficiently large to reduce the quantization error coming from the pixel size when the image is converted into digital form. Before the photograph was taken, the specimen was overviewed at a low magnification of 8000 to find a relatively large area of isolated particles. To decrease the possible particle shrinkage, the beam intensities was adjusted as low as possible to produce
Fig. 1. The measurement procedure of 100-nm sphere with TEM (a) for different exposure times (bold type numbers) (b).
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viewing screen illumination just visible in total darkness by the dark-adjusted eye. Only particles in the same negative were compared in order to avoid any variation of magnification depending on the different batches of shot. For a selected group of mixed particles on a negative, eight pictures were taken with eight different exposure times. The exposure times chosen are 20, 30, 40, 50, 60, 70, 80 and 200 s. Those include, as seen in Fig. 1b, the unavoidable exposure required before the first shot, the 3 s for taking a picture, and the intentional exposure. In order to investigate
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the effect of the beam condition on the particle shrinkage, a set of negatives with different exposure time, were obtained for a range of beam conditions. The set of conditions is comprised of one of the accelerating voltages of 80, 100 and 120 kV, and currents of either 300 or 720 pA. At the acceleration voltage of 60 kV, the image becomes unstable, thus the corresponding experiment was not performed. All of the negatives were scanned by a commercial scanner (HP 4c), and converted into digital files. The scanner has a resolution of 1200 DPI (1200 pixels per inch),
Fig. 2. Image processing being performed to calculate the size of 100- and 300-nm particles, respectively.
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Fig. 3. The change of particle lines (circular) as the grayscale threshold increases. The lines at the threshold of 49 and 63 are not good. The other circles between them are good, although they look almost the same at the bandwidth of the threshold between 52 and 58. Then the center value, 55 is chosen for the radius determination, and the bandwidth of 6 (from 52 to 58) produces the corresponding uncertainties.
Fig. 4. Comparison of intensity profiles of 100- and 300-nm particles. The intensity profiles of 300 nm are scaled down.
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and 256 gray levels. For processing of the scanned image, the commercial image analysis program (GLOBAL LAB) was used. The program uses grayscale threshold values to separate the pixels in an image into particle and background, and from the number of pixels inside, the particle diameter is determined in terms of pixels. The edge of the particle image on a negative is not sharp; rather, it has a distributed intensity profile. The best circle, which might represent the actual peripheral edge of the particle image, should be found before determining the diameter from the circle area. Fig. 2 shows how the image analysis is performed for 100- and 300-nm particles, respectively. The area of the region enveloped by yellow line is shown at the top and left. The best circle is chosen when the circle is judged as the clearest while increasing the ‘threshold’. The process is well illustrated in Fig. 3. The lines at the threshold of 49 and less, or 63 and greater are not good. The other circles at the threshold between 52 and 58 look best. Then the center value, 55 is chosen for the radius determination, and the bandwidth of 6 (from 52 to 58) becomes the interval of the corresponding error. This method is applied the same way to both particles, 100 and 300 nm, since their intensity profiles are nearly the same except the scale as can be seen in Fig. 4. As the boundary of the particle is fixed, then the interior area is calculated in the unit of pixels to convert into the diameter for the circle of the same area. For optimal accelerating voltage (80 kV) and beam current (300 pA), which were chosen after comparing the results of aforementioned experiments, photographs were taken of mixtures of 100 and 300 nm, and finally 17 negatives, including eighty-two 100-nm particles in total, were obtained for analysis as shown in Table 1. The numbers in ‘300 nm’ and ‘100 nm’ columns of Table 1
Table 1 The list of TEM negatives used for the study Negative no.
Number of 300-nm particle
Number of 100-nm particle
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Total
2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 20
3 3 2 4 4 4 6 3 3 6 4 7 6 7 9 6 5 82
The numbers in ‘300 nm’ and ‘100 nm’ columns represent the number of particles existing in the corresponding negatives.
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represent the numbers of particles existing in the corresponding negatives. Unfortunately, the sample preparation technique did not allow a sufficient number of both particles to be obtained in a negative. Development of the efficient deposition technique on the TEM specimen will save much time, and make this sizing method more powerful. The 300-nm particle diameter, or the average if there are two, on each photograph has been used as the calibration diameter for the measurement of 100-nm particle diameters on the photograph. Then the individual 100-nm particle diameters thus obtained are used to calculate the mean and standard deviation.
3. Results and discussion Figs. 5 and 6 show the exposure time versus measured particle size curves. The diameters for zero exposure time in each graph are not the measured values. They are extrapolated from the measured sizes with different exposure times, which was varied from 20 to 200 s. Fig. 5 shows the size change obtained for four specimens with two electron beam currents of 300 and 700 pA at the accelerating voltage of 120 kV. Pictures of two of the specimens (Fig. 5a and b) were taken with the beam current of 300 pA, while the others (Fig. 5c) were taken with 700 pA. There is a case (b) where the increase in size happened with 300 pA, while the remaining three cases where the usual shrinkage happened as expected. It is not certain to the authors whether such an increase came from an unusual contamination or from an unknown effect due to high acceleration voltage. Such a behavior, however, was not observed for other acceleration voltages, 100 and 80 kV, throughout the study. The results in Fig. 5 are further summarized in Fig. 6a and b, where each dot represents an averaged size over the particles in a negative corresponding to a specific exposure. In other words, each curve represents a change of the averaged particle size in a negative as the exposure varies. Fig. 6c,d and e,f shows the equivalent results for the accelerating voltages of 100 and 80 kV, respectively. In all cases, the sizes decrease monotonically with increasing exposure time, as expected. The rate of shrinkage is different from specimen to specimen even under similar conditions, so that the difference in the mean diameter significantly changes as the exposure increases in Fig. 6. Although the shrinkage does not show any noticeable dependence on the voltage and current, the shrinkages at 80 kV and 300 pA looks more consistent that under at any other condition. Therefore, the condition of 80 kV and 300 pA has been chosen to measure the diameter of 100-nm standard sphere. The choice also rests upon the idea that lower voltage and current will bring less damage to the particles, and our measurement results will be affected less from the beam conditions. Even for spheres of the same material and undergoing the same beam conditions, it is observed that the shrinkage ratio can differ slightly from particle to particle, and from
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Fig. 5. The exposure time versus particle size curves at the accelerating voltage of 120 kV. Each graph corresponds to each negative, and each dot in the graph represents the size of the individual particle.
specimen to specimen. Fig. 7 shows the shrinkage for the spheres on three specimens ing exposure time, respectively. The 300spheres seem to have the same shrinkage
examples of with increasand 100-nm behavior. A
shrinkage of 3 –10% is observed after an exposure of 1– 4 min, which is consistent with the result of Ref. [9]. It should be noted that the additional shrinkage occurs if the specimen is exposed further. That means the measured
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Fig. 6. The exposure time versus averaged particle size curves at the accelerating voltage of 120 kV (a, b); 100 kV (c, d); 80 kV (e, f). Two graphs at each voltage are with different beam currents.
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Fig. 7. The exposure time versus shrinkage ratio shown for the three samples out of 17 samples in total. The shrinkage at the zero exposure (extrapolated) is set to zero.
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particle diameter is affected by the measurement time, which means that the extrapolation to zero exposure time diameter is needed. As another evidence of the finding that shrinkage rates are similar, the mean shrinkage rates, over the first 20 s, are computed for each set of 100- and 300nm particles, respectively. Then the ratios of the mean shrinkages for each photograph are obtained and plotted in Fig. 8. The difference in shrinkage rates does not exceed 0.3% in standard deviation, which can be given as the standard uncertainty due to any slight difference in the shrinkage rates. In order to measure the mean and the standard deviation of the 100-nm standard sphere, 17 negatives were obtained where 100- and 300-nm spheres appear together for comparison. On average, one to two 300-nm particles, and three to seven 100-nm particles are included in each negative. In total, twenty 300 nm-spheres, as internal calibrators for the photograph where they are found, and eighty-two 100-nm spheres were taken, and are listed in Table 1. Fig. 9 is a histogram of the obtained diameters of eighty-two 100-nm spheres. The measured mean and the standard deviation of 100-nm particle are 109.2 and 3.2 nm, respectively. There was no outlier when the criterion of 4r (r: standard deviation) is used—that is, no particles deviated from their mean by more than 4r. Measurement uncertainties are summarized in Table 2. The uncertainties can be categorized into two evaluations, type ‘A’ and ‘B’. While type A evaluation is calculated from series of the repeated observations, type B evaluation uses available knowledge [11]. Type A uncertainty comes from the finite number of spheres taken to determine the mean diameter. The corresponding standard uncertainty is then given by the standard deviation of the 100-nm sphere, divided by the square root of the number of particles. The apparent standard deviation 3.2 nm obtained as described above, however, is broadened because of the breadth of the size distribution of the 300-nm particles. The apparent
Fig. 9. Size distribution of the measured diameters of 100-nm sphere.
relative standard deviation, 3.2 nm/109.2 nm will be therefore given by the square root of the sum of the squares of the relative standard deviations for the 300- and 100-nm spheres. The standard deviation of the 300-nm particles is 6 nm, according to TEM measurement results [10], and the standard deviation of the 100 sphere is computed as 2.1 nm (1.9%). Type B uncertainties have six sources. (1) Magnificationassociated uncertainty in the transfer of the particle image from a negative to a digital file. The image can be distorted due to the spatial inhomogeneity of the scanner magnification, the thermal bending of the negative, and different magnification along the horizontal and vertical direction. To estimate the uncertainty, one particle image was scanned
Table 2 Summary of the TEM measurement uncertainties of 100-nm standard sphere Uncertainty type
Source of uncertainty
Standard uncertainty (nm)
Type A
Finite sample size (N = 82; rD = 2.1) Scanner magnification Edge location of the particle image Uncertainties of the certified values of the reference sphere (300 nm) Finite sample of 300-nm particles Difference in shrinkage rates for 100- and 300-nm spheres Pixel size uc=(u21 + u22 + . . .)1/2
0.2
Type B
Fig. 8. The ratios of 300- to 100-nm particle shrinkage rates for the first 20-s exposure.
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Combined standard uncertainty Expanded uncertainty
U = 2uc
0.4 0.2 1.0
0.5 0.3
0.002 1.3 2.6
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in five different positions; center, up, bottom, left and right. The measured radii in the unit of pixel are 309.37, 308.39, 309.39, 309.66, 309.03 (mean = 309.2; 1r = 0.5, 0.2%) for the 300-nm particle, and 122.44, 121.44, 121.93, 121.85, 121.51 (mean = 121.8; 1r = 0.4, 0.3%) for the 100-nm particle. The positions of both particles (300 and 100 nm) in a negative affect the results through the inter-comparison. The corresponding standard uncertainty for the magnification is calculated as [(0.5/309 109)2+(0.4/122 109)2]1/2 = 0.4 nm for 109 nm. (2) Edge location uncertainty in the process of determining the threshold for the best circle as described previously. The maximum uncertainty due to this error was estimated for the case of the largest bandwidth, which is illustrated in Fig. 3. The shape of the circle is maintained best as the intensity of the threshold changes from 52 to 57. The corresponding areas enclosed by the ‘best’ circle are 43,358, 43,191, 43,065, 42,977, 42,891 and 42,815 pixels. The average area is 43,050 and the standard deviation is 200 or 0.47% of the average area. Considering that the relative error of diameter is given by a half of that of the area, the corresponding uncertainty is 0.2 nm for 109 nm. (3) Uncertainty of the certified diameter of the 300-nm particle. The 300-nm particle used for internal calibrator is originally certified as 269 F 7 nm by TEM, and 275 F 7 nm by QELS [10]. The uncertainty cited here approximately corresponds to the expanded uncertainty at the confidence level of 95%, although the total uncertainty is taken as the linear sum, instead of the square sums recommended by ISO [11,12]. For the vial used for the experiment, the mean diameter was re-measured as 273 nm by QELS at KRISS [13], with the combined standard uncertainty (1r) is 3 nm, which is used to give the equivalently standard uncertainty of 1 nm for the diameter of 109 nm. (4) Uncertainty due to the finite number of the 300-nm particle as internal calibrators, The uncertainty of the mean value for a set of n particles is expressed by the standard deviation of the size distribution divided by the square root of n. It is calculated to be 1.34 nm since twenty 300-nm particles in total are used, and the standard deviation is 6 nm [10], which then gives the corresponding standard uncertainty of 0.5 nm to the obtained mean diameter of 100-nm particles. (5) Uncertainty associated with the different shrinkage rates between 300- and 100-nm particles. The standard uncertainty is 0.3 nm or 0.3% of the diameter as given above. (6) Quantization-associated uncertainty due to the finite pixel size. Since the particle area is obtained in terms of the number of finite pixel area d2, there is a corresponding quantization error in the obtained diameter, whose standard uncertainty is given by pixel size divided by the circumference, which can be easily derived. The particle area is expressed as A = pD2/ 4 = Nd2, where A, D, d2 and N are the particle area, particle diameter, pixel area, and the number of pixels inside the particle threshold, respectively. The standard deviationpof ffiffiffi the area due to the ‘resolution’ is rA ¼ pDrD =2 ¼ d2 =2 3. The standard uncertainty, therefore, pffiffiffi is given by the standard deviation in diameter rD ¼ d2 = 3pD, which is 0.002 nm
for D = 109 nm, and 0.0008 nm for D = 309 nm with d = 1.2 nm. This uncertainty is obtained twice since both particles, 300 and 100 nm, are involved, and the resultant uncertainty is [(0.0008/309 109)2 + 0.0022]1/2 = 0.002 nm for 109 nm. It is negligible compared with the other uncertainties. The values of uncertainties are listed in Table 2, in terms of standard uncertainty from corresponding source, standard combined uncertainty, and finally the expanded uncertainty with the coverage factor of 2, which nearly represents the confidence interval at the confidence level of 95%.
4. Conclusion The diameters of 100-nm polystyrene sphere have been measured with the improved TEM method. The mean and the combined standard deviation are 109.2 and 2.1 nm, respectively over the 82 participant particles. The expanded uncertainty of the mean diameter is 2.6 nm at the confidence level of 95%. The measured mean diameter is 9% greater than the value reported by the manufacturer. This coincides well with the values obtained by DMA method at NIST [4] and quasiMillikan method at NRLM [5], which are also 10% and 9% larger, respectively. In conclusion, TEM can be used to calibrate the diameter of around the 100-nm polystyrene sphere, through the comparison with a larger particle whose diameter is already accurately known. The method described here, however, is very time-consuming at its current stage. It will be a very efficient way of calibrating 100-nm or less polystyrene spheres if we can deposit particles more densely and more uniformly on the TEM specimen. By then, the process could be easily automated because the analysis deals with the separated particle. Further improvements has yet to be done. Although the same material particles are treated in the present study, this method, in principle, can be applied to the comparison of different material particles. The extrapolated zero exposure size, which is used for direct comparison, is supposed to be the initial size before the shrinkage, and material-independent. Therefore, the method described here will potentially extend the use of TEM in the precise particle size measurement.
Acknowledgements We sincerely thank Dr. Youn Joong Kim and Young Boo Lee at Korea Basic Science Institute for lots of TEM measurement and discussion.
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