Ultramicroscopy ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Lattice imaging at an accelerating voltage of 30 kV using an in-lens type cold field-emission scanning electron microscope Mitsuru Konno n, Takeshi Ogashiwa, Takeshi Sunaoshi, Yoshihisa Orai, Mitsugu Sato Hitachi High-Technologies Corporation, 882, Ichige, Hitachinaka, Ibaraki 312-8504, Japan
art ic l e i nf o
Keywords: Low-voltage STEM Lattice imaging FE-SEM
a b s t r a c t We reported investigation of lattice resolution imaging using a Hitachi SU9000 conventional in-lens type cold field emission scanning electron microscope without an aberration corrector at an accelerating voltage of 30 kV and discuss the electron optics and optimization of observation conditions for obtaining lattice resolution. It is possible to visualize lattice spacings that are much smaller than the diameter of the incident electron beam through the influence of the superior coherent performance of the cold field emission electron source. The defocus difference between STEM imaging and lattice imaging is found to increase with spherical aberration but it is possible to reduce the spherical aberration by reducing the focal length (f) of the objective lens combined with an experimental sample stage enabling a shorter distance between the objective lens pre-field and the sample. We demonstrate that it is possible to observe the STEM image and crystalline lattice simultaneously. STEM and Fourier transform images are detected for Si{222} lattice fringes and reflection spots, corresponding to 0.157 nm. These results reveal the potential and possibility for a measuring technique with excellent precision as a theoretically exact dimension and established the ability to perform high precision measurements of crystal lattices for the structural characterization of semiconductor materials with minimal radiation beam damage. & 2013 Elsevier B.V. All rights reserved.
1. Introduction Transmission electron microscopes (TEM) operating at accelerating voltages of 200 kV or 300 kV have been widely applied for structural characterization of semiconductor devices, metals and ceramic materials. More recently, with the size of semiconductor device structures shrinking to below the 20 nm technology node, TEM lamella thickness requirements must be made prohibitively thin to prevent structural overlaps in the projected image. Technological developments suggest that inorganic carbon materials such as nanotubes and graphene, and organic polymeric materials will be developed more actively. The demands for fine structural, elemental, and chemical characterization of these materials by electron microscopes are rapidly increasing. Unfortunately, these materials are susceptible to beam damage leading to a reduction in the structural order and image contrast. Low energy microscopy has a reduced probability for knock-on damage; however, the resolution degrades due to an increase in electron wavelength. Accordingly, it is necessary to determine methods to improve the contrast at lower voltage operation without loss of resolution.
n
Corresponding author. Tel.: þ 81 293541970. E-mail address: [email protected] (M. Konno).
There has been a recent technical trend to develop low energy transmission electron microscopes and low energy scanning electron microscopes (SEM) in partnership between research institutes, universities and product manufactures. For example, in 2010 in Japan, Dr Suenaga of the National Institute of Advance Industrial Science and Technology (AIST), and JEOL Co. Ltd. have developed a low energy electron microscope ( 30 kV) with a spherical aberration and chromatic aberration corrector for atomically resolved observation for soft materials and they reported that example of the application of structural characterization of carbon materials [1–2]. In 2011 Dr. Kaiser of the Ulm University in Germany, and Zeiss Co. Ltd. developed a low energy transmission electron microscope ( 20 kV) with an aberration corrector and electronic monochromator which successfully resolved the 0.272 nm spacing Si{220} lattice fringes [3]. In addition, Hokkaido University in Japan and Hitachi Ltd. developed an electron diffraction microscope based on a conventional SEM for obtaining atomic-level resolution images [4]. The imaging resolution using this 30 kV field emission (FE) SEM with a scanning TEM (STEM) function has recently been significantly improved. It is important to reduce the spherical aberration of the objective lens and the energy fluctuation of electron gun (ΔE) for obtaining images at atomic resolution at low accelerating voltage operation. In order to respond to such demands, we have developed the Hitachi SU9000, a cold FE-SEM (CFE-SEM) with an in-lens type of objective lens,
0304-3991/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ultramic.2013.09.001
Please cite this article as: M. Konno, et al., Lattice imaging at an accelerating voltage of 30 kV using an in-lens type cold field-emission scanning electron microscope, Ultramicroscopy (2013), http://dx.doi.org/10.1016/j.ultramic.2013.09.001i
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capable of high resolution phase contrast STEM imaging. Through using this technique on this microscope, it is possible to routinely achieve lattice resolution of the graphite {002} planes with a spacing of 0.34 nm [5]. In this study, we have improved the electron optics and optimization of observation condition for obtaining lattice resolution enhancement in STEM imaging at an accelerating voltage of below 30 kV and its application for semiconductor devices.
2. Principle of lattice imaging 2.1. Behavior of the electron beam incident to the crystalline sample Fig. 2-1 shows the behavior of the electron beam incident on a crystalline sample in a transmission geometry. When the primary electron beam is incident on a crystalline sample with lattice spacing d, transmitted electrons are scattered by elastic and inelastic mechanisms. Elastically scattered electrons are scattered at an angle of twice the Bragg angle, θB, given by Bragg's law: 2θB ¼ λ=d
ð2 1Þ
Here λ is the electron wavelength which for the case of low accelerating voltages (Vacc), is given by λ ¼ √ð1:5=V acc Þ ðnmÞ
2.2.2. αi 42θB In the case where αi 42θB, three electron waves which include the central disk and disks on either side formed by the elastically scattered electrons overlap, so that interference fringes appear at the center of the signal detection surface as shown in Fig. 2-2(c). Some fraction of the interference fringes passing the STEM aperture on the center of the detection surface are detected as the signature of the elastic interaction between the electron beam and the sample. These interference fringes are shifted by scanning the primary electron beam across the crystalline sample. As shown in Fig. 2-3, when the primary electron beam moves by only one lattice spacing, these interference fringes are shifted by one pitch. By moving these interference fringes, the STEM signal is varied and generates the phase contrast lattice image observed. In the next section, we will discuss the optimum optical condition of the beam convergence semi-angle and primary beam focus for obtaining the lattice images with a 30 kV FE-SEM.
3. Optical condition for STEM imaging and lattice imaging 3.1. Optimum beam convergence semi-angle (αi) for STEM imaging and lattice imaging
ð2 2Þ
As mentioned above, if the lattice spacing, d, and accelerating voltage, Vacc, are fixed, the scattering angle of the elastically scattered electron is determined through Eq. (2-1). When the sample is a multi wall carbon nanotube (MWCNT) with a 0.34 nm lattice spacing, the scattering angle is 2θB ¼7.3 mrad at Vacc ¼ 200 kV and 2θB ¼ 21 mrad at Vacc ¼30 kV. 2.2. Principle of lattice image contrast generation When the convergent electron beam of a STEM is incident on a crystalline sample with a convergence semi-angle αi, the inelastically and elastically scattered electrons are spread radially at the same angle as αi, as shown in Fig. 2-2(a). In order to understand the principle of lattice image contrast generation, the interference state of the electron wave according to the relation between Bragg angle 2θB and beam convergence semi-angle αi must be considered. 2.2.1. θB oαi≦2θB In the case where θB oαi r2θB, the inelastic and elastic scattered electrons are both transmitted and their wavefronts partly overlap, forming a constructive interference pattern of fringes as shown in Fig. 2-2(b).
Fig. 3-1 shows the schematic of the Hitachi SU9000 FE-SEM optical system used to observe the STEM image. The beam convergence semi-angle, αi, of the incident beam on the sample can be set by changing the objective aperture size, or changing the beam crossover point by the strength of the second condenser lens. Fig. 3-2 shows the relation between the beam convergence semi-angle αi and the theoretical resolution R. R is limited by electron diffraction associated with the Raleigh criterion and the impact of the spherical aberration which is the limiting aberration of the system. There is an optimum beam convergence semi-angle for minimum theoretical resolution. In case of SU9000 FE-SEM, this optimum beam convergence semi-angle is approximately 10 mrad at 30 kV the maximum accelerating voltage. Normally this optimum beam convergence semi-angle is chosen when observing the real objective image because the image resolution is at its best. As discussed in Section 2.2.2, lattice image observation requires the beam convergence semi-angle αi 42θB. At the accelerating voltage of 30 kV, observation of carbon lattice fringes (d¼0.34 nm) requires αi 420.5 mrad, and for Si {111} lattice fringes (d¼ 0.314 nm) requires αi 422.5 mrad. Therefore, in order to obtain the phase contrast lattice image of Carbon or Si at 30 kV FE-SEM, a larger beam convergence semi-angle than normally used is required.
3.2. Behavior of the optimum defocus for STEM imaging and lattice imaging We have found from experiment that there is the gap of defocus value between optimum STEM imaging and optimum lattice imaging. In the following sections, we study this phenomenon.
Fig. 2-1. Behavior of the electron beam incident on a crystalline sample.
3.2.1. Theoretical model of the optimum defocus for STEM imaging The optimum defocus setting, Δf STEM , for STEM imaging as measured from the Gaussian image plane is found at which the STEM image is best. In order to determine Δf STEM , we applied the Information Passing Capacity (IPC) method [6] to calculate the model of optimum resolution. The IPC method applies information theory [7] to characterize the beam performance for an optical image.
Please cite this article as: M. Konno, et al., Lattice imaging at an accelerating voltage of 30 kV using an in-lens type cold field-emission scanning electron microscope, Ultramicroscopy (2013), http://dx.doi.org/10.1016/j.ultramic.2013.09.001i
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Fig. 2-2. Generation of the interference fringes by convergent beam.
Fig. 2-3. Generation of the lattice fringes contrast.
Fig. 3-2. Relation between theoretical resolution and lattice imaging condition.
Here τbeam is the two-dimensional Fourier Transform of the beam intensity distribution, and ν is the dimensionless special frequency in the radial direction normalized to the diffraction unit of length (λ=αi ) as λ qffiffiffiffiffiffiffiffiffiffiffiffiffiffi ν2x þ ν2y ð3 2Þ ν¼ αi
Fig. 3-1. Optical system for STEM imaging by Hitachi SU9000 FE-SEM.
The IPC parameter, ρH , is calculated by
ρH ¼
π ðλ=αi Þ2 ln 2
Z
2
ln 0
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! S 1 þ jτbeam ðνÞj2 νdν ðbit=nm2 Þ N
ð3 1Þ
Here νx and νy are the spatial frequencies for x and y directions, respectively. S/N corresponds to signal-to-noise ratio of the optical image. ρH represents the maximum capability of the information content in the optical image that is transferred from 1 nm2 area in a specimen. Because τbeam varies with the defocus Δf measured from Gaussian image plane, ρH in Eq. (3-1) is a function of Δf . Fig. 3-3 shows an example of behavior of the IPC ρH as a function of Δf near the optimum focus. In Fig. 3-3, an optimum defocus Δf STEM is found at which ρH is maximum. In the IPC method, the resolution R of an optical system is modeled by the following equation calculated at Δf ¼ Δf STEM . sffiffiffiffiffiffiffiffiffiffiffi λ ρideal H ð3 3Þ R ¼ 0:61 αi ρH
Please cite this article as: M. Konno, et al., Lattice imaging at an accelerating voltage of 30 kV using an in-lens type cold field-emission scanning electron microscope, Ultramicroscopy (2013), http://dx.doi.org/10.1016/j.ultramic.2013.09.001i
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Here ρideal is the IPC for aberration free optical system for a point H source where a beam intensity distribution is the Airy pattern. In Eq. (3-3), ρH and ρideal are calculated using the same value of H S/N. From Eq. (3-3), the resolution is given by Rayleigh's criterion (0.61λ=α) when the optical system is an aberration-free optical system for a point source, i.e., ρH ¼ ρideal . H 3.2.2. Behavior of spatial resolution R and optimum defocus Δf STEM Fig. 3-4 shows an example of resolution R and defocus Δf STEM as a function of beam convergence semi-angle αi at a specimen surface. The plot of resolution is V-shaped and has a minimum value at P1. The beam convergence semi-angle (αopt ) at P1 is called the optimum convergence semi-angle and the resolution at αopt is the attainable resolution of an optical system. When an optical
system is suffering from spherical aberration, the IPC ρH is maximum when the following condition is satisfied: B¼
1 C s α3i ¼1 4ðλ=αi Þ
ð3 4Þ
Here B represents the effect of spherical aberration in wave optics. From Eq. (3–4), we obtain the optimum convergence semi-angle αopt as: 1=4 4λ ð3 5Þ αopt ¼ Cs When Cs ¼2 mm and λ ¼0.00707 nm (at 30 kV), αopt becomes 11 mrad as shown Fig. 3-4. When beam convergence semi-angle αi is near αopt or smaller, Δf STEM is given as [8] Δf STEM ¼ Δf 1 ¼ 0:5C s α2i
ð3 6Þ
By applying Eqs. (3-5) and (3-6), the optimum defocus (See P2 in Fig. 3-4) at αopt is written as pffiffiffiffiffiffiffi Δf 1 ¼ C s λ ð3 7Þ Eq. (3-7) corresponds to the Scherzer defocus [9] for phase contrast STEM imaging. When the beam convergence semi-angle αi is large compared to αopt , Δf STEM becomes constant of αi and it is written as [8] pffiffiffiffiffiffiffi Δf STEM ¼ Δf 2 ¼ 1:15 C s λ ð3 8Þ
Fig. 3-3. Behavior of the IPC ρH as a function of defocus Δf.
The points P3 and P4 in Fig. 3-4 indicate defocuses Δf 2 (Eq. (3-8)) and Δf 1 (Eq. (3-6)), respectively, when αi ¼ 20 mrad (4 αopt ). Figs. 3-5 and 3-6 show beam intensity distributions and optical transfer functions (OTFs), respectively, calculated at defocuses for P3 and P4. If we simply compare the FWHM of beam intensity distributions in Fig. 3-5, the defocus for P4 seems to be better for higher resolution. However due to higher level of the beam tail produced at defocus for
OTF
1.2 1.0
P3
0.8
P4
0.6 0.4 0.2 0.0 -0.2
0
1
2
3
4
5
Spatial frequency (nm-1) Fig. 3-4. Behavior of the resolution and optimum defocus for STEM imaging as a function of beam opening angle.
Fig. 3-6. Comparison of optical transfer functions (OTFs) obtained at defocuses for P3 and P4.
Fig. 3-5. Comparison of beam intensity distributions obtained at defocuses for P3 and P4.
Please cite this article as: M. Konno, et al., Lattice imaging at an accelerating voltage of 30 kV using an in-lens type cold field-emission scanning electron microscope, Ultramicroscopy (2013), http://dx.doi.org/10.1016/j.ultramic.2013.09.001i
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P4, the OTF curve for P4 degrades in a wide range of special frequencies as shown in Fig. 3-6. This means that the important structural information degrades seriously at the defocus for P4. Therefore we see that the defocus for P3 is suitable to the observation of structural information compared to the defocus for P4. 3.3. Optimum defocus Δf Lattice for lattice imaging In order to observe the lattice of a CNT using 30 kV beam voltage, it is necessary to use a beam convergence semi-angle of 21 mrad or larger. The optimum condition for an optical system given by Eq. (3-4) at αi ¼21 mrad is satisfied when Cs ¼0.15 mm. However, we have obtained lattice images of CNT's using noncorrected FE-SEM where Cs is much larger than 0.15 mm. We also found from experiment that a discrepancy exists of the optimum defocus between STEM imaging and lattice imaging which varies with Cs. When Cs is close to the optimum value satisfying Eq. (3-4), optimum defocus for lattice imaging is given by [10] Δf Lattice ¼ C s θ2B
ð3 9Þ
Because spherical aberration in our experiment for lattice imaging is much larger than the optimum value satisfying Eq. (3-4), we compared the optimum defocus found from experiment for lattice imaging of CNT with those given by Eq. (3-9). The optimum defocus for lattice imaging can be measured as a function of defocus Δf a from the STEM images. Since the optimum defocus Δf STEM is now considered as Δf 2 (see Eq. (3-8)), the optimum defocus (Δf ex ) for lattice imaging, measured from Gaussian image plane, is expressed as Δf ex ¼ Δf 2 þ Δf a
ð3 10Þ C s θ2B
for lattice imaging Fig. 3-7 shows comparison between Δf ex and of CNT's at various Cs values. We see from Fig. 3-6 that the discrepancy between Δf ex and C s θ2B is decreased with decreasing Cs value.
Fig. 3-7. Relation between optimum defocus for lattice imaging of CNT and spherical aberration coefficient Cs.
5
4. Experimental study 4.1. The focus gap between the lattice and in focus Fig. 4-1 shows BF-STEM images of a graphite particle at an accelerating voltage of 30 kV. Fig. 4-1(a) is in an optimum defocus condition for STEM imaging (Δf STEM ) which clearly shows a particle configuration, layer construction and crystal orientation. Fig. 4-1(b) is optimized for defocus for lattice imaging (Δf Lattice ) showing that it is possible to slightly resolve the C{002} planes, which have a spacing of 0.34 nm. As demonstrated, switching from the initial imaging conditions to lattice fringe phase contrast conditions requires to underfocus the electron probe significantly. For this reason, it is difficult to observe the structural formations of the subject and its lattice fringes by simultaneously.
4.2. Optimizing the imaging condition by changing the sample height The defocus difference between STEM imaging and lattice imaging is found to increase with spherical aberration. It is possible to reduce the spherical aberration by reducing the focal length (f) of the objective lens combined with an experimental sample stage enabling a shorter distance between the objective lens pre-field and the sample (Fig. 4-2). The experimental sample stage used here for STEM observation has a hole in the center allowing for transmission observation where the TEM sample mounts at the upper position of the holder. This special stage permits a focal length 1.5 mm shorter than the standard sample position with a sample height adjustment of 70.3 mm. Fig. 4-3 shows the comparison of image resolution and amount of Δf for STEM imaging with those for lattice imaging. We have observed BF-STEM images of a graphite particle and lattice fringes in a squared area at four positions as per Table 4-1. The working distance and spherical aberration coefficient (Cs) according to computation are 3.0 mm, 2.0 mm at sample position A, 2.7 mm, 1.7 mm at B, 2.5 mm, 1.5 mm at C, 1.8 mm, 1.0 mm at D, respectively. Line A is a standard STEM observation position and line D is the upper limit of the special stage at an accelerating voltage of 30 kV setting. The amount of defocus difference between the lattice image and the in-focus image
Fig. 4-2. The experimental sample stage for changing sample height. (a) Top view and (b) cross section view of top along the line A-A'
Fig. 4-1. BF-STEM images graphite particle at an accelerating voltage of 30 kV. Magnification: 2,000,000
Please cite this article as: M. Konno, et al., Lattice imaging at an accelerating voltage of 30 kV using an in-lens type cold field-emission scanning electron microscope, Ultramicroscopy (2013), http://dx.doi.org/10.1016/j.ultramic.2013.09.001i
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Fig. 4-3. The comparison of image resolution and amount of Δf for STEM imaging with those for lattice imaging obtained at various Cs values.
(Δf) is calculated by the value of digital analog converter (DAC) at each focus point. As the focal length is shortened to decrease the spherical aberration coefficient and the sample height is brought up to the cross-over plane, the difference in defocus between STEM imaging (Δf STEM ) and lattice imaging (Δf Lattice ) is found to significantly decrease. At sample position D, the amount of defocus has been shortened to 25 nm and it is possible to observe the STEM image and crystalline lattice simultaneously. 4.3. Investigation of image resolution Fig. 4-4 shows high resolution phase contrast –STEM images observed along the Si〈1 1 0〉 zone axis at an accelerating voltage of 30 kV, with inset indexed Fast Fourier Transforms (FFT) of each image. The standard condition (WD: 3 mm, Cs: 2 mm) was used for Fig. 4-4 (a) and the optimized condition (WD: 1.8 mm, Cs: 1 mm) was used for Fig. 4-4(b). The sample was thinned by an Ar þ ion milling technique to a sample thickness of about 20 nm. Not surprisingly both BF-STEM images show the Si {111} planes, with an inter-planar spacing of 0.314 nm with the corresponding reflections in the FFT. However, in the optimized condition, the image sharpness of Si {111} lattice fringes and the associated FFT reflections are detected including the Si {200} spots, corresponding to 0.272 nm. This result using the optimized
condition reveals the potential for high contrast visualization without loss of resolution in semiconductor devices and any carbon materials with minimal radiation beam damage. Next we have investigated the image resolution when changing the amount of defocus. Fig. 4-5 shows the BF-STEM images of Si〈011〉 single crystal by a through-focus method at an accelerating voltage of 30 kV, and Fourier transform of each BF-STEM image. The amount of defocus (Δf) in the BF-STEM images were 0 nm (a) which focused on the sample (in focus), 86 nm (b), 223 nm (c) and 341 nm (d), respectively. Image resolution was changed depending on the extent of Δf, and BF-STEM image of Δf¼ 341 nm demonstrates the best result which shows the Si {222} planes, with an interplanar- spacing of 0.157 nm and Fourier transform image also detect the Si {222} reflection spots. BF-STEM and Fourier transform images of Δf¼ 223 nm shows the Si (220) plane, which has a spacing of 0.192 nm. This result emphasizes that high resolution imaging at less than 200 pm is possible without an aberration corrector and creates new possibilities and applications of low energy STEM image. 4.4. Application of semiconductor devices. Fig. 4-6 shows the cross sectional BF-STEM images of NAND flash memory (a) and the magnified BF-STEM image (b) observed along the Si〈011〉 zone axis for a sample prepared using a focused
Please cite this article as: M. Konno, et al., Lattice imaging at an accelerating voltage of 30 kV using an in-lens type cold field-emission scanning electron microscope, Ultramicroscopy (2013), http://dx.doi.org/10.1016/j.ultramic.2013.09.001i
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Fig. 4-4. High resolution BF-STEM images observed along the Si〈110〉 zone axis with accelerating voltage of 30 kV, and Fourier transform of each BF-STEM image. Magnification: 3,000,000 .
Fig. 4-5. BF-STEM images of Si〈011〉 single crystal by a through-focus method at an accelerating voltage of 30 kV. Magnification: 3,000,000 .
Fig. 4-6. The cross sectional BF-STEM images of NAND flash memory (a) and the magnified BF-STEM image (b) observed along the Si〈011〉 zone axis.
ion beam fabrication technique. The sample thickness was around 30 nm. Fig. 4-6a clearly shows the semiconductor device structure such as a floating gate, interlayer dielectric and gate insulating layer with great clarity by a low energy operation. In Fig. 4-6b, the magnified BF-STEM image shows Si {111} lattice fringes (spacing of 0.314nm) simultaneously with the fine structure of the gate
dielectric layer. Fig. 4-7 shows the Fourier transform image from the 512×512 pixel area in the center of the BF-STEM image observed along the Si o0114 zone axis. Because the spots for 0.314nm spacing are clearly detected in Fig. 4-7, the information of the spacing for Si {111} can be applied to the calibration of the critical dimension measurement for devices.
Please cite this article as: M. Konno, et al., Lattice imaging at an accelerating voltage of 30 kV using an in-lens type cold field-emission scanning electron microscope, Ultramicroscopy (2013), http://dx.doi.org/10.1016/j.ultramic.2013.09.001i
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5. Conclusions
Table 4-1 The working distance and spherical aberration. Sample position
A
B
C
D
Working distance (mm) Spherical aberration (mm)
3.0 2.0
2.7 1.7
2.5 1.5
1.8 1.0
We report here STEM observations of lattice fringes in graphite (lattice spacing of C{002} is 0.34 nm) and Silicon (lattice spacing of Si {002} and Si{222} are 0.272 nm and 0.157 nm, respectively) using an in-lens type FE-SEM without aberration corrector at an accelerating voltage of 30 kV. This technique needs a larger convergence angle than an optimum convergence angle for standard SEM and STEM observation; however it is possible to visualize the lattice spacing that is much smaller than the diameter of the incident electron beam through the influence of the superior coherent performance in cold field emission electron source. By applying the lattice observation used by conventional in-lens type FE-SEM, it is possible to provide a measuring technique with excellent precision as a theoretically exact dimension and established the ability to perform high precision measurements of crystal lattices for the structural characterization of semiconductor materials. Through a smaller degree of defocus, spherical aberration is reduced which allows simultaneous observation of the STEM image and lattice image.
Acknowledgments
Fig. 4-7. Fourier transform image of BF-STEM image observed along the Si〈011〉 zone axis.
We would like to thank Dr. David Joy, University of Tennessee for interpretational discussions, and Dr. Yoshifumi Taniguchi, Mr. Kuniyasu Nakamura and Dr. Tom Schamp of Hitachi HighTechnologies Corporation for technical assistance. References
Dimensions of Si device in BF-STEM image recorded digitally are calculated by Ndimension Lpixel, where Ndimension is a number of pixels corresponding to the measurement area and Lpixel is the dimension of pixel. Fig. 4-7 shows the Fourier transform image from the 512 512 pixel area in the center of the BF-STEM image (Magnification: 3,000,000 , area: 1280 960 pixels) observed along the Si〈011〉 zone axis. The distance between spot A which is a Si{111} reflection spot (coordinate: 221,204) and the image center (coordinate: 256,256) is 63 pixels, and the known spacing of Si {111} is 0.314 nm. From these results, the pixel size of BF-STEM image is 0.039 nm/pixel. Here, it is possible to obtain highly accurate measurement using pixel size calibrated by lattice spacing. These results demonstrate the ability to perform high precision measurements of crystal lattices for the structural characterization of semiconductor materials.
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Please cite this article as: M. Konno, et al., Lattice imaging at an accelerating voltage of 30 kV using an in-lens type cold field-emission scanning electron microscope, Ultramicroscopy (2013), http://dx.doi.org/10.1016/j.ultramic.2013.09.001i
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Lattice imaging at an accelerating voltage of 30 kV using an in-lens type cold field-emission scanning electron microscope Mitsuru Konno n, Takeshi Ogashiwa, Takeshi Sunaoshi, Yoshihisa Orai, Mitsugu Sato Hitachi High-Technologies Corporation, 882, Ichige, Hitachinaka, Ibaraki 312-8504, Japan
art ic l e i nf o
Keywords: Low-voltage STEM Lattice imaging FE-SEM
a b s t r a c t We reported investigation of lattice resolution imaging using a Hitachi SU9000 conventional in-lens type cold field emission scanning electron microscope without an aberration corrector at an accelerating voltage of 30 kV and discuss the electron optics and optimization of observation conditions for obtaining lattice resolution. It is possible to visualize lattice spacings that are much smaller than the diameter of the incident electron beam through the influence of the superior coherent performance of the cold field emission electron source. The defocus difference between STEM imaging and lattice imaging is found to increase with spherical aberration but it is possible to reduce the spherical aberration by reducing the focal length (f) of the objective lens combined with an experimental sample stage enabling a shorter distance between the objective lens pre-field and the sample. We demonstrate that it is possible to observe the STEM image and crystalline lattice simultaneously. STEM and Fourier transform images are detected for Si{222} lattice fringes and reflection spots, corresponding to 0.157 nm. These results reveal the potential and possibility for a measuring technique with excellent precision as a theoretically exact dimension and established the ability to perform high precision measurements of crystal lattices for the structural characterization of semiconductor materials with minimal radiation beam damage. & 2013 Elsevier B.V. All rights reserved.
1. Introduction Transmission electron microscopes (TEM) operating at accelerating voltages of 200 kV or 300 kV have been widely applied for structural characterization of semiconductor devices, metals and ceramic materials. More recently, with the size of semiconductor device structures shrinking to below the 20 nm technology node, TEM lamella thickness requirements must be made prohibitively thin to prevent structural overlaps in the projected image. Technological developments suggest that inorganic carbon materials such as nanotubes and graphene, and organic polymeric materials will be developed more actively. The demands for fine structural, elemental, and chemical characterization of these materials by electron microscopes are rapidly increasing. Unfortunately, these materials are susceptible to beam damage leading to a reduction in the structural order and image contrast. Low energy microscopy has a reduced probability for knock-on damage; however, the resolution degrades due to an increase in electron wavelength. Accordingly, it is necessary to determine methods to improve the contrast at lower voltage operation without loss of resolution.
n
Corresponding author. Tel.: þ 81 293541970. E-mail address: [email protected] (M. Konno).
There has been a recent technical trend to develop low energy transmission electron microscopes and low energy scanning electron microscopes (SEM) in partnership between research institutes, universities and product manufactures. For example, in 2010 in Japan, Dr Suenaga of the National Institute of Advance Industrial Science and Technology (AIST), and JEOL Co. Ltd. have developed a low energy electron microscope ( 30 kV) with a spherical aberration and chromatic aberration corrector for atomically resolved observation for soft materials and they reported that example of the application of structural characterization of carbon materials [1–2]. In 2011 Dr. Kaiser of the Ulm University in Germany, and Zeiss Co. Ltd. developed a low energy transmission electron microscope ( 20 kV) with an aberration corrector and electronic monochromator which successfully resolved the 0.272 nm spacing Si{220} lattice fringes [3]. In addition, Hokkaido University in Japan and Hitachi Ltd. developed an electron diffraction microscope based on a conventional SEM for obtaining atomic-level resolution images [4]. The imaging resolution using this 30 kV field emission (FE) SEM with a scanning TEM (STEM) function has recently been significantly improved. It is important to reduce the spherical aberration of the objective lens and the energy fluctuation of electron gun (ΔE) for obtaining images at atomic resolution at low accelerating voltage operation. In order to respond to such demands, we have developed the Hitachi SU9000, a cold FE-SEM (CFE-SEM) with an in-lens type of objective lens,
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capable of high resolution phase contrast STEM imaging. Through using this technique on this microscope, it is possible to routinely achieve lattice resolution of the graphite {002} planes with a spacing of 0.34 nm [5]. In this study, we have improved the electron optics and optimization of observation condition for obtaining lattice resolution enhancement in STEM imaging at an accelerating voltage of below 30 kV and its application for semiconductor devices.
2. Principle of lattice imaging 2.1. Behavior of the electron beam incident to the crystalline sample Fig. 2-1 shows the behavior of the electron beam incident on a crystalline sample in a transmission geometry. When the primary electron beam is incident on a crystalline sample with lattice spacing d, transmitted electrons are scattered by elastic and inelastic mechanisms. Elastically scattered electrons are scattered at an angle of twice the Bragg angle, θB, given by Bragg's law: 2θB ¼ λ=d
ð2 1Þ
Here λ is the electron wavelength which for the case of low accelerating voltages (Vacc), is given by λ ¼ √ð1:5=V acc Þ ðnmÞ
2.2.2. αi 42θB In the case where αi 42θB, three electron waves which include the central disk and disks on either side formed by the elastically scattered electrons overlap, so that interference fringes appear at the center of the signal detection surface as shown in Fig. 2-2(c). Some fraction of the interference fringes passing the STEM aperture on the center of the detection surface are detected as the signature of the elastic interaction between the electron beam and the sample. These interference fringes are shifted by scanning the primary electron beam across the crystalline sample. As shown in Fig. 2-3, when the primary electron beam moves by only one lattice spacing, these interference fringes are shifted by one pitch. By moving these interference fringes, the STEM signal is varied and generates the phase contrast lattice image observed. In the next section, we will discuss the optimum optical condition of the beam convergence semi-angle and primary beam focus for obtaining the lattice images with a 30 kV FE-SEM.
3. Optical condition for STEM imaging and lattice imaging 3.1. Optimum beam convergence semi-angle (αi) for STEM imaging and lattice imaging
ð2 2Þ
As mentioned above, if the lattice spacing, d, and accelerating voltage, Vacc, are fixed, the scattering angle of the elastically scattered electron is determined through Eq. (2-1). When the sample is a multi wall carbon nanotube (MWCNT) with a 0.34 nm lattice spacing, the scattering angle is 2θB ¼7.3 mrad at Vacc ¼ 200 kV and 2θB ¼ 21 mrad at Vacc ¼30 kV. 2.2. Principle of lattice image contrast generation When the convergent electron beam of a STEM is incident on a crystalline sample with a convergence semi-angle αi, the inelastically and elastically scattered electrons are spread radially at the same angle as αi, as shown in Fig. 2-2(a). In order to understand the principle of lattice image contrast generation, the interference state of the electron wave according to the relation between Bragg angle 2θB and beam convergence semi-angle αi must be considered. 2.2.1. θB oαi≦2θB In the case where θB oαi r2θB, the inelastic and elastic scattered electrons are both transmitted and their wavefronts partly overlap, forming a constructive interference pattern of fringes as shown in Fig. 2-2(b).
Fig. 3-1 shows the schematic of the Hitachi SU9000 FE-SEM optical system used to observe the STEM image. The beam convergence semi-angle, αi, of the incident beam on the sample can be set by changing the objective aperture size, or changing the beam crossover point by the strength of the second condenser lens. Fig. 3-2 shows the relation between the beam convergence semi-angle αi and the theoretical resolution R. R is limited by electron diffraction associated with the Raleigh criterion and the impact of the spherical aberration which is the limiting aberration of the system. There is an optimum beam convergence semi-angle for minimum theoretical resolution. In case of SU9000 FE-SEM, this optimum beam convergence semi-angle is approximately 10 mrad at 30 kV the maximum accelerating voltage. Normally this optimum beam convergence semi-angle is chosen when observing the real objective image because the image resolution is at its best. As discussed in Section 2.2.2, lattice image observation requires the beam convergence semi-angle αi 42θB. At the accelerating voltage of 30 kV, observation of carbon lattice fringes (d¼0.34 nm) requires αi 420.5 mrad, and for Si {111} lattice fringes (d¼ 0.314 nm) requires αi 422.5 mrad. Therefore, in order to obtain the phase contrast lattice image of Carbon or Si at 30 kV FE-SEM, a larger beam convergence semi-angle than normally used is required.
3.2. Behavior of the optimum defocus for STEM imaging and lattice imaging We have found from experiment that there is the gap of defocus value between optimum STEM imaging and optimum lattice imaging. In the following sections, we study this phenomenon.
Fig. 2-1. Behavior of the electron beam incident on a crystalline sample.
3.2.1. Theoretical model of the optimum defocus for STEM imaging The optimum defocus setting, Δf STEM , for STEM imaging as measured from the Gaussian image plane is found at which the STEM image is best. In order to determine Δf STEM , we applied the Information Passing Capacity (IPC) method [6] to calculate the model of optimum resolution. The IPC method applies information theory [7] to characterize the beam performance for an optical image.
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Fig. 2-2. Generation of the interference fringes by convergent beam.
Fig. 2-3. Generation of the lattice fringes contrast.
Fig. 3-2. Relation between theoretical resolution and lattice imaging condition.
Here τbeam is the two-dimensional Fourier Transform of the beam intensity distribution, and ν is the dimensionless special frequency in the radial direction normalized to the diffraction unit of length (λ=αi ) as λ qffiffiffiffiffiffiffiffiffiffiffiffiffiffi ν2x þ ν2y ð3 2Þ ν¼ αi
Fig. 3-1. Optical system for STEM imaging by Hitachi SU9000 FE-SEM.
The IPC parameter, ρH , is calculated by
ρH ¼
π ðλ=αi Þ2 ln 2
Z
2
ln 0
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! S 1 þ jτbeam ðνÞj2 νdν ðbit=nm2 Þ N
ð3 1Þ
Here νx and νy are the spatial frequencies for x and y directions, respectively. S/N corresponds to signal-to-noise ratio of the optical image. ρH represents the maximum capability of the information content in the optical image that is transferred from 1 nm2 area in a specimen. Because τbeam varies with the defocus Δf measured from Gaussian image plane, ρH in Eq. (3-1) is a function of Δf . Fig. 3-3 shows an example of behavior of the IPC ρH as a function of Δf near the optimum focus. In Fig. 3-3, an optimum defocus Δf STEM is found at which ρH is maximum. In the IPC method, the resolution R of an optical system is modeled by the following equation calculated at Δf ¼ Δf STEM . sffiffiffiffiffiffiffiffiffiffiffi λ ρideal H ð3 3Þ R ¼ 0:61 αi ρH
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Here ρideal is the IPC for aberration free optical system for a point H source where a beam intensity distribution is the Airy pattern. In Eq. (3-3), ρH and ρideal are calculated using the same value of H S/N. From Eq. (3-3), the resolution is given by Rayleigh's criterion (0.61λ=α) when the optical system is an aberration-free optical system for a point source, i.e., ρH ¼ ρideal . H 3.2.2. Behavior of spatial resolution R and optimum defocus Δf STEM Fig. 3-4 shows an example of resolution R and defocus Δf STEM as a function of beam convergence semi-angle αi at a specimen surface. The plot of resolution is V-shaped and has a minimum value at P1. The beam convergence semi-angle (αopt ) at P1 is called the optimum convergence semi-angle and the resolution at αopt is the attainable resolution of an optical system. When an optical
system is suffering from spherical aberration, the IPC ρH is maximum when the following condition is satisfied: B¼
1 C s α3i ¼1 4ðλ=αi Þ
ð3 4Þ
Here B represents the effect of spherical aberration in wave optics. From Eq. (3–4), we obtain the optimum convergence semi-angle αopt as: 1=4 4λ ð3 5Þ αopt ¼ Cs When Cs ¼2 mm and λ ¼0.00707 nm (at 30 kV), αopt becomes 11 mrad as shown Fig. 3-4. When beam convergence semi-angle αi is near αopt or smaller, Δf STEM is given as [8] Δf STEM ¼ Δf 1 ¼ 0:5C s α2i
ð3 6Þ
By applying Eqs. (3-5) and (3-6), the optimum defocus (See P2 in Fig. 3-4) at αopt is written as pffiffiffiffiffiffiffi Δf 1 ¼ C s λ ð3 7Þ Eq. (3-7) corresponds to the Scherzer defocus [9] for phase contrast STEM imaging. When the beam convergence semi-angle αi is large compared to αopt , Δf STEM becomes constant of αi and it is written as [8] pffiffiffiffiffiffiffi Δf STEM ¼ Δf 2 ¼ 1:15 C s λ ð3 8Þ
Fig. 3-3. Behavior of the IPC ρH as a function of defocus Δf.
The points P3 and P4 in Fig. 3-4 indicate defocuses Δf 2 (Eq. (3-8)) and Δf 1 (Eq. (3-6)), respectively, when αi ¼ 20 mrad (4 αopt ). Figs. 3-5 and 3-6 show beam intensity distributions and optical transfer functions (OTFs), respectively, calculated at defocuses for P3 and P4. If we simply compare the FWHM of beam intensity distributions in Fig. 3-5, the defocus for P4 seems to be better for higher resolution. However due to higher level of the beam tail produced at defocus for
OTF
1.2 1.0
P3
0.8
P4
0.6 0.4 0.2 0.0 -0.2
0
1
2
3
4
5
Spatial frequency (nm-1) Fig. 3-4. Behavior of the resolution and optimum defocus for STEM imaging as a function of beam opening angle.
Fig. 3-6. Comparison of optical transfer functions (OTFs) obtained at defocuses for P3 and P4.
Fig. 3-5. Comparison of beam intensity distributions obtained at defocuses for P3 and P4.
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P4, the OTF curve for P4 degrades in a wide range of special frequencies as shown in Fig. 3-6. This means that the important structural information degrades seriously at the defocus for P4. Therefore we see that the defocus for P3 is suitable to the observation of structural information compared to the defocus for P4. 3.3. Optimum defocus Δf Lattice for lattice imaging In order to observe the lattice of a CNT using 30 kV beam voltage, it is necessary to use a beam convergence semi-angle of 21 mrad or larger. The optimum condition for an optical system given by Eq. (3-4) at αi ¼21 mrad is satisfied when Cs ¼0.15 mm. However, we have obtained lattice images of CNT's using noncorrected FE-SEM where Cs is much larger than 0.15 mm. We also found from experiment that a discrepancy exists of the optimum defocus between STEM imaging and lattice imaging which varies with Cs. When Cs is close to the optimum value satisfying Eq. (3-4), optimum defocus for lattice imaging is given by [10] Δf Lattice ¼ C s θ2B
ð3 9Þ
Because spherical aberration in our experiment for lattice imaging is much larger than the optimum value satisfying Eq. (3-4), we compared the optimum defocus found from experiment for lattice imaging of CNT with those given by Eq. (3-9). The optimum defocus for lattice imaging can be measured as a function of defocus Δf a from the STEM images. Since the optimum defocus Δf STEM is now considered as Δf 2 (see Eq. (3-8)), the optimum defocus (Δf ex ) for lattice imaging, measured from Gaussian image plane, is expressed as Δf ex ¼ Δf 2 þ Δf a
ð3 10Þ C s θ2B
for lattice imaging Fig. 3-7 shows comparison between Δf ex and of CNT's at various Cs values. We see from Fig. 3-6 that the discrepancy between Δf ex and C s θ2B is decreased with decreasing Cs value.
Fig. 3-7. Relation between optimum defocus for lattice imaging of CNT and spherical aberration coefficient Cs.
5
4. Experimental study 4.1. The focus gap between the lattice and in focus Fig. 4-1 shows BF-STEM images of a graphite particle at an accelerating voltage of 30 kV. Fig. 4-1(a) is in an optimum defocus condition for STEM imaging (Δf STEM ) which clearly shows a particle configuration, layer construction and crystal orientation. Fig. 4-1(b) is optimized for defocus for lattice imaging (Δf Lattice ) showing that it is possible to slightly resolve the C{002} planes, which have a spacing of 0.34 nm. As demonstrated, switching from the initial imaging conditions to lattice fringe phase contrast conditions requires to underfocus the electron probe significantly. For this reason, it is difficult to observe the structural formations of the subject and its lattice fringes by simultaneously.
4.2. Optimizing the imaging condition by changing the sample height The defocus difference between STEM imaging and lattice imaging is found to increase with spherical aberration. It is possible to reduce the spherical aberration by reducing the focal length (f) of the objective lens combined with an experimental sample stage enabling a shorter distance between the objective lens pre-field and the sample (Fig. 4-2). The experimental sample stage used here for STEM observation has a hole in the center allowing for transmission observation where the TEM sample mounts at the upper position of the holder. This special stage permits a focal length 1.5 mm shorter than the standard sample position with a sample height adjustment of 70.3 mm. Fig. 4-3 shows the comparison of image resolution and amount of Δf for STEM imaging with those for lattice imaging. We have observed BF-STEM images of a graphite particle and lattice fringes in a squared area at four positions as per Table 4-1. The working distance and spherical aberration coefficient (Cs) according to computation are 3.0 mm, 2.0 mm at sample position A, 2.7 mm, 1.7 mm at B, 2.5 mm, 1.5 mm at C, 1.8 mm, 1.0 mm at D, respectively. Line A is a standard STEM observation position and line D is the upper limit of the special stage at an accelerating voltage of 30 kV setting. The amount of defocus difference between the lattice image and the in-focus image
Fig. 4-2. The experimental sample stage for changing sample height. (a) Top view and (b) cross section view of top along the line A-A'
Fig. 4-1. BF-STEM images graphite particle at an accelerating voltage of 30 kV. Magnification: 2,000,000
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Fig. 4-3. The comparison of image resolution and amount of Δf for STEM imaging with those for lattice imaging obtained at various Cs values.
(Δf) is calculated by the value of digital analog converter (DAC) at each focus point. As the focal length is shortened to decrease the spherical aberration coefficient and the sample height is brought up to the cross-over plane, the difference in defocus between STEM imaging (Δf STEM ) and lattice imaging (Δf Lattice ) is found to significantly decrease. At sample position D, the amount of defocus has been shortened to 25 nm and it is possible to observe the STEM image and crystalline lattice simultaneously. 4.3. Investigation of image resolution Fig. 4-4 shows high resolution phase contrast –STEM images observed along the Si〈1 1 0〉 zone axis at an accelerating voltage of 30 kV, with inset indexed Fast Fourier Transforms (FFT) of each image. The standard condition (WD: 3 mm, Cs: 2 mm) was used for Fig. 4-4 (a) and the optimized condition (WD: 1.8 mm, Cs: 1 mm) was used for Fig. 4-4(b). The sample was thinned by an Ar þ ion milling technique to a sample thickness of about 20 nm. Not surprisingly both BF-STEM images show the Si {111} planes, with an inter-planar spacing of 0.314 nm with the corresponding reflections in the FFT. However, in the optimized condition, the image sharpness of Si {111} lattice fringes and the associated FFT reflections are detected including the Si {200} spots, corresponding to 0.272 nm. This result using the optimized
condition reveals the potential for high contrast visualization without loss of resolution in semiconductor devices and any carbon materials with minimal radiation beam damage. Next we have investigated the image resolution when changing the amount of defocus. Fig. 4-5 shows the BF-STEM images of Si〈011〉 single crystal by a through-focus method at an accelerating voltage of 30 kV, and Fourier transform of each BF-STEM image. The amount of defocus (Δf) in the BF-STEM images were 0 nm (a) which focused on the sample (in focus), 86 nm (b), 223 nm (c) and 341 nm (d), respectively. Image resolution was changed depending on the extent of Δf, and BF-STEM image of Δf¼ 341 nm demonstrates the best result which shows the Si {222} planes, with an interplanar- spacing of 0.157 nm and Fourier transform image also detect the Si {222} reflection spots. BF-STEM and Fourier transform images of Δf¼ 223 nm shows the Si (220) plane, which has a spacing of 0.192 nm. This result emphasizes that high resolution imaging at less than 200 pm is possible without an aberration corrector and creates new possibilities and applications of low energy STEM image. 4.4. Application of semiconductor devices. Fig. 4-6 shows the cross sectional BF-STEM images of NAND flash memory (a) and the magnified BF-STEM image (b) observed along the Si〈011〉 zone axis for a sample prepared using a focused
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Fig. 4-4. High resolution BF-STEM images observed along the Si〈110〉 zone axis with accelerating voltage of 30 kV, and Fourier transform of each BF-STEM image. Magnification: 3,000,000 .
Fig. 4-5. BF-STEM images of Si〈011〉 single crystal by a through-focus method at an accelerating voltage of 30 kV. Magnification: 3,000,000 .
Fig. 4-6. The cross sectional BF-STEM images of NAND flash memory (a) and the magnified BF-STEM image (b) observed along the Si〈011〉 zone axis.
ion beam fabrication technique. The sample thickness was around 30 nm. Fig. 4-6a clearly shows the semiconductor device structure such as a floating gate, interlayer dielectric and gate insulating layer with great clarity by a low energy operation. In Fig. 4-6b, the magnified BF-STEM image shows Si {111} lattice fringes (spacing of 0.314nm) simultaneously with the fine structure of the gate
dielectric layer. Fig. 4-7 shows the Fourier transform image from the 512×512 pixel area in the center of the BF-STEM image observed along the Si o0114 zone axis. Because the spots for 0.314nm spacing are clearly detected in Fig. 4-7, the information of the spacing for Si {111} can be applied to the calibration of the critical dimension measurement for devices.
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5. Conclusions
Table 4-1 The working distance and spherical aberration. Sample position
A
B
C
D
Working distance (mm) Spherical aberration (mm)
3.0 2.0
2.7 1.7
2.5 1.5
1.8 1.0
We report here STEM observations of lattice fringes in graphite (lattice spacing of C{002} is 0.34 nm) and Silicon (lattice spacing of Si {002} and Si{222} are 0.272 nm and 0.157 nm, respectively) using an in-lens type FE-SEM without aberration corrector at an accelerating voltage of 30 kV. This technique needs a larger convergence angle than an optimum convergence angle for standard SEM and STEM observation; however it is possible to visualize the lattice spacing that is much smaller than the diameter of the incident electron beam through the influence of the superior coherent performance in cold field emission electron source. By applying the lattice observation used by conventional in-lens type FE-SEM, it is possible to provide a measuring technique with excellent precision as a theoretically exact dimension and established the ability to perform high precision measurements of crystal lattices for the structural characterization of semiconductor materials. Through a smaller degree of defocus, spherical aberration is reduced which allows simultaneous observation of the STEM image and lattice image.
Acknowledgments
Fig. 4-7. Fourier transform image of BF-STEM image observed along the Si〈011〉 zone axis.
We would like to thank Dr. David Joy, University of Tennessee for interpretational discussions, and Dr. Yoshifumi Taniguchi, Mr. Kuniyasu Nakamura and Dr. Tom Schamp of Hitachi HighTechnologies Corporation for technical assistance. References
Dimensions of Si device in BF-STEM image recorded digitally are calculated by Ndimension Lpixel, where Ndimension is a number of pixels corresponding to the measurement area and Lpixel is the dimension of pixel. Fig. 4-7 shows the Fourier transform image from the 512 512 pixel area in the center of the BF-STEM image (Magnification: 3,000,000 , area: 1280 960 pixels) observed along the Si〈011〉 zone axis. The distance between spot A which is a Si{111} reflection spot (coordinate: 221,204) and the image center (coordinate: 256,256) is 63 pixels, and the known spacing of Si {111} is 0.314 nm. From these results, the pixel size of BF-STEM image is 0.039 nm/pixel. Here, it is possible to obtain highly accurate measurement using pixel size calibrated by lattice spacing. These results demonstrate the ability to perform high precision measurements of crystal lattices for the structural characterization of semiconductor materials.
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