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On the spatial resolution limit of direct-write electron beam lithography
Microelectronic Engineering 168 (2017) 41–44
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Research paper
On the spatial resolution limit of direct-write electron beam lithography Nan Jiang Department of Physics, Arizona State University, Tempe, AZ 85287-1504, United States
a r t i c l e
i n f o
Article history: Received 14 July 2016 Received in revised form 11 October 2016 Accepted 18 October 2016 Available online 22 October 2016 Keywords: Direct-write electron beam lithography Scanning transmission electron microscopy Electric field Spatial resolution
a b s t r a c t The mechanism for direct-write electron-beam lithography in insulating resists is introduced in this letter, and it is based on damage by the induced electric field in transmission electron microscope. Under this mechanism, the direct-write EBL is electron dose-rate dependent, and there is a dose-rate threshold, below which the lithographic process does not operate, regardless of the total electron dose. The spatial resolution is determined by the strength of the induced electric field. In theory, the highest spatial resolution should be set by the dimension of the electron beam, and thus the EBL should be able to create nanostructures at the atomic scale. So far, the best resolution obtained was in the direct write of conductive nanochannels in Li4Ti5O12, in which 1.5 nm isolated features and a 1.0–1.5 nm half-pitch array of nanochannels were achieved. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Electron-beam lithography (EBL), a well-established high resolution patterning technique, has been widely used in nanotechnology and is the basis of much of the semiconductor device industry [1,3,9,22,26]. Understanding the limits of the spatial resolution in EBL is therefore very important in order to optimize the lithographic process. In brief, the resolution is determined by the following two processes: exposure (i.e. electron-resist interaction) and development in a developer [7, 18]. For direct-write (one-step) EBL using self-developing resist, which is the focus of the current study, the latter does not apply, so that the resolution is only determined by the interaction range of the beam electrons with the resist. So far, it has been reported in all experiments that the lateral sizes of the lithographic features are always larger than the probe size of the beam [5]. The broadening due to elastic scattering of the beam electrons has not been considered to play a limiting role, instead, the limit of spatial resolution of EBL is believed to be set by secondary electrons (SEs) [14,20,27]. This SE model is supported by Monte Carlo simulations of SE trajectories, which calculate range of SEs in the resist. It was found that the broadening of the point-spread function (PSF) matches the extension of the SEs [14,20, 27]. However, controversial results have also been reported. When Monte Carlo simulations track the energy deposited in the resist by SEs, instead of the range, the SEs have only slight, if any, effect on final resolution [4,5]. Besides SEs, delocalization of inelastic scattering of the beam electron has also been considered, and it has a similar interaction range as SEs [15]. Recently, attempts have been made to measure the EBL PSF directly using an aberration-corrected energyfiltered transmission electron microscopy (EFTEM) [17]. It was suggested that the volume plasmons should be more important than SEs in the limit of spatial resolution at the sub-10 nm scale. Even though
http://dx.doi.org/10.1016/j.mee.2016.10.016 0167-9317/© 2016 Elsevier B.V. All rights reserved.
the origins of these interactions are different, the delocalization effect is common in all the models. It seems that this delocalization effect provides a fundamental limit on efforts to achieve atomic resolution in EBL, although the finest electron beam can be focused within less than one tenth of a nanometer in diameter in the state-of-the-art electro-optical system [21]. Beside delocalization, all these existing models consider that EBL is an electron-dose dependent process, and thus different resists have different dose thresholds. Above the threshold (enough exposure), there are sufficient bond scission events to be developed by the developer [20] or atomic displacements to form a nanostructure in the directwrite EBL [17]. However, these models ignore important experimental evidence associated with EBL. In studies of hole-drilling in inorganic materials, it was discovered that the drilling process depends on the electron dose rate but not on total electron dose; prolonged exposure below the dose-rate threshold did not result in drilling [23]. In studies of nanofabrication using electron beams, it was found that the sizes of nanocylinders and nanowalls created by the electron beam is independent of specimen thickness [12,13]. Apparently, these observations violate the dose-dependent principle, and cannot be explained by these existing models. Recently, these phenomena have been interpreted by a revised mechanism of damage by the induced electric field (DIEF) [10,11]. In this study, we extend this mechanism to the EBL process, and especially discuss its impact to the limit of spatial resolution of direct-write EBL. Our results are based on experimental and theoretical analysis of thin, self-supporting films studied in scanning transmission electron microscope (STEM), free of backscattering. Although EBL has been studied for decades, the current study presents a very different view on the resolution limit from conventional beliefs. If this new model can be extended to more general situations, the atomic-level resolution could be achieved in EBL industry.
42
N. Jiang / Microelectronic Engineering 168 (2017) 41–44
2. Experimental For EBL in TEM or STEM, the specimen must be thin enough to allow incident electrons to pass through. Here there are two types of specimen, as illustrated in Fig. 1. One is equivalent to the self-supporting resist thin film (on the center in Fig. 1) and the other is equivalent to the resist thin film on a substrate (on the side). The specimen used for demonstration was 10Na2O-20B2O3-70SiO2 (in mol%) glass, and was obtained by the conventional melt-and-quench method. TEM specimen was prepared by grinding the glass into powder in acetone, and picking them up using a Cu grid covered with a lacy carbon thin film. The EBL was carried out using the Cornell VG HB501 100 kV STEM, equipped with electron energy-loss spectroscopy (EELS). The probe size was about 0.25 nm in diameter, at which the probe current was about 0.4 nA. 3. Results and discussion If the resist is insulating to electrons, the holes left by emissions of SEs and Auger electrons cannot be neutralized rapidly, resulting in accumulation of positive charges [2,8,10,11]. In the DIEF mechanism, the electric field is produced by these positive charges [10,11]. In the transmission geometry, for a thin self-supporting film, all the beam electrons traverse a thin slab of resist without depositing electrons inside it. In this case, the distribution of the induced electric field inside the resist is relatively simple. In most EBL systems, electron beams are highly focused, and their lateral dimensions are usually b0.5–1.0 nm, which is much smaller than the effective mean-free-path (MFP) of SEs and Auger electrons (e.g. N1.0 nm [24]). As illustrated in Fig. 2, most emitted electrons travel approximately perpendicular to the beam direction and scatter in a larger region around the beam column. This is equivalent to that incident electrons ionize the specimen into a positive inner core (nano-column) surrounded by a thick negative shell, and their volume ratio is r20/r2 (Fig. 2). Considering that r0 b 0.5 nm and r = 1–100 nm [24], the volume of positively charged inner core is much smaller than the negatively charged shell, and thus the charge density of the positively charged electron-probed region is much higher than the negatively charged surrounding. Therefore, the exposed region can be considered as a positively charged nano-column, with the diameter of the electron probe and a length given by the resist's thickness for the case of a selfsupporting thin film. Assuming that it is charged uniformly, the magnitude of the induced electric field for a given induced charge density ρ (Coulomb per length) can be simplified as [10] jEj ¼
ρ 2πε0 εr R
ð1Þ
in which R is the shortest distance to the electron beam. Its direction points outward perpendicular to the beam. Thus the induced electric field has an approximately cylindrical symmetry around the beam [10]. This theory is supported by experimental observations of nanocylinders in silicate glasses [6,12,13] and nanochannels in Li4Ti5O12 crystal [25] formed by a STEM probe. It should be noticed that for the sake of simplicity, we ignored the negative surrounding in deriving Eq. (1). This simplification does not affect the conclusion obtained, since including
Fig. 1. Cartoon drawing showing the definition of self-supporting thin film.
Fig. 2. Inner cylinder has net positive charges and larger outer one has net negative charges. r0 is the radius of the electron probe, and r represents the range of emitted electrons.
these emitted electrons may further enhance the strength of the induced electric field, and thus lower the threshold beam current density. The range of r may not affect the resolution. This is because in this model the displacements of atoms are driven by the electric field, not by the ionization of secondary or plasmon electrons. Interestingly, according to Eq. (1), the strength of the induced electric field is independent of the specimen thickness [10]. This is a unique characteristic of the DIEF mechanism in STEM, which distinguishes it from other dose-dependent mechanisms, such as knock-on and radiolytic processes. This thickness-independent characteristic has also been observed in previous direct-write EBL [6,12,13]. In resists, ionic bonds between anions and cations are polarized. Under a strong electric field, polar bonds can be ruptured, resulting in cation and/or anion displacements. To displace a bonded ion in a solid, the work done by the electric field on this ion as it moves from one site to the nearest available site must be equal to or larger than the activation energy Ua for ion migration, i.e. site2 Z
qEðrÞ dr ≥U a
W¼
ð2Þ
site1
in which q is the electric charge of the ion. The distance d between the two nearest minimum energy sites for the ion should be in order of the nearest atomic distance, which is several angstroms. Assuming that | E(r)| does not vary significantly over such a small distance, the minimum work required for an atomic displacement can be simplified as Wmin ¼ qETh ind d ¼ U a
ð3Þ
Therefore, the threshold strength | ETh ind | = Ua/qd, below which the lithographic process will not happen. Fig. 3 shows some nanocylinders created by STEM probe in a Na borosilicate glass. The formation of the nanocylinder is due to the accumulation of mobile cations driven by the induced electric field [10–13]. Therefore, it is reasonable to consider that the strength of the electric field at the boundaries should be approximately equal to | ETh ind |. Na migration in silicate glasses has been extensively studied; in a glass containing 10 mol% Na, Ea ≈ 0.9 eV [19]. The simplest approximation for the charge q of Na ion is to use its formal valence charge, i.e. q = + 1(e), where e = 1.602 × 10−19C (see S.I.). Here we set d = 0.3 nm, which is about the Na–Na distance in silicates. Inserting all these values in Eq. (3), we can estimate that | ETh ind | = 3.0 V/nm. This is the minimum electric field required in order to displace a Na ion in the [SiO4]
N. Jiang / Microelectronic Engineering 168 (2017) 41–44
Fig. 3. Left panel: Annular dark-field (ADF) image of nanocylinders created by STEM probe in the Na borosilicate glass. Right panel: The diameters of nanocylinders and the corresponding maximum electric field for different exposure time. The dotted line represents the modeling of the induced electric field versus irradiation time. It consists of two parts: initially increases rapidly and then keeps a constant.
tetrahedral network. As shown in Fig. 3, the diameter of the nanocylinder increases with exposure time. Using Eq. (1), the maximum electric field strengths at the edge of the electron probe for various exposure times can be estimated and the result are also plotted in Fig. 3. It shows that the induced electric field initially increases with exposure time, but not indefinitely. In this case, it reaches a maximum after about 10 s of exposure, thereafter keeps a constant. The EBL process driven by the DIEF mechanism is schematically illustrated in Fig. 4. In the DIEF model, the charge accumulation does not reach a maximum immediately after the exposure, instead, it increases rapidly with exposure time before it reaches the maximum at time t0, and so does the electric field [10,11]. For a current density J with Emax(J) = |ETh ind |, this is the threshold current density JTh (or threshold dose rate), below which the lithographic process cannot operate, regardless of the total electron dose [23]. As illustrated in Fig. 4, even though J N JTh, the lithographic process does not occur until the exposure time t ≥ tA, which is the time threshold for the DIEF mechanism [10,11], akin to charging a capacitor. Therefore, for any current density (J N JTh), the lateral size of the lithographic feature R should be between Rmin and Rmax, as illustrated in Fig. 4. Rmin is the smallest size that EBL can achieve in this resist, which is independent of beam current density but determined by the size of the beam. Rmax is the upper limit of lithographic feature size under this current density, and thus it is current density dependent. It should be pointed out that lithography is a dynamic process, i.e. it also changes the properties of the resist, and so changes the charge
43
accumulation process as well. In other words, the actual Emax may be either higher or lower than that predicted in Fig. 4, depending on the change of resistivity in the probed resist [10,11]. If the lithographic process increases the resistivity, Rmax becomes larger, while if the process decreases the resistivity, Rmax becomes smaller. Therefore the difference between Rmax and Rmin becomes narrower in the latter case. The lithographic process in the former resists is divergent, while it is convergent in the latter. A direct deduction from this mechanism is that, for self-supporting thin-films, the theoretical spatial resolution of EBL should be Rmin. It should be pointed out that the value of Rmin is generally determined by the size of electron beam. However, one should consider broadening effects due to both elastic scattering and convergent angle. Nevertheless, EBL should be able to create atomic-scale nanostructure using the state-of-the-art aberration-corrected STEM in thin films. However, current results have not been even close to this goal. One of the reasons is that the previous knowledge of EBL mechanism does not consider the dose rate as a crucial parameter, nor the exposure time. In addition, the materials that have been used as EBL resists are extremely susceptible to electron beam damage (to increase the efficiency), and thus the threshold current densities can be very low. As a consequence, previous efforts have sought the lowest Rmax, rather than the Rmin. There is also a practical difficulty in seeking low Rmin in these resists: finding the proper tool to detect these tiny features. Imaging using either STEM or TEM, operating at normal conditions, may destroy the lithographic features or introduce new ones. Therefore, we suggest that the materials that are suitable for achieving atomic-resolution lithography should be “convergent” for beam damage, i.e. their resistivity should decrease due to the lithographic process. In these materials, Rmax can be close to Rmin. One example is the creation of conductive nano-channels in Li4Ti5O12 crystals [25]. As shown in that work, the nanochannels have a diameter of 1.5 nm, and the separation of two channels can be as small as 1 nm. In other words, using a STEM as the exposure tool 1.5 nm isolated features and a 1.0–1.5 nm half-pitch array of nanochannels can be fabricated in Li4Ti5O12 [25]. These values are better than the previously reported highest resolution patterns of EBL in thin films [16]. It should be pointed out that these values are definitely not the limit of the resolution that we can achieve in the EBL. As mentioned above, Rmax is also dependent on the resistivity of resist. Generally, the lower the resistivity, the weaker the induced electric field, and thus the smaller the Rmax. In theory, if Rmax b Rmin, in which the latter is independent of the resistivity, the lithographic process cannot be initiated by the DIEF mechanism alone. This suggests that the DIEF mechanism may not play a dominant role in the lithography of semiconductors and conductors, unless the current density of the electron beam is much higher than that currently used in the conventional TEM. However, the induced electric field may lower the activation energies for certain species in these types of resists, and thus it may not be appropriate to ignore the effect of the induced electric field. Therefore, there are two crucial parameters in this EBL model. One is the resistance to electrons, which determines Rmax, and the other is the conductivity of ions (i.e. activation energy of ion migration), which determines Rmin. It should be pointed out that the electron-beam transparency is not a necessary condition to apply the DIEF mechanism. The condition is only for the convenience of discussion and straightforward experimental observations. However, in bulk samples, either very thick resists or thinfilm resists on very thick substrates, the induced electric field can be much more complicated than that in the beam-transparent thin films due to the contributions from both deposit and backscattering of the beam electrons. The details of this more general situation should be discussed thoroughly when experimental data are available. 4. Conclusion
Fig. 4. Schematic drawing showing the DIEF mechanism for the EBL. Left vertical axis (E) is the strength of electric field and the right one (R) is the diameter of the lithographic feature. Rmin represents the smallest diameter and Rmax is largest for a current density J.
In conclusion, the mechanism based on DIEF has been introduced to describe direct-write EBL in self-supporting thin films of insulating
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N. Jiang / Microelectronic Engineering 168 (2017) 41–44
resists. Under this mechanism, the direct-write EBL is electron dose-rate dependent and there is a dose-rate threshold. The spatial resolution is determined by the strength of the induced electric field. In theory, the highest resolution should be only limited by the dimension of the electron beam, and thus it should be possible to achieve the atomic-scale resolution EBL in thin films in the near future. Acknowledgement Discussions with Prof. J. C. H. Spence of Arizona State University and Dr. D. Su of Brookhaven National Laboratory are very helpful. Appendix A. Supplementary data Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.mee.2016.10.016. References [1] A. Broers, M. Molzen, J. Cuomo, N. Wittels, Appl. Phys. Lett. 29 (1976) 596–598. [2] J. Cazaux, Correlations between ionization radiation damage and charging effects in transmission electron microscopy, Ultramicroscopy 60 (1995) 411–425. [3] Y. Chen, Nanofabrication by electron beam lithography and its applications: a review, Microelectron. Eng. 135 (2015) 57–72. [4] B.M. Cord, J. Yang, H. Duan, D.C. Joy, J. Klingfus, K.K. Berggren, Limiting factors in sub10 nm scanning-electron-beam lithography, J. Vac. Sci. Technol. B 27 (2009) 2616–2621. [5] H. Duan, V.R. Manfrinato, J.K.W. Yang, D. Winston, B.M. Cord, K.K. Berggren, Metrology for electron-beam lithography and resist contrast at the sub-10 nm scale, J. Vac. Sci. Technol. B 28 (2010), C6H13. [6] L. Gontard, J.R. Jinschek, H. Ou, J. Verbeeck, R.E. Dunin-Borkowski, Three-dimensional fabrication and characterisation of core-shell nano-columns using electron beam patterning of Ge-doped SiO2, Appl. Phys. Lett. 100 (2012) 263113. [7] R. Howard, H. Craighead, L. Jackel, P. Mankiewich, M. Feldman, J. Vac. Sci. Technol., B 1 (1983) 1101–1104. [8] C.J. Humphreys, T.J. Bullough, R.W. Devenish, D.W. Maher, P.S. Turner, Electron beam nano-etching in oxides, fluorides, metals and semiconductors, Scan. Electron Microsc. Supplement 4 (1990) 185–192.
[9] M. Isaacson, A. Murray, J. Vac. Sci. Technol. 19 (1981) 1117–1120. [10] N. Jiang, Damage mechanisms in electron microscopy of insulating materials, J. Phys. D. Appl. Phys. 46 (2013) 305502. [11] N. Jiang, Electron beam damage in oxides: a review, Rep. Prog. Phys. 79 (2016) 016501. [12] N. Jiang, J. Qiu, A. Garta, J. Silcox, Nanoscale modification of optical properties in Ge doped SiO2 glass by electron-beam irradiation, Appl. Phys. Lett. 80 (2002) 2005–2007. [13] N. Jiang, G.G. Humbree, J.C.H. Spence, J. Qiu, F.J.G. de Abajo, J. Silcox, Nanoring formation by direct-write inorganic electron-beam lithography, Appl. Phys. Lett. 83 (2003) 551–553. [14] D.C. Joy, The spatial resolution limit of electron lithography, Microelectron. Eng. 1 (1983) 103–119. [15] M.I. Lutwyche, The resolution of electron beam lithography, Microelectron. Eng. 17 (1992) 17–20. [16] V.R. Manfrinato, L. Zhang, D. Su, H. Duan, R.G. Hobbs, E.A. Stach, K.K. Berggren, Resolution limits of electron-beam lithography toward the atomic scale, Nano Lett. 13 (2013) 1555–1558. [17] V.R. Manfrinato, J. Wen, L. Zhang, Y. Yang, R.G. Hobbs, B. Baker, D. Su, D. Zakharov, N.J. Zaluzec, D.J. Miller, E.A. Stach, K.K. Berggren, Determining the resolution limits of electron-beam lithography: direct measurement of the point-spread function, Nano Lett. 14 (2014) 4406–4412. [18] H. Namatsu, T. Yamaguchi, M. Nagase, K. Yamazaki, K. Kurihara, Microelectron. Eng. 42 (1998) 331–334. [19] M.L.F. Nascimento, E. Nascimento, W.M. Pontuschka, M. Matsuoka, S. Watanabe, Test of Anderson-Stuart model in sodium silicate glasses and the general Arrhenian conductivity rule in wide composition range, Cerâmica 52 (2006) 22–30. [20] A. Raghunathan, J.G. Hartley, Influence of secondary electron in high-energy electron beam lithography, J. Vac. Sci. Technol. B 31 (2013) 011605. [21] RMS — Royal Microscopical Society, in: R. Brydson (Ed.), Aberration-corrected Analytical Electron Microscopy, John Wiley & Sons, Lts., 2011 [22] M.S.M. Saifullah, Sub-10 nm direct patterning of oxides using an electron beam — a review, Cosmos 5 (2009) 1–21. [23] I.G. Salisbury, R.S. Timsit, S.D. Berger, C.J. Humphreys, Nanometer scale electron beam lithography in inorganic materials, Appl. Phys. Lett. 45 (1984) 1289. [24] M.P. Seah, W.A. Dench, Quantitative electron spectroscopy of surfaces: a standard data base for electron inelastic mean free paths in solids, Surf. Interface Anal. 1 (1979) 2–11. [25] D. Su, F. Wang, C. Ma, N. Jiang, Engineering nano-composite Li4Ti5O12 anodes via scanning electron-probe fabrication, Nano Energy 2 (2013) 343–350. [26] O. Wells, T. Everhart, R. Matta, IEEE Trans. Electron Devices ED12 (1965) 556–563. [27] B. Wu, A.R. Neureuther, Energy deposition and transfer in electron-beam lithography, J. Vac. Sci. Technol. B 19 (2001) 2508–2511.
Contents lists available at ScienceDirect
Microelectronic Engineering journal homepage: www.elsevier.com/locate/mee
Research paper
On the spatial resolution limit of direct-write electron beam lithography Nan Jiang Department of Physics, Arizona State University, Tempe, AZ 85287-1504, United States
a r t i c l e
i n f o
Article history: Received 14 July 2016 Received in revised form 11 October 2016 Accepted 18 October 2016 Available online 22 October 2016 Keywords: Direct-write electron beam lithography Scanning transmission electron microscopy Electric field Spatial resolution
a b s t r a c t The mechanism for direct-write electron-beam lithography in insulating resists is introduced in this letter, and it is based on damage by the induced electric field in transmission electron microscope. Under this mechanism, the direct-write EBL is electron dose-rate dependent, and there is a dose-rate threshold, below which the lithographic process does not operate, regardless of the total electron dose. The spatial resolution is determined by the strength of the induced electric field. In theory, the highest spatial resolution should be set by the dimension of the electron beam, and thus the EBL should be able to create nanostructures at the atomic scale. So far, the best resolution obtained was in the direct write of conductive nanochannels in Li4Ti5O12, in which 1.5 nm isolated features and a 1.0–1.5 nm half-pitch array of nanochannels were achieved. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Electron-beam lithography (EBL), a well-established high resolution patterning technique, has been widely used in nanotechnology and is the basis of much of the semiconductor device industry [1,3,9,22,26]. Understanding the limits of the spatial resolution in EBL is therefore very important in order to optimize the lithographic process. In brief, the resolution is determined by the following two processes: exposure (i.e. electron-resist interaction) and development in a developer [7, 18]. For direct-write (one-step) EBL using self-developing resist, which is the focus of the current study, the latter does not apply, so that the resolution is only determined by the interaction range of the beam electrons with the resist. So far, it has been reported in all experiments that the lateral sizes of the lithographic features are always larger than the probe size of the beam [5]. The broadening due to elastic scattering of the beam electrons has not been considered to play a limiting role, instead, the limit of spatial resolution of EBL is believed to be set by secondary electrons (SEs) [14,20,27]. This SE model is supported by Monte Carlo simulations of SE trajectories, which calculate range of SEs in the resist. It was found that the broadening of the point-spread function (PSF) matches the extension of the SEs [14,20, 27]. However, controversial results have also been reported. When Monte Carlo simulations track the energy deposited in the resist by SEs, instead of the range, the SEs have only slight, if any, effect on final resolution [4,5]. Besides SEs, delocalization of inelastic scattering of the beam electron has also been considered, and it has a similar interaction range as SEs [15]. Recently, attempts have been made to measure the EBL PSF directly using an aberration-corrected energyfiltered transmission electron microscopy (EFTEM) [17]. It was suggested that the volume plasmons should be more important than SEs in the limit of spatial resolution at the sub-10 nm scale. Even though
http://dx.doi.org/10.1016/j.mee.2016.10.016 0167-9317/© 2016 Elsevier B.V. All rights reserved.
the origins of these interactions are different, the delocalization effect is common in all the models. It seems that this delocalization effect provides a fundamental limit on efforts to achieve atomic resolution in EBL, although the finest electron beam can be focused within less than one tenth of a nanometer in diameter in the state-of-the-art electro-optical system [21]. Beside delocalization, all these existing models consider that EBL is an electron-dose dependent process, and thus different resists have different dose thresholds. Above the threshold (enough exposure), there are sufficient bond scission events to be developed by the developer [20] or atomic displacements to form a nanostructure in the directwrite EBL [17]. However, these models ignore important experimental evidence associated with EBL. In studies of hole-drilling in inorganic materials, it was discovered that the drilling process depends on the electron dose rate but not on total electron dose; prolonged exposure below the dose-rate threshold did not result in drilling [23]. In studies of nanofabrication using electron beams, it was found that the sizes of nanocylinders and nanowalls created by the electron beam is independent of specimen thickness [12,13]. Apparently, these observations violate the dose-dependent principle, and cannot be explained by these existing models. Recently, these phenomena have been interpreted by a revised mechanism of damage by the induced electric field (DIEF) [10,11]. In this study, we extend this mechanism to the EBL process, and especially discuss its impact to the limit of spatial resolution of direct-write EBL. Our results are based on experimental and theoretical analysis of thin, self-supporting films studied in scanning transmission electron microscope (STEM), free of backscattering. Although EBL has been studied for decades, the current study presents a very different view on the resolution limit from conventional beliefs. If this new model can be extended to more general situations, the atomic-level resolution could be achieved in EBL industry.
42
N. Jiang / Microelectronic Engineering 168 (2017) 41–44
2. Experimental For EBL in TEM or STEM, the specimen must be thin enough to allow incident electrons to pass through. Here there are two types of specimen, as illustrated in Fig. 1. One is equivalent to the self-supporting resist thin film (on the center in Fig. 1) and the other is equivalent to the resist thin film on a substrate (on the side). The specimen used for demonstration was 10Na2O-20B2O3-70SiO2 (in mol%) glass, and was obtained by the conventional melt-and-quench method. TEM specimen was prepared by grinding the glass into powder in acetone, and picking them up using a Cu grid covered with a lacy carbon thin film. The EBL was carried out using the Cornell VG HB501 100 kV STEM, equipped with electron energy-loss spectroscopy (EELS). The probe size was about 0.25 nm in diameter, at which the probe current was about 0.4 nA. 3. Results and discussion If the resist is insulating to electrons, the holes left by emissions of SEs and Auger electrons cannot be neutralized rapidly, resulting in accumulation of positive charges [2,8,10,11]. In the DIEF mechanism, the electric field is produced by these positive charges [10,11]. In the transmission geometry, for a thin self-supporting film, all the beam electrons traverse a thin slab of resist without depositing electrons inside it. In this case, the distribution of the induced electric field inside the resist is relatively simple. In most EBL systems, electron beams are highly focused, and their lateral dimensions are usually b0.5–1.0 nm, which is much smaller than the effective mean-free-path (MFP) of SEs and Auger electrons (e.g. N1.0 nm [24]). As illustrated in Fig. 2, most emitted electrons travel approximately perpendicular to the beam direction and scatter in a larger region around the beam column. This is equivalent to that incident electrons ionize the specimen into a positive inner core (nano-column) surrounded by a thick negative shell, and their volume ratio is r20/r2 (Fig. 2). Considering that r0 b 0.5 nm and r = 1–100 nm [24], the volume of positively charged inner core is much smaller than the negatively charged shell, and thus the charge density of the positively charged electron-probed region is much higher than the negatively charged surrounding. Therefore, the exposed region can be considered as a positively charged nano-column, with the diameter of the electron probe and a length given by the resist's thickness for the case of a selfsupporting thin film. Assuming that it is charged uniformly, the magnitude of the induced electric field for a given induced charge density ρ (Coulomb per length) can be simplified as [10] jEj ¼
ρ 2πε0 εr R
ð1Þ
in which R is the shortest distance to the electron beam. Its direction points outward perpendicular to the beam. Thus the induced electric field has an approximately cylindrical symmetry around the beam [10]. This theory is supported by experimental observations of nanocylinders in silicate glasses [6,12,13] and nanochannels in Li4Ti5O12 crystal [25] formed by a STEM probe. It should be noticed that for the sake of simplicity, we ignored the negative surrounding in deriving Eq. (1). This simplification does not affect the conclusion obtained, since including
Fig. 1. Cartoon drawing showing the definition of self-supporting thin film.
Fig. 2. Inner cylinder has net positive charges and larger outer one has net negative charges. r0 is the radius of the electron probe, and r represents the range of emitted electrons.
these emitted electrons may further enhance the strength of the induced electric field, and thus lower the threshold beam current density. The range of r may not affect the resolution. This is because in this model the displacements of atoms are driven by the electric field, not by the ionization of secondary or plasmon electrons. Interestingly, according to Eq. (1), the strength of the induced electric field is independent of the specimen thickness [10]. This is a unique characteristic of the DIEF mechanism in STEM, which distinguishes it from other dose-dependent mechanisms, such as knock-on and radiolytic processes. This thickness-independent characteristic has also been observed in previous direct-write EBL [6,12,13]. In resists, ionic bonds between anions and cations are polarized. Under a strong electric field, polar bonds can be ruptured, resulting in cation and/or anion displacements. To displace a bonded ion in a solid, the work done by the electric field on this ion as it moves from one site to the nearest available site must be equal to or larger than the activation energy Ua for ion migration, i.e. site2 Z
qEðrÞ dr ≥U a
W¼
ð2Þ
site1
in which q is the electric charge of the ion. The distance d between the two nearest minimum energy sites for the ion should be in order of the nearest atomic distance, which is several angstroms. Assuming that | E(r)| does not vary significantly over such a small distance, the minimum work required for an atomic displacement can be simplified as Wmin ¼ qETh ind d ¼ U a
ð3Þ
Therefore, the threshold strength | ETh ind | = Ua/qd, below which the lithographic process will not happen. Fig. 3 shows some nanocylinders created by STEM probe in a Na borosilicate glass. The formation of the nanocylinder is due to the accumulation of mobile cations driven by the induced electric field [10–13]. Therefore, it is reasonable to consider that the strength of the electric field at the boundaries should be approximately equal to | ETh ind |. Na migration in silicate glasses has been extensively studied; in a glass containing 10 mol% Na, Ea ≈ 0.9 eV [19]. The simplest approximation for the charge q of Na ion is to use its formal valence charge, i.e. q = + 1(e), where e = 1.602 × 10−19C (see S.I.). Here we set d = 0.3 nm, which is about the Na–Na distance in silicates. Inserting all these values in Eq. (3), we can estimate that | ETh ind | = 3.0 V/nm. This is the minimum electric field required in order to displace a Na ion in the [SiO4]
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Fig. 3. Left panel: Annular dark-field (ADF) image of nanocylinders created by STEM probe in the Na borosilicate glass. Right panel: The diameters of nanocylinders and the corresponding maximum electric field for different exposure time. The dotted line represents the modeling of the induced electric field versus irradiation time. It consists of two parts: initially increases rapidly and then keeps a constant.
tetrahedral network. As shown in Fig. 3, the diameter of the nanocylinder increases with exposure time. Using Eq. (1), the maximum electric field strengths at the edge of the electron probe for various exposure times can be estimated and the result are also plotted in Fig. 3. It shows that the induced electric field initially increases with exposure time, but not indefinitely. In this case, it reaches a maximum after about 10 s of exposure, thereafter keeps a constant. The EBL process driven by the DIEF mechanism is schematically illustrated in Fig. 4. In the DIEF model, the charge accumulation does not reach a maximum immediately after the exposure, instead, it increases rapidly with exposure time before it reaches the maximum at time t0, and so does the electric field [10,11]. For a current density J with Emax(J) = |ETh ind |, this is the threshold current density JTh (or threshold dose rate), below which the lithographic process cannot operate, regardless of the total electron dose [23]. As illustrated in Fig. 4, even though J N JTh, the lithographic process does not occur until the exposure time t ≥ tA, which is the time threshold for the DIEF mechanism [10,11], akin to charging a capacitor. Therefore, for any current density (J N JTh), the lateral size of the lithographic feature R should be between Rmin and Rmax, as illustrated in Fig. 4. Rmin is the smallest size that EBL can achieve in this resist, which is independent of beam current density but determined by the size of the beam. Rmax is the upper limit of lithographic feature size under this current density, and thus it is current density dependent. It should be pointed out that lithography is a dynamic process, i.e. it also changes the properties of the resist, and so changes the charge
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accumulation process as well. In other words, the actual Emax may be either higher or lower than that predicted in Fig. 4, depending on the change of resistivity in the probed resist [10,11]. If the lithographic process increases the resistivity, Rmax becomes larger, while if the process decreases the resistivity, Rmax becomes smaller. Therefore the difference between Rmax and Rmin becomes narrower in the latter case. The lithographic process in the former resists is divergent, while it is convergent in the latter. A direct deduction from this mechanism is that, for self-supporting thin-films, the theoretical spatial resolution of EBL should be Rmin. It should be pointed out that the value of Rmin is generally determined by the size of electron beam. However, one should consider broadening effects due to both elastic scattering and convergent angle. Nevertheless, EBL should be able to create atomic-scale nanostructure using the state-of-the-art aberration-corrected STEM in thin films. However, current results have not been even close to this goal. One of the reasons is that the previous knowledge of EBL mechanism does not consider the dose rate as a crucial parameter, nor the exposure time. In addition, the materials that have been used as EBL resists are extremely susceptible to electron beam damage (to increase the efficiency), and thus the threshold current densities can be very low. As a consequence, previous efforts have sought the lowest Rmax, rather than the Rmin. There is also a practical difficulty in seeking low Rmin in these resists: finding the proper tool to detect these tiny features. Imaging using either STEM or TEM, operating at normal conditions, may destroy the lithographic features or introduce new ones. Therefore, we suggest that the materials that are suitable for achieving atomic-resolution lithography should be “convergent” for beam damage, i.e. their resistivity should decrease due to the lithographic process. In these materials, Rmax can be close to Rmin. One example is the creation of conductive nano-channels in Li4Ti5O12 crystals [25]. As shown in that work, the nanochannels have a diameter of 1.5 nm, and the separation of two channels can be as small as 1 nm. In other words, using a STEM as the exposure tool 1.5 nm isolated features and a 1.0–1.5 nm half-pitch array of nanochannels can be fabricated in Li4Ti5O12 [25]. These values are better than the previously reported highest resolution patterns of EBL in thin films [16]. It should be pointed out that these values are definitely not the limit of the resolution that we can achieve in the EBL. As mentioned above, Rmax is also dependent on the resistivity of resist. Generally, the lower the resistivity, the weaker the induced electric field, and thus the smaller the Rmax. In theory, if Rmax b Rmin, in which the latter is independent of the resistivity, the lithographic process cannot be initiated by the DIEF mechanism alone. This suggests that the DIEF mechanism may not play a dominant role in the lithography of semiconductors and conductors, unless the current density of the electron beam is much higher than that currently used in the conventional TEM. However, the induced electric field may lower the activation energies for certain species in these types of resists, and thus it may not be appropriate to ignore the effect of the induced electric field. Therefore, there are two crucial parameters in this EBL model. One is the resistance to electrons, which determines Rmax, and the other is the conductivity of ions (i.e. activation energy of ion migration), which determines Rmin. It should be pointed out that the electron-beam transparency is not a necessary condition to apply the DIEF mechanism. The condition is only for the convenience of discussion and straightforward experimental observations. However, in bulk samples, either very thick resists or thinfilm resists on very thick substrates, the induced electric field can be much more complicated than that in the beam-transparent thin films due to the contributions from both deposit and backscattering of the beam electrons. The details of this more general situation should be discussed thoroughly when experimental data are available. 4. Conclusion
Fig. 4. Schematic drawing showing the DIEF mechanism for the EBL. Left vertical axis (E) is the strength of electric field and the right one (R) is the diameter of the lithographic feature. Rmin represents the smallest diameter and Rmax is largest for a current density J.
In conclusion, the mechanism based on DIEF has been introduced to describe direct-write EBL in self-supporting thin films of insulating
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resists. Under this mechanism, the direct-write EBL is electron dose-rate dependent and there is a dose-rate threshold. The spatial resolution is determined by the strength of the induced electric field. In theory, the highest resolution should be only limited by the dimension of the electron beam, and thus it should be possible to achieve the atomic-scale resolution EBL in thin films in the near future. Acknowledgement Discussions with Prof. J. C. H. Spence of Arizona State University and Dr. D. Su of Brookhaven National Laboratory are very helpful. Appendix A. Supplementary data Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.mee.2016.10.016. References [1] A. Broers, M. Molzen, J. Cuomo, N. Wittels, Appl. Phys. Lett. 29 (1976) 596–598. [2] J. Cazaux, Correlations between ionization radiation damage and charging effects in transmission electron microscopy, Ultramicroscopy 60 (1995) 411–425. [3] Y. Chen, Nanofabrication by electron beam lithography and its applications: a review, Microelectron. Eng. 135 (2015) 57–72. [4] B.M. Cord, J. Yang, H. Duan, D.C. Joy, J. Klingfus, K.K. Berggren, Limiting factors in sub10 nm scanning-electron-beam lithography, J. Vac. Sci. Technol. B 27 (2009) 2616–2621. [5] H. Duan, V.R. Manfrinato, J.K.W. Yang, D. Winston, B.M. Cord, K.K. Berggren, Metrology for electron-beam lithography and resist contrast at the sub-10 nm scale, J. Vac. Sci. Technol. B 28 (2010), C6H13. [6] L. Gontard, J.R. Jinschek, H. Ou, J. Verbeeck, R.E. Dunin-Borkowski, Three-dimensional fabrication and characterisation of core-shell nano-columns using electron beam patterning of Ge-doped SiO2, Appl. Phys. Lett. 100 (2012) 263113. [7] R. Howard, H. Craighead, L. Jackel, P. Mankiewich, M. Feldman, J. Vac. Sci. Technol., B 1 (1983) 1101–1104. [8] C.J. Humphreys, T.J. Bullough, R.W. Devenish, D.W. Maher, P.S. Turner, Electron beam nano-etching in oxides, fluorides, metals and semiconductors, Scan. Electron Microsc. Supplement 4 (1990) 185–192.
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