Surface Structure Dependence of Mechanochemical Etching

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Surface Structure Dependence of Mechanochemical Etching: Scanning Probe-based Nanolithography Study on Si(100), Si(110), and Si(111) Chen Xiao, Xiaojun Xin, Xin He, Hongbo Wang, Lei Chen, Seong Han Kim, and Linmao Qian ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b00133 • Publication Date (Web): 22 Apr 2019 Downloaded from http://pubs.acs.org on April 22, 2019

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ACS Applied Materials & Interfaces

Surface Structure Dependence of Mechanochemical Etching: Scanning Probe-based Nanolithography Study on Si(100), Si(110), and Si(111) Chen Xiao†,‡, Xiaojun Xin§, Xin He‡, Hongbo Wang†, Lei Chen†, Seong H. Kim*,†,‡ and Linmao Qian*,† † Tribology Research Institute, State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China ‡ Department of Chemical Engineering and Materials Research Institute, Pennsylvania State University, University Park, Pennsylvania 16802, United States § Key laboratory of Magnetic levitation Technologies and Maglev Trains (Ministry of Education), Superconductivity and New Energy R&D Center, Mail stop 165#, Southwest Jiaotong University, Chengdu 610031, China

ABSTRACT: We employed a scanning probe-based lithography process on single-crystalline Si(100), Si(110), and Si(111) surfaces and studied effects of crystallographic surface structures on mechanochemical etching of silicon in liquid water. The facet angle and etching rate of

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the mechanochemical process were different from those of the purely chemical etching process. In liquid water, the shape of the mechanochemically-etched nanochannel appeared to be governed by thermodynamics of the etched surface, rather than stress distribution. Analyzing the etch rate with the mechanically-assisted Arrhenius-type kinetics model showed that the shear-induced hydrolysis activity varies drastically with the crystallographic structure of silicon surface.

KEYWORDS: Silicon, scanning probe-based lithography, mechanochemical etching, crystallographic anisotropy, surface energy


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Lithographic fabrication of nanoscale structural units on semiconductor materials is of great importance for the manufacture of various electronic, optical and mechanical nanodevices.1-5 Recently, a scanning probe-based lithography (SPL) method was demonstrated for maskless and chemical-free etching of surface patterns on a silicon (100) wafer surface.6 This new method relies on mechanochemical reactions occurring at the sliding interface of a silicon oxide scanning probe tip surface and the silicon surface in humid air.6, 7 The water molecules adsorbed from humid air facilitate hydrolysis reactions of silicon surfaces only in the region sheared by the silicon oxide tip (Scheme 1).6-10 Because the mechanochemical reactions occur only at the topmost surface, it is possible to control the etch depth to a single atomic layer without causing any subsurface structural damage.6-9 If such precision nanofabrication method is applied to various materials with a capability of simultaneous processing of multiple patterns, it could open a new nanomanufacturing paradigm.

Scheme 1. (a) Schematic representation of the mechanochemical etching test on single crystal silicon surface against silica tip in DI water using an AFM with external liquid cell. (b) Illustration showing the mechanochemical etching process adapted from Ref. 6. The


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process can be conceived as three stages: (i) generation of surface hydroxyl groups by reaction of silicon atoms with water molecules, (ii) formation of interfacial bridge bonds (SiO-Si) via dehydration reaction between two surface hydroxyl groups across the interface, and (iii) dissociation of the substrate bonds under the mechanical shear action, leading to the removal of silicon atom from the substrate.6 In this paper, we report the dependence of mechanochemical etching in SPL on the crystallographic structure of a single crystalline silicon surface in liquid water. The arrangement of atoms exposed at the surface varies with the crystallographic orientation. Thus, the mechanochemical reactions leading the removal of atoms from the topmost surface may vary depending on the crystallographic structure of the surface. This study focuses on Si(100), Si(110), and Si(111) surfaces. The crystallographic structure dependence of the mechanochemically-etched nanopattern is found to be different in liquid water and humid air conditions. The etch pattern shape and rate are tentatively explained with the surface energy and mechanically-assisted Arrhenius-type kinetics arguments. Mechanochemical etching of three crystallographic silicon surfaces was conducted with a silica sphere with a radius of 1 µm attached to an atomic force microscopy (AFM) cantilever in DI water. Details of AFM experiments are provided in the Supporting Information. After sliding the silica sphere in a line scan mode for 100 reciprocating cycles at an applied load of 3 μN in liquid water, the line-scanned regions were imaged with a sharp silicon nitride tip with a nominal curvature of 15 nm at a low applied load (0.9 nN) in dry air. Figure 1 displays the mechanochemically-etched lines (topographic trenches) produced on the Si(100), Si(110) and Si(111) surfaces after 100 cycles of shearing with the silica sphere at various line scan


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directions with respect to the crystallographic axes. The cross-section profiles across the trenches show that the etch depth and shape are fairly insensitive to the scan direction on one surface, but they vary significantly among three surfaces. The trenches produced on Si(111) are narrow and deep, while those on Si(110) are wide and those on Si(100) are shallow. The depth and width of the mechanochemically-etched channels are 3.4  0.4 nm and 241  21 nm on Si(100), 7.3  0.8 nm and 578  34 nm on Si(110), 8.1  0.5 nm and 183  31 nm on Si(111), respectively.

Figure 1. AFM images (5 µm × 5 µm) (I) and cross-sectional profiles (II) of nanochannels produced by sliding a SiO2 microsphere (radius = 1 μm) along various directions (III) in pure water. The applied normal load was 3 μN, the sliding length was about 5 m, and the number of reciprocating cycles was 100. The reciprocating cycle dependence of the width and depth of the mechanochemicallyetched channels reveals the differences in the material removal pattern on three surfaces (Figure S1a in the Supporting Information). As the number of shear cycles increases, the nanochannels on the Si(111) surface becomes deeper at a rate higher than those of the


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Si(100) and Si(110) surfaces (Figure S1b). In contrast, the nanochannels on the Si(110) surface become wider laterally at a rate faster than those on the Si(100) and (111) surfaces (Figure S1c). The volumetric removal rate of the mechanochemical etch process appears to be fairly constant over a wide range of number of cycles at a given surface (Figure S1d). The rate is slightly faster (7500220 nm3/cycle for a silica sphere with a 1 m radium sliding over a 2 m long track at a 3 N applied load) for Si(110), intermediate (5700440 nm3/cycle) for Si(111), and slowest (3400270 nm3/cycle) for Si(100). This trend is quite different from the chemical etching rates in strong base solutions. In KOH or tetramethyl ammonium hydroxide (TMAH) solutions, the etch rate is about one order of magnitude lower for Si(111) than Si(100) and Si(110) and the rates of Si(100) and Si(110) are relatively comparable to each other.11-14 These differences in the anisotropic etch rate imply that the mechanochemical etching process is different from the chemical etching process. In addition to the etch rate, the etch pattern is also different from chemical etching. For example, the side wall of the etch pit produced on Si(100) in base solutions is the (111) facet which is exactly at 54.7o with respect to the (100) surface.14-16 On the Si(111) surface, the chemical etching proceeds faster in the lateral direction than the depth direction.17, 18 The cross-sectional topography profiles of the mechanochemically-produced nanochannels are shown in Figure 1. The side wall angle of the nanochannel with respect to the top surface is measured to be 2.70.4o on Si(100), 3.60.5o on Si(110), and 9.20.7o on Si(111), regardless


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the scan direction. Obviously, these angles are quite different from the values observed for the same surfaces etched in the KOH or TMAH solution.14, 15 The mechanochemical reaction is limited at the topmost surface only and do not cause any subsurface damage under mild load conditions.6-9 Thus, based on these measured angles, one can estimate the atomic structure of the nanochannel side wall produced in Si(100), Si(110) and Si(111). Figure 2 illustrates the crystallographic termination of the nanochannel wall created by cutting the crystal structure at the measured wall angle. The crystallographic structure of the sidewall of the nanochannel produced by mechanochemical etching would be close to the (22, 1, 0) facet on Si(100) when the sliding direction is along the direction. On the Si(110) surface, it would be close to the (10, 9, 0) facet at the same sliding direction. On the Si(111) surface, the facet would be close to the (7, 7, 10) structure if the sliding direction is along the direction.


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Figure 2. Atomic structures of the nanochannel side wall produced on Si(100), Si(110) and Si(111) surfaces through mechanochemical reactions at the sliding interface with silica in liquid water. The cross-sectional contour of the nanochannel mechanochemically produced in liquid water does not tightly correlate with the curvature of the silica counter-surface. Figures 3a – 3c show the AFM images of the silica sphere after scanned for 400 cycles against the silicon substrates in water. Figures 3d – 3f overlay the measured silica counter-surface profile on top of the cross-sectional profile of the nanochannels made with the same sphere. On the Si(100) and (111) surfaces, the mechanochemically-etched nanochannels are much narrower and deeper than the silica counter-surface curvature. In contrast, the nanochannel on Si(110) is wider than the silica counter-surface curvature. These observations are quite different from those observed for mechanochemical etching in humid air conditions (Figure S2).9 In humid air conditions, the mechanochemical reaction products (wear of the substrate materials) are adhered to the silica sphere surface, altering the counter-surface profile as the sliding cycle continues. The results shown in Figure 3 and Figure S2 suggest that the physical factor governing the shape of mechanochemically etched nanochannel varies depending on the process environment. In humid air (Figure S2), the close match between the etch pattern and the counter-surface contour implies that the stress distribution within the sliding contact region is an important factor determining the etch pattern. In liquid water (Figures 3), the mechanochemical reaction products may readily dissolve into the liquid phase (probably in a


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form of silicic acid, Si(OH)4), instead of adhering to the counter-surface.8 If diffusion or transport of such products is not fast enough, some of them may be redeposited onto the etched surface and alter the etch pattern. This backward reaction may assist the etch surface to reach a thermodynamically more stable structure.

Figure 3. (a, b, c) AFM images and (d, e, f) cross-sectional profiles (red lines) of the silica sphere after sliding 400 reciprocating cycles in water overlaid with the cross-section profiles (black lines) of the corresponding nanochannels produced on Si(100), Si(110) and Si(111). The applied normal load was 3 μN and the sliding amplitude was 2 μm. Hypothesizing that surface energy may be a key factor determining the final shape of the nanochannel produced in the liquid water process, density functional theory (DFT) calculations were carried out to estimate the surface energy of the nanochannel facets as well as the initial surfaces. DFT calculations were performed using the Vienna ab initio simulation


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package (VASP)19 with the projector augmented wave (PAW) potentials for core electrons and the Perdew-Burke-Ernzerhof (PBE)20 form of the generalized gradient approximation (GGA) for exchange and correlation functionals. Details of DFT calculations are provided in the Supporting Information. Since the scan direction dependence is very weak (Figure 1), we just considered the simplest case that we can predict for each surface (Figure 2). The calculation results are summarized in Figure 4a. The trend in calculated surface energies of different crystal facets is qualitatively consistent with literature values.21, 22 Note that these values are calculated for the facets exposed to vacuum; in liquid water, they may get further stabilized by reactions with water molecules. The simulation considering both dynamics and energetics during and after mechanochemical reactions may require more complicated methods that are beyond our capability at this moment.


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Figure 4. (a) DFT calculation results for surface energies (eV/Å2) of pristine Si(100), Si(110), and Si(111) and nanochannel facets produced on those surfaces by mechanochemical etching. (b) Semi-log plot of the volumetric etch rate versus the applied contact pressure for mechanochemical etching of Si with SiO2 in liquid water. The applied normal load ranged from 0.5 to 3 μN and the number of sliding cycles was 100. (c) Schematic energy diagram along the hypothetical reaction coordinate leading to the mechanochemical removal on Si(100), Si(110) and Si(111) by SiO2 microsphere in liquid water. The DFT calculation result supports the hypothesis that thermodynamics may play important roles governing the shape of nanochannels produced by the mechanochemical etching. On the Si(110) surface, the (10,9,0) facet is more stable than the top terrace by 0.017 eV/Å2; thus, increasing the nanochannel width can lead to lowering of the system surface energy. In contrast, the (7,7,10) facet is less stable than the (111) terrace by +0.014 eV/Å2. Thus, spreading of the nanochannel width may increase the system surface energy. Instead, the nanochannel may get deeper to keep the stable (111) surface area as much as possible. In the case of the Si(100) surface, the newly produced (22,1,0) facet appears to have a surface energy similar to the terrace. Thus, the nanochannel width-to-depth ratio is intermediate compared to the Si(110) and Si(111) cases. The chemical etching of silicon surface in liquid water near pH 7 is negligible, which means the activation energy (Ea) for such reaction is significantly higher than the thermal energy (~RT where R is the gas constant, 8.314 J/K, and T is 300 K). The fact that simply rubbing the silica counter-surface against the silicon surface in the same chemical and thermal condition leads to effective material removal (etching) implies that Ea is significantly reduced by the mechanical shear action.6, 29 If the mechanical shear action is to lower Ea and


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its magnitude is expressed as Em, the effective activation energy could be expressed as following,23-25

Eeff = Ea – Em

(1)

This means that the mechanochemical etching reaction can be viewed as a mechanicallyassisted thermal reaction.24-26 Modifying the Arrhenius equation for the reaction with an activation energy, the mechanochemical etching rate constant (k) can be expressed as:23, 27-29 k  A  exp

( Ea  Em ) kbT

(2)

where A is the pre-exponential factor which will vary depending on the unit of the left-hand side of the equation, kb is the Boltzmann constant (1.38 × 10−23 J/K), and T is the average temperature of the sliding interface. By assuming that the mechanical assistance term (Em) is proportional to the contact pressure (P) and the proportionality constant is the friction coefficient (), one could obtain the following relationship (see the Supporting Information for derivation):24, 29, 30

ln(k ) 

V   P kbT

(3)

where V* is the critical activation volume involved in the mechanochemical reaction process, which is a measure of how readily the reaction would be facilitated by mechanical stress. The mechanochemical etch volume measured as a function of applied contact pressure (P) was normalized with the total sliding time (over 100 cycles) to obtain the etch rate constant


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(k). Figure 4b displays the plot of ln(k) versus P. By multiplying kbT/ to the slope of the linear regression, ΔV* is estimated to be 115±10 Å3 for Si(100), 72±2 Å3 for Si(110), and 87 ± 6 Å3 for Si(111). For the chemical etching in base solutions, Ea of Si(100) is about 10% larger than that of Si(110).13, 15 The larger Ea would give a lower intercept value in the ln(k) versus P plot, which is consistent with the trend seen in Figure 4b. The data in Figure 4b indicate that the mechanical assistance effect is the largest on the Si(100) surface, comapred to the Si(110) and Si(111) surfaces. But, it should be noted that the wear rate is still the smallest for the Si(100) surface, implying that the Eeff is still the largest in our experimental conditions. In summary, the crystallographic structure dependence of the mechanochemical etch of Si surfaces in liquid water is elucidated. Putting the data in Figures 4a and 4b together, the surface structure dependence of the mechanochemical etching process can be explained with the energy diagram schematically shown in Figure 4c. The shape or facet of the mechanochemically-etched trench appears to be governed by the surface energy change, i.e., thermodynamics. The material removal rate seems to be governed by the susceptibility to mechanical activation or assistance as well as the chemical activation energy. The mechanical assistance component can be determined from the load dependence of the mechanochemical etch rate; but, the exact value of activation energy of chemical reactions in this process could not be determined from this study.


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ASSOCIATED CONTENT Supporting Information. Summary of previous results on mechanochemical wear processes; details of material preparation and AFM experiments; computational details; more information about stress-assisted Arrhenius-type kinetics equation. Corresponding Author *Email: [email protected]; [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interest. ACKNOWLEDGMENT This work was supported by the Natural Science Foundation of China (Grant No. 51527901 and 51875486), Self-developed Project of State Key Laboratory of Traction Power (2017TPL_Z02) and the National Science Foundation of the USA (Grant No. CMMI1435766). C.X. is supported by China Scholarship Council and Doctoral Innovation Fund Program of Southwest Jiaotong University. REFERENCES


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Surface Structure Dependence of Mechanochemical Etching

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