A New Method of AFM‐Based Nanolithography Using Frequency Enhanced Electrochemical Pressure Solution Etching

A new method of direct‐write nanolithography that is able to rapidly etch silica surfaces under a scanning atomic force microscopy (AFM) probe in tapping mode (TM) is reported. In this lithography technique, silica surfaces are etched using a recently described electro‐chemo‐mechanical phenomenon of frequency enhanced electrochemical pressure solution (FEEPS). In FEEPS, the tapping of the AFM tip generates oscillations of the Stern potential at the silica‐water interface that can accelerate the silica dissolution kinetics by more than 5–6 orders of magnitude when surface resonance states are achieved; i.e., when the oscillation frequency is in phase with the dynamics of interfacial chemical reaction steps. By scanning silica surfaces in TM, silica is selectively dissolved below the tapping tip as it is scanned. The FEEPS accelerated silica dissolution rates can generate etched features with depths of more than 60 nm in a single AFM tip pass. The rate of etching can be controlled easily by varying the scanning rate or by modulating the tapping frequency. This fine control over the silica etching process and because material is removed (dissolved) rather than displaced as with nanoscratching, the FEEPS process lends itself to gray‐scale nanolithography which is demonstrated.

Nanoscratching is the process by which a material is plastically deformed, and features designed by the application of high levels of load and shearing forces. This typically uses a diamond AFM probe enabling pressures in the range of several tens of GPa to be applied. Nanoscratching has been performed on various materials including polymers, semiconductors, and metals. [10][11][12] However, nanoscratching possesses several critical limitations that have prevented it from becoming a widely used nanolithography technique beyond a few niche applications. First, the shear forces applied always result in tip damage [13] thus leading to a gradual decrease of pressure for the same force applied and result in inhomogeneous features designed. Second, when performing nanolithography on crystalline materials, depending on the geometry of the tip, fractures can occur resulting in the formation of irregular cracks on the edges of the features. [14][15] These defects even if they are subsurface, can have important undesired effects in the resulting lithograph. It has been demonstrated that subsurface defects could alter the performances of GaAs-based devices. [16] Additionally, because nanoscratching results in material displacement rather than material removal, it gives rise to hillock formations surrounding the features as well as debris within features. [14,17] The consequence is a much-increased surface roughness and a lack of control over the shape and edge-sharpness of the desired features.
Interestingly it has been observed that nanoscratching could be carried out at lower pressures with the only requirement that it then has to be done in aqueous (or highly humid) environments. [18] In fact, the scratch volume was found to increase with increasing relative humidity (RH). [19][20] Reduction in size or outright disappearance of debris pileup has been observed when nanolithography is performed in water or humid environments. [18,[21][22] The underlying mechanism to account for these curious features has remained elusive as of now but still, it means that the scratching mechanism can no longer be 100% mechanical in origin and tribochemistry effects have to be taken into account. [23] The current and widely adopted explanation of the underlying tribochemical mechanism involves 3 stages: 1) creation of surface hydroxyl species via reactions with surrounding water molecules 2) generation of SiOSi bridges between the two surfaces by dehydration reactions; and 3) Si removal from the substrate via the action of shear forces. [24] A major implication that arises from such a mechanism is that, if valid, the process should be limited to metal-metal oxide tribopairs that is, systems in which both the substrate and the sliding surface display a similar chemistry (at least silicon based). However, it has been demonstrated that tribochemical lithography could be achieved on GaAs surfaces using silicon AFM tips. In the latter study, the contact pressure was kept below the yield stress of GaAs and it was found that an increased RH gave rise to higher wear rates. [25][26] It has also been observed that tribochemical wear of diamond-like carbon (DLC) films could be achieved when sliding the substrate against Si 3 N 4 balls. [27] Due to the very dissimilar chemical nature of the probe and the substrate, these last two results are inconsistent with the above mentioned bridging bond chemical mechanism.
It should be noted that the conditions necessary for tribochemistry and FEEPS are essentially the same; namely, two (usually dissimilar) surfaces pressed together in the presence of water. In addition, shear forces required for tribochemical wear likely create the right set of conditions for surface resonance processes to take place. [9] This surface "wear" or etching usually attributed to tribochemistry may instead be due to FEEPS. It is therefore proposed that poorly described features of tribochemical wear will find a complementary explanation by acknowledging that electrochemical pressure solution is taking place congruently (or in lieu of) the SiOSi bond bridging mechanism. Consideration of such a dual mechanism will also shine a new light onto the enhanced calcite dissolution in aqueous environments observed at the contact interface with a static silicon-based AFM tip. [28] In this work, we demonstrate the ability of FEEPS to rapidly and locally remove silica materials under a scanning AFM tip making intermittent contact with the silica surface at frequencies that greatly enhance its rate of dissolution, leading to etching depths of more than 60 nm in a single tip pass. The use of the AFM in tapping mode (TM) greatly increases the tip longevity as low to no tip wear is recorded. Further, the use of intermittent contact mode in etching experiments where little to no shear is present [29] enables us to rule out any traditional tribochemical wear, bond bridging like mechanism and confirm the presence of a FEEPS like etching behavior in our system. Additionally, gray-scale lithography becomes feasible by controlling the time allocated to the tip to dissolve the substrate, simply by varying its velocity across the surface. The mechanism of action shares many common characteristics with another powerful AFM-based lithography technique called thermal scanning probe lithography (t-SPL) with the main difference being the mechanisms of material removal (i.e., thermal degradation vs dissolution) and the fact the t-SPL can only pattern polymers when FEEPS can pattern directly into inorganic substrates. In this regard, FEEPS etching provides an easy way of achieving truly maskless direct write lithography on inorganic substrates.
Finally, a side-by-side comparisons of FEEPS with nanoscratching in humid air as well as contact mechanics considerations enable us to present evidences of the presence of a FEEPS mechanism in processes traditionally understood as tribochemical phenomena.

Chemicals and Materials
High purity deionized water (> 18 MΩ cm) was used for surface cleaning procedures as well as for the pressure solution/lithography study.
The fused silica surfaces were custom designed and fabricated by the South Australia node of the Australian National Fabrication Facility (ANFF). They consisted of a fused silica wafer etched with a grid of 200 × 200 µm 2 squares. Each grid has a registration number to facilitate finding the etched features in cases where tips had to be changed between experiments.

Atomic Force Microscopy
All AFM experiments were conducted using a JPK Nanowizard Sense. The pressure solution/lithography experiments were carried out using a Bruker model AD-40-AS AFM tip with nominal tip radius of 10 nm, nominal spring constant of 40 N m −1 and a nominal resonant frequency of 180 kHz. In practice, the tips used in this report show a much broader measured radius, because they were previously extensively used for other indentation and scratching works resulting in tip wear. Also, the AD-40-AS model of AFM tip possesses a boron doped conductive diamond coating.
Imaging was carried out in ambient air and in tapping mode using the same AFM tip used for the lithography experiments. In order to try to reduce the tip wear inherent to the method, all FEEPS and imaging were carried out at a relative setpoint (Rs, defined as the ratio between the cantilever tapping oscillation amplitude and the free oscillation amplitude) close to 0.75. This setpoint was chosen as it is close to the empirically determined value shown by Su et al. [30] to produce relatively low tapping mode tip wear (i.e., Rs = 0.8 that corresponds to the "light tapping" regime).
The AFM tip radius calculation was performed via imaging a calibration grating TGT1 [31] consisting of a 3D array of sharp tips of nominal height 300-500 nm and tip radius curvature < 10 nm, designed on a silicon wafer surface. For the radius calibration process, the TGT1 surface is imaged in contact mode and the upper region (apex) of each sharp tip captured on the image is fitted with a spherical/circular model. The radius of the AFM tip is thus obtained using the radius of the fitting sphere/circle minus the tip radius curvature (10 nm) [32] (see the Supporting Information S1 for the method. MATLAB analysis code will be made available upon reasonable request).

Surface Preparation
In order to remove the protective photoresist resin covering the fused silica grids, the surfaces were soaked in an acetone bath under stirring for 30 min. The silica grids were then rinsed with absolute ethanol (100%, Chem-supply) and dried with nitrogen gas. To ensure that the surfaces would not be displaced when subjected to strain by the AFM tip, they were glued to the bottom of a petri dish using a UV curable epoxy (Norland Optical Adhesive 81) exposed to UV light of wavelength 254 nm (-Pen-Ray standard Mercury UV lamp model 11SC-1). Finally, the fused silica surfaces were again rinsed with absolute ethanol (100%, Chem-supply) and cleaned in a UV-ozone cleaner (BioForce Nanoscience) for 15 min.

Method Used for FEEPS Experiments
In these experiments, performed in DI water (Milli-Q), the AFM was used in tapping mode (TM, unless explicitly mentioned), tuned to a frequency off the main resonance peak and the tips were pressed against fused silica surfaces at an average "tapping" force calculated using the method provided by Kowalewski et al. [33] who describe the average tip-sample force in TM AFM. The model assumes the AFM cantilever to be a damped driven harmonic oscillator. [33] When the separation distance between the tip and the surface is large enough, the only external force that has to be taken into account is the Van der Waals (VdW) interaction between a sphere and an infinite flat plane. However, as the piezoelectric material drives the probe down, the tip begins to interact with the surface and the tip-sample interaction is then described using the Derjaguin-Muller-Toporov (DMT) model. [34] DMT is an elastic model of contact that only differs from the Hertzian model [35] via the addition of attractive forces outside the contact area, [36] that is, the pressure distribution within the contact area is still Hertzian.
According to Kowalewski et al. [33] when tuning the cantilever off-resonance to dampen the amplitude of the cantilever oscillations, the average force exerted by the AFM probe on the sample can be approximated using Equation (1) where a 0 is the drive amplitude applied through the piezoelectric material, k is the cantilever spring constant, and A 0 is the free cantilever oscillation amplitude. Figure 1 is representative of the method used in this report to approximate the average force applied in tapping mode. Figure 1 shows a cantilever tuning in tapping mode and displays the values of a 0 and A 0 used in Equation (1). Prior to carrying out any AFM experiment, the AFM cantilever spring constant and sensitivity were calibrated using contact-based methods. The sensitivity is measured in air by performing a force-distance measurement against a hard surface (clean fused silica) and by fitting the linear region of the separation curve in order to obtain the slope (i.e., the sensitivity, in nm V −1 ). The AFM tip is then disengaged from the surface and lifted up in order to ensure a separation of a few micrometers. Then, the spring constant is determined using the thermal method [37][38] that is, the spring constant is obtained from the free fluctuations of the cantilever. If needed for the experiment, the AFM tip is then placed in deionized water and the sensitivity is again measured using the same method described previously in air.  Additionally, the contact pressure between the tip and the surface can be obtained as a first approximation from the force applied (calculated as described previously) using the Hertzian contact theory which indicates that the maximum contact pressure between a sphere of radius R and an infinite flat surface is given by Equation (2) [39] 3 2 a max 2 p F av π = (2) with a 3 4 1 1 where (νi,Ei) are the Poisson ratio and Young's modulus of the indenter and the substrate, R is the radius of the AFM tip, a is the contact radius and F av is the average force given by Equation (1).
For all the pressure calculations, the Poisson ratio and Young's modulus for diamond were taken equal to 0.2 and 1050 GPa respectively, [40] whereas the same constants for fused silica were taken equal to 0.17 and 72 GPa. [41]

AFM Images Analysis
All the AFM images were processed using JPK data processing software (version 6.0.26). In order to obtain the radius of the tip, the JPK images were turned into XYZ files using Gwyddion visualization and analysis software (version 2.50) [42] and processed in MATLAB R2017a (version 9.2.0.556344) (MATLAB analysis code will be made available upon reasonable request).

Localized Silica Etching Using Frequency Enhanced Electrochemical Pressure Solution
The FEEPS process has recently been studied in detail by the authors, however focusing on static AFM dissolution experiments carried out at a single location without dragging the AFM probe. [8] In this report, the AFM probe is dragged on the surface in order to design lithography. It is however used in intermittent contact mode (minimal to no shear) and the operating conditions are such that the contact pressures used (≈4.1 GPa) are well below a typical nanoscratching experiment (14.1-33.4 GPa) [43] implying that material is primarily being removed by dissolution rather than simply being displaced through shearing. We note that it is possible however that the way FEEPS is performed still involves superficial elements of nanoscratching and tribochemistry. As a FEEPS etching driven process, a relationship between the tip velocity and the etching depth is expected since slower velocities lead to longer dissolution times. Additionally, previous work on static AFM FEEPS etching have found that the etching depth was proportional to the contact time power a coefficient β measured to be 0.39 ± 0.03 indicating that the depth continues to increase so long as pressure is applied. [8] This is in sharp contrast with nanoscratching in which scratch depth has been reported independent of the AFM tip velocity. [44][45] Additionally, even though a precise relationship between the tribochemical wear of silica and the AFM tip velocity has yet to be established, Yan et al. [46] have shown that the tribochemical wear was nonexistent below 0.5 ± 0.3 µm s −1 and became visible from 0.8 to 4 µm s −1 .
To ascertain a relationship between the rate of silica etching and the scanning velocity of the AFM tip, a series of trenches were etched using the off-resonance TM method at a fixed frequency of 301 kHz at different tip velocities. Conductive diamond AFM tips were placed into intermittent contact against a fused silica surface in DI at an average "tapping" force of 7300 nN calculated as described previously (see Figure 2A for the tip and cantilever characteristics as well as the experimental parameters used). The intermittent pressure generated by the tapping AFM tip causes the rapid dissolution of silica beneath the tip, resulting in an etched "trench" as the tip is scanned. In fact, the tapping AFM cantilever establishes a resonating electric field at the substrate surface due to the dissimilarity of the tip to the substrate. These resonating fluctuations in the stern layer lead to an enhanced dissolution as the equilibrium rates of dissociation of the charged surface species is alternated. A more detailed explanation of the mechanism can be found in previous work by the authors. [8] An AFM image of the etched trenches obtained at different tip velocities is displayed in Figure 2B as well as the corresponding cross sections. What is immediately noticeable is the high inverse dependence of the etched trench depth with the AFM tip velocity; the depth decreases from 65 nm at a velocity of 0.2 µm s −1 down to 0.76 nm at 600 µm s −1 . It was found that the obtained data were well fitted (correlation coefficient of 0.97) using the power law, characteristic of FEEPS processes [8] (see Equation (3)) where h is the trench depth, v is the AFM tip velocity, and α,β are fitting parameters. This is equivalent to the FEEPS etching process kinetics law because in this experiment, the "residency time" of the tip over any particular region will be inversely proportional to the velocity. A more detailed analysis of the impact of the tip velocity upon the depth of the etched trenches is presented in Figure 2C, where the average depth of each trench is plotted as a function of the tip velocity used to design it. It is important to note that Equation (3) is functionally identical to the power law describing the static (no strain forces) kinetics of FEEPS etching and it turned out that the coefficient β was found equal to 0.41±0.03; the same as the value of 0.39±0.03 measured for FEEPS etching processes of silica surfaces. [8] We note, that the scan speed is equivalent to the etching time introduced for static experiments, [8] since it determines how much time the probe spends over a region of the surface during the etching process. Consequently, we demonstrate that the FEEPS equation still holds even under a scanning AFM tip. Previous experiments investigating the time and pressure dependence of silica dissolution under an oscillating conductive diamond AFM tip demonstrated that the rate of dissolution increases with the pressures, and that the dependence of the etching depth with time always followed the same power-law relationship. The presence of this power law relationship in our lithographic experiments indicates that the mechanism responsible for the trenches is FEEPS driven silica etching. We also note that the slow speeds produce more etching than the fast speeds despite the shear stress component of the force being higher. Indeed, given that a frequency of 301 kHz was used, also given the length of the trenches (1 µm) we can estimate the lateral distance travelled by the probe between each tap cycle using Equation (4) d where d is the distance between taps, v is the tip velocity, l is the trench length, and f is the tapping frequency. At the slowest speed (0.2 µm s −1 ) the lateral distance travelled per "tap" is estimated to be equal to just 0.7 pm, whereas at the highest speed (600 µm s −1 ) the sliding distance increases slightly 2 nm. We also note, that the AFM probe is in contact with the silica for a fraction of the tap cycle so the "shearing distance" is even less than the lateral distances calculated.
The wear mechanism studied herein is therefore of a different nature to traditional tribochemistry, shear induced processes as indeed 1) more shear leads less wear and 2) the power law observed is characteristic of FEEPS induced processes. [8] Further, the use of intermittent contact mode in etching experiments where little to no shear is present [29] enables us to rule out any traditional tribochemical wear, bond bridging like mechanism, and confirm the presence of a FEEPS like etching behaviour in our system.
In order to characterize how much faster FEEPS etching is happening compared to the normal dissolution rate of silica in water (reported to be 10 −11.5 mol m −2 s −1 at pH 5.7), [47] the FEEPS apparent etching rate was calculated to be ≈5 × 10 −6 mol m −2 s −1 . This is an estimate based on the etched volume, surface area and time required to design the trench obtained at 0.2 µm s −1 (see the Supporting Information S2 for the calculation), thus demonstrating a 5-6 orders of magnitude enhanced rate, comparable to what has been previously reported for FEEPS etching [8] thus again, indicating that the etching process is primarily driven by FEEPS.
In addition, it can be seen from Figure 2B that upon increasing the velocity, there comes a point where the depth of the etched trench loses its homogeneity, starting to display a wavy interference pattern, which may be a frequencydependent artefact (given the frequency at which the tip is tapping on the surface) stemming from the superposition of tapping frequency in both trace and retrace motions, giving rise to constructive interference-observed as higher depth profiles-in the patterned features, while out-of-phase trace and retrace motions would result in more homogeneous features. We note that the trenches designed at 1.   (1) and maximum contact pressure at the apex of the tip, given by the Hertz model. In tapping mode, the AFM tip makes intermittent contact depending on oscillatory frequency and tip velocity. B) AFM image obtained after a trench velocity variation experiment in DI and corresponding cross sections; the arrows indicate the order in which the trenches were designed. The above line (blue cross section) was designed first, then the below line (orange cross section). The frequency of the AFM tip was chosen to be equal to 301 kHz. The tip velocity was varied between each trench, from 0.2 to 5 µm s −1 . C) Depth of the trenches plotted as a function of the tip velocity and fit using the frequency enhanced electrochemical pressure solution power law. C') Identical set of data plotted on a Log-Log scale.
phase for the slower velocities (<1.4 µm s −1 ) but the interference pattern may be too small (as a result of a higher number of taps) to become apparent. This is further evidence that the observed features cannot be due to shear forces and have to be the product of dissolution underneath the oscillating tip. We note that while not currently possible given the standard control software of the JPK AFM, introducing a slight off-set in the trace and retrace velocities would probably avoid any constructive interference patterns from arising thus resulting in more homogeneous features.
Because the etching is achieved using tapping mode where the AFM tip makes intermittent contact with the surface rather than being dragged/sheared against it, the FEEPS lithography is expected to be gentler and less damaging to the AFM tip. In order to assess tip wear and/or damage incurred during the etching of the trenches in Figure 2B, the radius of the AFM tip was measured before and after the trench experiment and was found to be unchanged at 200 ± 20 nm indicating negligible tip wear (see the Supporting Information Figure S1 for the method, Table S1 for the tip radius values and Figure S2 (Supporting Information) for actual AFM scans on the TGT1 grating before and after the experiment).
Our results demonstrate a significant modulation of the trench depth as a function of the AFM tip velocity in contrast to the findings of Jiang et al. [44] who, in nanoscratching experiments performed on silicon substrates, found that the tip velocity did not have much impact upon the depth of the features designed, ranging from 3.09 nm at 10 µm s −1 down to 2.73 nm at 0.1 µm s −1 . The inverse relationship reported here between the feature depth and tip velocity remains in sharp contrast with observations made in nanoscratching processes. [44] The features observed in nanoscratching experiments are due only to material displacement (i.e., plastic deformation) of the substrate subjected to high forces. In this regard then, the depth is mainly controlled by the loading force and an independence of the depth versus AFM tip velocity is the expected result. In contrast to nanoscratching, as Figure 2B clearly shows, higher etching volumes and deeper features are obtained at the slower velocity. Such a relationship is consistent with a rate limited process rather than the energy input limitation found in most tribochemical wear processes [13,48] because the etching rate is more or less constant but the residency time of the tip on the silica surface (i.e., the total number of "taps") changes with the tip velocity. It is also in sharp contrast with the tribochemical removal kinetics of silica investigated by Yan et al. [46] showing that the etching depth is small at low velocities and becomes more pronounced at higher speeds. Therefore, the mechanism responsible for the material removal and hence, the trench formation is FEEPS and any plastic deformation or tribochemical wear by any other mechanism is either neglectable or not taking place.

Demonstration of FEEPS Lithography
Because the silica is dissolved rather than displaced under the tapping AFM tip, FEEPS has the potential to be able to etch features more uniformly and consistently compared with nanoscratching processes. In order to evaluate the capability of FEEPS etching to fabricate uniform and repeatable nanofeatures with little to no tip wear/damage, a series of 3 µm long, parallel nanochannels were etched onto silica. The AFM tip radius was measured before and after the lithography experiment and was found to remain unchanged at 200 ± 20 nm (see Figure S1 for the method, Table S1 for the tip radius values, and Figure S3 for actual AFM scans on the TGT1 grating before and after the experiment, Supporting Information). An AFM image of the resulting feature is displayed in Figure 3A as well as a cross section and a zoomed-in 3D plot. The AFM image consists in very well defined nanochannels of constant depth (4-5 nm) obtained in a single trace and retrace AFM pass. This depth value can be compared with the results obtained by Guo et al. [49] who obtained nanolithography features via chemomechanical etching, using a silica AFM tip against a silica surface, in an atmosphere containing a relative humidity of 50%. They obtained etching depths of 18 nm over 500 trace and retrace imaging scans, that is about 0.4 Å per scan using forces of 2 µN. The conclusion then being that our intermittent contact method for nanolithography allows the design of features 2 orders of magnitude deeper using similar physical parameters, in addition to minimal tip damage because of the absence of large shear forces. Previous work by the authors also suggest that the dissolution rate could even be increased further by selecting the right working frequency. [8] Because one of the two dissolution enhancing electro-chemo-mechanical mechanisms of FEEPS involves a surface resonance phenomenon, the observed rate was found highly dependent on the frequency applied, [8] indicating that the maximum material removal rate was obtained in the low kHz domain (<100 kHz).
This effect as well as the velocity dependence of material removal was utilized to design a more complex lithography feature composed of 2 layers: an image of the Australian flag. An AFM image of the flag is displayed in Figure 3B as well as its corresponding cross section. By making minor changes to the tip velocity and oscillation frequency, we are able to achieve a very high dynamic range of etching depths using a single pass to etch. The flag outline and stars (red fields) are etched at ≈1 nm, while the different parts of the cross (white fields) are etched at 20 and 35 nm, respectively, for the large and small crosses.

FEEPS as a Potential Gray-Scale Lithography Tool
The ability to control the depth of the features designed by changing the tip velocity can be used in order to create easy onestep gray-scale lithography directly onto fused silica surfaces. These are features that have always proved difficult to design using traditional photolithography methods. In fact using these methods, the polymer resist films have to be exposed to various intensities of light in order to create the gray levels and it is thus, difficult to control. [50] AFM-based gray-scale lithography has currently only been possible in polymer photoresist substrates using the recently developed NanoFrazor-thermal scanning probe lithography (t-SPL)-type techniques. [51] While the t-SPL technique is powerful and impressive in its capabilities, a significant limitation remains that many applications require that the patterned polymer substrates be transferred, using wet or dry etch techniques [52] onto silicon or other functional inorganic substrate. [53][54] However, we note some important similarities between our FEEPS method and the NanoFrazor system. First, both are AFM based and thus, can take advantage of the AFM's precise positioning system to etch features in a "direct write" fashion. Second, they are rapid enough for features to be designed within a few minutes [52] thus making them amenable to rapid prototyping.
In order to evaluate the potential of FEEPS to etch gradient depth features using only tip velocity control, FEEPS etching was performed using a tip velocity ramp (see Figure 4A,A′ for the velocity parameters used in this experiment). A conductive diamond AFM probe was tapped against a fused silica surface, in DI. The AFM was switched to TM imaging and a tip velocity ramp applied. A frequency of 250 kHz was chosen after a preliminary screening of frequencies to determine which produced the greatest etching rate, and the AFM was tuned off peak so that the tip/sample interaction model described at the beginning was applicable. The maximum pressure calculated using this model was found to equal just 4.8 GPa, 15% less than the silica yield stress. [55] The AFM tip radius was measured before and after the lithography experiment and was found to be unchanged, equal to 200±20 nm (see Figure S1 for the method, Table S1 for the tip radius values, and Figure S3 for actual AFM scans on the TGT1 grating before and after the experiment, Supporting Information).
An AFM image of the resulting lithography feature is displayed in Figure 4A″ as well as 5 corresponding cross sections taken from low to high tip velocity regions, showing depths constantly decreasing ranging from 65 to 40 nm. Also displayed is the good depth homogeneity recorded at low tip velocities. A 3D plot of the trench is also displayed detailing the level of grayscale depth control achieved. Again observed in the 2D-line traces in Figure 4A is the wavy/interference pattern that arises at velocities equal or higher than 3.8 µm s −1 . Engineering controls like off-setting the trace and retrace velocities (or tapping frequencies) could be used to remove this interference pattern and obtain more homogeneous features. This, however, is currently not possible with the standard JPK control software.
In order to test the consistency and reproducibility of our tip velocity variation method, we designed a more complex feature involving 2 velocity ramps of opposite direction. That is, the velocity is first increased, then decreased again (see Figure 4B,B′). An AFM image of the resulting feature is displayed in Figure 4B″ as well as its corresponding 3D plot. Note in Figure 4B″ that the profiles in the 2D and 3D-depth plots are not symmetric, and that is because the velocity variation ramp was not symmetric either as displayed in Figure 4B,B′. In fact, the velocity gradient controls the slope of the trench bottom. The tip velocity variation results in a curved bottom whose depth is in between 80 and 60 nm. Also note the 2 lines (blue and green color) symbolizing the area where the tip velocity  was equal to 2 µm s −1 . The corresponding cross sections are also displayed in Figure 4B″. The consistency of the depth (≈60 nm) then confirms the reproducibility of the method and that the final feature depth remains strongly correlated with the velocity. Note the overall higher depth obtained during this experiment compared to the single velocity ramp trench presented in Figure 4A″. This is explained by the higher pixel density used in this last experiment that is, a higher scanning line density and hence more time allowed for dissolution. Essentially, the method described herein only requires the use of an AFM in TM and in an aqueous environment and has proven to be capable of designing features several tens of nm deep directly onto a silica surface as well as the ability to carry out simple gray-scale lithography. Besides, deeper and more complex features can be easily fabricated by repeated scans over the same area. All in all, the etching process presented in this report, if combined with an appropriate control software (of the kind used by the NanoFrazor community), has the potential to turn any standard AFM, into a lithography instrument as powerful as a NanoFrazor but able to pattern inorganic substrates of different kind (silica demonstrated in this report. Although not studied in detail, preliminary etching results were obtained utilizing FEEPS onto GaN and Si substrates. [8] This material can be found in the Supporting Information). [8] Last, the machining dimensional accuracy of the method is closely related to the chord theorem, where the width of a feature on the surface is given by Equation (5), as a function of its depth (d) and the AFM tip radius R Given the radius of the AFM probe (200 nm) and the maximum depth obtained (80 nm), the chord theorem is used to predict the width of an 80 nm deep trench. It is found that such a feature would be 160 nm wide, which corresponds to the smallest trench that can be obtained using this method and this AFM probe.

Comparison of FEEPS with Traditional Nanoscratching Lithography Methods
In order to confirm that our etching process does not involve any significant nanoscratching element to it, an attempt was made to replicate the trenches experiments described in Figure  2B in ambient air which then replicates the conditions used in many nanoscratching-like experiments. [56][57] We show that there is no nanoscratching involved in the FEEPS etching process.
To this end, the AFM was used in contact mode that is, the AFM tip is dragged on the surface without any oscillations (i.e., not "tapped"), and in air (RH 50%). The radius of the AFM conductive diamond probe was measured at the beginning of the experiment and found equal to 100 ± 10 nm (see Figure S1 for the method, Table S1 for the tip radius values, and Figure S4A for actual AFM scans on the TGT1 grating before the experiment, Supporting Information). The contact pressure could then be calculated using Equation (2). First, to allow a comparison with the set of experiment presented in Figure 2, the maximum contact pressure was fixed to 4.1 GPa and it was found that sliding the diamond tip on the surface at various velocities (3; 1; 0.2 µm s −1 ) did not give rise to any visible material wear or any visible features, that is, under the same conditions of maximum contact pressures used in the tapping mode experiments, there is no plastic deformation (i.e., no scratching) of the surface. These experiments are not shown because no detectible features were obtained. The lack of features in these constant load experiments highlights the importance of the pressure oscillations in enhancing the silica etching process. However, wear became visible upon increasing the maximum contact pressure to 5.8 GPa. In this case, trenches were obtained at 3 different velocities (3; 1; 0.2 µm s −1 ) and an AFM image of the resulting features is presented in Figure 5A, as well as the corresponding cross-section. First of all, note that the measured depth is no more than 1 nm, in contrast to the experimental data presented in Figure 2 which shows depths ranging from 20 nm to more than 60 nm depending on the tip speed. Second, material pile-up is also observed in Figure 5A near the edge of the trenches. Also important to note is the quality of the image itself, which is comparatively worse than for the similar experiments run in water and in TM. Poor image quality can be explained as due to tip wear that was recorded in this set of experiments but also the "wavy" nature of the trenches presented in Figure 5A, arising from thermal and piezoelectric drifts which are worse in air than in a liquid environment.
Next, an experiment was designed to compare the uniformity and consistency of the etched/scratched features. Experimental conditions were similar to the nanoscratching-like experiment presented previously, that is, the experiment was performed in contact mode and in air (RH = 50%). Only the sliding speed was kept constant equal to 2.4 µm s −1 . An AFM image of the channels is displayed in Figure 5B as well as cross sectional data obtained on 2 different locations of the AFM image: in the middle and on the end of the channels. Similar to what was measured from Figure 5A, the maximum depth of the channels is in the range 1.5-2 nm. It can be noted on the AFM image presented in Figure 5B that the width of the channels slightly increases from left to right which corresponds with the order in which the channels were created. Zoom-ins of the cross-section data taken in the middle of the channels and labeled as Figure  5B',B″ confirm the width increase of the channels from left to right. Moreover, the latter zoom-ins cross-section data display a ploughed field on the left side in contrast with proper channels on the right side. This evolution in channel morphology and dimension is evidence of tip wear/damage which was confirmed by comparing tip radius measurements performed before and after the experiment in Figure 5B″ that found the radius to increase from 100 nm (±10 nm) to 170 nm (±17 nm) (see Figure  S1 for the method, Table S1 for the tip radius values, and Figure  S4 for actual AFM scans on the TGT1 grating before and after the experiment, Supporting Information). Thus, we arrive at the conclusion that our tapping mode FEEPS method for carrying out lithography work gives rise to incomparably deeper features than what could be obtained using nanoscratching-like methods as well as a better reproducibility due to a minimal tip wear and material removal instead of displacement.
As was observed in Figure 5A and common to all nanoscratching processes, material pile-up and debris are again present, both on the sides and at the end of the channels, as displayed on both cross-section data present in Figure 5B. Contact mechanics considerations can give an insight as to whether or not these material piles and debris are really due to plastic deformation. First, we consider that the maximum shear stress (τ max ) is given by Equation (6) where p 0 is the maximum Hertzian contact pressure, υ is the Poisson ratio for fused silica, a is the indentation contact radius, and z is the indentation depth.  Figure 5C, which shows that the maximum shear stress τ max is equal to 0.34p 0 and occurs at a depth z = 0.44a. From this, we use the Von Mises criterion for plastic deformation which states that for plastic deformation to occur, the maximum shear stress must be at least half the yield stress (τ max ≥ 0.5σ) [39] and we obtain that the critical pressure (P C ) for plastic deformation to occur is given by Equation (7) [22] 1.47 Given a yield stress of 5.5 GPa for fused silica, [55] we obtain a critical pressure of 8.1 GPa, 28% higher than the maximum Hertzian contact pressure used in this series of experiments. We therefore demonstrate that the material pile-up observed is unlikely to be the result of plastic deformation and in this regard, nanoscratching as traditionally understood only plays an insignificant role in the formation of the features obtained herein. In the absence of a plastic deformation mechanism, the origin of the material piles arises from a chemically driven mass transport process which, in this system consisting of a silica surface covered by a molecularly thin water film, is most likely a dissolution-reprecipitation process. Similar dissolutionreprecipitation has been reported in other tribochemical systems; [25] however, the condition used in these "nanoscratching" experiments, i.e., dissimilar surfaces bridged by an interfacial water film, high contact pressure, and mechanical vibrations (from friction), are also associated with enhanced surface etching via a FEEPS mechanism. This opens up the possibility that many reported "tribochemical" phenomena may also include an underlying or hidden FEEPS mechanism.

Potential Role of a FEEPS-Like Mechanism in Reported Tribochemical Phenomena
Considerations regarding the shear stresses used to generate the features presented in Figure 5 as well as the use of Von Mises criterion for plastic deformation to occur lead to a strong evidence that the material pile-up observed in Figure 5 could be due to dissolution/reprecipitation processes and not mechanical ploughing. However, the question we want to ask is whether this is tribochemically or FEEPS driven (or some combination of both). We note that if the material mounds are due (or influenced by) a FEEPS-like mechanism, then, oscillating the contact pressure will enhance the FEEPS etching rate and therefore produce higher rates of dissolution/reprecipitation (i.e., material deposits). Moreover, oscillating the contact pressure does not lead to higher shear forces so long as the maximum contact pressure between the oscillating and nonoscillating systems are the same. That is, since tribochemical models indicate that tribochemical wear rates are dependent  on the magnitude of shear stress alone, if the material mounds are the result of tribochemical wear, then oscillating the contact pressure should have no effect at all. In fact, since the pressure oscillation reduces the normal force from the maximum load, the average shear stress will actually be reduced and less tribochemical wear may actually be observed.
To this effect, the experiment presented in Figure 5A was repeated using the oscillating pressure condition. The AFM was used in force modulation Mode (FMM) that is, physical oscillations of small amplitude are applied to the AFM tip which never breaks contact with the surface (i.e., no tapping). The reason being that in FMM the force is never constant and in fact a constant average force (i.e., midpoint) F 0 is applied to the surface while a small sinusoidal force oscillation component (amplitude F 1 , F 1 <F 0 , frequency f) is added. This can be summarized by Equation (8) where F is the total force applied to the surface and t is the time. Consequently, the AFM tip never lifts off the surface, replicating the experimental conditions of experiments presented in Figure 5, while the pressure oscillation ensures the FEEPS process to take place at a much faster rate. The maximum Hertzian contact pressure for this experiment was chosen equal to 5.8 GPa (the frequency of the oscillating pressure was 20 kHz) that is, similar to the experiments presented in Figure 5A,B. The AFM tip radius was measured before and after the experiment and was found to be unchanged, equal to 150 ± 15 nm (see Figure S1 for the method, Table S1 for the tip radius values, and Figure S5 for actual AFM scans on the TGT1 grating before and after the experiment, Supporting Information). The AFM tip was dragged along the surface in regions scanned at 3 different tip velocities: 0.2; 1; and 3 µm s −1 , resulting in the features shown in Figure 6 which presents an AFM image as well as cross-section data and 3D plots of the features. First of all, visible on both the AFM image and the cross-section data, the regions scanned at 1 and 3 µm s −1 are actually 1-2 nm high mounds (confirmed by the 3D plot of the mound obtained at 3 µm s −1 ) and no trace of material removal is visible. From a mechanistic point of view, the formation of a mounds cannot be driven by material displacement so that it has to be of a chemical origin. This is only possible by an expansion of the SiO 2 volume in the scanned region which indicates the rapid breaking and reformation of SiO bonds within the region. Also, the trench designed at a smaller tip velocity (0.2 µm s −1 ) is actually a trench 5-6 nm deep and some material deposit is visible. This is the natural outcome of the SiO bonds breakingreformation only, the process continues for longer periods of time thus leading to material being removed. As a matter of fact, FEEPS etching is an accelerated dissolution phenomenon but which fundamental chemical mechanism is no different from traditional dissolution processes in which-for the case of silica-water hydrolyzes 4 SiO bonds in order to liberate a silicic acid Si(OH) 4 unit that is then carried away by diffusion. To understand how the changing AFM tip velocity leads from mounds to trenches, one must recognize that this is essentially what happens underneath the AFM tip, in the local and highly confined region, thus giving rise to material removal. However, it can also happen that the tip is going fast enough to not provide enough time for the hydrolyses reaction to occur fully. That is, instead of hydrolyzing 4 SiO bonds, only 1, 2, or 3 are being hydrolyzed thus creating free volume in the material (decreased density) and forming a mound. Concomitantly, within the molecularly thin water film it becomes easy for the silicic acid units that are being released from the surface to immediately exceed the solubility thus leading to reprecipitation underneath the tip. The combination of these 2 effects can  well account for the formation of mounts at high tip velocities and trenches at low tip velocities. Finally, comparisons can now be made between this oscillating pressure in humid air experiment and the constant pressure in humid air experiment presented in Figure 5A. The trench obtained at the smaller speed is much deeper in the case of oscillating pressure (5-6 nm) compared to its constant pressure experiment analogous (≈1 nm) presented in Figure 5A thus showing signs of material removal rates enhancement due to the application of an oscillatory pressure, consistent with a FEEPS-like mechanism.
Last, the SiOSi bond bridging tribochemical mechanism fails to provide a reasonable explanation to the features observed in the experiments presented in Figure 6, for at least 3 reasons: first, the substrate used is silica and the tip is diamond that is, the probe and the substrate display a very dissimilar chemical nature, while this does not support a tribochemical wear mechanism, the surface dissimilarity supports a FEEPS-like mechanism. [8] As discussed earlier, the chemistry of this covalent bond (bridge) formation is unclear and, in any case, limited to metal-metal oxide tribopairs which is clearly not part of the experimental conditions of the experiment presented in Figure  6. Second, in the bond bridging mechanism, material removal is obtained by the action of shear forces alone which provides the energy necessary to overcome the activation energy barrier and carries the SiOSi(OH) 3 unit away, thus similar levels of shear forces should result in similar tribochemical removal rate, which is not the case when comparing the results of Figures 5A and 6 which demonstrates behavior consistent with a higher rate of material dissolution/hydration via the application of an oscillatory force (the maximum pressure being kept constant, i.e., constant shear stress). Third, in our experiment, wear becomes more pronounced at low velocity (0.2 µm s −1 ) which is the exact opposite to what was found by Yan et al. [46] in experiments studying the tribochemical wear of silica. Last, we would like to point out that the SiOSi mechanism has been corroborated by simulations [58] but direct experimental evidence of materials transfer from substrate to the tip have remained elusive despite such evidence seeming rather easy to come by.
Interestingly, this exact same mound to trench evolution has been previously reported in experiments performed by He et al. [59] when performing nonoscillating pressure in humid air (RH = 40%) experiments investigating tribochemical phenomena in soda lime glass, using a diamond tip against a silica glass surface. The tip they used had a radius of 550 nm and they used forces of 5; 10; 20; and 30 µN (maximum Hertzian contact pressure from 2.5 to 4.5 GPa). They recorded the formation of a 1 nm high mound at the lowest pressure, gradually replaced by a trench at higher pressures. A major difference between the results obtained by He et al. [59] and the results presented here though, is that the experiments they performed involved scanning the surface 400 times. Here, mounds of similar heights (≈1 nm) are obtained in a single AFM tip pass. However, the underlaying mechanism must necessarily be identical. In their report, He et al. [59] proposed a stress enhanced corrosion mechanism which, in essence, is identical to the one described herein, that is, the application of the pressure accelerates the rate at which the water hydrolyses the SiO bonds (they however, do not provide any physical or electrochemical mechanism describing how the pressure accelerates the apparent cor-rosion rate). We only go a step further and demonstrate that electrochemical pressure solution is responsible for the wear of silica produced by the action of a diamond tip in humid air, and only in our case, the process is happening at a much faster rate because it is further accelerated by the oscillating pressure, as demonstrated by the comparison of Figures 5A and  6, thus becoming the FEEPS process detailed in this report. A more detailed discussion of the electro-chemo-mechanical enhancement mechanism can be found in previous work by the authors. [8] Again, compared with a constant pressure experiment, if oscillating the pressure while keeping the average pressure identical overall enhances the effect, it must necessarily be dominated by a FEEPS mechanism rather than a bond bridging mechanism.
All in all, we are driven to the conclusion that FEEPS is the dominant mechanism for the tribochemical wear of silica and by extension silicon since a silicon surface is always covered by a silica oxide layer in humid environments. [60]

Conclusion
Our tapping mode (TM) under water AFM experiments demonstrate the feasibility of using the (FEEPS etching to carry out nanolithography work on fused silica surfaces. Experiments investigating the effect of varying the AFM tip velocity upon the depth of the etched features showed that the process obeyed the same power law relationship between "contact time" and etching depth as was previously observed in hole etching experiments, [8] thus demonstrating the etching observed herein is dominated by the FEEPS etching mechanism. By varying the velocity of the AFM tip and hence, the dissolution time, gray-scale lithography that has proven challenging to obtain by others means became thus not only possible but also easy to design, giving features as deep as 60 nm in a single AFM tip pass (trace and retrace), comparable to what can be obtained on thermally sensitive polymers using a heated AFM probe. The advantages of the FEEPS technique compared to t-SPL are, first: etching is carried out directly onto inorganic substrates and so does not require the pattern to be transferred via reactive ion etching [61] and second, the AFM tip does not need to be heated to high temperatures (700 °C). [62] Consequently, FEEPS has the potential of turning any standard AFM into a t-SPL (nanoFrazer-like) instrument using appropriate controls software.
Experimental results on stress-enhanced dissolution (material removal) of calcite using AFM tips demonstrated the possibility of obtaining enhanced calcite dissolution rates both in the case of a sliding AFM tip but also in the case of a static AFM tip. [28] This last result where similar effects are observed both with and without the presence of shear forces seem to rule out any mechanism only taking into account bond bridges phenomena between the substrate and the tip surface, for the simple reason that shear forces represent a necessary component for the tribochemical bond bridging mechanisms to take place. [24] Comparing the results of the contact mode, nanoscratching-like and the force modulation mode experiments presented in this report, it is observed that nanoscratching leads tip wear (i.e., greater friction) compared to force modulation mode. However, greater etching is observed in force modulation mode. The etching method presented herein is therefore of a different nature than any tribochemical, friction induced chemistry mechanism.
The widely accepted mechanism explaining tribochemical wear and tribochemical phenomena appear to be flawed and we have provided experimental evidence that FEEPS may in fact be responsible for the removal of silica (and by extension Si) in these systems.
Again, the fact that our novel nanolithography method presents the same kinetics as the FEEPS process may help shine a new light onto tribochemical processes that have remained unclear until now. Mainly, that it is possible to tribochemically etch GaAs or DLC using silicon-based AFM tips. [25,27] Instead, our experiments demonstrate that it is possible to "etch" inorganic surfaces via a mechanism which does not invoke covalent bridging bonds. [22,49] In this respect, pressure solution dissolution occurs so long as the surfaces in contact display a sufficiently distinct surface potential and the mechanical vibrations generated during the sliding of the tip are likely to create the right set of conditions for FEEPS to happen.
Other well-know yet poorly understood phenomena involve similar physical conditions as the ones described above. Namely, bringing two electrochemically distinct surfaces into close proximity in a humid/liquid environment and adding a component of shear. An example is the concept of chemical mechanical polishing (CMP) where softer colloids dispersed in a slurry are used to polish much harder substrates like sapphire. [63][64] Our FEEPS centered etching mechanism may provide some clarifications regarding the CMP polishing rate dependency upon the shear rate [63,65] as shear forces are likely to liberate phonons (i.e. pressure waves) of the right frequency for FEEPS processes to take place. Furthermore, still using the framework of FEEPS, the polishing rate should be much reduced when both the surface potential of the colloid and the substrate are matching and thus, our new mechanism of electrochemical pressure solution may help giving a better understanding of the selectivity of CMP. It has indeed been observed that particular slurries are capable of polishing certain surfaces but not others. [66][67] Last, the CMP polishing rate dependency upon the pH [68] may find an explanation by acknowledging that a change in pH changes the surface potential difference between colloid and surface and therefore, alters the electrochemical pressure solution rate. [8]

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.