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To calibrate the optical trap, we monitor the fluctuations of an isolated, optically trapped TiO2 nanocylinder using a position-sensitive detector (PSD) (DL100-7PCBA3, Pacific Silicon Sensor, The Netherlands) that acquires at 100 kHz (Fig. S7†). The nanocylinder trapping position is ~7 µm above from the bottom surface of the flow cell channel, to conserve the similar measurement conditions with the case of DNA-tethered nanocylinders.11 We can calculate the restoring force acting on a nanocylinder displaced from the trap center, by multiplying the measured displacement with the calibrated trap stiffness. Precise linear translation of the flow cell is possible using a piezo-actuator (P-517.3CD, Physik Instrumente, Germany) in x, y, and z directions.
For the force-induced DNA-extension experiments, we move the flow cell along the axis of laser beam propagation (axial direction) at a constant speed (~1 µm/s) while maintaining the laser beam at a fixed position.
As the flow cell moves away from the laser beam focus, the increased DNA-tethered nanocylinder’s displacement from the trap center induces higher axial force to the DNA molecule. For the DNA coiling experiments, a constant axial force should be applied to the trapped, DNA-tethered nanocylinder since whether the DNA twists or forms plectonemic supercoils strongly influenced by the tension applied to the molecule.12 We use a feedback loop between the piezo-actuator and PSD to clamp the axial force at the specified setpoint. By simultaneously rotating the linear input polarization of the laser beam, we apply torque to the TiO2 nanocylinder, coiling the DNA molecule. The polarization can be rotated either by manual rotation of a half-wave plate (PWPS-1064-10-2, CVI Melles Griot, Germany), or by a fast electro-optical modulator (EOM) (LM 0202-LT, LINOS, Germany) in combination with quarter-wave plates (PWPS-1064-10-4, CVI Melles Griot, Germany).
Dry etching conditions for single-crystal TiO2 during optimization of the CHF3-RIE process We show the representative etching conditions (Table S1†) used during optimization of the CHF3-based plasma etching of single-crystal TiO2 in an RIE system. Throughout the optimization, we fix the flow rate of CHF3 gas, the main etchant, at the maximum value of 50 sccm, and set the flow rate of O2 gas at 5 sccm which is the median value of our target range (0–10 sccm). More accurate comparisons are possible within the same batches of the applied Cr etch mask, designated as Ra (H: 100 nm, D: 535 nm) and Rb (H: 100 nm, D: 345 nm).
The samples Ra1 and Rb1 are the reference samples, while the other samples differ by a single process parameter (designated as bold red numbers in Table S1†).
As an elevated RF power increases the etch rates of TiO2 while maintaining nearly constant etch selectivity (compare samples Ra1, Ra2, and Ra3 in Table S1†), we select the highest available power (200 W).
We find that an increase in the chamber pressure (from 10 to 50 µbar) enhances the etch selectivity by increasing the TiO2 etch rates and decreasing the Cr etch rates (compare samples Ra1 and Ra4 in Table S1†).
However, we do not utilize chamber pressures exceeding 50 µbar, as higher values result in excessive deposition of fluorocarbon passivation layers13 that are sufficiently thick to reduce the TiO2 etch rates again.
With these parameters fixed, we vary the gas composition. The addition of Ar gas, which results in harsher physical etching by heavy ions, generally increases etch rates.14 Indeed, upon its addition (at 30 sccm) both the Cr and TiO2 etch rates are increased; however, as the increase in the Cr etch rate surpasses that of TiO2, a deteriorated etch selectivity results (compare samples Rb1 and Rb2 in Table S1†). Our optimized process condition thus consists of CHF3 at 50 sccm, a chamber pressure of 50 µbar, and an RF power of 200 W. With these fixed parameters, we vary O2 gas flow rate from 0 sccm to 10 sccm to control sidewall profiles (Fig. S3†), and vertical sidewall can be obtained with 0.5 sccm of O2.
a) The bold red letters denote the main etchant gas in each condition.
Dry etching conditions for single-crystal TiO2 nanofabrication We use etching systems that are denoted as F1 (Fluor Z401S, Leybold Heraeus, Germany), F2 (Fluor Z401S, Leybold Heraeus, Germany), F3 (AMS100 I-speeder, Adixen, France), and F4 (Plasmalab System 100, Oxford Instr., UK). The F1 and F2 are two nominally identical RIE systems, while F3 and F4 are two distinct ICP-RIE systems. We summarize the etching conditions for each batch of TiO2 nanocylinders in Table S2†.
S7 Table S3. Dimensional analysis of high and low aspect-ratio TiO2 nanocylinders.
Dimensional analysis of high and low aspect-ratio TiO2 nanocylinders We have analyzed SEM images of high and low aspect-ratio nanocylinder batches to quantify both the local and global structural uniformity. We summarize the obtained statistical parameters for each batch of TiO2 nanocylinders in Table S3†, and present the corresponding graphs in Fig. 3d-f (high aspect-ratio: 3.6) and Fig.
S4d-i† (low aspect-ratio: 1.6).
Fig. S1. Diverse applications of TiO2 at the nanoscale. (a) Overview of the chemical, electrical, and optical properties that make TiO2 a versatile material for different applications. (b) Illustrations of nanoscale applications of TiO2 (yellow). Top, left to right: a TiO2 nanoparticle serves as a photocatalyst for water splitting into oxygen and hydrogen gases (ℎν: input radiation energy, CB: conduction band, VB: valence band, e-: electron, h+: hole); a TiO2 nanopillar array acts as a gas sensor (gray: metal electrodes, green: gas molecules, A: current as a sensing signal); a TiO2 thin
film acts as a tunable resistance material in a resistive random access memory device (gray: metal electrodes, orange:
TiO2-x, V: voltage as a read/write signal); a TiO2 thin film can be used as a channel layer in a transparent transistor (gray: metal electrodes, blue: gate insulator, purple: transparent electrode, VS, VD, and VG denote voltages at source, drain, and gate terminals, respectively). Bottom, left to right: a TiO2 nanorod array acts as a photoanode in a solar cell (ℎν: radiation energy from the sun, gray: metal electrode, purple: transparent electrode, magenta: sensitization layer e.g. dye molecules or quantum dots, brown: electrolyte, A: current as converted energy); a nanostructured TiO2 forms the core of a strip waveguide to support lightwave propagation (blue: cladding layers, red: confined lightwave);
a two-dimensional TiO2 photonic crystal slab used to manipulate the flow of lightwave (blue: cladding layers, red:
confined lightwave); an optically trapped TiO2 nanoparticle used as a force transducer (red: focused laser beam, dotted circle: trap center, F: force induced by the displacement of the nanoparticle).
S9 Fig. S2. The etch rates and etch selectivities of different mask materials. (a) The etch rates for substrate (blue bars) materials (TiO2: (100)-cut rutile single crystal, ~140 nm/min; SiO2: X-cut quartz single crystal, ~220 nm/min) and mask (red bars) materials (a-Si: amorphous silicon layer deposited by a plasma-enhanced chemical vapor deposition system (Plasmalab 80 Plus, Oxford Instr., UK), ~300 nm/min; ER: spin-coated and baked e-beam resist layer (NEBA2E, Sumitomo Chemical, Belgium), ~110 nm/min; W: tungsten layer deposited by an e-beam evaporator (Temescal FC-2000, Ferrotec, Germany), ~60 nm/min; Cr: chromium layer deposited by the same evaporator, ~5 nm/min). All results are obtained under the same dry etching conditions (using the F3 etching system; etching conditions in Table S2†). (b) Etch selectivity of each mask material for single-crystal TiO2 dry etching, which is the etch rate of TiO2 divided by that of the mask material (a-Si: 0.5, ER: 1.3, W: 2.3, Cr: 28).
S10 Fig. S3. Control of sidewall profiles and etch characteristics in single-crystal TiO2 nanocylinders by variation of O2 flow rate in the CHF3-RIE process. (a-e) SEM images of single-crystal TiO2 nanocylinders produced under identical etching conditions (using the F1 etching system; etching conditions in Table S2†) apart from the O2 flow rate (values shown at the bottom of each image). Scale bars denote 500 nm. Top surfaces of the nanocylinders are marked with yellow lines because the remaining Cr masks are also visible in these images. The insets in top-right corner illustrate (to scale) the corresponding three-dimensional shapes of the nanocylinder SEM images. The types of obtained nanocylinder shapes include (a) positive sidewall angles, (b) vertical sidewall angles, (c) negative sidewall angles, (d) symmetric hourglass shapes, and (e) asymmetric hourglass shapes. In (b) and (e), the insets in top-left corner (scale bars denote 500 nm) show top-view SEM images of nanocylinders cut at their middle, displaying cross-sections that are (b) circular or (e) diamond-shaped. (f) For the analysis of sidewall angles (θ), we use two-dimensional models as defined here. The definition of sidewall angles is illustrated for the cases of positive, vertical, and negative angles, using the measured heights (H) and diameters of top (Dt) and bottom (Db). The hourglass-shaped nanocylinders possess two sidewall angles and heights for both top (θt, Ht) and bottom (θb, Hb) sides, and an additional waist diameter (Dw). (g-i) The etch characteristics are shown as a function of the O2 flow rate: the etch rates of (g) TiO2, (h) Cr, and (i) the resulting etch selectivities (TiO2:Cr).
The measured dimensions extracted from the SEM images (a-e) are as follows: (a) Dt: 285 nm, Db: 395 nm, H: 500 nm, θ: 84°; (b) Dt = Db: 275 nm, H: 545, θ: 90°; (c) Dt: 305 nm, Db: 260 nm, H: 520 nm, θ:
-88°; (d) Dt = Db: 260 nm, Dw: 175 nm, Ht = Hb: 555 nm, -θt = θb: 86°; (e) Dt: 245 nm, Db: 370 nm, Dw: 135 nm, Ht: 385 nm, Hb: 1085 nm, θt:
-82°, θb: 84°.
Control mechanism for sidewall profiles in CHF3-etched single-crystal TiO2 nanocylinders We observe that tuning the O2 flow rate during the single-crystal TiO2 etching process allows us to control the sidewall profile of the nanostructures. We attribute the formation of different sidewall profiles (positive, vertical, negative, and hourglass-shaped) to underlying changes in the thickness of a sidewall passivation layer that result from the interplay between CHF3 and O2 plasma. The thickness variation permits both the formation S11 of positive sidewall angles in the absence of O2 flow and the formation of vertical (or negative) sidewall angles at an O2 flow of 0.5 (1.0) sccm (Fig. S3a-c†). The hourglass-shaped etch profiles likely result from substantially reduced TiO2 surface passivation combined with the random trajectories of reactive ions15,16 (Fig. S3d,e†).
Control mechanism for cross-sectional shapes and etch selectivity in CHF3-etched single-crystal TiO2 nanocylinders We find that the single-crystal TiO2 nanocylinders etched at low O2 flow rates (0−1 sccm) exhibit circular crosssections (Fig. S3b†, inset in top-left corner), while those etched at high O2 flow rates (5−10 sccm) feature diamond-shaped cross-sections (Fig. S3e†, inset in top-left corner). These differences may result from changes in the predominant etching mode: at low O2 flow rates, the initial shape of the etch masks (circular in the case of Fig. S3†) should be directly transferred to the etched nanostructures, as the dominance of physical etching by ion bombardment results in the same etch rate independently of crystallographic orientation; conversely, at high O2 flow rates, chemical etching may predominate than physical etching, resulting in etch rates that vary per orientation of the crystal planes in the single-crystal TiO2 substrates.17 Moreover, the above reasoning is supported by the fact that TiO2 etch rates (Fig. S3g†) increase significantly (~3-fold) while Cr etch rates (Fig.
S3h†) remain nearly the constant (~3 nm/min), as we increase O2 flow rate. The removal of Cr mask layer is possible only by the physical etching but not by the chemical etching based on fluorine chemistry while both etching modes induce TiO2 etching. We attribute this to a decreased thickness of the CHF3 plasma-generated fluorocarbon passivation layer on TiO2 surfaces in the presence of O2 plasma.18 As such a layer protects TiO2 surfaces from chemical reaction with etching species, its decreased thickness results in an increase of the TiO2 etch rates whilst those of Cr remain nearly unaffected, enhancing etch selectivity (Fig. S3i†).
The reproducibility of different sidewall profiles in CHF3-etched single-crystal TiO2 nanocylinders A repetition of this experiment in the second nominally identical RIE system yields the similar trends but at slightly altered O2 flow rates (using the F2 etching system; etching conditions in Table S2†). For example, etching nanocylinders with vertical sidewall angles requires an O2 flow rate of 4−8 sccm (compared to ~0.5 sccm in the first RIE system (Fig. S3b†)). Similarly, etching nanocylinders into hourglass-shapes requires an O2 flow rate of ~16 sccm (compared to 5−10 sccm in the first RIE system (Fig. S3d,e†)). We attribute this discrepancies in parameters to the differences in instrument calibration, e.g. of the mass flow controllers for the control and measurement of O2 flow rates.
S12 Fig. S4. Dimensions of fabricated single-crystal TiO2 nanocylinders. (a-c) SEM images of etched single-crystal TiO2 nanocylinders (light gray). Scale bars denote 1 µm. (a) Top-view of a single-crystal TiO2 substrate with partially cleaved nanocylinders. An array of rigidly fixed nanocylinders is visible in the top left corner, and the cleaved substrate surface is bottom right corner. The released nanocylinders are positioned at the interface of these regions.
(b) Top-view of a substrate with etched nanocylinders. The inset shows a zoom-in as an example for image analysis.