2.1.

Laser Interference Lithography

LIL, also known as holographic lithography, consists of the direct transfer of laser interference patterns on a photoresist, without the need of a lithography mask [Fig. 1(a)]. LIL combines the ease and speed of a direct illumination in a simple optical setup for applications, where large area ($\sim {\mathrm{cm}}^2$) patterns of lines or dots are needed,^15,16 as in our case [Fig. 1(b)]. The linear interference pattern resulting from the coincidence of two plane wavefronts has a spatial period given by

Fig. 1

Scheme of LIL. (a) Scheme of the optical setup employed to produce the interference fringes. (b) Result of the sum of two interference patterns. (c) Interference patterns generated by two light beams intersecting at an angle $\theta$. (d) Schematic view of the aspect ratio of the exposed photoresist as a function of exposure.

The optical setup used in our experiments is depicted in Fig. 1(a). A 30-mW laser with $\lambda =405\mathrm{nm}$ produces a Gaussian beam, which is focused on a $10\mu \mathrm{m}$ wide pinhole, resulting in a coherent light beam propagating from the aperture with a coherence length larger than 10 m. The divergent beam strikes two adjacent mirrors oriented at an angle $\theta$, creating two beams interfering at the plane where the sample, coated with photoresist, is placed. This interference region is about $3\mathrm{cm}\times 3\mathrm{cm}$ in our setup and the illuminance is $0.16\mathrm{mW}{\mathrm{cm}}^{-2}$, which imposes minute-long exposures for common photoresists. By adjusting the angle $\theta$ between the two mirrors, according to Eq. (1), we can continuously tune the spatial period of the interference and generate patterns with a pitch from 400 nm up to $2\mu \mathrm{m}$. The exposure duration is set to provide the required optical dose to completely cross-link the photoresist at the location of constructive interference. By controlling the exposure time, it is also possible to tune the ratio of exposed versus nonexposed photoresist and hence, to adjust the lines width or dots diameter while keeping a constant pitch [Fig. 1(d)].

2.2.

Optical Torque Wrench

Depending on their spin, photons carry positive or negative angular momentum, which corresponds to the two left- and right-circular polarization components. Because of the birefringence, the polarization state of the trapping beam is modified during the propagation through the particle trapped in the laser focus. This results in a change in the total spin angular momentum of the laser beam, which reflects the torque transferred to the particle. The induced dipole moment $\overrightarrow{P}$ and the laser electric field $\overrightarrow{E}$ are generally not parallel in the birefringent crystal. The angle between the two vectors results in a restoring torque $\overrightarrow{\tau }=\overrightarrow{E}\times \overrightarrow{P}$ on the particle.⁶ As a consequence, the extraordinary axis of the quartz cylinder tends to orient parallel to the linear polarization of the laser. The optical torque transferred to the particle can be written as

Our optical setup is described in detail in Refs. 8 and 18. Briefly, the trap consists of an infrared laser ($\lambda =1064\mathrm{nm}$, 100-mW CW at the optical trap, ${\mathrm{TEM}}_{00}$) focused by a large numerical aperture objective ($\mathrm{NA}=1.2$) in a flow cell containing cylinders dispersed in water. The orientation of the linear polarization of the laser is dynamically controlled by an electro-optical modulator (EOM) combined with a quarter waveplate.^7,8 In our experiments, we control the frequency $\omega$ of rotation of the linear polarization by driving the EOM with a sawtooth voltage signal of variable frequency. The polarization can be set in rotation in both directions with $\omega$ in the range from 0 to few kHz.

The transferred torque is measured by analyzing the imbalance of the circular components of the polarization at the output of the trap with respect to the input. After calibration of the angular trap,¹⁸ absolute measurements of torque are performed at 20-kHz sampling rate.

3.1.

Quartz Microcylinders Fabrication

We depict the microfabrication process in Fig. 2. First, a chromium layer of 30 nm is sputtered onto a $24\times 24{\mathrm{nm}}^2$ single-crystal quartz substrate (X-cut), previously cleaned with a Piranha solution. Second, we spin-coat a thin layer of AZ 701 MIR photoresist (Merck Performance Materials GmbH) at 4000 rpm for 30 s, followed by soft baking at 95°C for 1 min. The photoresist is diluted (2∶1) to achieve a final thickness of 600 nm. The quartz sample is then exposed on the LIL setup, prepared for a fixed interference period (typically $1\mu \mathrm{m}$). Exposure is made in two steps of 130 s each, rotating the sample by 90 deg in the interference plane. After exposure, the sample is postbaked at 110°C for 1 min and developed with AZ 726 developer for 17 s under smooth agitation. Figures 3(a) and 3(b) show two SEM images of lines and dots arrays obtained after development. The next step consists in transferring the photoresist pattern onto the quartz substrate. To achieve the high anisotropy required by the cylindrical geometry, we use inductive coupled plasma reactive ion etching (ICP-RIE). To improve the selectivity of the technique (which is low especially when using photoresists), the key is to use a hard mask, as a chromium layer, and a two-step ICP-RIE process, as described below. Hard masks are often used in plasma etching, in particular to prevent photoresist shrinking,¹⁹ and the materials employed include Ni, Al, or ZnO. Abe and Esashi²⁰ reported the etching of $90\text{-}\mu \mathrm{m}$ deep quartz trenches by using a $4\text{-}\mu \mathrm{m}$ Ni metal mask with ${\mathrm{SF}}_6$, ${\mathrm{SF}}_6/\mathrm{Ar}$, and ${\mathrm{SF}}_6/\mathrm{Xe}$ RIE gas plasma. Also, a SU8 thick photoresist has been used as a hard mask for quartz etching.²¹ In our case, we find that the submicron dimensions of the quartz cylinders require a thin (30 nm) hard mask layer. Following LIL patterning, the chromium layer is etched with an Ar plasma in the absence of oxygen, using a Corial 250D ICP RIE (200 W RF and 400 W LF). The absence of oxygen prevents the photoresist from shrinking during etching, allowing the unprotected hard mask to be completely removed in 6 min with sufficient selectivity. Etching of quartz is achieved by a second ICP-RIE process, using a mixture of ${\mathrm{CHF}}_3$ (200 sccm) and ${\mathrm{O}}_2$ (100 sccm), an internal pressure of 1.2 mTorr, and incoming power of 200 W RF and 800 W LF. In these conditions, the etching rate of quartz is about $100\mathrm{nm}/\min$.

Fig. 2

Steps of the microfabrication process: (a) initial stack, photoresist on a 30-nm chromium layer on quartz substrate, (b) LIL and development of the photoresist, plasma sputter etching of chromium, (c) plasma etching of quartz, and (d) cleavage by microtome blade.

Fig. 3

(a) and (b) SEM pictures of the photoresist patterns obtained by LIL: (a) lines with 800 nm pitch. (b) Dots with $1\text{-}\mu \mathrm{m}$ pitch. (c) SEM image of ICP-RIE etched quartz cylinders (45-degtilt). (d) SEM image of cylinders mechanically cleaved from the substrate.

The cylinders obtained are slightly conical, with a wall angle of about 80 deg [Fig. 3(c)]. Aiming at an aspect ratio of $\sim 3$, we can adjust the etching time to produce cylinders with heights ranging from 900 nm to $1.6\mu \mathrm{m}$, with a homogeneity across the sample of 3% to 5%. After etching, the cylinders are mechanically cleaved and removed from the substrate by using a microtome blade, as can be observed in Fig. 3(d). They are finally collected and stored in water (a surfactant can be used to avoid coalescence). Before cleavage, the top surface of the pillars can be specifically functionalized.¹³ Given the dimensions of the wafer ($2\times 2{\mathrm{cm}}^2$) and the pitch of the structures ($1\mu \mathrm{m}$), the production of $\approx 4\times {10}^8$ cylinders would be expected. However, irregularities in the thickness of the photoresist near the edges of the substrate decrease the efficiency of the process from 60% to 70% of the total area. The distribution of sizes obtained for the cleaved cylinders, shown in Fig. 3(d), is summarized in Table 1.

Table 1

Cylinder size statistics for the 1-μm period series shown in Fig. 3(d) (N=35).

3.2.

Optical Torque Measurement on a Trapped Birefringent Cylinder

In Fig. 4, we show the dynamical measurements of the transferred torque on a single cylinder in the optical trap [sketched in Fig. 4(a)], performed for different frequencies of rotation $\omega$ of the linear polarization of the laser at the optical trap. As predicted by Eq. (2), when the linear polarization rotates at a frequency $\omega$, the dynamical response of the system is “excitable” and can be well described by the one-dimensional motion of a particle along a tilted periodic potential.^8,18 For low $\omega$, the extraordinary axis of the cylinder follows the polarization rotation in phase. In this regime, the average optical torque transferred to the particle is linearly proportional to $\omega$, as seen in Fig. 4(b). The time resolved torque traces are characteristic of confined Brownian motion of an angularly trapped particle, as shown in Fig. 4(c). When $\omega$ reaches the critical value ${\omega }_{\mathrm{c}}={\tau }_{\mathrm{o}}/\gamma$ (with ${\tau }_{\mathrm{o}}$ given in Eq. (2) and $\gamma$ the angular drag coefficient of the cylinder), the cylinder cannot follow in phase the rotation of the polarization. In this regime, thermal noise triggers stochastic escape events of the particle axis from the potential created by the rotating laser polarization. The average torque transferred to the particle decreases with increasing $\omega$ [Fig. 4(b)], and the escape events are apparent as spikes in the torque signal [Fig. 4(d)]. For larger $\omega$, the rotation of the polarization is too fast to allow the particle to follow it in phase, and the average torque falls to zero [Fig. 4(b)]. The cylinder axis remains quasistatic in the trap, leading to a quasiperiodic torque trace [Fig. 4(e)]. The calibration of the optical signal allows absolute measurements of torque in physical units (pN nm) and provides a value for the angular drag coefficient $\gamma$ of the particle immersed in water.¹⁸ Trapping one cylinder from the batch shown in Fig. 3(d), whose dimensions are distributed as indicated in Table 1, the calibration yields a value of $\gamma$ of $1.1\pm 0.2\mathrm{pN}\mathrm{nm}\mathrm{s}$. This is compatible with the theoretical value of 0.9 pN nm s for a cylinder with the same dimensions.²² This dynamical behavior of the trapped cylinder, well described by the model, confirms that optical torque in the range of pN nm, relevant in single-molecule essays, can be transferred and measured on these birefringent cylinders trapped in an OTW.

Fig. 4

Torque measurements on a trapped cylinder. (a) Sketch of the cylinder in the optical trap: at equilibrium, the geometrical axis of the cylinder is parallel to laser propagation direction. The extraordinary axis of the crystal ${\chi }_e$ and the polarization of the laser $P$ are shown. (b) Average torque transferred to the particle as a function of the polarization rotation frequency $\omega$. Laser power = 55 mW (blue), 92 mW (orange). (c)–(e) The instantaneous torque traces recorded at the indicated values of $\omega$, as shown also in (b).