Fabrication and Operation of a Nano-Optical Conveyor Belt

1. Design the C-shaped Engraving (CSE) Array

1. Design the array pattern.

Figure 1. CSE Layout. Depiction of conveyor belt repeating element. Successful transport has been achieved using d_y = 320 nm and d_x = 360 nm. Adjacent pairs of engravings have a 60º relative rotational offset. Please click here to view a larger version of this figure.

1. Determine the desired path of particles across a planar substrate.
2. Using a CAD program, generate a double-linear array of C-shaped polygons along the path, each polygon in each pair consecutively rotated 30 ± 90° about its convex hull as shown in Figure 1. Because a particle’s own volume roughly determines its handoff range²², leave no more than one particle diameter separating consecutive pairs, and leave no more than 90% of this distance between polygon centers in a pair.
   Note: For reference, previous studies have indicated that polystyrene spheres of 390 nm in diameter and above are most suitable for transport along such a CSE array. Beads as small as 200 nm can be manipulated, though not reliably. However, beads larger than 500 nm feel stronger competing forces from a focused illumination beam.

2. Verify handoff forces along the array pattern using a numerical method to solve Maxwell’s equations. While the procedure described herein pertains to the Finite Element Method (FEM) implemented by the commercial software COMSOL, it is possible to adapt this method for other numerical methods and implementations.
   1. Draw up a numerical method geometry which accommodates the planar pattern dimensions and extends at least 200 nm below the pattern plane and 600 nm above the plane. Below the plane, include a domain to represent the substrate and above the plane a domain to represent the fluid chamber. Extrude the planar C-shaped pattern 150 nm downwards into the substrate, creating 3D domains to represent the interior of the engravings. Introduce a particle domain with the desired shape.
      1. Make sure that there is at least 200 nm of space between the top of the particle and the ceiling of the simulation volume and adjust the simulation extents as necessary. Add perfectly-matched layers at least 500 nm in thickness to the open boundaries of the simulation to absorb outward radiation.
   2. Set the electromagnetic material properties of the domain above the interface to those of water, the material properties of the interior of the C-shaped engravings to those of hydrogen-silsesquioxane (HSQ), and the material properties of the remaining material to those of gold. Set the material properties of the particle to those of polystyrene or another material of choice. For simplicity, use linear electromagnetic material models.
      Note: A sample complete 3D geometry is shown in Figure 2. In this case, PML material domains at the Cartesian ±x, ±y, and +z boundaries absorb fields meant to propagate to infinity. PML thickness is defined to be 5 times the maximum tetrahedral mesh element size, equal to 5 x 100 nm = 500 nm.
   3. If permittivity ɛ_r and permeability µ_r are required inputs for the numerical solver at hand, use a relative permittivity of 1.96 for HSQ, 1.77 for water, and -52.15 – 3.57i for gold. Set all relative permeabilities to 1. If an electromagnetic material property other than permittivity and permeability are required, use these values to derive the required inputs according to standard electromagnetic identities. Use the appropriate sign of the imaginary part of gold according to the complex time harmonic sign convention of the numerical solver (it should be negative under the exp(+iωt) convention and positive under the exp(-iωt) convention).

Figure 2. Simulation Geometry. Example of numerical simulation geometry in the commercial Finite Element Method software COMSOL. Two conveyor belt periods are simulated with d_y = 320 nm and d_x = 360 nm and a 500 nm diameter sphere. Shaded material regions are a) HSQ, b) polystyrene, c) gold, and d) water. Please click here to view a larger version of this figure.

4. Discretize the simulation volume with an adaptive tetrahedral mesh. Constrain the maximum size of the mesh elements to no larger than 100 nm in the bulk. Furthermore, constrain the maximum size of mesh elements to 30 nm on the sphere surface and 30 nm on the engraving surfaces to increase accuracy on critical structures. A moderate mesh growth rate of about 1.4 should be used to preserve mesh element quality in those regions, and a minimum mesh size can also be defined in the volume to limit unpredictable adaptive mesh behavior.
5. For optical excitation, define a background harmonic plane wave with a free space wavelength of 1,064 nm which is normally incident and reflected off of the planar gold substrate as if the engravings and particle were absent. Use the Fresnel equations evaluated at a normal angle of incidence to calculate plane wave reflection and transmission coefficients. Choose the polarization of this wave such that the electric field is aligned with the ridge of a C-shaped engraving. Normalize the intensity of the plane wave to 1 mW/µm².
6. Solve for the scattered electromagnetic fields in a batch of simulations, sweeping the particle position parameter from one end of the path to the other while holding the particle’s altitude constant at just a few nanometers off the surface. Altitudes as low as 5 nm tend to predict very strong trapping potentials, while greater altitudes predict smoother trapping potentials. In fact, Brownian motion will ensure that a real particle will explore a variety of altitudes above the surface.
   Note: Computational resources and time will vary with numerical system size, numerical method, and computer hardware.
7. Repeat steps 1.2.5 and 1.2.6 for polarization aligned with each of the other two polarization-distinct C-shape orientations, as polarization angle is taken modulo 180°.
8. For each simulation in the three batches, calculate the net force on the particle by integrating the flux of the Maxwell-Minkowski Stress Tensor through a surface which completely encloses the particle but does not cross any material interfaces.
9. For each polarization, calculate the work done against optical forces by performing a path integral of the negative net optical force over the path that the particle follows in each batch, as shown in Figure 3.

Figure 3. Trapping Verification. Stable trapping can be demonstrated by plotting the optical potential of activation states. A single period of just three CSEs is analyzed for simplicity. Indeed, overall trap depth is sufficient (> 10 k_BT) for stable trapping at the activated engraving for each state A, B, and C. Please click here to view a larger version of this figure.

Figure 4. Handoff Verification. Handoff can be demonstrated by plotting the optical potential of old (light red) and new (bright red) activation states in sequence. A single period of just three CSEs is analyzed for simplicity. During handoff from A to B and B to C, the potential barrier in the direction of desired motion between those two positions is both small (1 k_BT) and smaller than that in the opposite direction, indicating that controlled handoff is likely. Handoff from C to A is most difficult because the inter-trap barrier remains sizable at all polarizations. Please click here to view a larger version of this figure.

10. Verify for each polarization A, B, and C that there is an energy barrier of at least 10 k_BT in height on either side of the potential minimum in each period of three Cs. Refer to Figure 3 for a visual identification of the potential minima and barriers.
    Note: This step determines whether the particle will be stably trapped on the proposed conveyor belt without skipping back and forth. Due to the linearity of electromagnetic waves and the use of linear material models, the energy barrier is proportional to the exciting plane wave intensity.
11. Verify that the energy barriers between adjacent A traps and B traps dip below 1 k_BT when the polarization is continuously rotated from A to B during particle handoff. Repeat for polarization rotation from B to C, and from C to A. Refer to Figure 4 for a visual identification of these handoff transition potential minima and barriers.
    Note: This step determines if the particle will reliably transfer from a trap A to a trap B during polarization rotation. A particle will easily overcome a barrier of height 1 k_BT to move to a deeper potential well.
12. If there is any insufficient energy barrier in step 1.2.10 or any energy barrier which is too strong in step 1.2.11, adjust the design. In general, to raise energy barriers, increase the space dividing C-shaped engravings. To lower energy barriers, bring the engravings closer together. Avoid bringing them closer together than two skin depths (40 nm), as engravings which are too close together may disrupt one another's resonance currents, which lowers overall trapping effectiveness. Repeat step 1.2 to re-verify the optical potential.

2. Fabricate the CSE Array

Note: The process diagram is shown in Figure 5. This process is inspired by the work in ref. 25 and 26.

Figure 5. CSE Process. Process flow diagram of the dual-layer template-stripping process. E-beam lithography with 100 keV energy is used to expose the conveyor pattern on the HSQ resist. The thin PMMA layer underneath the HSQ is intended to facilitate the final strip-off (release) of the device from the Si substrate. Please click here to view a larger version of this figure.

1. Acquire a clean, polished silicon wafer and bring it to a clean room equipped for silicon lithography processes.
2. Clean the silicon wafer to remove organic contamination and oxides on the surface.
   1. Immerse the wafer in a 9:1 H₂SO₄:H₂O₂ solution at 100 °C for 10 min. A bath of at least 1 L ensures robust cleaning, though less chemical may permit safer and easier wafer processing as facilities require.
   2. Dip the wafer in a 50:1 HF solution for 30 sec. A bath of at least 1 L ensures robust cleaning, though less chemical may permit safer and easier wafer processing as facilities require.
   3. Thoroughly rinse the wafer with DI water and spin-dry it.
3. Spin coat 50 nm PMMA (thickness is not critical).
   1. Singe bake the wafer at 150 °C for 30 min.
   2. Spin coat a polished, clean silicon wafer with 2% 950k poly-methyl-methacrylate (PMMA) at 5,000 rpm for 40 sec. Apply the PMMA with a pipette, landing 20-25 drops of resist on the center of the wafer before beginning the spin.
   3. Post bake PMMA resist on hotplate at 200 °C for 2 min.
4. Spin coat 150 nm HSQ (same day as following step).
   1. Spin on HSQ negative tone resist at 900 rpm for 1 min. Apply the HSQ with a plastic pipette, again landing 20-25 drops of resist on the center of the wafer before beginning the spin.
   2. Post bake HSQ resist on hotplate at 80 °C for 2 min.
5. Expose and develop the pattern using electron beam lithography techniques (same day as previous step). The process follows from the PMMA/HSQ dual-layer demonstration in ref. 27.
   1. Translate the silhouette design to GDSII format for electron beam patterning in a dose array. Include alignment marks and annotations which are at least 5 µm in size in order to identify the nanostructures under an optical microscope. The dose array should range from 800-4,000 µC/cm².
   2. Use an electron beam lithography exposure tool to expose the array at 100 kV accelerating voltage and an aperture of 60 µm, which produces a current of 500 pA. Electron beam exposure is also possible under lower accelerating voltages provided the beam current, dose, and proximity pattern correction are adjusted accordingly.
   3. Develop the exposed HSQ by submerging the wafer in a 2.2% tetramethylammonium hydroxide (TMAH) developer solution for 90 sec. Gently agitate the solution by jostling the developer dish every 10 sec. After the development time has passed, immediately stop the development by flushing the surface with water for 60 sec.
6. Coat a layer of gold 200 nm in thickness, followed by a layer of copper 1,000 nm in thickness, by magnetron sputtering. Make sure to use a sputtering tool whose gold sputtering rate has been calibrated so that the target thickness is achieved within 20%. Sputtering rates will vary among tools. Overshoot in gold thickness is acceptable, as is overshoot in copper.
7. Glue a 1 cm x 1 cm quartz back plate onto patterned substrate with UV-curable epoxy.
   1. Spread a single drop of UV-curable epoxy onto the copper side of the sample in a 1 cm x 1 cm square covering the patterned device area.
   2. Apply a quartz/glass back plate to the copper surface, making sure that it completely covers the patterned device area.
   3. Put on UV safety goggles.
   4. Rest the back plate and wafer on a level surface, and illuminate the epoxy from above with a UV flood lamp for approximately 30 min.
   5. Turn off the UV flood lamp and remove the cured sample.
8. Release the device from the silicon substrate in an acetone bath.
   1. Using a sharp knife, score a smooth, closed path around the quartz back plate, making sure that the cut is deep enough to penetrate all the way through the two metal layers and the PMMA layer above the silicon wafer.
   2. Submerge the substrate in an acetone bath for 6-8 hr.
   3. If after 8 hr the device sample has not yet been released from the silicon wafer naturally, carefully pry the device (including the quartz back plate and both metal layers) away from the silicon wafer using a thin wedge or knife.
   4. Rinse the resulting sample with acetone for about 1 min and dry it with N₂ or clean air.
   5. If there are rough edges of metal or glue remaining around the back plate, carefully trim them away with a razor or lab shears. This will improve the fluid dynamics during a trapping experiment by ensuring uniform evaporation around the chip edges.
   6. Store the sample in a clean, dust-proof container for transport to the optical lab.

3. Prepare the Specimen Sample

1. Prepare a fluorescent polystyrene bead solution.
   1. Dilute a fluorescent polystyrene bead solution from the manufacturer’s concentration to 1×10⁹/ml– 1×10¹⁰/ml by adding the appropriate volume to 1 ml of water.
   2. Add 0.05 ml of surfactant (octyl phenol ethoxylate) to the specimen sample. The surfactant reduces the tendency of the colloidal beads to stick to any surfaces, and it also slightly increases the viscosity of the host fluid.

4. Calibrate the Focus of the Optical Columns

Note: A schematic of the apparatus can be referenced in Figure 8.

1. Calibrate the focus of the specimen imaging camera.
   1. Acquire a spare, patterned, and flat reflective surface for testing and calibration. A dummy sample with alignment marks works well.
   2. Turn on the microscope mercury lamp and wait until the light level has stabilized, then open the lamp shutter.
   3. Place the patterned test surface into the microscope field of view and move its edge into the field of view center. Adjust light attenuators to make sure that the light is not too bright to observe through the eyepiece, then look through the eyepiece and bring the edge into focus.
   4. Move the microscope stage so that a pattern is now in the center of the field of view, and adjust the focus knob to maximize the sharpness of the pattern.
   5. Turn on the specimen imaging camera and adjust the brightness and contrast to the microscope illumination level.
   6. Adjust the specimen camera focus until the pattern is also in focus for the camera. The pattern should be in focus in both the camera's view and in the eyepiece without having to make any focal adjustments when switching between the two.
2. Calibrate the beam imaging column to ensure that the laser beam imaging camera focuses on the substrate.
   Note: It is assumed that the near-IR laser has already been roughly collimated and aligned with the microscope imaging columns. An IR sensor card is a useful tool to perform this alignment. It is recommended to build the whole system on a pre-aligned support such as a cage system so that all of the optics can be centered on the same axis automatically. Dichroic mirrors inserted to separate beam and imaging wavelengths are standard, but for safety should not leak more than 1% of the laser wavelength.
   1. Ensure that each researcher in the room puts on laser safety goggles with an extinction of at least 10⁷ at the wavelength of laser operation (1,064 nm) and ensure that the laser beam shutter is closed.
   2. Turn on the laser power supply and cooling system, but leave the beam shuttered. Warm up the laser gain medium.
   3. Once the goggles are in place and the shutter is confirmed closed, turn on the laser. Place a beam block in front of the laser and open the shutter to measure the output of the laser beam and verify, using a power meter, that the laser power output has stabilized. Keep the beam block in place.
   4. To protect the specimen imaging camera from damaging levels of laser light, make sure beam attenuators are in place in front of the specimen imaging camera, as well as a dichroic mirror to direct the remaining beam energy to a separate beam imaging camera. Also, modulate the power of the laser using attenuators or a polarizing beam splitter so that only a moderate amount of power (10 mW) passes through to the apparatus.
   5. Remove the beam block and allow the beam to travel through the apparatus and fall onto the beam imaging camera detector.
   6. Turn on the beam imaging camera and adjust the brightness and contrast to the laser light level.
   7. Defocus the laser beam so that a wide area of the patterned reflector is illuminated by laser light.
   8. Adjust the focus of the beam imaging camera until the features of the pattern are in focus simultaneously with the white light image of the specimen imaging camera, and translate the camera so that its field of view is centered on the field of view of the specimen imaging camera. The effective focal offset between the white light image and the beam image counteracts the focal length discrepancy of the optics between the laser and visible wavelengths.
3. Bring the laser into focus with the beam imaging camera.
   1. Using the calibrated focus in the beam imaging camera, adjust the laser beam focus until it focuses to a tight spot, and adjust the beam's focus position so that it falls in the center of the field of view. Using annotation software or another method of choice, mark the location of the beam in the specimen camera's field of view.
   2. Close the laser beam shutter.

5. Trap and Manipulate Specimen with Optical Energy

Note: A schematic of the apparatus can be referenced in Figure 8.

1. Image the fluorescent polystyrene beads.
   1. Replace the dummy sample and cover slip with a clean coverslip in the sample holder of the microscope.
   2. Place a tip on the discharge end of the micro-pipette and extract 2-4 µl of diluted fluorescent particle solution with the pipette.
   3. Slowly discharge the solution onto the coverslip. If there are bubbles, remove them by gently blowing clean air onto the drop of solution.
   4. Carefully place the device on top of the solution blob with gold surface facing down. The solution should spread across the entire area under the device.
   5. Move the microscope stage so that an edge of the resonator array chip is near the center of the field of view. Establish focus on the edge of the chip.
   6. Translate the microscope stage so that the resonator pattern is near the center of the field of view. Focus on the nanostructures by bringing dark alignment marks into focus, and note that the resonators themselves appear as dark spots in the bright reflector background.
   7. Insert a narrow band-pass filter in front of the mercury lamp which blocks all colors other than that corresponding to the fluorescent beads' absorption peak.
   8. Insert a narrow band-pass filter in front of the specimen imaging camera which blocks all colors other than that corresponding to the fluorescent beads' emission peak.
   9. Bring the fluorescent image of the beads into focus, noting their collective average drift velocity against their individually random Brownian motion. Wait until the beads' average drift velocity slows to less than 10 µm/sec.
      Note: Due to evaporation at the edges of the chip, and due to dynamic settling forces of the fluid underneath the chip's weight, there may be visibly apparent currents (tens of µm/s or more) in the specimen fluid. If the evaporation is not too asymmetric along the edge of the chip, these currents will eventually diminish to acceptable levels to perform an experiment.
2. Use the focused laser beam to trap a polystyrene bead.
   1. Ensure that all researchers put on appropriate laser safety goggles, and then turn on the laser while keeping the laser beam shutter closed. Make sure that the laser output is less than 10 mW. Ensure that the laser power has stabilized by testing the beam output with a beam block in place which prevents laser radiation from entering the microscope.
   2. Once the laser power has stabilized, remove the beam block and note the laser spot in the beam image. If the spot is out of focus, adjust the laser focus until minimal spot focus is achieved.
   3. While ensuring that sufficient attenuators are placed in front of the beam image to prevent beam detector saturation, gradually increase laser output power until a drifting bead can be captured stably at the beam focus. Scanning the microscope stage can assist in trapping a bead which is off-center.
   4. Verify that the trapped bead is located at or near the mark made earlier to track the laser focus position in the specimen image. If there is a difference between the bead position and the laser focus mark, correct the laser focus mark to match the new bead position.
   5. Now, adjust the beam contractor built in to the beam path until the beam spot is expanded to 9 µm in diameter FWHM when it is fully in focus. Measure this as a straight intensity cross section through the center of the beam spot in the beam image.
   6. If the original trapped bead was lost during this adjustment, use the translation stage to search for and trap another bead.
      1. If widening the beam spot has de-stabilized the optical trap (due to a decreased intensity gradient), increase the beam power as necessary to achieve stable optical trapping. If increasing the focal spot size has moved the center of the beam away from its original position, re-mark the average position of the trapped bead in the specimen image as the beam center.
3. Establish near-field trapping and manipulate a polystyrene bead on a C-shaped engraving array.
   1. Turn on the background illumination lamp and increase its power until the substrate pattern can be seen in the background behind the images of fluorescent beads.
   2. With a bead trapped by the loosely-focused beam, use the microscope stage to move the substrate pattern so that the end of an array of resonators can be seen directly behind the trapped bead. If the bead's random Brownian motion becomes significantly reduced, this means the bead is trapped by the near field of an excited resonator.
      Note: If the bead has not yet been trapped by the optical near field, adjust the position of the plasmonic resonator array underneath the bead. This adjustment might bring the bead into closer contact with a resonator which is better aligned with the current polarization of the laser light. If this process does not induce near-field trapping, the beam focus may be slightly above the substrate plane. In this case, adjust the laser focus slightly so that the focal spot approaches the surface of the substrate.
   3. If after small stage and laser focus adjustments the bead has still not yet been trapped by the optical near field, find another array on the substrate and repeat the near-field trapping process, starting with step 5.3.2.
      Note: Fabrication defects cause both systematic and random variations in resonator performance. Non-functioning resonator arrays are common until the fabrication results have been fully characterized and are repeatable.
   4. Once near-field trapping has been established, move the microscope translation stage so that the center of the laser spot resides more near to the center of the conveyor. This action will tend to pull the bead along with the center of the focused laser, so only small adjustments can be made in this way. If a bead becomes dislodged, reduce the motion. This is the amount of beam displacement tolerable by the near-field traps.
   5. After displacing the beam slightly in the previous step, rotate a half-wave plate placed in the laser beam path to rotate the angle of linear polarization. This activates resonators in a sequence down the array and induces controlled, linear motion in the fluorescent bead. A motorized rotary stage can help produce more steady rotation in the half-wave plate and therefore more steady bead motion.
   6. To track the progress of the bead and capture data on its position, turn off the background illumination lamp and use a video capture utility to capture frames of the bead motion. Post-processing of the particle motion can be achieved using the provided MATLAB script.