Synthesis and Operation of Fluorescent-core Microcavities for Refractometric Sensing

1. Preparation of Materials

1. Microcapillaries Obtain silica capillaries from a commercial supplier. We purchase our capillaries from Polymicro Technologies . Choose a small inner diameter (~25 – 30 μm) for more widely separated spectral resonances (i.e. a larger free spectral range) or a larger inner diameter (~100 μm) for more closely spaced resonances with higher quality factors. A large outer diameter ensures the FCMs are durable and easily manipulated.
   1. The capillaries come with a colored polyimide jacket, which must first be removed. Cut approximately 10-cm pieces of capillary from the roll, using diamond fiber cleaver. Each piece constitutes a single sample. Heat these in a tube furnace at 650 °C for one hour in oxygen to burn off the coating. This process removes the jacket material, exposing the silica capillary inside. After cooling to room temperature, remove the capillaries from the heating boat.
2. Hydrogen silsesquioxane solutions Hydrogen silsesquioxane (HSQ) is reported to consist of H₁₂Si₈O₁₂ molecules with a cage-like structure.¹⁴ This material is commercially available from Dow Corning. Purchase the HSQ in one of its FOx-series (flowable oxide) solutions, such as FOx-15. These solutions are expensive and have a limited shelf life, so careful planning is needed. Evaporation of the MIBK solvent provides an HSQ concentration of approximately 18% by weight. If the HSQ concentration is too low, quantum dots may not form in the film. If it is too high, the films may be too thick and delaminate from the capillary channel surface. In our experience, for a capillary with a 25-30 μm inner diameter, a FOx solution containing ~25 wt.% HSQ is best. Thus, it may be necessary to evaporate or add more HSQ solvent (making sure that it is dry) in order to adjust the concentration. Whether a dilution or concentration is necessary is difficult to determine without trial and error; i.e. make some samples and examine the results, as discussed below.

2. Fabrication of Coated Capillaries

1. Filling the capillary Take the pieces of capillary prepared in step 1.1 and dip them into the FOx solution. When a capillary is dipped into the solution, you should be able to visually follow the meniscus up the channel, as the solution is drawn into the capillary (Figure 2a).
   1. When the meniscus reaches the top, remove the capillary and place it in a glass annealing crucible. It should now be completely filled with FOx solution. Repeat this for as many samples as possible, to increase the chances of success. We typically run batches of 20-30 and use two different concentrations of HSQ solutions by weight. We fill the capillaries in air, but keeping the FOx solution chilled in a glovebox is recommended if possible, in order to minimize exposure of the solution to oxygen and water vapor. Even small exposures can result in gelation of the solution.
2. Annealing Anneal the capillaries in a two stage process. Annealing evaporates the solvent and collapses the HSQ cage structure, forming an SiO_x film adhering to the channel walls. Annealing at higher temperatures disproportionates the SiO_x film into Si quantum dots dispersed in a silica matrix. The annealing steps include a 30-minute ramp from room temperature to 300 °C, a dwell for 3 hr to evaporate the solvent, then a ramp to 1,100 °C in 45 min, and a dwell for one hour to precipitate the QDs.
   1. Let the capillaries slowly cool (~12 hr) back to room temperature. This helps to minimize stress-related cracking of the film deposited on the capillary wall. Other annealing protocols could probably be followed and may be more reliable, but a high-temperature anneal stage at 1,000-1,100 °C is always necessary to form the QDs. At the end of this step, one should (hopefully) have 20-30 capillaries with a layer of fluorescent QDs embedded in a silica matrix coating the channel walls.

3. Characterization

1. Sample check The fluorescence microscope on which the capillaries are mounted must perform both imaging and spectroscopy in the 700-900 nm wavelength range. Epifluorescence or confocal setups are suitable for this purpose. Place a row of the candidate capillaries on the stage so that it is easy to move between them for quick visual analysis (Figure 2b). Excite the capillary with blue or UV radiation either in free space on the microscope stage, or directly through the objective lens using a dichroic filter, and observe the fluorescence image using the eyepieces or a color camera.
   1. Observe the capillary fluorescence. If the fabrication was successful, the capillaries will exhibit a bright red fluorescence. This is the first indication of a favorable sample. Capillaries exhibiting orange-yellow fluorescence (instead of the red color associated with the QDs) in general do not have the desired optical characteristics. These samples also tend to form more often in solutions with a low HSQ concentration. Some capillaries may show no fluorescence at all; in this case the QD film did not form and the capillary can be discarded (glass sharps). This is an indication that the solution may not have been drawn into the capillary, or it may have been deficient in HSQ. Finally, some samples may show a cracked or textured film; these can also be discarded.
   2. Discard all the samples mentioned in the previous step except those that show the bright red fluorescence characteristic of silicon QDs.
2. Check for the presence of WGMs in the fluorescence spectra Ensure the image is aligned as desired on the entrance slit of the spectrometer and collect a fluorescence spectrum. Adjust the collection time so as to produce an acceptable signal-to-noise ratio. Perform wavelength and intensity calibrations as required. The QD spectra should be intense in the wavelength range from 700 to 900 nm. Spectra taken from the region corresponding to the capillary inner wall should show strong oscillations due to the presence of the cylindrical whispering gallery modes (WGMs); this is the second-to-last requirement of a successful refractometric sensor.
   1. Some samples may have a bright red QD fluorescence but lack WGM oscillations in the spectrum. This is an indication the QD film cracked or delaminated from the capillary wall, which destroys the optical resonances. Discard capillaries without WGMs. At this point, only the (typically small) fraction of samples that meet the sensor requirements remain. There is one final test to be performed.
3. Refractometric analysis Attach the candidate capillaries to polyethylene, tygon, teflon, or other tubing chemically compatible with the intended analyte solutions whose inner diameter should be slightly larger than the capillary outer diameter. The choice of tubing should be made so as not to react with the solutions to be pumped into the capillary.
   1. Use a good adhesive to attach the glass capillary to the tubing; otherwise the capillary-tubing interface will leak. We have reasonably good success using Norland NOA-76 or Mascot instant adhesive gel. The choice of glue depends on its adhesion to the glass capillary and the tubing, and a lack of reaction with the channel fluids. Use care to prevent the adhesive from seeping into the capillary channel and blocking it.
   2. Interface the tubing via a syringe to a micropumping system. Compounds with well-known refractive indices such as methanol, ethanol, and water can be used to determine the refractometric sensitivity of the device. This is the final test of a successful sensor. Pump each fluid, one at a time, into the capillary, making sure not to burst the adhesive seal between the capillary and the tubing (Figure 2c).
   3. Collect spectra with each liquid inside the capillary. Use an analyzer in the light path to distinguish between TE-polarized WGMs (analyzer parallel to capillary axis) and TM-polarized WGMs (analyzer perpendicular to capillary axis). There should be a shift in the wavelength of the WGM resonances, either TE or TM, with each different solution in the capillary. If there is no observable shift, the quantum-dot film is too thick and the WGMs do not sufficiently sample the channel medium. In successful samples we observe sensitivities typically between 5 and 15 nm per solution refractive index unit (RIU). Almost all the samples that do show WGMs demonstrate a measurable sensitivity; however, typically only a small fraction of prepared capillaries will show WGMs.

4. Data Analysis

1. Obtaining the fluorescence spectra Take a spectrum of the fluorescence of your sample. For biosensing applications, the channel surface has first to be functionalized for specific analytes. The surface of the QD film is essentially silica, so many surface modification recipes exist. Regardless of the application, the final step is the data processing and analysis.
   1. Achieving low detection limits requires measuring small spectral shifts- ideally the “shift resolution” should be significantly smaller than the nominal spectrometer resolution or pitch. Care must be exercised in the spectral processing due to this. In particular, on many imaging spectrometers the spectrum may not be projected perfectly horizontally onto the CCD; thus if, between analyses, the sample image drifts vertically on the slit, false spectral shifts may be obtained. Use whatever means are necessary to ensure that this doesn’t happen; e.g. use a calibration standard to determine the angle of the projected spectrum and correct for it, minimize sample drift, and ensure that the same CCD pixels are used to obtain all the spectra.
      An example spectral image is shown in Figure 3, where the modes appear as strong oscillations at locations corresponding to the channel walls. Use a Mathematica computer code (or what your group prefers) to import the spectral images, output the 1D spectral data, and perform curve fitting and Fourier analysis of the WGM shifts, as described below.
2. Curve fitting Determine the WGM peak wavelength to measure small spectral shifts due to analytes in the FCM channel. Fit a single mode to a function that describes the spectral shape – this is a common way to obtain the peak position. In the ideal case, this will be a Lorentzian function (with proper conversion from wavelength to frequency units via δλ = │-cδf/f²│ where c is the speed of light):
   
   In Eq. 1, A is a scaling parameter and f₀ is the central frequency. Unfortunately, FCMs are not an ideal case.
   1. In cylindrical cavities the WGMs are skewed toward higher frequencies, likely owing to the development of spiraling resonances (WGMs with a non-zero axial component of the wavevector).¹⁵ Lorentzian fits therefore perform poorly for determining the peak position. Unfortunately, there is no function that will fit a distribution of overlapping Lorentzians from the spiraling WGMs. In previous work ¹⁶ we suggested that a skewed Lorentzian ¹⁷ would give a better fit:
      
      Here, a and B are skewing parameters. As can be seen in Figure 4, Eq. 2 does give a better fit to the data than Eq. 1, but unfortunately it has no physical basis in the theory of WGMs.
3. Fourier shift analysis Alternatively, the data can be processed using a discrete Fourier transform, and the corresponding phase shifts measured from the Fourier spectrum. This method takes advantage of the periodicity of the whole spectrum, as opposed to using a single arbitrary WGM. It does not measure the peak wavelength position, but instead measures an overall shift of a given WGM spectrum with respect to an arbitrary reference spectrum.
   1. Use the phase difference Δφ for the high-power Fourier component that corresponds to the main WGM spectral oscillation to obtain the spectral shift. This corresponds to a real WGM frequency shift of:
      δf = Δφ(f_max – f_min)/(2πk),
      where f_min and f_max are the minimum and maximum frequency in the spectra. However, much information can be discarded if only the main component is used; additionally, truncation issues may make it difficult to determine which component is the main one. Often, the best results require some trial and error as to which Fourier components to select.
   2. The shift theorem instead uses all of the Fourier components. Accordingly, for a pure shift, each individual component is shifted proportional to k (with k being the component number). In other words, δφ_k = mk, where the proportionality m is a measure of the real shift. The total frequency shift is thus given by:
      δf = m(f_max – f_min)/(2π) .
      This requires m to be obtained from a linear fit to the phase differences ΔΦ_k for some or all of the Fourier components.
   3. For real data, the linear relation ΔΦ_k = mk will have uncertainty due to noise and background signal, which can have a significant effect in the low-power Fourier components. Thus, we recommend a weighted linear fit, in which the weight for each component is proportional to its power, in order to obtain the slope of the ΔΦ_k vs. k graph. The spectrum can be filtered around the main component prior to fitting, to remove both high frequencies (noise) and low frequencies (uncoupled fluorescence background). The frequency shifts from Eq. 4 are then converted into wavelength units.
   4. Unlike the case for curve fitting, a WGM “wavelength” is never obtained, but instead a wavelength shift is measured over the whole spectrum with respect to an arbitrary reference spectrum. The procedure is then repeated for every spectrum to be analyzed. The steps for this procedure are as follows:
      1. Convert the spectra into frequency units to ensure a constant free spectral range.
      2. Choose the reference dataset (i.e. the first WGM fluorescence spectrum) from which all shifts will be measured.
      3. Interpolate the spectra to obtain uniform frequency spacing.¹⁸
      4. Perform a discrete Fourier transform to obtain the power and phase components of each spectrum.
      5. Find the phase differences for all k components of a given WGM spectrum for which the shift value is desired, with respect to the reference spectrum.
      6. Find the phase shift using the phase difference of either the main Fourier component only, or a weighted linear fit to the selected components. This will give the phase shift δf or δλ between the WGM spectrum and the reference spectrum.
      7. The errors in the spectral shifts (the detection limit) can be measured by collecting repeated spectra for the same analyte. An uncertainty in the sensitivity can be obtained from the error in the weighted linear fits, if multiple components are used.

Repeat Steps 1-7 for every analysis. While this procedure sounds complicated, after the initial implementation the procedure is simple to automate, so that large data sets can be batch processed to find the shifts. We use a Mathematica code written specifically for this procedure, so that complete data sets can be batch processed “with the press of a button”. In principle, the spectral shifts can even calculated “live”, although we have not done this yet.