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Abstract
We study the use of nanopatterned silicon membranes to obtain optically-induced heating in water. We show that by varying the detuning between an absorptive optical resonance of the patterned membrane and an illumination laser, both the magnitude and response time of the temperature rise can be controlled. This allows for either sequential or selective heating of different patterned areas on chip. We obtain a steady-state temperature of approximately 100 °C for a 805.5nm CW laser power density of 66 µW/μm2 and observe microbubble formation. The ability to spatially and temporally control temperature on the microscale should enable the study of heat-induced effects in a variety of chemical and biological lab-on-chip applications.
© 2017 Optical Society of America
1. Introduction
The use of laser illumination to generate heat has led to valuable applications in several fields, such as nanochemistry [1], optofluidics [2] and biosensing [3, 4]. Noble metal nanoparticles have widely been used as nanoheaters, due to enhanced light absorption at their plasmonic resonances [5–7]. Lithographically-defined structures offer further advantages, including increased absorption strength, the ability to tune the resonance wavelength, and control over the heat pattern [5, 8].
Recent work by the authors [9] has introduced a dielectric alternative for laser-induced microheaters. In contrast to previous work on metallic particles and films, we use silicon photonic-crystal slabs as efficient heaters. We have shown that a highly absorptive optical mode can be obtained by patterning a 2D periodic array of holes inside a silicon slab and operating in the 700-1000 nm wavelength range, falling within the biological transparency window. Our silicon microheater features a much narrower resonance linewidth than plasmonic structures. As a result, heating occurs suddenly and rapidly after a controllable delay on the order of hundreds of microseconds, which we call the response time. In this article, we show that the narrow linewidth allows two additional capabilities: the ability to sequentially or selectively heat different regions on chip within a single laser spot.
This paper is organized as follows. We first explain the concepts of sequential and selective heating schematically and describe how the absorptive resonance and laser wavelengths should be chosen to achieve each function. We then design microheaters for operation in water and characterize their optical spectrum and time-dependent transmission experimentally. We use a opto-thermo-fluidic model to identify a signature of sudden heating in the time-dependent transmission curve. We then show that by varying the detuning between a single laser and the absorptive resonance of the device, the response time can be varied. For two devices with closely spaced resonances, corresponding to slightly different detunings from a single laser, we show that the devices heat up sequentially upon illumination. For two devices with widely spaced resonances, we show that by using two laser wavelengths, we can selectively heat either one device or the other. Lastly, we measure the steady-state temperature rise in our microheaters as a function of optical power and note that stable microbubbles appear at a temperature close to 100°C.
2. On-chip sequential and selective heating
The photonic crystal microheaters that we have introduced in Ref [9]. exhibit unique temperature behavior as a function of time. After the laser turns on, the temperature slowly increases and then suddenly jumps. This is a consequence of using a relatively narrow absorptive resonance for heating [9]. The elapsed time between laser turn-on and jump is called the response time. In this paper, we consider how our heaters could be used for either sequential or selective heating.
In the schematic of Fig. 1(a), different areas of a chip are patterned with devices with different resonance wavelengths. For concreteness, we show two device types (maroon and black circles) with corresponding resonances at λ1 and λ2. If the two devices are designed to have closely spaced resonances, the response times (τi) and temperature rises after the jump (Ti) will be different, when illuminated by the same laser. The two devices will thus heat sequentially, as illustrated schematically in Fig. 1(b). Alternatively, if the two devices are designed to have widely separated resonances, two different lasers aligned with these resonances could be used to selectively heat one device type or the other, as shown in Figs. 1(c) and (d).
Fig. 1 (a) Schematic of an array of microheaters. Maroon and black circles are devices with different resonance wavelengths, λ1 and λ2. (b) Sequential heating (closely-spaced resonance wavelengths): upon illumination by a single laser, the device type with resonant wavelength closer to the laser wavelength will heat up first. τ1 and τ2 represent the response times and T1, T2 the steady-state temperatures. (c-d) Selective heating (widely-spaced resonance wavelengths): illumination by a laser close to λ1 will predominantly heat devices with resonant wavelength at λ1 (c); illumination by a laser close to λ2 will predominantly heat those with resonant wavelength at λ2 (d).
In the remainder of this paper, we design and measure the prototypical microheater devices needed to realize this vision. In contrast to our previous paper, where we demonstrated microheaters in air, we design, characterize, and operate our heaters in water with an eye towards lab-on-chip applications.
2.1 Design and measurement of an absorptive resonance in water
We begin our experimental work by studying the time-dependent response of a microheater in water. Schematic diagrams of unpatterned and photonic-crystal slabs are shown in Figs. 2(a) and 2(b). Light is normally incident on the slabs. The photonic crystal is formed by patterning a square array of circular holes in the slab [10].
Fig. 2 (a,b) Schematic of a (a) plain silicon slab and (b) a photonic crystal microheater slab, each illuminated at normal incidence by a plane wave. (c) The corresponding measured transmission spectrum and FDTD fitted transmission and absorption spectra for the unpatterned slab. (d) Measured and CMT-fitted transmission spectra of the microheater slab; dotted blue and red lines show the laser wavelengths used in measurements. (e,f) Transmitted power from the unpatterned (e) and photonic-crystal (f) slabs, normalized to the incident power.
We fabricated the photonic crystal device using a silicon slab thickness of 340 nm, a lattice constant of 450 nm, and a hole diameter of 135 nm. The total patterned area is circular, with a diameter of 100 μm, and a 1.5 mm-thick fluidic channel filled with DI water was formed on top of the device. The normal-incidence transmission spectra of the photonic crystal, as well as that of an unpatterned slab of the same thickness in the same chamber, were characterized using a broadband white-light source and spectrometer (Ocean Optics USB 4000). A detailed description of the fabrication and measurements methods is given in the Appendix.
The measured transmission spectra are depicted by the black lines in Figs. 2(c) and 2(d). The unpatterned slab (Fig. 2(c)) has a nearly featureless transmission spectrum. The small slope in transmission results from Fabry-Perot effects; the Fabry-Perot fringe width is significantly larger than the wavelength range shown. The transmission spectrum of the photonic crystal slab (Fig. 2(d)) has a prominent Fano resonance near 970 nm. The origin of its characteristic, asymmetric lineshape is described in detail in Ref [10]; the resonance wavelength can be tuned by changing the photonic crystal hole size or spacing [11].
The calculated absorption spectra are shown in Figs. 2(c) and 2(d). For the unpatterned slab, we used the Lumerical finite-difference time-domain (FDTD) solver to calculate transmission and absorption. Figure 2(c) shows that the unpatterned slab has only about 0.5% light absorption for the given thickness and wavelength range. For the photonic crystal slab, we used the methods in the Appendix to fit the experimental transmission spectrum to the coupled-mode theory (CMT) model in Eq. (1) and obtained the fitting parameters of, , , and. Figure 2(d) shows that fitted and experimental results are in good agreement. Using the given fitting parameters, we obtain the absorption spectrum shown in Fig. 1(d). At resonance, the absorption is 45%. We may conclude that by patterning the slab, the absorption is enhanced by a factor of about 90.
2.2 Time-dependent optical resonance and heating
Due to heating, the optical transmission through the photonic crystal changes as a function of time. Using simulations, we can identify a signature of the response time for heating in the optical transmission.
Figures 2(e) and f show the experimentally-measured transmission as a function of time for the unpatterned and photonic-crystal slabs, respectively. In Fig. 2(e), the unpatterned slab shows a nearly flat transmission as a function of time after laser turn-on. This is true over the entire range of laser powers shown (93–212 mW). In contrast, for the photonic crystal slab, the transmission exhibits a downward peak at the highest power levels (Fig. 2(f)).
The origin of the peak can be understood by referring to Fig. 2d. From the absorption curve in Fig. 2(d), for a laser detuning of 6 nm from resonance (laser wavelength of 976 nm), nearly 10% of the incident power is absorbed at t = 0. Consequently, the slab starts to gradually heat up. Due to the positive thermo-optic coefficient of silicon, the transmission spectrum incurs a redshift, i.e. shifts to the right. As the spectrum shifts across the laser wavelength, the transmission decreases with time until it hits a minimum and then rises again. Figure 2(f) shows that the response time, defined as the time elapsed from turning the laser on to the sharp, upward jump in the transmission, can be controlled by varying the incident power. As the power is increased, the response time is shortened.
In previous work on similar microheaters operating in air, it was shown that the sudden rise in transmission corresponds to a sudden temperature rise [9]. Here we show that a similar conclusion applies in water. To model the temporal heating and absorption profiles, we use COMSOL Multiphysics to solve for the temporal heat distribution using coupled optical, thermal, and fluidic modules, following the methods in Refs [9]. and [2]. A detailed description of the simulation is given in the Appendix. The simulation incorporates a fluidic module to explicitly account for convective flow and convective cooling.
The blue curves in Fig. 3 correspond to the illumination of the photonic crystal by a 976 nm wavelength laser (6nm detuning from the photonic crystal resonance). Figure 3(a) shows the time-dependent transmission for 200 mW laser power. The shape of the curve is in good agreement with the measurements in Fig. 2(f). The corresponding temperature profile in Fig. 3(b) (blue line) shows that the initial smooth decrease in transmission with time corresponds to the gradual heating of the slab. After a response time of around 320 μs, sudden jumps in both transmission and temperature occur simultaneously. Figure 2(c) further shows that light absorption by the slab reaches its peak at the jump. This indicates that the sudden rise in transmission and temperature occur when the resonance wavelength shifts through the laser wavelength.
2.3 Effect of detuning and sequential heating
The red curves in Figs. 3(a), (b), and (c) show the effect of reducing the detuning between the laser wavelength and the resonance to 4 nm. For a smaller detuning, the transmission dip (Fig. 3(a)) and temperature jump (Fig. 3(b)) happen faster. This is because the closer the laser wavelength is to resonance, the higher the absorption is at t = 0, as shown in Fig. 3(c). From Fig. 3(b), we see that the temperature after the jump also varies with detuning. For smaller detuning, the temperature after the jump is smaller.
This result demonstrates the concept of sequential heating. For multiple microheater devices on the same chip, the response time will increase with detuning from the laser wavelength. For the results of Fig. 3(b), the device with 4 nm detuning will experience a temperature jump 270 µs sooner than the device with 6nm detuning.
The concept of sequential heating can be extended to multiple device types and arrangements. While Fig. 2(a) shows two device types in a checkerboard pattern, three or more device types can easily be designed by varying the photonic crystal hole size and spacing [11]. The device types can be arranged in arbitrary patterns, whether periodic or aperiodic, across the area of the chip, for customized sequential heating patterns.
The effects of detuning can also be demonstrated using a single device and two different wavelength lasers. In the experiment of Fig. 4, we achieved detunings of 4 nm and 6 nm by using 974 nm and 976 nm lasers and the device of Fig. 2(b). The results show that the response time can be increased by increasing the laser detuning, in agreement with simulations.
Fig. 4 Experimental transmitted power through the photonic-crystal microheater, normalized to the incident power of 201 mW. Detunings of 4 nm and 6 nm are achieved using laser wavelengths of 974 nm and 976 nm, respectively.
2.4 Selective heating
Our microheaters also allow for selective heating of particular regions on chip. To demonstrate this idea, we designed two devices with resonances at widely separated wavelengths. We will call the device measured in Figs. 2 and 4 above device 1; it has a resonance near 976 nm. We fabricated a second photonic-crystal device with a lattice constant of 430 nm and a hole diameter of 129 nm, which we will call device 2. It is designed to have a resonance near 805.5 nm.
The measured spectra of the two devices are shown in Figs. 5(a) and (b) in the spectral regions near the two laser wavelengths. Device 1 has a strong resonance near 976 nm (blue, dashed line in Fig. 5(a)) and a nearly flat transmission spectrum near 805.5 nm (green, dashed line in Fig. 5(b)). Device 2 has a strong resonance at 805.5 nm and a nearly flat response at 976 nm.
Fig. 5 (a,b) The measured spectra of the two fabricated devices around (a) 805nm and (b) 970nm. Inset shows the proposed use of these structures on a larger chip. (c,d) Experimental transmitted power through both devices, normalized to the incident power of 140 mW using laser wavelengths of 805.5 nm (green) and 976nm (blue).
We characterized the time-dependent transmission for each device for laser wavelengths of 976 nm and 805.5 nm. The laser power used was 140mW, and the spot size of each laser was 10 µm. The results are shown in Figs. 5(c) and 5(d). Device 1 shows a transmission dip, indicating heating, when illuminated near 976 nm (blue line, Fig. 5(c)). We note that the “noisy” transmission observed at later times for 976nm (blue line) may be associated with bubble formation, discussed below. For device 2, illumination at 805.5 nm yields a strongly time-dependent response, indicating heating. Due to the alignment of the laser at the center of the resonance (as shown in Fig. 5(b), Device 2), the spectral shift results in a time-dependent transmission rise, rather than a dip. Each device therefore heats up in response to its own laser wavelength. When illuminated with the opposite device’s laser wavelength, the time-dependent transmission is flat (green curve, Fig. 5(c) and blue curve, Fig. 5(d)). The steady-state temperature rise of device 2 is measured in the next section.
These results indicate that by varying the hole size and/or spacing of the photonic crystal, microheaters can be designed that respond selectively to a particular laser wavelength. In this measurement, the devices were fabricated on different chips. We envision that by incorporating different photonic-crystal designs on a single chip, the spatial heating profile could be written in to the nanopatterned design. Lasers at two different wavelengths λ1 and λ2 could be used to selectively heat the corresponding microheaters.
2.5 Temperature measurement and bubble generation
In the sections above, we used the time-dependent transmission as a signature of heating in order to measure the response time. We can also measure the steady-state temperature via the steady-state shift in the optical spectrum. We first perform a calibration experiment. We use a Thorlabs temperature-controlled lens tube to heat device 2 to known temperatures and measure the spectral shift as shown in Fig. 6(a). The actual temperature of the device is measured using a Seek Thermal Compact camera as shown in Fig. 6b. The spectral shift is plotted with temperature in Fig. 6(c) (red curve). We also performed FDTD simulations to calculate the spectral shift with temperature, using the temperature-dependent refractive indices of glass, silicon and water [12–14]. The results are plotted by the black line in Fig. 6(c) and show good agreement with experiment.
Fig. 6 (a) Measured spectra (monitored around 940 nm) of device 2, under electric heating using a Thorlabs temperature-controlled lens tube, (b) temperature measurements of the sample using the Seek Thermal Compact camera, and (c) experimental and simulation of spectral shift for elevated temperature up to 100°C.
We next measure the spectral shift under CW 805.5 nm laser illumination using a spectrometer (Ocean Optics USB 4000). A Thorlabs - NF808-34 notch filter was used to attenuate the laser power, and the spectrum was monitored around 940nm. As shown in Fig. 7a, the device spectrum redshifts with increasing power. Using the simulation curve in Fig. 6c, the temperature rise was plotted for each power in Fig. 7b. From the data, we conclude that the device is heated by 0.58 K/mW of incident laser power.
Fig. 7 (a) Measured spectra of device 2 as a function of laser power for CW illumination at 805.5 nm. Inset is a microscopic image of the bubble (black circle to the left) and an unilluminated device of 100 µm diameter (grey circle to the right). (b) Sample temperature versus illumination power (error bar determined by experimental resonance linewidth).
When our device is heated beyond 98.7 ± 4°C vapor microbubbles are formed, as shown in the inset of Fig. 7a. Due to light scattering by the bubble, the transmission spectrum magnitude decreases when the power is increased beyond 127 mW. While bubbles are not a main focus in this paper, photothermal microbubble generation has several applications in photoacoustic imaging [15–17], microparticle trapping [18–21], and lab-on-chip devices [22]. The proposed microheaters could offer the ability to control the optical power threshold of the bubble formation. Namely, devices 1 and 2 shown in Fig. 5 have 93 mW and 127 mW bubble thresholds, under 976 nm and 805.5 nm laser excitation, respectively, with all other conditions kept the same. Both the resonance quality factor and detuning of the laser contribute to this shift in the bubble threshold.
3. Conclusions
We have introduced and demonstrated an all-silicon, laser-activated microheater operating in water. Our approach enables sequential or selective heating of different areas on-chip. The microheater is based on a photonic crystal slab, which is designed to resonantly enhance the absorption at a particular wavelength. Using a coupled opto-thermo-fluidic model, we simulated the temporal response of our microheater in water. The simulations show that the temperature experiences a sudden jump some time after the laser is turned on. The jump results from the shift of the photonic crystal resonance through the laser illumination wavelength. Defining the response time as the delay between laser turn-on and temperature jump, we show that the response time and maximum temperature rise can be “programmed in” to the device via design of the nanopattern.
We have demonstrated time-dependent heating experimentally via measurement of the optical transmission. Changes in transmission serve as an optical signature of the temperature rise. We have further demonstrated thermal generation of microbubbles at approximately 100 °C.
The controllable, time-dependent temperature response of our device opens the door for spatial and temporal control of heat on the microscale. We anticipate a variety of applications in biology and nanochemistry. Intriguingly, the heating rates in our devices can be up to two orders of magnitude higher than for PCR [23, 24], suggesting, for example, the possibility of microscale control of genetic replication. Moreover, the silicon platform we use will enable facile integration into larger microsystems based on CMOS technology and fabrication processes.
4 Appendix: methods
Device fabrication: We followed the fabrication procedure in Ref [25]. and transferred the silicon membrane to a 1.6 mm-thick, ground and polished glass disc. A 1.5 mm-thick fluidic chamber filled with water was created on top of the device, using a lens-holder with a rubber O-ring as a sidewall pressed against an identical glass disc on the top of the chamber.
Measurement methods: To measure the time-dependent optical transmission, we illuminated the slabs with a near-infrared, 3S Photonics, CHP1999 laser operating at 976 nm. The laser is passed through a 19 mm lens and focused through an objective onto the sample. This results in a Gaussian beam with a spot size of 30 μm on the sample. The laser intensity is modulated using a laser diode controller (Thorlabs) using a square pulse with modulation frequency of 5 Hz and 0.3% duty cycle. The rise time of the laser pulse is approximately 1 μs. The transmitted beam collected by the objective is fed to a fiber-coupled trans-impedance amplifier (Thorlabs) with a response time on the order of a few picoseconds.
Simulation setup: We simulated an axisymmetric structure consisting of a silicon disk of thickness 340 nm with a 5 μm water layer on top. The simulation cell has a radius of 0.5 mm. We take the bottom surface of the disk to be thermally insulated, and the top boundary of water to be an open fluidic and thermal boundary, to mimic the much taller fluidic channel of 1.6mm thickness used in experiment. The sidewalls of the disk and water are fixed at room temperature. A heat source with a Gaussian spatial profile (full width at half maximum of 30 μm) is positioned at the center of the disk. To approximately model the effect of the holes, we use the same modified silicon parameters as in Ref [9].
Opto-thermo-fluidic model: We use Comsol Multiphysics to solve for the temporal heat distribution using coupled optical, thermal and fluidic modules, following the methods in Refs [9]. and [2].
The transmission spectrum is given by coupled mode theory (CMT) [26] as
where is the operating frequency of the laser, is the decay rate of the resonance due to radiation loss, is the decay rate due to material absorption loss, and and are the direct transmission and reflection coefficients, respectively. The frequency of the guided resonance mode, depends on the time-dependent temperature of the slab as
where is the initial frequency of the guided resonance mode (e.g., the frequency at room temperature, in the absence of laser heating), is the thermo-optic coefficient of silicon, and is the refractive index at room temperature (). Since silicon has a positive thermo-optic coefficient, the frequency in Eq. (2) goes down as the temperature increases in time, redshifting the spectrum.
The temporal temperature distribution inside the photonic crystal slab is governed by the 3D heat diffusion equation:
where is the thermal conductivity of silicon, its density, and its specific heat capacity at constant pressure. The heat source is determined by the optical power absorbed at resonance, which from coupled mode theory is [27]We neglect the absorption in water, since the absorption coefficient is 3 orders of magnitude lower than that of silicon at 976 nm; thus. Hence, the heat distribution in the surrounding water is governed by the following equation [28]:
where is the fluid velocity, is the thermal conductivity of water, its mass density, and its specific heat capacity at constant pressure. Due to the temperature increase that takes place within the fluid around the structure, the fluid experiences some reduction of its mass density, which yields upward convection. The general equation governing the fluid velocity profile is the Navier Stokes equation [28]:Where is the viscosity of water and is the force per unit mass due to temperature non-uniformity. This thermal force can be estimated using the Boussinesq approximation [28]. This approximation accounts for the temperature dependence of the mass density by adding an external buoyancy force term that is dependent on the temperature distribution;where g is the gravitational acceleration, β the dilatation coefficient of water, is the temperature increase, and is the upward unit vector in the z direction.At each time step, we use a COMSOL model including coupled heat transfer in solids/ fluids and laminar flow to solve eq. 2 through eq. 5 self-consistently for , , and, given the parameters , and, using methods similar to Refs [2]. and [9]. Note that throughout the COMSOL simulation, we assume implicitly that and are functions of position ; to obtain , we use the values at the center of the microheater .
Acknowledgment
A.M. was supported by an Army Research Office PECASE Award under Grant W911NF0910473, and R. B. was supported by a National Science Foundation CAREER Award under Grant No. 0846143. Computational resources were provided by the University of Southern California Center for High-Performance Computing and Communications (www.usc.edu/hpcc).
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