All‐Optical Thermometry with Infrared Emitting Defects in Diamond

Diamond color centers (optically active defects) can be used for all‐optical thermometry for non‐invasive and localized temperature measurements. The visible to near‐infrared photoluminescence of these defects is greatly attenuated in optical fibres and biological samples and therefore limits their use. A color center in Si‐doped diamond with emission coinciding with the O‐band and a major biological transparency window has recently been reported. It has a zero phonon line (ZPL) at 1221 nm and well‐resolved phonon side‐band features. In this work, a strong temperature dependence above 150 K is observed, allowing for accurate temperature measurements up to approximately 420 K. The temperature can be determined via spectral shifts or thermal broadening of the ZPL and through the intensity ratio between the ZPL and the phonon side‐band to a maximum temperature resolution of 0.57 K/ Hz$\sqrt {Hz}$ . Thermometry using these micro‐diamonds is demonstrated for both electronic and biological applications highlighting their versatility. The potential for further enhancements in sensitivity is discussed.


Introduction
Luminescence thermometry involves the measurement of local temperature variations with possible nanometer spatial resolution and has important applications in nanotechnology, DOI: 10.1002/adsr.202300086biotechnology and other fields. [1]Electronic devices and batteries may benefit from such diagnostics to understand durability, efficiency, and function. [2]In biology, luminescence thermometry can also provide insights into temperature sensitive biological phenomena such as reactions catalyzed by enzymes [3] and denaturation of protein behavior [4] to name a few.
Recently, optically active point defects in diamond, also known as color centers, have shown promise in nanoscale photoluminescence (PL) thermometry.The wide bandgap and high Debye temperature of diamond results in PL that is often bright, stable and with emission in a narrow spectral band.In addition, diamond does not contain any toxic elements making it compatible with biological applications. [5]Furthermore, its excellent thermal properties ensures intimate thermal contact with its environment.
Common color centers in diamond with temperature dependent PL are the negatively charged nitrogen-vacancy (NV), [6][7][8] the Ni complex [9,10] and a range of group-IV-vacancy defects including the negatively charged silicon vacancy (SiV − ), [11,12] Ge vacancy (GeV), [13,14] , and tin vacancy (SnV). [15]The temperature dependence may manifest as shifts or broadening in the zero phonon line (ZPL) component of the spectrum, changes in intensity or the intensity ratio between separate spectral components of the PL.Spin-based resonance methods are also possible with the NV center albeit at the expense of a more complex experimental setup. [16]or optical-based sensing in biological environments (especially in small animal models) the NIR-II window (1000 -1700 nm) is unquestionably superior to shorter wavelengths at which these color centers emit light.First, the visible to near-infrared spectral range can be strongly attenuated by both optical fibres and biological tissues. [17,18]This impacts the time required to collect the emitted light and hence affects the temperature resolution (as defined in [19] and measured in K/ √ Hz).Excitation with short wavelength light can also cause heating for some materials and auto-fluorescence of biological compounds.The latter can distort the detected spectral lineshape [20] but is virtually nonexistent for wavelengths longer than 1200 nm. [21]While absorption is not necessarily lower than in the NIR-I (700-1000 nm) window due to the vibrational bands of water, the reduction in the scattering coefficient with increasing wavelength [22] makes it possible to obtain higher resolution fluorescence images at larger tissue depths. [23,24]n this work, we consider a recently discovered color center in diamond that emits in the second near-infrared transparency window, 1000-1700 nm (NIR-II). [25]In this wavelength range absorption and scattering in biological tissue are significantly lower than in the spectral region below 1000 nm. [22,26]This defect center has a ZPL at 1221 nm (at a temperature of T = 0 K) and a number of distinct quasi-local vibrations that dominate the phonon sideband (PSB).These phonons have an energy of 42 meV suggesting a weak coupling to the diamond lattice.Visible spectra from these particles has also been reported previously showing strong PL from the SiV − , silicon-boron (SiB), and negatively charged substitutional nickel center (Ni − s ). [27]The strong intensity of the 1221 nm defect also suggests that it consists of one or more of the main impurities in the diamond and has been tentatively assigned to a SiV 2 :H (− ) defect. [25,28]It is also interesting to note that the PL lineshape is similar to the so-called 1.660 eV (746.9 nm) line with a phonon sideband energy of 59 meV found in Ni-doped diamond. [29]urther to previous work on this defect, we present a detailed analysis of the PL temperature dependence and consider a number of methods to extract the temperature from the PL line-shape.Potential applications as local temperature probes for electronic devices and biological specimens are also explored.

Results and Discussion
A schematic of the custom-built confocal microscope used to study the temperature dependence of the 1221 nm defect PL in Si-doped micro-diamonds is shown in Figure 1a.Further details are provided in the experimental section below.Figure 1b) shows the PL spectra at three different temperatures.These spectra are normalized to the intensity of the ZPL.The main features of the PSB of this defect are labeled as PSB1 and PSB2.A third phonon replica appears around 1400 nm but its intensity is much reduced and is not considered further here.The PL emission is stable and increases linearly with excitation power, characteristic of a large ensemble of color centers.
Additional peaks at shorter wavelengths are also observed.The peak at 1170 nm is attributed to the same 1221 nm defect system (marked with an asterisk in Figure 1b).The remaining peaks at 1110 and 1150 nm are associated with an as-yet unidentified defect.These peaks have intensities that vary independently of the 1221 nm defect when observed in different micro-diamonds.We also note that these shorter wavelength PL features do not appear in bulk diamonds that also contain the 1221 nm defect. [25]Diamond particles made from such material could be beneficial for reducing the background within the 1221 nm defect PL range but is not considered here.
Figure 1c shows a typical fit of the spectra with the sum of three Lorentzians, where x = ( −  i )/(Γ i /2).The values I i ,  i , and Γ i are the intensity, peak position, and full width at half maximum of the ith peak It consists of a 980 nm laser, which is directed onto a dichroic mirror (DM) and NIR optimized objective mounted on an XYZ piezoelectric stage.The PL is collected with the same objective and passes through a 1075 nm long pass (LP) filter.b) PL spectra of the Si-doped micro-diamonds in the NIR range, measured at temperatures of 5, 288, and 352 K.The zero phonon line (ZPL, 1221 nm), first (PSB1, 1275 nm), and second (PSB2, 1330 nm) phonon side-band features are indicated.Features at shorter wavelengths arise from a separate defect system, except for the 1170 nm feature identified with an asterisk, which is also a part of the 1221 nm system.c) Typical fit to data using Equation ( 1) and a linear background.c) the PSB1/ZPL intensity ratio.Data from ref. [25] is included for comparison.Lines are fits using the models discussed in the text.
(i.e., the ZPL, PSB1, and PSB2 peaks).A linear fit is employed to account for the background signal which most likely arises from the PL from other defects with ZPL at shorter wavelengths.This Lorentzian model provides an excellent fit over the full temperature range considered (5-420 K) and was employed throughout this work (see Figure S1, Supporting Information for a comparison with other models).
The temperature dependence of the PL line-shape was investigated over the 5-420 K temperature range.The variation in  i , Γ i and the intensity ratio, PSB1/ZPL, with temperature is shown in Figure 2.These will now be discussed in turn.
Generally, the ZPL red-shift is a consequence of lattice expansion and electron phonon coupling.For the case of the 1221 nm line, this shift can be described by the equation, The fit shown in Figure 2a (with energy scale indicated on the right axis) results in fitting parameters of  = (−2.7 ± 0.1) × 10 −10 meVK −4 and  = (−6 ± 2) × 10 −6 meVK −2 .Here, the T 2 term, which is related to the softening of bonds dominates the T 4 term, related to hard phonon modes. [30]Our data agree well with those reported previously in ref. [25] (crosses in Figure 2a).Equation (2) can also be conveniently solved for temperature.
A fit with a modified Varshni equation with a similar T 4 scaling (ΔE = (T 4 )/(T + ) 2 with  = 1.1 × 10 −6 eV.K −4 and  = 1.5 × 10 3 K) is also included for comparison as it has been employed previously to describe ZPL line shifts in diamond. [31]It can be observed here that  is of the same order of magnitude as the Debye temperature (2300 K for diamond).These values are also comparable to those obtained for the NV center in diamond with  = 5.3 × 10 −7 eV.K −4 and  = 725 K. [31] A strong thermal broadening is also observed for the 1221 nm ZPL and presented in Figure 2b.We find the temperature dependence to be well-described by the expression, [32] Γ = aT 3 + Γ 0 (3)   with the fitting parameters a = (2.24 ± 0.05) × 10 −7 nm K −3 and a zero-temperature width of Γ 0 = 3.81 nm.A similar T 3 dependence has been observed previously for both charge states of the NV center and the SiV − center. [32]The T 3 dependence has been attributed to defect-defect interactions [33] or the softening of the local phonon modes of the defect involved in the electronic transition. [30]At temperatures above 400 K there is an apparent decrease in the broadening, which is actually due to the growing uncertainties in the fit caused by heavy thermal quenching of the ZPL peak.At these temperatures the signal to noise ratio is much reduced (spectra included in Figure S2, Supporting Information).For our confocal system this temperature represents an approximate upper limit at which this PL can be used as an optical thermometer.
The thermal quenching is expected to be proportional to the empirical relation, (1 − C exp (ΔE a /k B T)) −1 where ΔE is the activation energy, k B is Boltzmann's constant, and C is a dimensionless constant.Since the 1221 nm defect has a well-resolved PSB, the intensity ratio, PSB1/ZPL can also be used to determine a temperature.The advantage of taking a ratio is that the measurement will be less susceptible to fluctuations due to excitation laser intensity and variations in the optical absorption of biological samples over time.The total PL intensity also varies depending on the number of defects that are addressed during measurement.Furthermore, the integrated intensity in the ZPL and PSB spectral bands may be collected simultaneously via appropriate band pass filters to determine temperature without any post-processing, although the accuracy then becomes more sensitive to background PL.
The intensity ratio, follows the Arrhenius equation, [34] A exp(−ΔE∕k B T) where A is the proportionality factor and B is an offset.For the fit in Figure 2c, A = 2.2 ± 0.4 and ΔE = (55 ± 6) meV.This is in good agreement with the ZPL -PSB energy separation, ΔE = 42.8 ± 1.9 meV. [25]The scatter in the intensity ratio data appears to be slightly greater than that observed for the ZPL position and width data.The intensity ratio determined with Equation (1) inherently contains more noise and is more susceptible to background signals.This will be discussed further with reference to Figure 3.
It is noted that the PL lineshape of small diamond particles is susceptible to variations.This is a common issue where the peak position and width suffer from inhomogeneous broadening caused by variations in the local strain around the defect due to proximity of the surface, fabrication damage, or impurity density fluctuations within the diamond lattice.The intensity ratio itself may also vary due to phonon confinement effects. [35]We further note that the 1221 nm defect is fairly robust against environmental changes such as pH (data included in Figure S3, Supporting Information) or magnetic noise.
With the temperature dependence of the 1221 nm PL established, the temperature resolution, , to changes in temperature is now explored.A series of spectra were continuously collected with a 1 s exposure time while the sample was at room temperature.The ZPL peak position, width and PSB1/ZPL intensity ratio were extracted from a fit using Equation ( 1) and converted to temperature (using the fits in Figure 2).The measured temperature over time is plotted for the 1000 measurements in Figure 3a-c with the corresponding histograms plotted in Figure 3d-f.The FWHM of these histograms include drifts in temperature over the course of the measurement and have values of (0.958 ± 0.006) K, (0.93 ± 0.01) K, and (2.20 ± 0.03) K, respectively, indicating that the peak position and width are the most accurate indicators of temperature using the 1221 nm defect.This is consistent with the general scatter of data observed in Figure 2c.The spectral noise density is determined with a fast Fourier transform of the experimental data in Figure 3a-c and plotted in Figure 3g.It shows no dependence on frequency as expected and has a geometric mean of 0.63, 0.57, and 1.36 K∕ √ Hz (dashed lines), respectively.The Allan variance (Figure 3h), also determined from the experimental data, shows a decrease in the detected RMS temperature with measurement time, proportional to 1/ (dashed line).This dependence is due to the uncertainties related to the fitting procedure as confirmed with simulations provided in Figure S4 (Supporting Information).The Allan variance reaches a minimum between 10-40 s before the long term drifts of the temperature during measurement start to become noticeable.A minimum value of around 0.014 K for the temperature determined with the ZPL position and width and 0.16 K for the intensity ratio is determined.
The temperature resolution is expected to follow the relation,  =  √ Δt|df ∕dT| −1 , where t is the measurement time,  is the uncertainty, and f is , Γ, or PSB1/ZPL intensity ratio. [36]The |df/dT| −1 term increases dramatically below 150 K as observed in Figure 2. At higher temperatures thermal quenching will cause the uncertainty to increase due to a loss in the signal to noise ratio (SNR) of the measured spectrum.Indeed, the temperature resolution determined from any of the parameters considered here is proportional to 1∕ optical thermometry using 1221 nm PL is best suited for temperatures between approximately 150-350 K.The upper limit can be extended further by improving the collection efficiency or brightness of the PL.
To investigate the potential for micro-scale thermometry, the Si-doped micro-diamonds were drop-cast onto a micro-heater fabricated on a Si platform, as shown in Figure 4a.Fabrication details are included in the Experimental Section below.Confocal maps of the surface a laser were then collected in and PL modes across the same region and are shown in Figure 4b,c, respectively.The higher reflectivity of the circuit can clearly be seen with micro-diamonds distributed over the entire field of view (both on and off the microheater).In Figure 4c the outline of the micro-heater is indicated by white dashed lines.An aggregate of bright micro-diamonds located on the micro-heater is circled.Assuming that the resistance for the micro-heater remains constant, and that all of the power applied to the circuit is dissipated as an increase in temperature, the applied current was used to control the temperature produced by the micro-heater.The PL spectra were collected first at room temperature and then as a function of an applied current between 0-39 mA.
The change in the PSB1/ZPL intensity ratio is shown in Figure 4d, as a function of the square of the applied current.The temperature corresponding to the PSB1/ZPL intensity ratio is indicated on the right axis.A linear fit (slope=(1.09± 0.07) × 10 −4 mA −2 and intercept=0.646± 0.007) is also shown, demonstrating that the change in the PSB1/ZPL ratio is directly proportional to the power applied to the micro-heater.The temperature variation is approximately linear over this PSB1/ZPL ratio range.This technique could be further extended to have mapping capabilities as previously demonstrated for nano-diamond arrays in ref. [36] for example.
To assess the suitability of the 1221 nm color center for deep tissue imaging in biological applications, the PL from microdiamonds were imaged through a phantom (Figure 5).This phantom is commonly used to mimic tissue-like materials since it has similar optical properties. [37]he micro-diamonds were first suspended in DI water and dispersed using sonication.The suspension was transferred to cuvette and immediately imaged.Sedimentation is expected over minutes for these micron sized particles, but this has no effect on the measurements performed here.Imaging was performed with an 808 nm excitation laser and the PL was collected with a NIR camera, through a 1200 nm longpass filter.The resultant map is shown in Figure 5a.A tissue phantom with a thickness varying from 5 -12 mm (from left to right in Figure 5b) was then placed on the cuvette and remeasured.The thicker part of the phantom is at the right-side end of the cuvette in Figure 5b where the PL is attenuation by around 60%.This attenuation plotted as the ratio between the PL intensity with (I P , Figure 5b) and without the tissue phantom (I NoP , Figure 5a) is plotted in Figure 5c.The dashed blue lines indicate the region over which the attenuation was determined.
Finally, the the PL attenuation versus tissue phantom thickness is presented in Figure 5d.A exponential fit using, exp (− t), with t the phantom thickness, gives an attenuation coefficient of  = 3.45 ± 0.15 cm −1 , which is comparable to reported values. [17]or a thickness of 10 mm the PL intensity drops by about half.Under these conditions, we may expect a temperature resolution degradation by a factor of √ 2. PL emission may be further improved by using a longer wavelength excitation source up to ≈1200 nm.

Conclusion and Outlook
The temperature dependence of the 1221 nm defect PL in Sidoped micro-diamonds was investigated in detail.The ZPL position, width and intensity were all considered for thermometry applications.The shift and width were found to have the greatest temperature resolution at 0.63, and 0.57 K∕ √ Hz, respectively.Although the intensity ratio of the PSB to ZPL was less sensitive, this metric may allow fast temperature sensing via spectral filtering given the well resolved features of the PL lineshape, without the need for a fitting routine and therefore have a shot-noise limited sensitivity.In the case of our current microdiamond material this was not considered given the presence of background PL from defects emitting at shorter wavelengths.Higher sensitivities may be obtained with material that is fabricated without these defects.
Demonstrations of local area temperature probes were explored for both electronic devices and biological contexts highlighting the versatility of these materials.This together with the convenient wavelength range of the diamond color center make this sensor a competitive technology for local temperature sensing.

Experimental Section
For all-optical NIR temperature sensing, high temperature-high pressure (HPHT) silicon-doped micro-diamonds were used.The size distribution of the particles is presented in Figure S5 (Supporting Information).The distribution was skewed with a mode, mean, and median of 89, 245, and 193 nm, respectively.However, the larger particles, around 1 μm in diameter, exhibited the brightest PL and tended to be studied in more detail (the PL versus particle size is presented in Figures S5 and S6, Supporting Information ).The particles were obtained from Ad ḿas Nanotechnologies and synthesized by Hyperion M&T. [25,27]s noted in earlier work, [27] these particles did not contain any noticeable amount of the nitrogen-vacancy defect but about 19 ppm of substitutional nitrogen impurities were detected.The silicon center was present to about ppm with smaller concentrations of the neutral charge state (0.06 ppm).Given that Ni was a common solvent catalyst used in diamond growth, around 1 ppm of the substitutional negatively charged nickel defect was also present.
The diamonds were dispersed in deionized water and subjected to ultrasonication to break down large aggregates.The final solution was dropcast onto a substrate for study.
PL spectroscopy and mapping were conducted using the custom-built confocal microscope with diffraction-limited spatial resolution schematically shown in Figure 1a.A 980 nm diode laser was employed for excitation filtered with a 980 nm notch and variable density filters.The laser power was typically kept below 1 mW.Laser heating became noticeable for powers of 5 mW and above.
The laser was directed through a NIR-optimized objective (Olympus, × 50, 0.65 NA IR LCPlan N) mounted on a three-axis piezo scanning stage (Physik Instrumente, PI P-545.xC8S).A 980 nm longpass dichroic mirror was used to filter the PL emitted by the sample, before further filtering with 980 and 1075 nm longpass filters.The PL was then focused into a 62.5 μm diameter core multimode fibre, which acted as the confocal pinhole.The fibre could be directed into either an InGaAs/InP photon counter (ID Quantique ID230) for confocal PL mapping or a InGaAs spectrometer (Princeton Instruments PyLoN-IR, IsoPlane SCT-320) for spectral analysis.For the optical reflection confocal maps, the 1075 nm longpass was replaced by a 1000/50 nm bandpass filter and the laser was heavily attenuated to avoid saturating the detector.
The temperature of the sample during measurement was controlled with either a Montana cryostat (4-300 K) or a Linkam THMS600 (>300 K).
The on-chip heater patterns were defined using photolithography on a 1×1 cm 2 silicon substrate with a 200 nm surface oxide.Ti and Au were electron beam evaporated to thicknesses of 5 and 100 nm, respectively.
The phantom was prepared from 1% intralipid (Sigma-Aldrich, 20% emulsion) as described in ref. [37].While still liquid, the phantom was poured into a right-angled triangular prism mold with a thickness increasing from 0 to 12 mm over a length of 22 mm.This was placed over a cuvette (Thorlabs, CV1Q035AE), which contained the microdiamonds suspended in water.A defocused 808 nm diode laser was used to illuminate the cuvette and the PL was captured with a Princeton Instruments NIRvana HS focal plane array fitted with a 1200 nm longpass filter.

Figure 1 .
Figure 1.a) Schematic of the confocal microscope employed in this work.It consists of a 980 nm laser, which is directed onto a dichroic mirror (DM) and NIR optimized objective mounted on an XYZ piezoelectric stage.The PL is collected with the same objective and passes through a 1075 nm long pass (LP) filter.b) PL spectra of the Si-doped micro-diamonds in the NIR range, measured at temperatures of 5, 288, and 352 K.The zero phonon line (ZPL, 1221 nm), first (PSB1, 1275 nm), and second (PSB2, 1330 nm) phonon side-band features are indicated.Features at shorter wavelengths arise from a separate defect system, except for the 1170 nm feature identified with an asterisk, which is also a part of the 1221 nm system.c) Typical fit to data using Equation (1) and a linear background.

Figure 2 .
Figure 2. The temperature dependence of a) the ZPL peak position, b) widthand c) the PSB1/ZPL intensity ratio.Data from ref.[25] is included for comparison.Lines are fits using the models discussed in the text.

Figure 3 .
Figure 3.The variation in temperature measured with a) the peak shift, b) the peak width, and c) the PSB1 to ZPL intensity ratio extracted from fits of spectra collected for 1 s with 3 mW of laser power.The corresponding histograms are shown in (d-f).g) The spectral noise density and h) the Allan variance determined from (a-c) as a function of averaging time of the measurement, .The dashed line indicates a slope proportional to 1/.

√Figure 4 .
Figure 4. a) Schematic of setup to test spectral responses to changes in temperature on-chip.Confocal maps in (b) reflectivity and (c) NIR PL modes of the same region.The dashed lines in (c) denote the perimeter of the heater.d) The temperature as determined with the ZPL position and width of the particle cluster circled in (c) as well as other particles at greater distances from the heater.The grey lines show linear fits to the data.

Figure 5 .
Figure 5. PL widefield images of micro-diamonds in a quartz cuvette (shown by white dotted lines) a) without and b) with a tissue phantom placed on top.c) The PL intensity ratio between (b) and (a) determined in the region indicated by the dashed blue boxes in (b) and (a).d) The intensity ratio versus the thickness of the phantom.A fit with exp (− t) is also shown giving an attenuation coefficient,  = 1.75 ± 0.06 cm −1 .