Optimal architecture for diamond-based wide-field thermal imaging

Thermal imaging, enabling fast and accurate monitoring of heat distribution at sub-micron scales, has become decisive in a broad range of fields from exploratory research up to prototyping and manufacturing in nanomaterials science, nanoelectronics, nanophotonics, or nanochemistry. Various detection schemes are being explored in this respect.¹ These schemes include tip-enhanced infrared or Raman thermometry,^2,3 scanning thermal microscopy (SThM),^4,5 SQUID-based nano-thermometry,⁶ or nanoscale fluorescence thermometry, making use of fluorescent nanoparticles either dispersed on the probed sample or attached to the tip of an atomic force microscope (AFM).⁷ However, none of these techniques can simultaneously provide fast, sensitive (in the sub-K/$Hz$ range), and quantitative thermal imaging with a sub-micron spatial resolution under ambient conditions.

Nitrogen-vacancy (NV) centers in diamonds have garnered growing attention in the last decade, notably because their electron spin resonance can be detected optically⁸ and strongly depends on various external perturbations. This dependence has enabled the implementation of highly sensitive NV-based quantum sensors capable of locally probing several physical quantities including strain^9,10 and electric^11,12 and magnetic fields.^13–15 The sensing capabilities of the NV center have also been extended to thermometry,¹⁶ building on the variation of the zero-field splitting parameter of its electron spin sublevels with temperature.¹⁷ A thermal sensitivity in the range of 100 mK/$Hz$ was demonstrated for single NV centers hosted in nanodiamonds¹⁸ and can reach values down to few mK/$Hz$ while using NV centers with long spin coherence times embedded in ultrapure bulk diamond samples.^16,18–20 Besides building on the temperature dependence of spin resonance, temperature sensing with NV centers in diamonds can utilize the temperature dependence of their optical response such as the Debye–Waller factor, zero-phonon line, or anti-Stokes photoluminescence wavelength.^21,22 These all-optical schemes have also been extended to other point defects in diamonds, e.g., SiV, GeV, or SnV colored centers.^23–25 Last but not least, the temperature sensitivities of NV centers can be pushed down to few tens of μK/$Hz$ by relying on a transduction of temperature gradients on magnetic fields probed by their electronic spins.^26,27

These thermal sensing modalities can be exploited for thermal imaging. A first strategy consists in grafting a NV-doped nanodiamond at the apex of either an optical fiber or an AFM tip, which is scanned above the surface of the sample to be probed.^28–30 The spatial resolution of thermal imaging is then ultimately limited by the nanodiamond size. Such a scanning-NV configuration however requires a complex experimental apparatus and suffers from long acquisition times. In addition, the thermal sensitivity is impaired by the short spin coherence time of NV centers hosted in nanodiamonds. Another approach makes use of stationary NV centers in a wide-field detection scheme.^18,19,31 Although the spatial resolution is then fundamentally limited by diffraction (∼500 nm), this approach offers faster acquisition times and a simple experimental configuration. To date, wide-field thermal imaging has been solely demonstrated with NV-doped nanodiamonds directly dispersed on the surface of a target sample.

In this paper, we investigate whether this method could be extended to NV centers hosted in an ultrapure bulk diamond sample in view of improving the thermal sensitivity, thanks to the improved NV spin coherence time. To this end, we first experimentally analyze the temperature distribution induced by a micron-sized heat source deposited on the surface of a bulk diamond material. The results are then compared to numerical simulations performed for a bulk diamond, a 100-nm thin diamond membrane deposited on quartz, and nanodiamonds directly dispersed on the heat source. This study shows that any detection scheme based on bulk diamonds is highly perturbative due to the large thermal conductivity of diamonds. Dispersions of nanodiamonds, in the vicinity of a heat source, appear as the most relevant configuration for invasive-less wide-field thermal imaging, while thin diamond membranes could provide an effective option for thermal imaging at microscale.

The heat source here consists of an array of gold nanoparticles illuminated at their plasmonic resonance wavelength.^32,33 We consider 10 × 10 µm² assemblies of gold cuboids with the thickness t = 40 nm, width w = 60 nm, and length l ranging from 90 nm to 210 nm. As illustrated in Fig. 1(a), the metallic cuboids are arranged in periodic two-dimensional rectangular patterns, each with constant cuboid dimensions and with a side-to-side distance of 100 nm along the cuboid’s width direction and of 1, 6 × l along the cuboid’s length direction. These thermoplasmonic arrays were fabricated on two substrates, namely, an ultrapure electronic grade diamond substrate grown by chemical vapor deposition (element 6) and on a quartz substrate used as a reference. The process combines an electron-beam lithography step, the deposition of 5 nm of titanium and 35 nm of gold, followed by a lift-off. Under continuous near-infrared laser illumination at their absorption resonance, the thermoplasmonic structures give rise to a delocalized temperature distribution, fairly uniform throughout the array.^33,34 The increase in temperature induced by the array is then governed, inter alia, by the absorption cross-section σ_abs of each cuboid, the number N of cuboids forming the array, and the intensity $I$ of the infrared laser illumination.

Temperature variations induced by the thermoplasmonic structures were imaged using quadriwave lateral shearing interferometry³⁵ [see Fig. 1(b)]. This technique uses a wavefront analyser to indirectly provide temperature distributions with a diffraction-limited spatial resolution and an accuracy of about 1 K. It relies on the temperature-dependent refractive index of a surrounding water layer covering the thermoplasmonic arrays. The heat generated by the arrays results in a steady-state temperature distribution, which provokes modifications in the refractive index in the water. These spatial variations in the refractive index result in a wavefront distortion of a white light source illuminating the sample in a Köhler configuration. Such local distortions are recorded on a wavefront analyser, providing spatially-resolved optical path difference (OPD) maps. A typical OPD map recorded for a thermoplasmonic array deposited on quartz is shown in Fig. 1(c). Post-processing of these data then enables the retrieval of the spatial distribution of the heat power density (HPD) [Fig. 1(d)] and the spatial temperature variations δT [Fig. 1(e)]. This processing relies on a modeling of heat diffusion based on Green’s function formalism.³⁵ 

The plasmonic resonance wavelength of the heating structures varies with respect to both the substrate and the shape of the metallic cuboids. In order to obtain a reliable comparison between the heat generated on an ultrapure diamond substrate and on a quartz substrate, experimental conditions leading to similar absorption cross-sections of the thermoplasmonic arrays were carefully selected. As explained in detail in Ref. 35, the absorbed power P_abs can be inferred through a spatial integration of the HPD image. The absorption cross-section is then given by $σabs=Pabs/(I×N)$⁠, where $I$ is the infrared laser intensity (power per unit area), and N is the number of cuboids forming the thermoplasmonic array. Similar absorption cross-sections, σ_abs ∼ 2 × 10⁴ nm², were found for (i) 60 × 120 nm² cross-section cuboids illuminated at 760 nm on the quartz substrate and (ii) 60 × 90 nm² cross-section cuboids illuminated at 710 nm on the diamond substrate.

Under such experimental conditions, thermal images were recorded while increasing the absorbed infrared laser power P_abs. As shown in Fig. 2, the maximum local heating δT_max evolves linearly with P_abs for both substrates, as expected. However, for equivalent absorption powers, the heating induced by the thermoplasmonic array on the quartz substrate is much higher than the one observed on the diamond substrate. A difference of two orders of magnitude is observed, with a maximum heating per absorbed power of 38 K/mW and 0.2 K/mW for quartz and diamond substrates, respectively. This discrepancy results from the large difference in thermal conductivity κ of the substrates. While κ is about 1.4 W/(m K) in quartz, it reaches values almost three orders of magnitude higher in diamonds, with κ = 1000–3300 W/(m K) depending on its purity. Consequently, while heat dissipation in a quartz material is rather low, heat transfer in diamonds is highly efficient. As such, the diamond substrate acts as a thermal sink that cools the heat source.³⁶ Any architecture of thermal imagers based on bulk diamonds will thus be perturbative: the measured temperature, though recorded with a high sensitivity, will be the temperature of the heat source however significantly cooled by the diamond substrate hosting the NV centers probes and down to temperatures that may be too small to be measured. This precludes the use of bulk diamond samples for wide-field thermal imaging.

In order to reduce heat dissipation in bulk diamonds, one alternative approach could be to rely on a thin diamond membrane bonded on a low thermal conductivity substrate, such as quartz. Figure 3 gathers finite-difference time-domain (FDTD) simulations based on heat conduction modeling of temperature increase as a function of heat power for three different diamond-based architectures: (i) a bulk diamond, (ii) a 100-nm thin diamond membrane on quartz, and (iii) nanodiamonds dispersed on the heat source. The achieved temperature increase in the diamond–quartz heterostructure is much higher than the one predicted for bulk diamonds and gets closer to the one expected on quartz. This stems from the strongly reduced effective thermal conductivity of the diamond–quartz heterostructure, in which the effective heat release through diamonds occurs no longer in three but in two dimensions. In view of applications for thermal imaging, this partly lifts the limitations encountered with bulk diamonds. However, the heat diffusion throughout the diamond layer would still yield a lateral spreading of temperature distribution over a length scale of a few μms, thus limiting the spatial resolution.

Conversely, the temperature of nanodiamonds exactly matches the one expected on the low thermal conductivity quartz substrate (see Fig. 3), with a homogenous temperature distribution across the entire nanodiamond volume. This thermalization of the nanodiamonds with the local thermal bath, combined with the constant temperature profile within the nanoparticle, allows for a non-perturbative measurement of the heat source temperature, despite the randomness in the position of the NV spin sensor inside the nanodiamond.

These results enable us to specify the optimal configuration for NV-based wide-field thermal imaging. Although bulk diamond imagers would provide the highest temperature sensitivity due to increased spin coherence times, efficient heat transfer in such high thermal conductivity material unavoidably leads to significant cooling of the sample to be probed, thus preventing any effective temperature mapping at sub-micron scales. Engineered heterostructures stacking thin diamond membranes over low conductive substrates feature significantly reduced heat diffusion, providing a valuable option for imaging at microscale. The most relevant configuration for non-invasive wide-field thermal imaging yet consists of random or ordered dispersions of diamond nanostructures on the hot sample to be probed. These thermal imagers may bring competitive imaging modalities with implications in the fields of micro- and nano-electronics, nanoplasmonics, or chemistry at nanoscale.

The authors acknowledge financial support from the French Research National Agency (through the ANR THESEUS Grant), the Center National de la Recherche Scientifique (through the CNRS TEMPO Grant), and the European Commission (through H2020 program’s ASTERIQS, TSAR, and ThermoQuant grants). This work was also partly supported by the French RENATECH network.