We demonstrate an all-optical thermometer based on an ensemble of silicon-vacancy centers (SiVs) in diamond by utilizing the sensitivity of the zero-phonon line wavelength to temperature, Δλ/ΔT=0.0124(2) nm K–1 [6.8(1) GHz K–1]. Using SiVs in bulk diamond, we achieve 70 mK precision at room temperature with a temperature uncertainty σT=360mK/Hz. Finally, we use SiVs in 200 nm nanodiamonds as local temperature probes with 521 mK/Hz uncertainty and achieve sub-Kelvin precision. These properties deviate by less than 1% between nanodiamonds, enabling calibration-free thermometry for sensing and control of complex nanoscale systems.

Luminescent thermometers1 utilize the sensitivity of optical transitions to temperature in order to probe thermal variations on the nanometer scale. Although these systems have lower sensitivity than, for example, scanning probes,2,3 they are non-invasive, enabling a broad class of experiments including in vivo biological measurements.1,4 Current platforms for luminescent thermometry are often limited by intrinsic emitter properties: broad inhomogeneous distributions,5,6 weak transition dipoles,3,7–9 photobleaching,10,11 and small Debye-Waller factors.12 These properties result in thermometers which require long acquisition times5,8,9,12 and typically require individual calibration10–14 in order to measure temperature variation.

Diamond based platforms have proven to be versatile for a wide range of sensing applications. The diamond crystal is chemically inert, making it naturally robust to extreme environments, and biologically compatible, capable of being located within nanometers of the sensing volume. Nitrogen vacancy color centers (NVs) in diamond, for example, utilize microwave and optical control to measure temperature12,14 (as well as magnetic,15,16 electric,17 and strain18 fields) with nanoscale resolution and low uncertainty. While thermometry with NVs features high sensitivity, it requires simultaneous optical and microwave control, and due to inhomogeneous broadening, each emitter must be individually calibrated before use as a thermometer. The negatively charged silicon-vacancy color center (SiV) in diamond has recently emerged as a superior optical emitter, belonging to a family of interstitial defects whose favorable optical properties arise from inversion symmetry.19–21 SiVs have stable optical properties featuring bright, narrowband emission, allowing for fast, accurate measurements which are consistent between emitters. This means that SiVs can be used as high-resolution, non-photobleaching thermometers without the need for calibration. In this letter, we take advantage of the SiV's zero-phonon line (ZPL) frequency, linewidth, and quantum efficiency temperature sensitivity to realize all-optical thermometry with SiV ensembles both in bulk and in nanodiamonds.

Following previous studies,22–25 we first focus on the photoluminescence (PL) spectrum of an ensemble of SiVs in bulk diamond at room temperature [Figs. 1(a) and 1(b)]. We fit the ZPL spectrum26,27 and use the ZPL peak position as the thermometry signal (PL thermometry, supplementary material). Although the SiV ZPL frequency shifts non-linearly from 5 K to room temperature,22–25 for a small range (295±5K), it deviates by less than 1% from the linear approximation [Fig. 1(c)]. We measure the sensitivity of the peak wavelength to temperature, Δλ/ΔT=0.0124(2) nm K−1 [6.8(1) GHz K−1], consistent with previous low-resolution measurements.22–25 The origin of this shift is thermal lattice expansion which reduces the orbital overlap between dangling carbon bonds.24 

FIG. 1.

SiV PL thermometry in bulk diamond. (a) Diamond with a high SiV density is excited off resonance, and SiV fluorescence spectra are measured (supplementary material). (b) Typical spectra at 15 °C (blue) and 29 °C (red). The ZPL peak shifts to the red at higher temperatures. (c) Peak position as a function of temperature. The peak sensitivity to temperature is Δλ/ΔT=0.0124(2) nm K–1 [6.8(1) GHz K–1]. Error bars (±1σ) for this measurement are the size of the data points. (d) Temperature uncertainty (σT) of the thermometer as a function of integration time. Solid line is a fit to shot noise 1/Nph. The uncertainty is 360 mK/Hz.

FIG. 1.

SiV PL thermometry in bulk diamond. (a) Diamond with a high SiV density is excited off resonance, and SiV fluorescence spectra are measured (supplementary material). (b) Typical spectra at 15 °C (blue) and 29 °C (red). The ZPL peak shifts to the red at higher temperatures. (c) Peak position as a function of temperature. The peak sensitivity to temperature is Δλ/ΔT=0.0124(2) nm K–1 [6.8(1) GHz K–1]. Error bars (±1σ) for this measurement are the size of the data points. (d) Temperature uncertainty (σT) of the thermometer as a function of integration time. Solid line is a fit to shot noise 1/Nph. The uncertainty is 360 mK/Hz.

Close modal

To estimate the precision of SiV thermometry, we measure uncertainty in the peak position as a function of integration time at a fixed temperature [Fig. 1(d)] and extract a temperature uncertainty σT=360mK/Hz, giving 70 mK temperature precision after 50s integration time. This measurement uncertainty follows the shot-noise limit 1/Nph [Fig. 1(d)], suggesting that the precision can be improved by increasing photon collection rates from the sample, either by increasing SiV density28,29 or by improving collection efficiency. The stability of this thermometer is also measured by keeping the sample stage at a fixed temperature (as measured by an external temperature sensor) and recording the peak position every minute for 2 h. In this way, we extract a repeatability uncertainty of 152 mK for a 10 s integration time, which is comparable to the measured temperature uncertainty for the same integration time.

While measurements in bulk confirm that SiVs can be used for thermometry, many applications require localized probes for in situ measurements. To address this, we next demonstrate nanometer-scale thermometry using SiV-containing nanodiamonds. For these experiments, we use 200(70) nm high-pressure high-temperature nanodiamonds grown with silicon included in the growth chamber (supplementary material). The count rates in these nanodiamonds are 200–400 kHz, suggesting that they contain fewer SiVs (<10) in the probe volume than for the bulk diamond (> 10 MHz, ∼100 SiVs). With a smaller photon flux, longer integration times are needed in order to achieve the same precision. For our spectrometer CCD (Synapse BIUV), we have a readout noise of 10 counts per bin and a total of 1500 bins, which limits the detection bandwidth to 0.6 Hz for 10:1 signal to noise using the measured count rates, making the measurement sensitive to slow drifts. To overcome this limitation, we introduce a different thermometry technique based on photoluminescence excitation (PLE) spectroscopy, the near-resonant excitation of the SiV ZPL transition.

For PLE thermometry, instead of exciting SiVs off resonance and measuring the ZPL spectrum, we excite on resonance (738 nm at room temperature) and collect emission into the phonon sideband, effectively probing the absorption cross-section of the ZPL as a function of temperature. Physically, increasing the temperature red-shifts the ZPL peak and reduces the peak intensity when the SiVs are excited below saturation, caused by non-radiative decays from the excited state becoming more favorable at higher temperatures.24 Both of these effects contribute to a reduced absorption cross-section (blue) of the resonance peak. We therefore excite the nanodiamonds at an experimentally determined wavelength (λp) of maximum contrast [Fig. 2(a)]. For this technique, we use an avalanche photodiode (APD) with 50 dark counts per second, giving a detection bandwidth of 200 Hz, much larger than PL thermometry for the same signal to noise. This high-bandwidth measurement also enables lock-in techniques (described below), which further mitigate slow experimental drifts.

FIG. 2.

SiV PLE thermometry with nanodiamonds (a) Scheme for PLE thermometry: Excite SiVs near resonance at λp and measure PLE fluorescence as a function of temperature (ΔI). (b) ∼200 nm nanodiamonds are drop-cast onto a gold targeting grid. Heat is applied via a green laser at position rh, which is probed via the nanodiamond at position rp. (c) Lock-in fluorescence contrast vs. temperature for PLE thermometry. The heating laser power Ph is modulated, and PLE fluorescence is measured. The signal sensitivity to temperature is ΔII0/ΔT=1.3(1)%/K with an uncertainty of 521mK/Hz. ΔT=TPh0TPh=0.

FIG. 2.

SiV PLE thermometry with nanodiamonds (a) Scheme for PLE thermometry: Excite SiVs near resonance at λp and measure PLE fluorescence as a function of temperature (ΔI). (b) ∼200 nm nanodiamonds are drop-cast onto a gold targeting grid. Heat is applied via a green laser at position rh, which is probed via the nanodiamond at position rp. (c) Lock-in fluorescence contrast vs. temperature for PLE thermometry. The heating laser power Ph is modulated, and PLE fluorescence is measured. The signal sensitivity to temperature is ΔII0/ΔT=1.3(1)%/K with an uncertainty of 521mK/Hz. ΔT=TPh0TPh=0.

Close modal

We demonstrate PLE thermometry by patterning an array of 2 μm wide, 50 nm thick gold pads onto a glass slide using photolithography and drop casting an isopropyl alcohol solution of nanodiamonds containing SiVs [Fig. 2(b)]. The gold pads absorb light at 520 nm30 and act as a local heat source when illuminated. A nanodiamond at position rp [Fig. 2(b)] is continually monitored while the power Ph of a heating laser applied at rh is modulated. This gives rise to a PLE thermometry signal (ΔII0) defined by the normalized difference in counts between Ph = 0 and Ph0.

Unlike in PL thermometry, here we modulate the heat source rapidly in order to utilize lock-in detection. Because of this, the sample never reaches a global thermal equilibrium, necessitating a different calibration technique (supplementary material). The temperature sensitivity of the intensity signal, ΔII0/ΔT=1.3(1)%/K [Fig. 2(c)], varies by less than 1% between different nanodiamonds. Therefore, SiV incorporated nanodiamonds do not need to be individually calibrated in order to be a precise relative thermometer. The temperature uncertainty is also measured to be 521 mK/Hz which, in contrast to bulk measurements, is not shot noise limited but saturates at 700 mK. This is most likely limited by residual fluorescence noise not rejected by the lock-in technique. Although we should be able to operate at a 200 Hz lock-in modulation frequency based on count rates, the optimal sensitivity occurs around 80 Hz, suggesting that the bandwidth for this measurement is limited by the speed at which we can modulate the heat source. While the uncertainty of this technique is higher than that measured for bulk diamond, it involves probing a much smaller volume (∼0.004 μm3 compared to ∼4 μm3 in bulk). When normalized by sensor volume, this technique performs twenty times better than PL thermometry.

Finally, we scan the position of the heating laser, rh, across our sample and measure the temperature response at the probe position, rp. Whenever the heating laser passes over a gold pad, the temperature at the nanodiamond increases, leading to the observed pattern in Fig. 3(a). This map is a measurement of the temperature difference ΔT at rp induced by the heating laser at rh. According to the steady-state heat equation for a point-source load in half-space,31 we expect ΔT(r)=ϵPta4πk|rr0|, where P is the applied laser power, t is the transmission efficiency of the objective, a is the absorption of a 50 nm gold pad illuminated at 520 nm, and k is the thermal conductivity of the glass slide. Due to fabrication imperfections, it is possible for a to deviate from the theoretical value. We account for this with a free parameter ϵ=0.7. For these measurements, the spatial resolution is limited by the nanodiamond size and the precision with which one can focus the heat source. Although not fundamental, these experiments were limited by the latter, which is the confocal microscope's optical resolution (∼300 nm). By using plasmon resonances of gold nanoparticles14 as a heat source and smaller nanodiamonds, this resolution can be improved by an order of magnitude.

FIG. 3.

Measuring local heating via PLE thermometry. (a) Away from the nanodiamond, heating corresponds to the gold array (overlaid boxes). Near the nanodiamond (inset), off-resonant fluorescence from the heating laser dominates the signal. (b) Temperature change on gold pads vs. their distance from the nanodiamond. These points follow a 1/|rprh| dependence as expected from solving the steady-state 2D heat equation31 and are consistent with the absorption of a 50 nm gold film at 520 nm.30 

FIG. 3.

Measuring local heating via PLE thermometry. (a) Away from the nanodiamond, heating corresponds to the gold array (overlaid boxes). Near the nanodiamond (inset), off-resonant fluorescence from the heating laser dominates the signal. (b) Temperature change on gold pads vs. their distance from the nanodiamond. These points follow a 1/|rprh| dependence as expected from solving the steady-state 2D heat equation31 and are consistent with the absorption of a 50 nm gold film at 520 nm.30 

Close modal

This letter demonstrates nanoscale thermometry based on SiV centers in diamond and achieves a temperature uncertainty of 360 mK/Hz in bulk diamond and 521 mK/Hz in 200 nm-sized nanodiamonds. The uncertainty of PL thermometry follows shot-noise limited scaling, which is not the case for PLE thermometry. We therefore infer that systematic effects dominate the uncertainty of PLE thermometry at longer integration times. This is most likely due to an inability to fully reject fluorescence intensity noise in the lock-in measurement. To address this, one can modify the lock-in technique by modulating two resonant lasers placed on the red and blue sides of the ZPL transition. Since this method does not rely on modulating the sample temperature, this modulation can be done at higher frequencies, which should further reduce noise in the measurement and improve the precision of this thermometry technique. Currently, each nanodiamond has <10 SiVs, so a straightforward method for reducing the measurement time would be to use nanodiamonds with higher SiV density. Unlike commercial nanodiamonds, which naturally contain many 1000s of NV centers,14 SiV nanodiamonds must be specifically fabricated and thus are not widely available.

SiV thermometry features several unique benefits compared to other luminescent thermometers, especially for biological applications. The all-optical scheme eliminates the necessity of microwaves and operates at low laser powers (∼100 μW resonant laser power), reducing measurement induced heating and potential damage to the target under investigation. In addition, SiVs have a narrow inhomogeneous distribution, which makes PL and PLE thermometry with SiVs effective as a thermometer even without individual calibration.

Other systems for luminescent thermometry6,8,9,32 also report absolute temperature uncertainties on the order of 1 K; however, due to their low spectral density and weak transition dipoles, these measurements typically require integration for several minutes to achieve sub-Kelvin uncertainty. Our approach is comparable in probe size to these techniques and achieves a similar absolute uncertainty but does so in significantly less time. This increased speed is crucial for many practical applications. For example, typical intracellular processes occur on the 1 s timescale, which can be resolved with our technique.33 Moreover, the SiV emission lies in the optical window for cellular imaging, a frequency-band of high transmission for a variety of biological materials typically between 650 nm and 1350 nm,34 rendering SiV thermometry a promising candidate for biological in vivo applications.1,4 Finally, recent studies show that color centers in nanodiamonds can also be used to vary the temperature of a local environment via optical refrigeration.35 Combining SiV thermometry with this technique would allow these nanodiamonds to be an integrated temperature sensor and actuator at the cellular level.

See supplementary material for details regarding diamond growth, as well as experimental details on calibrating PL thermometry in bulk diamond and PLE thermometry in nanodiamonds.

We thank J. Choi, H. Zhou, P. Maurer, and R. Landig for discussions and valuable insight regarding biological applications. Financial support was provided by the NSF, the Center for Ultracold Atoms, the Office of Naval Research MURI, the Gordon and Betty Moore Foundation, and the ARL. F.J. was supported by ERC and Volkswagen Stiftung. V.A.D. and L.F.K. thank the Russian Foundation for Basic Research (Grant No. 18-03-00936) for financial support. This work was performed in part at the Center for Nanoscale Systems at Harvard University, which is supported under NSF Grant No. ECS-0335765.

1.
Thermometry at the Nanoscale
, RSC Nanoscience and Nanotechnology edited by
L. D.
Carlos
and
F.
Palacio
(
The Royal Society of Chemistry
,
2016
).
2.
F.
Menges
,
P.
Mensch
,
H.
Schmid
,
H.
Riel
,
A.
Stemmer
, and
B.
Gotsmann
,
Nat. Commun.
7
,
10874
(
2016
).
3.
Z.
Cai
,
A.
Chardon
,
H.
Xu
,
P.
Féron
, and
G.
Michel Stéphan
,
Opt. Commun.
203
,
301
(
2002
).
4.
D. P.
O'Neal
,
L. R.
Hirsch
,
N. J.
Halas
,
J. D.
Payne
, and
J. L.
West
,
Cancer Lett.
209
,
171
(
2004
).
5.
G. W.
Walker
,
V. C.
Sundar
,
C. M.
Rudzinski
,
A. W.
Wun
,
M. G.
Bawendi
, and
D. G.
Nocera
,
Appl. Phys. Lett.
83
,
3555
(
2003
).
6.
H.
Liu
,
Y.
Fan
,
J.
Wang
,
Z.
Song
,
H.
Shi
,
R.
Han
,
Y.
Sha
, and
Y.
Jiang
,
Sci. Rep.
5
,
14879
(
2015
).
7.
I.
Sildos
,
A.
Loot
,
V.
Kiisk
,
L.
Puust
,
V.
Hizhnyakov
,
A.
Yelisseyev
,
A.
Osvet
, and
I.
Vlasov
,
Diamond Relat. Mater.
76
,
27
(
2017
).
8.
F.
Vetrone
,
R.
Naccache
,
A.
Zamarrón
,
A.
Juarranz de la Fuente
,
F.
Sanz-Rodríguez
,
L.
Martinez Maestro
,
E.
Martín Rodriguez
,
D.
Jaque
,
J.
García Solé
, and
J. A.
Capobianco
,
ACS Nano
4
,
3254
(
2010
).
9.
S.
Kalytchuk
,
K.
Poláková
,
Y.
Wang
,
J. P.
Froning
,
K.
Cepe
,
A. L.
Rogach
, and
R.
Zbořil
,
ACS Nano
11
,
1432
(
2017
).
10.
S.
Arai
,
S.-C.
Lee
,
D.
Zhai
,
M.
Suzuki
, and
Y. T.
Chang
,
Sci. Rep.
4
,
6701
(
2014
).
11.
J. S.
Donner
,
S. A.
Thompson
,
M. P.
Kreuzer
,
G.
Baffou
, and
R.
Quidant
,
Nano Lett.
12
,
2107
(
2012
).
12.
T.
Plakhotnik
,
H.
Aman
, and
H.-C.
Chang
,
Nanotechnology
26
,
245501
(
2015
).
13.
V. M.
Acosta
,
E.
Bauch
,
M. P.
Ledbetter
,
A.
Waxman
,
L. S.
Bouchard
, and
D.
Budker
,
Phys. Rev. Lett.
104
,
070801
(
2010
).
14.
G.
Kucsko
,
P. C.
Maurer
,
N. Y.
Yao
,
M.
Kubo
,
H. J.
Noh
,
P. K.
Lo
,
H.
Park
, and
M. D.
Lukin
,
Nature
500
,
54
(
2013
).
15.
J. M.
Taylor
,
P.
Cappellaro
,
L.
Childress
,
L.
Jiang
,
D.
Budker
,
P. R.
Hemmer
,
A.
Yacoby
,
R.
Walsworth
, and
M. D.
Lukin
,
Nat. Phys.
4
,
810
(
2008
).
16.
G.
Balasubramanian
,
I. Y.
Chan
,
R.
Kolesov
,
M.
Al-Hmoud
,
J.
Tisler
,
C.
Shin
,
C.
Kim
,
A.
Wojcik
,
P. R.
Hemmer
,
A.
Krueger
,
T.
Hanke
,
A.
Leitenstorfer
,
R.
Bratschitsch
,
F.
Jelezko
, and
J.
Wrachtrup
,
Nature
455
,
648
(
2008
).
17.
F.
Dolde
,
H.
Fedder
,
M. W.
Doherty
,
T.
Nobauer
,
F.
Rempp
,
G.
Balasubramanian
,
T.
Wolf
,
F.
Reinhard
,
L. C. L.
Hollenberg
,
F.
Jelezko
, and
J.
Wrachtrup
,
Nat. Phys.
7
,
459
(
2011
).
18.
M. W.
Doherty
,
F.
Dolde
,
H.
Fedder
,
F.
Jelezko
,
J.
Wrachtrup
,
N. B.
Manson
, and
L. C. L.
Hollenberg
,
Phys. Rev. B
85
,
205203
(
2012
).
19.
J. P.
Goss
,
P. R.
Briddon
,
M. J.
Rayson
,
S. J.
Sque
, and
R.
Jones
,
Phys. Rev. B
72
,
035214
(
2005
).
20.
T.
Iwasaki
,
F.
Ishibashi
,
Y.
Miyamoto
,
Y.
Doi
,
S.
Kobayashi
,
T.
Miyazaki
,
K.
Tahara
,
K. D.
Jahnke
,
L. J.
Rogers
,
B.
Naydenov
,
F.
Jelezko
,
S.
Yamasaki
,
S.
Nagamachi
,
T.
Inubushi
,
N.
Mizuochi
, and
M.
Hatano
,
Sci. Rep.
5
,
12882
(
2015
).
21.
T.
Iwasaki
,
Y.
Miyamoto
,
T.
Taniguchi
,
P.
Siyushev
,
M. H.
Metsch
,
F.
Jelezko
, and
M.
Hatano
,
Phys. Rev. Lett.
119
,
253601
(
2017
).
22.
T.
Feng
and
B. D.
Schwartz
,
J. Appl. Phys.
73
,
1415
(
1993
).
23.
E.
Neu
,
C.
Hepp
,
M.
Hauschild
,
S.
Gsell
,
M.
Fischer
,
H.
Sternschulte
,
D.
Steinmüller-Nethl
,
M.
Schreck
, and
C.
Becher
,
New J. Phys.
15
,
043005
(
2013
).
24.
K. D.
Jahnke
,
A.
Sipahigil
,
J. M.
Binder
,
M. W.
Doherty
,
M.
Metsch
,
L. J.
Rogers
,
N. B.
Manson
,
M. D.
Lukin
, and
F.
Jelezko
,
New J. Phys.
17
,
043011
(
2015
).
25.
S.
Lagomarsino
,
F.
Gorelli
,
M.
Santoro
,
N.
Fabbri
,
A.
Hajeb
,
S.
Sciortino
,
L.
Palla
,
C.
Czelusniak
,
M.
Massi
,
F.
Taccetti
,
L.
Giuntini
,
N.
Gelli
,
D. Y.
Fedyanin
,
F. S.
Cataliotti
,
C.
Toninelli
, and
M.
Agio
,
AIP Adv.
5
,
127117
(
2015
).
26.
D.
Foreman-Mackey
,
D. W.
Hogg
,
D.
Lang
, and
J.
Goodman
,
Publ. Astron. Soc. Pac.
125
,
306
(
2013
).
27.
J.
Goodman
and
J.
Weare
,
Commun. Appl. Math. Comput. Sci.
5
,
65
(
2010
).
28.
V. M.
Acosta
,
E.
Bauch
,
M. P.
Ledbetter
,
C.
Santori
,
K. M. C.
Fu
,
P. E.
Barclay
,
R. G.
Beausoleil
,
H.
Linget
,
J. F.
Roch
,
F.
Treussart
,
S.
Chemerisov
,
W.
Gawlik
, and
D.
Budker
,
Phys. Rev. B
80
,
115202
(
2009
).
29.
U. F. S.
D'Haenens-Johansson
,
A. M.
Edmonds
,
B. L.
Green
,
M. E.
Newton
,
G.
Davies
,
P. M.
Martineau
,
R. U. A.
Khan
, and
D. J.
Twitchen
,
Phys. Rev. B
84
,
245208
(
2011
).
30.
L.
Khriachtchev
,
L.
Heikkilä
, and
T.
Kuusela
,
Appl. Phys. Lett.
78
,
1994
(
2001
).
31.
A.
Tadeu
and
N.
Simões
,
Eng. Anal. Boundary Elem.
30
,
338
(
2006
).
32.
Y.
Yue
and
X.
Wang
,
Nano Rev.
3
,
11586
(
2012
).
33.
M.
Shamir
,
Y.
Bar-On
,
R.
Phillips
, and
R.
Milo
,
Cell
164
,
1302
(
2016
).
34.
A. M.
Smith
,
M. C.
Mancini
, and
S.
Nie
,
Nat. Nanotechnol.
4
,
710
(
2009
).
35.
M.
Kern
,
J.
Jeske
,
D. W. M.
Lau
,
A. D.
Greentree
,
F.
Jelezko
, and
J.
Twamley
,
Phys. Rev. B
95
,
235306
(
2017
).

Supplementary Material