Transition metal dichalcogenides (TMDCs) draw attention because their weak out-of-plane bonding enables easy isolation of their atomically thin constituents. Their extraordinary electrical and optical properties and mechanical flexibility make TMDCs excellent candidates for novel nanoscale electronic and optoelectronic devices. 1 As device features approach or reach the atomic limit, 2 nanometer-scale thermometry techniques are required to better understand their thermal transport and heat management.

The currently available temperature measurement techniques with submicrometer resolution are generally optical- 3,4 or scanning probebased. 5,6 Optical techniques (e.g., Raman, infrared detection) are noncontact, but diffraction limits their resolution to several hundred nanometers. Scanning probe techniques achieve $10 nm resolution, 7 but thermal contact requires perturbing the probed small volumes' temperature, introducing errors that are challenging to estimate and control.

Plasmon energy expansion thermometry (PEET) is a noncontact, nanoscale temperature mapping technique based on electron energy loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM). 8,9 This approach exploits the temperature dependence of a material's bulk plasmon energy: thermal expansion or contraction changes the local electron density, which, in turn, shifts the bulk plasmon energy. In PEET, a STEM equipped with EELS rasters a focused probe across the sample and collects a spectrum at each beam position (the 3D data array is called a spectrum image). Analyzing a spectrum image produces a plasmon energy map, which is subsequently converted into a temperature map, using the material's known thermal expansion coefficient (TEC). For materials with sufficiently sharp plasmon resonances, PEET provides a method for obtaining temperature maps with a nanometer-scale resolution.

Other TEM-based temperature measurements use diffractionbased detection of thermal expansion, 10 detailed balance using EELS, 11 or thermal population of Stokes/anti-Stokes excitations. 12 The phononbased measurements are a novel and more fundamental means to measure temperature, but phonons are more delocalized than plasmons. So far, temperature gradients in the TEM have only been observed with PEET, although other techniques have such potential.

In the work presented here, we apply PEET to the prototypical member of the TMDC family, molybdenum disulfide (MoS 2 ). We use an FEI NanoEx TM -i/v TEM microheater chip 13 [Fig. 1(a)] with a vendor-supplied calibration of temperature-vs-microheater resistance. Depositing a MoS 2 flake, we corroborate the vendor calibration using both conventional (diffraction limited) Raman thermometry and PEET. Finally, we use a homemade microheater chip [Fig. 1(b)] to create switchable, opposing, nanoscale temperature gradients across a MoS 2 flake that we map using PEET.

Few layer MoS 2 flakes are dry-transferred via mechanical exfoliation (scotch tape method) to a commercial or homemade TEM chip (Fig. 1), 14 avoiding some wet transfer contamination. 15 The MoS 2 is exfoliated first from the bulk material (SPI Supplies, Inc.) onto a transparent polydimethylsiloxane (PDMS) substrate, and then a thick flake (տ10 layers) is located using optical microscopy. 16 The target flake is transferred to the TEM chip using a home-built contact aligner. 17 The chips are wire bonded to PCB chip carriers customized for a TEM biasing holder (Hummingbird, Inc.), and electrical power is supplied by a Keithley 2400 Sourcemeter controlled with LabVIEW.

For Raman thermometry, the samples are placed in a cryostat (Cryo Industries, Inc.) with a base pressure of <10 À5 Torr. Raman spectra are collected using a Renishaw InVia confocal Raman microscope with 100 lW of a 532 nm laser excitation. TEM data are acquired in a JEOL JEM-2100F with a Gatan Quantum 963 GIF. Standard temperature mapping conditions used an 80 kV accelerating potential, a beam current of 0.3 nA, and a 12-14 mrad beam convergence semiangle (19-22 mrad spectrometer collection semiangle). PEET mapping conditions use a beam current of 0.3 nA, a 12-14 mrad beam convergence semiangle, a 19-22 mrad spectrometer collection semiangle, and a 0.025 eV/bin EELS dispersion. The calibrated heater experiment is performed with an accelerating potential of 200 kV and an EELS zero-loss peak (ZLP) full-width at half maximum (FWHM) of 0.95 eV, while the gradient experiment is performed with 80 kV and a ZLP FWHM of 0.65 eV.

Raman spectroscopy is a noncontact, nondestructive technique widely used to study mechanical and thermal properties of graphene and TMDCs. Raman peak positions shift and broaden with increasing temperature and have been measured for vapor-phase-grown, exfoliated, and hydrothermal-synthesized MoS 2 flakes. The in-plane mode E 1 2g and out-of-plane mode A 1g frequencies show a linear variation with temperature. 18,19 This temperature dependence can be mapped with $1 lm spatial resolution. Moreover, the temperature variation of these Raman frequencies is primarily due to thermal expansion. 18 Thus, the shifting of Raman peaks and bulk plasmon peaks is similar, making Raman thermometry, which is comparatively well-established, an appropriate technique for calibrating temperature measurements in MoS 2 via PEET.

Figure 1 shows the NanoEx chip with a $20 nm-thick MoS 2 flake and the shifts of the MoS 2 E 1 2g and A 1g Raman modes at elevated temperatures. Temperatures are determined from the calibrated heater resistance. Linear fitting gives first order temperature coefficients of cðE 1 2g Þ ¼ À1:60 6 0:03 Â 10 À2 cm À1 =K and c A 1g ð Þ ¼ À1:39 6 0:01 Â10 À2 cm À1 =K. We observe reasonable agreement ($10%) with the linear dependence reported by Livneh et al., 20,21 After confirming the MoS 2 flake temperature via Raman thermometry, we switch to plasmon thermometry. EELS spectra (5 of 29) of suspended MoS 2 at different temperatures are shown in Fig. 2(a). The plasmon peak's maximum shift is equivalent to just seven spectrometer bins in the 2048-bin spectrum. Spectrum images are acquired at different temperatures, and the plasmon energy shifts are determined by fitting the ZLP and the MoS 2 plasmon peak with Gaussian and Lorentzian functions, respectively. The measured bulk plasmon energy of MoS 2 is defined as the difference between the ZLP's and MoS 2 plasmon peak's fitted centers, eliminating common-mode effects caused by the beam shifting relative to the spectrometer.

The curve fit spectrum images produce plasmon energy maps showing a clear systematic shift with temperature (supplementary material, Fig. 1). Each map produces a normally distributed set of plasmon energies per temperature (supplementary material, Fig. 1), from which a mean and standard deviation are extracted.

According to the electron gas model, the bulk plasmon energy E p ¼ hx p ¼ h ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 4pne 2 =m p : At elevated temperatures, the valence electron number density n in the MoS 2 decreases due to thermal expansion according to the relation n T

and a 1 and a 2 are the first and second order volume (not to be confused with linear) TECs, respectively. [22][23][24] Temperature changes DT ¼ T À T 0 are measured relative to a reference temperature, here taken to be room temperature 300 K. Combining the equations for E p and n(T) gives the bulk plasmon energy as a function of temperature,

shows, as a function of temperature change DT, the measured bulk plasmon energies, along with predictions of E p and reported a V values 25,26 for comparison. Fitting the experimental values to a second order polynomial [green line in Fig. 2(b)] gives the estimates a 1 ¼ 1:9 6 0:1 Â 10 À5 K À1 and a 2 ¼ 5 6 8 Â 10 À10 K À2 in the range of 300-1100 K.

The literature values for the TECs of MoS 2 are various and confusing. In the 1970s, El-Malahaway and Evans, 26 and Murray and the same Evans, 27 measured MoS 2 's lattice parameters in the temperature ranges of 20-850 C and 10-320 K, respectively, using X-ray diffraction. Unfortunately, while the data are consistent in the overlap region, the lattice-constant fit parameters (from which the TECs are extracted) given by Murray and Evans, do not match their own data. Moreover, the low-temperature TECs in Ref. 27 are more than twice than the high-temperature TECs in Ref. 26, which is unphysical since TECs are expected to approach zero in the low-temperature limit. A more recent theory by Ding and Xiao 25 and Gan and Liu 28 matches this expectation, indicating that the MoS 2 TEC increases rapidly from zero below room temperature and then more slowly above room temperature. In quoting the X-ray data for comparisons, however, these 25,28 and other authors 29 note neither Murray and Evan's error nor that the hightemperature TECs 26 are referenced to 0 C and the low-temperature TECs 27 to 0 K, where, by all accounts, the TEC is very different. Huang and Zeng 30 and Hu et al. 29 have studied the in-plane thermal expansion of single and few-layer MoS 2 . Hu et al. used shifts in the plasmon energy to measure in-plane thermal expansion coefficient values, but unfortunately do not give bulk volume TEC values (no out-of-plane component is given); so, a comparison is not possible.

Given this state of affairs, we ignore the TEC data of Murray and Evans entirely. Table I lists the other values available. The values of El-Mahalawy and Evans are outliers and thus seem implausible, not only because of the small value of a 1 but also because their (linearized) volume TEC increases by a factor of 2a 2 DT/a 1 $4 over their measured temperature range of 20-850 C. For the other three entries (two of them theoretical), the corresponding increase is 15%. The value on the last line is the result of a quadratic fit of E p (T) to the data [Fig. 2(b)], where the errors are statistical and reflect the scatter in the data plotted.

To determine Raman-based temperatures in MoS 2 flakes, we invert the equations describing the peak shift's temperature dependence. We have

where x is the frequency, and c is the first order temperature coefficient, of the Raman mode. 18 In the case of PEET, we solve E p (T) for DT, finding

where the normalized change in the plasmon energy R ½E p T ð Þ ÀE p ðT 0 Þ=E p ðT 0 Þ. Here, we show the linear approximation to emphasize the similarity (the origin of the "2" is the square-root in the plasmon energy) with the Raman case. For the Raman-based determination of the MoS 2 flake's temperature, only two Raman spectra are acquired: room temperature and an elevated temperature. In contrast, for the PEET-based temperature determination, R is obtained at each point from two spectrum images. Raman thermometry provides point measurements on the lm-scale, while PEET can provide nm-scale maps.

When normalized for the integration time, the statistical precision of Raman thermometry and PEET are comparable in MoS 2 . Raman spectra, acquired in 30 seconds, have a statistical uncertainty of Plotting DT PEET and DT Raman vs the vendor-calibrated chip temperature DT holder (Fig. 3) shows that the Raman E 1 2g and A 1g peaks give values that are systematically þ9% and þ13% high, respectively. PEET values, calculated using the TEC values of Gan and Liu for illustration purposes, are systematically low by 22%. (The values in the last line of Table I would give perfect agreement by construction.) Clearly systematic errors dominate statistical errors in both Raman and PEET thermometry (their scatter is small). One possibility is that the chip calibration, specified to be good at 5%, is incorrect. The chip's heater/ thermometer could have been miscalibrated or altered, either during flake deposition or use. However, a different chip calibration would not make the Raman data agree with the PEET data. Thus, it appears that the temperature coefficients of the Raman modes, the available MoS 2 TEC values, the chip calibration, or some combination of these three are incorrect. Clearly, more work is required to demonstrate consistent and reproducible accuracy with these three thermometric techniques. On a more promising note, the lack of scatter in the data indicates that relative thermometry with precision at the few percent level is already possible. Because the Raman and the chip thermometries agree better than the other two pairs, we elect to take those values as more reliable and thus the value for MoS 2 's volume TEC given in the last line of Table I as the best available.

We now apply PEET to mapping a nanoscale temperature gradient in a suspended 30 nm-thick MoS 2 flake. To create temperature gradients, we use a homemade chip [Figs. 1(b) and 4(a)], applying heater power alternately on one side or the other (the heater on the opposing side is grounded). Spectrum images are acquired with neither heater powered (reference temperature T 0 ) and one heater powered (unknown temperature T), aligned to remove spatial drifts, and fit to give the plasmon energies. With the aligned maps of plasmon energies, the normalized change R is calculated for each pixel and then converted to a temperature map.

Applying 100 mW to the two heaters alternately gives two temperature maps [Fig. 4(b)]. Averaging the mapped region along the direction transverse to the gradient gives a 1D plot of temperature as a function of the position along the flake [Fig. 4(c)]. Fitting these temperature profiles reveals that the (switchable) temperature gradients are 70-90 K/lm (À90 K/lm for left heating, blue line, and 70 K/lm for right heating, red line). The error in temperature, determined from the normally distributed temperatures in the isothermal columns in Fig. 4(b)'s temperature maps, is 20 K.

From the temperature gradient of 80 K/lm and our 20 K temperature uncertainty, we can estimate our spatial resolution r R to be 250 nm (slope $ r T /r R ). This resolution is not limited by the thermometry technique's spatial resolution per se, which is determined by (see Ref. [8]) the image pixel size (6 nm) and the plasmon delocalization length ($2 nm, which is similar to our probe size of 1-2 nm), but by its precision and the temperature gradient's size. Our gradient of 80 K/lm ¼ 8 Â 10 5 K/cm is already large by macroscopic standards, but the ideal target for a resolution test would feature a step change in the temperature. Such a step is impossible to arrange and difficult to even approximate, since the thermal conductivities of real materials span only a few orders of magnitude (compare, e.g., electrical conductivities, which span many).

In summary, we apply Raman thermometry and PEET to a MoS 2 flake on a commercial, calibrated MEMS-style TEM heating chip. Ramping the chip temperature from room temperature to 1100 K (according to the chip calibration) gives corresponding Raman and PEET temperature curves that are internally consistent at the few percent level, but that gives values 10% high and 20% low relative to the chip temperature, respectively. These systematic discrepancies highlight the need for more careful studies of the TECs and Ramanpeak-frequency temperature coefficients in MoS 2 and other TMDCs. Interpreting the STEM EELS experiment as a measurement of the MoS 2 volume TEC gives a 1 ¼ (1.9 6 0.1)Â10 À5 K À1 and a 2 ¼ (5 6 8) Â10 À10 K À2 in the measured temperature range of 300-1100 K. We then used this TEC value to map 70-90 K/lm temperature gradients in a suspended flake of MoS 2 with a submicrometer spatial resolution. The basic procedure reported here, which determines the TEC if unknown and then maps the plasmon energy to determine the temperature, is general and can be most profitably applied in nanostructures made of materials (e.g., many semiconductors) with sharp plasmon resonances and sizable TECs.

See the supplementary material for two figures describing the curve fitting used to determine the plasmon energy, plasmon energy maps at different temperatures, a schematic of the experiment, and images of the connections to the MoS 2 flake. The first supplementary figure shows the plasmon energy maps and characteristics of the fitting, and the second shows an overview of how the Joule heaters are connected to the device.