Layered indium selenide (InSe) has emerged as a promising two-dimensional semiconductor due to its high electron mobility and direct optical bandgap in the few-layer limit. As InSe is integrated into high-performance electronic and optoelectronic systems, thermal management will become critical, thus motivating detailed characterization of intrinsic thermal properties. Here, we report the room-temperature thermal conductivity of exfoliated crystals of InSe along the through-plane and in-plane directions using conventional and beam offset time-domain thermoreflectance (TDTR), respectively. InSe crystals with varying thicknesses were prepared by mechanical exfoliation onto Si(100) wafers followed by immediate encapsulation with a 3-nm-thick AlOx passivation layer to prevent ambient degradation prior to coating with metal films for TDTR measurements. The measured thermal conductivity in the in-plane direction, Λin ≈ 8.5 ± 2 W/m K, is an order of magnitude higher than that in the through-plane direction, Λthrough ≈ 0.76±0.15 W/m K, which implies a high thermal anisotropy ≈11 ± 3. These relatively high anisotropy and low thermal conductivity compared to other layered semiconductors imply that InSe will require unique thermal management considerations when implemented in electronic, optoelectronic, and thermoelectric applications.

In the last decade, post-graphene layered semiconductors have emerged as promising electronic and optoelectronic materials due to their high charge carrier mobilities, diverse band structures, large oscillator strengths, unprecedented tunability, and access to novel spin and valley degrees of freedom.1–5 Layered solids with weak out-of-plane van der Waals bonding and strong in-plane covalent bonding also show large anisotropy in electronic, optical, magnetic, and thermal properties.5,6 Weak inter-layer van der Waals bonding not only allows isolation of monolayers and few-layer crystals through exfoliation but also enables diverse van der Waals heterojunctions through stacking assembly.1,7,8

Among layered semiconductors, transition metal dichalcogenides (TMDCs) have received significant attention for device applications due to their strong layer dependence, large exciton binding energies, and successful wafer-scale growth.1,2,9,10 However, most TMDC semiconductors only possess a direct bandgap in the monolayer limit, which hinders the utilization of thicker films that are optimal for many optoelectronic applications. On the other hand, post-transition metal chalcogenide (PTMC) semiconductors not only possess a direct bandgap in multi-layer films but also possess higher charge carrier mobilities than TMDCs.1,11 Among the PTMCs, layered indium selenide (InSe) is among the most promising n-type semiconductors as a result of its high electron mobility (>1000 cm2/V s) at room temperature.11,12 Furthermore, InSe has a direct bandgap at all beyond-monolayer thicknesses, which is desired for many photodetector and photovoltaic applications.11 For example, with a bandgap of 1.25 eV that approaches the ideal Shockley–Queisser limit (i.e., 1.34 eV) and a low surface recombination velocity (≈4 × 104 cm s−1), multi-layer InSe is ideal for ultracompact photovoltaics.11,13–16 InSe phototransistors also show a high photoresponsivity (≈107 A/W at 515.6 nm) and a ballistic avalanche photoresponse when paired with p-type black phosphorus.17–19 Few-layer InSe has further shown promise for heterogeneous catalysis, spintronic devices, and thermoelectric energy conversion.20–23 Specifically, the band dispersion of InSe results in a high Seebeck coefficient that enhances the thermoelectric figure of merit (ZT).23 

The realization of these InSe device concepts in scaled systems will require high-density integration with effective thermal management. Therefore, quantification of the thermal conductivity for exfoliated InSe in both the in-plane and through-plane directions is paramount for future application development. For example, the optimal design of low-noise InSe photodetectors and high-gain InSe avalanche photodiodes will require a detailed understanding of electron–phonon coupling and hot carrier dynamics.14,18,24 Moreover, ultracompact InSe photovoltaic cells will rely on effective heat dissipation strategies, especially in solar concentration schemes.15 However, there are limited experimental studies on the intrinsic thermal properties of bulk InSe crystals and no reports on exfoliated InSe flakes.25–27 A recent first-principles calculation on phonon transport in layered indium chalcogenides predicted a thermal conductivity of 8.2 W/m K for InSe at room temperature, but no anisotropic effects were examined.28 

Here, we experimentally determine the thermal conductivity tensor for exfoliated InSe flakes using time-domain thermoreflectance (TDTR).29–31 Thermal transport measurements of InSe in ambient conditions possess a technical challenge due to the high chemical reactivity of InSe that results in rapid oxidation and significant degradation of intrinsic properties.32 To circumvent this issue, we employed seeded atomic layer deposition (ALD) of an alumina encapsulation layer on exfoliated InSe flakes to impart ambient stability during TDTR measurements. In this manner, the thermal conductivity of exfoliated InSe is measured to be an order of magnitude higher in the in-plane direction, Λin ≈8.5 ± 2 W/m K, compared to the through-plane direction, Λthrough ≈0.76 ± 0.15 W/m K, which implies high thermal anisotropy ≈11 ± 3. These intrinsic thermal conductivity parameters are expected to inform the design of thermal management solutions for emerging InSe electronic, optoelectronic, and thermoelectric technologies.

InSe flakes were mechanically exfoliated in a controlled atmosphere N2 glovebox using scotch tape on Si(100) wafers covered with an ≈1-nm-thick native oxide (SiOx). Each layer of InSe has a hexagonal lattice that consists of two In and two Se close-packed sublayers with the stacking sequence Se–In–In–Se [Fig. 1(a)]. Thus, each monolayer of InSe consists of four covalently bonded sub-layers with an in-plane lattice constant of a = 4.084 Å. The out-of-plane lattice constant depends on the specific InSe polytype (e.g., β, ε, or γ), which defines the stacking configuration of the constituent monolayers. For example, the unit cell of β-InSe spans two layers that are rotated by 60°, resulting in a c-axis lattice constant of c = 16.64 Å.16,33,34 Following exfoliation, the InSe flakes were encapsulated with an ≈3-nm-thick aluminum oxide (AlOx) overlayer that provides protection against ambient degradation. In particular, the InSe flakes were first dipped in n-methyl-2-pyrrolidone in the glovebox, which results in an organic adlayer that promotes conformal atomic layer deposition (ALD). The AlOx encapsulation layer was subsequently grown using an established low-temperature ALD protocol without any ambient exposure using an ALD reactor that is directly connected to the glovebox.32 

FIG. 1.

(a) Schematic of a β-InSe crystal with a side view and top view. The unit cell spans over two AB stacked layers (rectangle in the side view), while only a monolayer is shown in the top view for clarity. (b) Optical micrograph of an InSe crystal exfoliated on an Si(100) substrate. (c) Atomic force microscopy image of the exfoliated InSe flake encapsulated with 3-nm-thick ALD AlOx from the region outlined by the dashed line in (b). The inset shows a height profile along the dashed blue line. (d) Raman spectrum of an InSe flake using an excitation wavelength of 532 nm, a 100× objective (NA = 0.9), and a 2400-grooves/mm grating.

FIG. 1.

(a) Schematic of a β-InSe crystal with a side view and top view. The unit cell spans over two AB stacked layers (rectangle in the side view), while only a monolayer is shown in the top view for clarity. (b) Optical micrograph of an InSe crystal exfoliated on an Si(100) substrate. (c) Atomic force microscopy image of the exfoliated InSe flake encapsulated with 3-nm-thick ALD AlOx from the region outlined by the dashed line in (b). The inset shows a height profile along the dashed blue line. (d) Raman spectrum of an InSe flake using an excitation wavelength of 532 nm, a 100× objective (NA = 0.9), and a 2400-grooves/mm grating.

Close modal

Figure 1(b) shows a representative optical microscopy image of an encapsulated InSe flake. After encapsulation, the thickness of the exfoliated InSe flakes was measured by tapping mode atomic force microscopy (AFM). InSe flakes with thicknesses ranging from 45 nm to 300 nm and lateral dimensions exceeding 20 × 20 μm2 were selected for thermal measurements [Figs. 1(b) and 1(c)]. The chemical structure of InSe was confirmed by Raman spectroscopy as shown in Fig. 1(d). β-InSe has D6h4 point group symmetry, characterized by a hexagonal lattice consisting of eight atoms in the unit cell and extending over two layers [Fig. 1(a)]. This structure results in three Raman-active vibrational modes at ≈113 cm−1 (A1g1), ≈175.5 cm−1 (E2g1), and ≈224 cm−1 (A1g2), as has been previously reported.17,35–38

The through-plane thermal conductivity of exfoliated InSe flakes encapsulated with AlOx was measured by conventional pump–probe TDTR, which utilizes surface heating via a train of laser pulses (pump beam at wavelengths near 788 nm) and monitors the resulting temperature variation through changes in optical reflectivity of the surface, which are sampled using a time-delayed probe beam with wavelengths near 783 nm. The pump beam frequency (f) is modulated for lock-in detection of the thermoreflectance signal. To analyze the data, the in-phase voltage (Vin) and out-of-phase voltage (Vout) of the measured thermoreflectance signals are monitored, with the ratio calculated using a thermal model.30 The modeling requires material parameters such as heat capacity (C), thickness (h), interface conductance (G), and thermal conductivity (Λ).

Before performing TDTR measurements, the encapsulated InSe flakes were coated with a 60-nm-thick NbV layer using dc magnetron sputtering, which acts as a transducer in the TDTR measurement. As a result, the samples possess at least five chemically distinct layers in the following structure (from the top): NbV/AlOx/InSe/SiOx/Si. Since the thicknesses of the AlOx layer (3 nm) and the SiOx native oxide layer (1 nm) are at the single nanometer scale, these layers were treated as part of the NbV/InSe interface conductance G1 and InSe/Si interface conductance G11, respectively. The thickness of the NbV transducer layer was measured using picosecond acoustics,39 assuming that the speed of sound in the NbV layer is 5.4 nm ps−1. In addition, the volumetric heat capacity of the InSe layer was assumed to be the bulk value of 1.3 J K−1 cm−3.25 

The remaining free parameters are the through-plane thermal conductivity of InSe (Λthrough), the thermal conductance of the NbV(metal)/InSe interface (G1), and the thermal conductance of the InSe/Si(substrate) interface (G11). For highly anisotropic materials, the anisotropy ratio of the in-plane thermal conductivity to the through-plane thermal conductivity should be included in the thermal model although its effect is significant only at a smaller modulation frequency (f = 1.12 MHz) and a smaller 1/e2 beam radius (w ≈3.2 μm). This effect can be observed in the sensitivity analysis of TDTR signals (−Vin/Vout) acquired with co-aligned pump and probe beams for different modulation frequencies and beam radii [see Fig. S2(d) of the supplementary material]. The sensitivity of the TDTR signal (−Vin/Vout) to a parameter (α) in the thermal model is evaluated using logVin/Voutlog(α).

FIG. 2.

Example of beam offset time-domain thermoreflectance data used to determine the in-plane thermal conductivity of a 297-nm-thick flake of InSe. The x-axis is the offset distance between the pump and probe beams. The out-of-phase signal acquired at a low modulation frequency of 1.1 MHz and a time delay of −50 ps is plotted as red solid circles vs the left-hand axis. The red line is a Gaussian fit to those data. The in-phase signal acquired at a high modulation frequency of 11 MHz and a time delay of 55 ps is plotted as black solid squares vs the right-hand axis. The black line is a Gaussian fit to those data to determine the 1/e2 radius of the pump and probe beams, w ≈ 3.2 μm.

FIG. 2.

Example of beam offset time-domain thermoreflectance data used to determine the in-plane thermal conductivity of a 297-nm-thick flake of InSe. The x-axis is the offset distance between the pump and probe beams. The out-of-phase signal acquired at a low modulation frequency of 1.1 MHz and a time delay of −50 ps is plotted as red solid circles vs the left-hand axis. The red line is a Gaussian fit to those data. The in-phase signal acquired at a high modulation frequency of 11 MHz and a time delay of 55 ps is plotted as black solid squares vs the right-hand axis. The black line is a Gaussian fit to those data to determine the 1/e2 radius of the pump and probe beams, w ≈ 3.2 μm.

Close modal

In the TDTR measurements of the through-plane thermal conductivity, a relatively high modulation frequency of f = 11 MHz and a relatively large 1/e2 beam radius of w ≈ 10.6 μm were used, thereby minimizing the sensitivity of the measurement to the in-plane thermal conductivity [Fig. S2(a)]. In this case, the through-plane analysis is performed iteratively. In particular, the analysis of the data acquired with a co-aligned pump and probe is iterated with the analysis of the beam-offset TDTR signals used to determine the in-plane thermal conductivity until a satisfactory convergence is reached. Example data for a beam-offset TDTR measurement are included in Fig. 2 and discussed further below. In this manner, the final values for the components of the thermal conductivity tensor do not depend on the initial guesses. At high modulation frequency and large beam sizes, the sensitivity of the TDTR signal to the conductance of the InSe/Si(substrate) interface (G11) is also negligible. To determine G11, measurements were conducted using f = 1.12 MHz and w = 3.2 μm, which results in optimal sensitivity as shown in Fig. S2(d).

Figure 3(a) shows that the measured through-plane thermal conductivities are essentially independent of the flake thickness for thicknesses h >100 nm to within experimental uncertainties. Error propagation from uncertainties in the NbV thickness (±5%) produces an uncertainty of ±10% in the measured through-plane thermal conductivity of h > 100-nm-thick layers. The error bars in Fig. 3(a) denote this measurement uncertainty. For thinner samples, h < 60 nm, the thermal conductivity is suppressed. We cannot, however, draw a firm conclusion about the mechanisms that produce this suppression because of the increasingly important role of the thermal conductance of the InSe/substrate interface, G11, in the analysis of the data. In the analysis of the data, G11 is fixed at 100 MW m−2 K−1. Uncertainty in G11 is not included in the error bars in Fig. 3(a).

FIG. 3.

Measured (a) through-thickness thermal conductivity (Λthrough) and (b) in-plane thermal conductivity (Λin) of exfoliated InSe flakes plotted as a function of flake thickness. The measurement uncertainties are denoted by error bars. In (a), the uncertainties of ±10% do not include the uncertainty in the thermal conductance of the InSe/substrate interface that becomes increasingly important for thinner samples. In (b), the uncertainties are ±20%.

FIG. 3.

Measured (a) through-thickness thermal conductivity (Λthrough) and (b) in-plane thermal conductivity (Λin) of exfoliated InSe flakes plotted as a function of flake thickness. The measurement uncertainties are denoted by error bars. In (a), the uncertainties of ±10% do not include the uncertainty in the thermal conductance of the InSe/substrate interface that becomes increasingly important for thinner samples. In (b), the uncertainties are ±20%.

Close modal

The average of the measured through-plane conductivity for samples with h > 100 nm is Λthrough ≈ 0.76 ± 0.15 W/m K. The interface conductance between the NbV and the InSe flake is relatively low, G1 < 60 MW m−2 K−1, as shown in Fig. S1, where G1 is plotted against the flake thickness. While this low interface conductance can be partially attributed to the low thermal conductivity of the AlOx encapsulation layer, it has also been observed previously for interfaces between metals and highly anisotropic layered materials.29,40–43

The in-plane thermal conductivities were measured for InSe flakes with a thickness larger than 100 nm using a beam-offset method.44,45 A relatively small spot size of w ≈ 3.2 μm and a low modulation frequency of f = 1.1 MHz were used to optimize sensitivity for the in-plane thermal conductivity. The laser beam intensity has a Gaussian shape, and the TDTR signal as a function of the relative position of the pump and probe also has a Gaussian shape with a slightly larger width. The full-width-at-half-maximum (FWHM) of the TDTR signal is used in the analysis.

In the beam-offset method, data were collected as the pump beam was translated relative to the probe. The FWHM of the out-of-phase thermoreflectance signal (Vout) measured at a negative time delay was used to determine the in-plane thermal conductivity along the direction of the beam offset. Additionally, the width of the in-phase signal (Vin) at a small positive time delay and high modulation frequency provides a measure of the spatial correlation of the pump and probe. Figure 2 shows an example of a beam-offset TDTR measurement for a 297-nm-thick InSe flake at 1.12 MHz. The FWHM of Vout at a low modulation frequency of 1.12 MHz and a negative time delay of −50 ps is ≈6.22 μm, which is larger than the FWHM of the laser beam profile ≈5.32 μm measured at a high modulation frequency of 11 MHz and a positive time delay of 55 ps. The in-plane thermal conductivity measurements were restricted to InSe flakes thicker than 100 nm due to the limited sensitivity of the measurement for thinner flakes.

The measured in-plane thermal conductivities are plotted against the flake thickness in Fig. 3(b). The in-plane thermal conductivity does not have a systematic dependence on the flake thickness within the experimental uncertainties. The measured in-plane conductivity is Λin ≈8.5 W/m K, resulting in a high anisotropy ≈11 for the measured in-plane to through-plane conductivity (Fig. 4). The uncertainty of the derived in-plane thermal conductivity of ±20% is calculated based on error propagation for the input parameters, predominantly from the uncertainty in the measurement of the FWHM of the TDTR signals. Variations in the defect densities or chemical purity of the InSe layers could potentially contribute to the sample-to-sample variations in the in-plane thermal conductivity, but we cannot draw a firm conclusion in that regard because the sample-to-sample variations in the data are not significantly larger than the variations that are expected for multiple measurements with an individual uncertainty of ±20%.

FIG. 4.

(a) Measured in-plane thermal conductivity (Λin) plotted against the measured through-plane thermal conductivity (Λthrough) for various exfoliated InSe flake thicknesses. (b) The measured anisotropy in thermal conductivity (ratio of Λin to Λthrough) is plotted as a function of exfoliated InSe flake thickness.

FIG. 4.

(a) Measured in-plane thermal conductivity (Λin) plotted against the measured through-plane thermal conductivity (Λthrough) for various exfoliated InSe flake thicknesses. (b) The measured anisotropy in thermal conductivity (ratio of Λin to Λthrough) is plotted as a function of exfoliated InSe flake thickness.

Close modal

In conclusion, the through-plane and in-plane thermal conductivity values for exfoliated InSe flakes have been measured using TDTR methods to be 0.76 W/m K and 8.5 W/m K, respectively. These ambient TDTR measurements were enabled by a conformal encapsulation layer (3-nm-thick ALD AlOx) that contributes negligibly to the interface thermal conductance. Both the through-plane and in-plane thermal conductivity values were found to be essentially independent of the flake thickness in the range considered here (≈100–350 nm). The extracted in-plane thermal conductivity of InSe is smaller than that of previously measured 2D semiconductors and semimetals such as MoS2, WS2, WSe2, WTe2, and ReS2, all of which possess values in the range of ≈20–100 W/m K,29,41–43 which implies that unique thermal management solutions will likely be required for high-density InSe electronic circuits. In addition, the anisotropy ratio between in-plane and through-plane thermal conductivities is also low for InSe (≈11) compared to that for transition metal dichalcogenides (≈20 to 100). Although the electron mobility of InSe does show high anisotropy (≈500),11,13,14,46 its thermal conductivity anisotropy is comparable to that of black phosphorus (≈10).40 Strong inter-layer coupling33 in InSe is likely to contribute to the reduced anisotropy of InSe compared to ReS2 (anisotropy >100), which has one of the weakest inter-layer couplings among 2D materials.47 Overall, the quantification of the thermal conductivity of exfoliated InSe will inform ongoing effort to utilize ultrathin InSe in electronic, optoelectronic, and thermoelectric applications.

See the supplementary material for materials characterization methods and additional TDTR measurements.

A.R. and V.K.S. contributed equally to this work.

A.R. and D.G.C. acknowledge support from National Science Foundation Grant No. EFRI-1433467. V.K.S., J.T.G., and M.C.H. acknowledge the National Science Foundation Materials Research Science and Engineering Center at Northwestern University (Grant No. DMR-1720139).

The data that support the findings of this study are openly available in the Materials Data Facility at http://doi.org/10.18126/lsg5-3utw.48 

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