Thickness-Dependent Thermal Conductivity of Suspended Two

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Thickness-Dependent Thermal Conductivity of Suspended Two-Dimensional Single-Crystal InSe Layers Grown by Chemical Vapor Deposition 2

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Shengwen Zhou, Xin Tao, and Yi Gu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b10905 • Publication Date (Web): 17 Feb 2016 Downloaded from http://pubs.acs.org on February 27, 2016

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The Journal of Physical Chemistry

Thickness-Dependent Thermal Conductivity of Suspended Two-Dimensional Single-Crystal In2Se3 Layers Grown by Chemical Vapor Deposition S. Zhou,* X. Tao,* and Y. Gu Department of Physics and Astronomy, Washington State University, Pullman, WA 99164-2814

ABSTRACT:

Using micro-Raman spectroscopy and finite-element simulations, we

determine the in-plane thermal conductivity of suspended two-dimensional single-crystal In2Se3 grown by chemical vapor deposition. The thermal conductivity shows a strong dependence on the layer thickness: it reaches ~ 60 W/m·K at the thickness of 35 nm, and it reduces to ~ 4 W/m·K for the 5 nm-thick layer. This dependence demonstrates the significance of phonon surface scattering, and also indicates changes to the phonon dispersion relations as the layer thickness decreases. The determination of the thickness-dependent thermal conductivity provides an important practical basis for advancing 2D In2Se3-based device technologies, and, more generally, also enables fundamental insight into the limiting mechanisms for 2D thermal transport.

*

These authors contributed equally to this work

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1. INTRODUCTION The discovery of graphene has led to extensive explorations of other two-dimensional (2D) materials that can exist in the form of single-atom or few-atom thick layers.1-7 Within these materials, the transition metal dichalcogenides are particularly promising for electronic and optoelectronic applications, such as field-effect transistors,8-13 light-emitting devices,14,15 solar cells,14,16-18 and valleytronics.19-23 Single- and few-layer black phosphorus has also been studied.24-29 Recently, indium selenide compounds, including InSe and In2Se3, have gained considerable interest: broadband photodetectors with the sensitivity superior to graphene and MoS2,30-32 high-mobility field-effect transistors,33 and electroluminescent devices34 have been demonstrated. One unique aspect of these compounds, compared to other more extensively studied 2D materials, is the potential applications in phase-change memory.35-37 In particular, our previous studies38 have shown the possibility to stabilize multiple crystalline phases of In2Se3 in 2D form, which can be used to encode data via their different electrical resistances. Further explorations of these materials in device applications are guided by a thorough understanding of material properties. Thermal properties, in particular, are central to the thermally driven phase-change memory operations, and are also important for developing efficient thermal management schemes for other electronic devices. In this work, by combining micro-Raman spectroscopy and finite-element simulations, we determine the in-plane thermal conductivity in suspended single-crystal In2Se3 layers grown by chemical vapor deposition (CVD). Our results show that the in-plane thermal conductivity of In2Se3 layers reaches ~ 60 W/mK at the thickness of 35 nm. On the other hand, the thermal conductivity reduces to ~ 4 W/mK for the 5 nm-thick layer. The strong thickness dependence of the thermal conductivity can be attributed, at least partially, to the surface phonon 2 ACS Paragon Plus Environment

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scattering. The possible changes to the phonon dispersion relations as the layer thickness decreases might also play a role. These results provide a practical guide for advancing 2D In2Se3-based device technologies, and, more generally, also enable fundamental insight into the limiting mechanisms for 2D thermal transport. 2. EXPERIMENTAL DETAILS The CVD growth of 2D In2Se3 was carried out following the procedures reported previously.39 Briefly, In2Se3 powers (99.99%, Alfa Aesar) were loaded into a quartz tube furnace and were heated to 850 oC. H2 was used as the carrier gas, with freshly cleaved mica substrates located in the downstream as the growth substrate. The growth time ranges from 5 to 40 mins. The as-grown layers were then transferred using a thermal release tape (Nitto Revalpha 3193 MS) to thin Si3N4 membranes and holey Si3N4/Si substrates for further studies. The Raman spectra were obtained by using a Renishaw InVia Raman microscope with a 632 nm laser excitation. 3. RESULTS AND DISCUSSION Figure 1 (a) shows a transmission electron microscopy (TEM) image of layers on a thin Si3N4 membrane. The electron diffraction pattern [inset to Fig. 1 (a)] demonstrates the single crystal nature of the as-grown layers. The hexagonal pattern can be indexed using the β-phase structure. The large-area growth allows us to suspend layers on holes with large diameters [from ~ 5 – 8 µm; Fig. 1 (b)]; this minimizes the impact of the uncertainty in the substrate-layer interfacial thermal conductance on the determination of the layer thermal conductivity (see also below). The Raman spectrum of an as-grown In2Se3 layer [Fig. 2 (a)] shows a dominant peak at ~ 110 cm-1 and a relatively weak peak at ~ 205 cm-1; in addition, a very weak peak can be seen at ~ 176 cm-1. To identify the phonon modes for these peaks, we note that the β-phase In2Se3 has the R-3m symmetry. According to the group theory, there are 3 ACS Paragon Plus Environment


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four Raman-active modes (2A1g + 2Eg). The A1g modes represent the out-of-plane lattice vibrations, and the Eg modes correspond to in-plane lattice vibrations. To differentiate between these modes, we conducted polarized Raman spectroscopy on a CVD-grown In2Se3 layer [inset to Fig. 2 (a)]. The z and ab axes represent the [0001] and arbitrary orthogonal in-plane directions, respectively. Under the cross polarization condition, z(ab)z, the 110 cm-1 and 205 cm-1 peaks vanish, with the 176 cm-1 peak as the only observable mode in this frequency regime. Based on the Raman tensor for the R-3m symmetry,40 we identify the 110 cm-1 and 205 cm-1 peaks as the A1g modes and the 176 cm-1 peak as the Eg mode. Since In2Se3 and the α-Bi2Se3 have similar lattice structures and belong to the same space group, we use the phonon modes of α-Bi2Se3 as the reference, and we further attribute the 110 cm-1, 176 cm-1, and 205 cm-1 peaks to the A1g1, Eg2, and A1g2 modes, respectively. We note that these modes in In2Se3 have higher frequencies than the corresponding modes in Bi2Se3, consistent with the larger mass of Bi compared to In.

We next discuss the temperature dependence of the phonon modes, which forms the basis for the thermal conductivity measurements. For these studies, samples were loaded into an Instec hot stage, and Raman measurements were conducted under a constant flow of ultrapure Ar to prevent oxidation at elevated temperatures. We focus on the A1g1 mode since it is the dominant Raman peak. To extract the phonon mode frequency as a function of temperature, we fitted the Raman spectra [Fig. 2 (b)] with Voigt functions; a background curve was added to account for the response of the laser line filter, which has a cut-off frequency at ~ 100 cm-1. The A1g1 mode frequency was found to decrease with increasing temperature, as shown in Fig. 2 (c). The generally lower phonon frequencies in the suspended layer can be attributed to the laser heating that leads to higher temperatures in the suspended geometry. For both 4 ACS Paragon Plus Environment

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substrate-supported and suspended layers, the temperature dependence of the frequency can be fitted with a linear function within the temperature range studied. Such a phenomenon has been observed in monolayer and few-layer MoS2,41 graphene,42 and black phosphorus.43 The slope of this linear function is the first-order temperature coefficient, χT. For substrate-supported and suspended layers, χT are – (0.0096 ± 0.0004) cm-1/K and – (0.0089 ± 0.0007) cm-1/K, respectively, from the data shown in Fig. 2 (c). The slight difference in χT in supported and suspended geometries, which is within the errors of the linear fitting, might originate from the strain due to the different thermal expansion coefficients of the layer and the substrate.44 Nonetheless, in light of this small difference, and since the suspended layers are prone to damage during the Raman measurements at elevated temperatures due to poor heat dissipation, we use χT obtained from the supported layers for the thermal conductivity measurements. We note that, as a justification of this approach, χT of supported layers does not show obvious dependence on the layer thickness [inset to Fig. 2 (c)], indicating minimal substrate effects. Having established the relation between the A1g1 mode frequency and the temperature, we next use this relation to measure the temperature rise of the suspended layers under a steady-state heating from a focused laser beam (632 nm), as shown schematically in Fig. 3 (b). To determine the optical power absorbed by the layers, we measured the optical absorption coefficient at the 632-nm wavelength by dispersing CVD In2Se3 layers on thin Si3N4 membranes, with the schematics shown in Fig. 3 (a). By measuring the transmitted laser power, with the layer thickness obtained by atomic force microscopy, we obtained the absorption coefficient of ~ 1.35×107 m-1. The evolution of the Raman spectra of a suspended 5 ACS Paragon Plus Environment


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layer under various absorbed laser power is shown in Fig. 3 (c). The A1g1 mode frequency as a function of the laser power [Fig. 3 (d)] can be fitted by a linear function, with the slope, χP, of – 10.507 ± 1.26 cm-1/mW. We then obtain the temperature rise of the suspended layers as a function of absorbed laser power via the ratio between χT and χP (χP/χT). Knowing χP/χT allows us to estimate the thermal conductivity of suspended layers. Specifically, we use finite-element simulations to calculate the temperature rise of the layer under laser heating, with the layer thermal conductivity as the varying parameter. These simulations assume diffusive heat transport, as Raman measurements are sensitive to the diffusive phonon transport.42 We note that, due to the absence of photoluminescence emission under laser excitation in multi-layer In2Se3,45 most of the absorbed laser energy is converted to thermal energy. By matching the simulated temperatures to the experimentally determined values (extracted from χP/χT), we can determine the layer thermal conductivity. The simulations were carried out in COMSOL, with the simulation geometry and an example of the simulated temperature map of a suspended In2Se3 layer under the laser heating shown in Figs. 4 (a) and (b), respectively. We incorporated the following aspects in the simulations, with material parameters listed in Supporting Information:

(1) We took into account the difference between in-plane (k//) and out-of-plane thermal conductivities (k⊥). This anisotropy is inherent in all 2D materials, as the in-plane atomic bonds are largely covalent, whereas the out-of-plane atomic interaction is dominated by the van der Waal force.

(2) We considered the layer-substrate (outside the hole) heat transfer by defining an interface 6 ACS Paragon Plus Environment

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thermal conductance (G).

(3) The layer-air heat transfer, which was shown to have a non-negligible impact on the thermal conductivity measurements in graphene,42 was also considered.

(4) The laser illumination was defined as a Gaussian beam. The full-width-at-half-maximum (FWHM) of the Gaussian beam was obtained from wavelength-adjusted spatially resolved autocorrelation scans.46 Details can be found in Supporting Information.

(5) The boundary condition is that the temperature at the back of the substrate remains 300 K (room temperature).

We next discuss the possible sources of errors in determining k//. First, the ratio between k// and k⊥ is unknown in In2Se3 (to the best of our knowledge). In graphene, k///k⊥ can reach beyond 100.47 As shown in Fig. 4 (c), the temperature profiles for k///k⊥ of 10 and 100 (with k// = 21 W/mK) exhibit noticeable differences. These differences lead to errors ranging from ~ 4% up to ~ 46% across different layers. We note that, in a previous study48 on multi-layer MoS2, the difference between k// and k⊥ was not considered. In multi-layer black phosphorus, the uncertainty of k⊥ was shown to be insignificant.43 The significant errors observed here can be attributed to the heat transfer at the layer-air interface, where the out-of-plane thermal conduction plays an important role. Another possible origin of errors is the thermal conductance (G) at the layer-substrate (Si3N4) interface. A value of 50 MW/m2K has been used for MoS2-Si3N4 substrate.41 Similar to the case of MoS2 and black phosphorus,43 we found negligible differences in the temperature profiles for G = 50 and 500 MW/m2K [Fig. 4 (d)]. This can be attributed to the sharp temperature decreases outside the laser heating area 7 ACS Paragon Plus Environment


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and small temperature rises close to the hole edge, which are due to the relatively low thermal conductivity and the large hole diameters (≳ 5 µm) relative to the laser beam diameter (FWHM ~ 544 nm) used in our studies. We also considered the possibility that the layer outside the hole (i.e. the substrate-supported layer region) might have a lower thermal conductivity (k´//) than the suspended layer region, due to the layer-substrate interaction. For k´///k// of 0.1 and 0.01 (with k// = 21 W/mK), we plotted the corresponding temperature profiles in Fig. 4 (e), which show negligible differences. This is also consistent with what has been observed in single-layer MoS2.41 Finally, the errors of the linear fitting to the phonon peak position vs. temperature and laser power, such as shown in Figs. 2 (c) and 3 (d), lead to the uncertainty of k// ranging from ~ 1 to 30 %. Figure 5 shows the k// as a function of the layer thickness (t), with the error bars corresponding to the uncertainty of k///k⊥ (between 10 and 100), which, as shown above, leads to the most significant errors. In general, k// increases with the increasing layer thickness; k// obtained from layers suspended on holes with different diameters shows the similar trend. Specifically, k// increases from ~ 4 W/mK to ~ 60 W/mK as t increases from ~ 5 nm to ~ 35 nm. A direct comparison of these values to that (< 1 W/mK)49 in bulk In2Se3 is difficult, because of the polycrystalline nature of the bulk sample. The k// vs. t relation observed here is opposite to that in graphene,50 where the Umklapp scattering is suppressed in single-layer graphene, leading to higher thermal conductivities. k// in single- and few-layer MoS2 was determined to be ~ 34.5 W/mK41 and ~ 52 W/mK,51 respectively. In black phosphorus,43 k// is ~ 12 – 18 W/mK at the thickness of ~ 10 nm, and reaches 20 – 45 W/mK at the thickness of ~ 30 nm. These studies show a similar trend of k// vs. t, which was attributed to the increasing 8 ACS Paragon Plus Environment

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significance of surface phonon scattering in thinner layers.43 Compared to MoS2 and black phosphorus with corresponding layer thicknesses, In2Se3 appears to have noticeably lower thermal conductivities in thin layers and comparable thermal conductivities in thicker layers. We note that the low thermal conductivity in thin In2Se3 layers is advantageous for phase-change memory applications, in that a higher temperature can be achieved via a lower electrical input.

To gain insight into the thickness dependence of k//, we use the Callaway model, with the characteristic length for the boundary scattering given by t, to fit the k// vs. t relation (details provided in the Supporting Information). The fitting results (dashed lines) are shown in Fig. 5 and its inset. The Callaway model can describe the general trend of k// vs. t; however, it does not lead to a good fit with the experimental data. While the various assumptions in the Callaway model can contribute to the fitting errors, a potentially important factor is that it does not consider the possible modifications to the phonon dispersion relations as the layer thickness decreases. We note that the phonon dispersion relations as a function of layer thickness were recently studied by first-principles calculations for MoS2,52 where k// of the tri-layer MoS2 approaches the bulk value. On the other hand, the interlayer vibrations in both MoS253 and graphene54, 55 were found to approach the bulk vibrational energies when the thickness becomes ≥20 layers. These interlayer vibrational modes might be related to k⊥. As shown and discussed in the manuscript, the value of k///k⊥ has a nontrivial impact on the determination of k//. Therefore, the discrepancy between our experimental data and the Callaway model might originate from the dependence of the k///k⊥ ratio on the layer thickness. Nonetheless, the strong thickness dependence of k// suggests the dominance of 9 ACS Paragon Plus Environment


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phonon-boundary (surface) scattering in the thermal transport process. Further studies, such as the theoretical calculations of phonon dispersion relations in single- and multi-layer In2Se3, are necessary to fully account for the k// vs. t relation. In summary, we have determined the in-plane thermal conductivity in CVD-grown suspended single-crystal In2Se3 layers. This thermal conductivity shows a strong dependence on the layer thickness: it increases from ~ 4 W/mK to ~ 60 W/mK as the layer thickness increases from ~ 5 nm to ~ 35 nm. These results provide a guide for further advancing In2Se3-based device technologies: for example, the low thermal conductivity in thin layers is ideal for realizing energy-efficient phase-change memory applications; whereas the higher thermal conductivity in thick layers is beneficial for transistors, light-emitting devices, and photodetectors, where the efficient heat dissipation is desired. From a fundamental perspective, our findings demonstrate the significance of phonon-surface scattering in thermal transport, and also indicate the need to take into account the effect of possible phonon dispersion relation changes as the layer thickness approaches the single layer limit. Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Determination of the full-width-at-half-maximum of the focused 632 nm laser beam, material parameters used in the simulations, procedures for determining the average simulated temperature, and details of the fitting using the Callaway model. Corresponding Author [email protected] Acknowledgement This work was supported by the National Science Foundation (DMR-1506480). 10 ACS Paragon Plus Environment

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(35) Jin, B.; Kang, D.; Kim, J.; Meyyappan, M.; Lee, J. S. Thermally Efficient and Highly Scalable In2Se3 Nanowire Phase Change Memory. J. Appl. Phys. 2013, 113, 164303-6. (36) Yu, B.; Ju, S. Y.; Sun, X. H.; Ng, G.; Nguyen, T. D.; Meyyappan, M.; Janes, D. B. Indium Selenide Nanowire Phase-Change Memory. Appl. Phys. Lett. 2007, 91, 133119-3. (37) Huang, Y. L.; Huang, C. W.; Chen, J. Y.; Ting, Y. H.; Lu, K. C.; Chueh, Y. L.; Wu, W. W. Dynamic Observation of Phase Transformation Behaviors in Indium(Iii) Selenide Nanowire Based Phase Change Memory. ACS Nano 2014, 8, 9457-9462. (38) Tao, X.; Gu, Y. Crystalline-Crystalline Phase Transformation in Two-Dimensional In2Se3 Thin Layers. Nano Lett. 2013, 13, 3501-3505. (39) Lin, M.; Wu, D.; Zhou, Y.; Huang, W.; Jiang, W.; Zheng, W. S.; Zhao, S. L.; Jin, C. H.; Guo, Y. F.; Peng, H. L.; et al. Controlled Growth of Atomically Thin In2Se3 Flakes by Van Der Waals Epitaxy. J. Am. Chem. Soc. 2013, 135, 13274-13277. (40) Lewandowska, R.; Bacewicz, R.; Filipowicz, J.; Paszkowicz, W. Raman Scattering in Alpha-In2Se3 Crystals. Mater. Res. Bull. 2001, 36, 2577-2583. (41) Yan, R.; Simpson, J. R.; Bertolazzi, S.; Brivio, J.; Watson, M.; Wu, X.; Kis, A.; Luo, T.; Hight Walker, A. R.; Xing, H. G. Thermal Conductivity of Monolayer Molybdenum Disulfide Obtained from Temperature-Dependent Raman Spectroscopy. ACS Nano 2014, 8, 986-993. (42) Chen, S. S.; Moore, A. L.; Cai, W. W.; Suk, J. W.; An, J. H.; Mishra, C.; Amos, C.; Magnuson, C. W.; Kang, J. Y.; Shi, L.; et al. Raman Measurements of Thermal Transport in Suspended Monolayer Graphene of Variable Sizes in Vacuum and Gaseous Environments. ACS Nano 2011, 5, 321-328. (43) Luo, Z.; Maassen, J.; Deng, Y.; Du, Y.; Garrelts, R. P.; Lundstrom, M. S.; Ye, P. D.; Xu, X. Anisotropic in-Plane Thermal Conductivity Observed in Few-Layer Black Phosphorus. Nat. Communi. 2015, 6, 8672-8 (44) Lee, J. U.; Yoon, D.; Kim, H.; Lee, S. W.; Cheong, H. Thermal Conductivity of Suspended Pristine Graphene Measured by Raman Spectroscopy. Phys. Rev. B 2011, 83, 081419. (45) Zhou, J.; Zeng, Q.; Lv, D.; Sun, L.; Niu, L.; Fu, W.; Liu, F.; Shen, Z.; Jin, C.; Liu, Z. Controlled Synthesis of High-Quality Monolayered α-In2Se3 Via Physical Vapor Deposition. Nano Lett. 2015, 15, 6400-6405. (46) Tao, X.; Mafi, E.; Gu, Y. Synthesis and Ultrafast Carrier Dynamics of Single-Crystal 14 ACS Paragon Plus Environment

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Figure 1

(a) A TEM image of the CVD-grown In2Se3 layers, with the

inset showing an electron diffraction pattern; (b) scanning electron microscopy image of suspended In2Se3 layers.


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Figure 2

(a) A typical Raman spectrum of a CVD-grown In2Se3 layers, with the inset

showing polarized Raman spectra of an as-grown layer; (b) variable-temperature Raman spectra (open circles) of a supported In2Se3 layer, with the red dashed lines and the blue dash-dotted lines as the Voigt functions and the background curves for the fitting, respectively; (c) A1g1 phonon mode frequency as a function of temperature for suspended and supported layers, with dashed lines as the linear fittings. Inset to (c): χT from supported layers as a function of layer thickness.



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Figure 3

Schematic experimental setup for (a) absorption coefficient and (b) laser

heating measurements; (c) Raman spectra (open circles) of a suspended In2Se3 layer with various absorbed laser powers, with the red dashed lines and the blue dash-dotted lines as the Voigt functions and the background curves for the fitting, respectively; (d) A1g1 phonon mode frequency as a function of absorbed laser power, with dashed line as the linear fitting.


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Figure 4

(a) Schematics for finite-element simulations; (b) a temperature map of an

In2Se3 layer under laser heating; temperature profiles across the layer for different values of (c) k⊥, (d) G, and (e) k´//.



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Figure 5 k// as a function of the layer thickness, with the dashed line representing the fitting using the Callaway model, with the inset showing the same data in a larger t regime.


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Thickness-Dependent Thermal Conductivity of Suspended Two

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