Temperature-dependent optical and vibrational properties of PtSe2 thin films

PtSe2 has received substantial research attention because of its intriguing physical properties and potential practical applications. In this paper, we investigated the optical properties of bilayer and multilayer PtSe2 thin films through spectroscopic ellipsometry over a spectral range of 0.73–6.42 eV and at temperatures between 4.5 and 500 K. At room temperature, the spectra of refractive index exhibited several anomalous dispersion features below 1000 nm and approached a constant value in the near-infrared frequency range. The thermo-optic coefficients of bilayer and multilayer PtSe2 thin films were (4.31 ± 0.04) × 10−4/K and (–9.20 ± 0.03) × 10−4/K at a wavelength of 1200 nm. Analysis of the optical absorption spectrum at room temperature confirmed that bilayer PtSe2 thin films had an indirect band gap of approximately 0.75 ± 0.01 eV, whereas multilayer PtSe2 thin films exhibited semimetal behavior. The band gap of bilayer PtSe2 thin films increased to 0.83 ± 0.01 eV at 4.5 K because of the suppression of electron–phonon interactions. Furthermore, the frequency shifts of Raman-active Eg and A1g phonon modes of both thin films in the temperature range between 10 and 500 K accorded with the predictions of the anharmonic model. These results provide basic information for the technological development of PtSe2-based optoelectronic and photonic devices at various temperatures.

Scientific Reports | (2020) 10:19003 | https://doi.org/10.1038/s41598-020-76036-y www.nature.com/scientificreports/ Most optical measurements of PtSe 2 thin films have been limited to room temperature [27][28][29] . The temperaturedependent optical properties of PtSe 2 thin films have not been reported. In this paper, we characterized the optical constants of PtSe 2 thin films over a wide range of photon energy (from 0.73 to 6.42 eV) and temperature (between 4.5 and 500 K) through spectroscopic ellipsometry. We found that bilayer PtSe 2 thin films exhibited an indirect band gap and that multilayer PtSe 2 thin films exhibited semimetal behavior at 300 K. Furthermore, the band gap of bilayer PtSe 2 thin films increased from 0.71 ± 0.01 to 0.83 ± 0.01 eV when temperature decreased from 500 to 4.5 K. Multilayer PtSe 2 thin films exhibited a band gap of approximately 0.04 ± 0.004 eV at 500 K. Additionally, we investigated the temperature-dependent Raman scattering spectra of PtSe 2 thin films from 10 to 500 K. The temperature dependence of E g and A 1g phonon modes was attributed to the anharmonic contributions to the interatomic potential energy, mediated by phonon-phonon interactions. These findings are highly promising for further development of PtSe 2 thin films in optoelectronic and photonic applications at various temperatures.

Experiment
Bilayer and multilayer PtSe 2 thin films were grown on sapphire substrates by using chemical vapor deposition method. Platinum (II) chloride (PtCl 2 ) and selenium (Se) were used as precursors. Both PtSe 2 samples with an area of approximately 1 cm 2 were formed at a temperature of 400 °C. The growth time ranged from 10 to 20 min for bilayer and multilayer thin films, respectively. The samples were prepared according to the method described in 21 . Figure 1 depicts the optical microscopic and atomic force microscopic images, and corresponding height  www.nature.com/scientificreports/ profiles of two thin films. The thickness of these two thin films was approximately 1.4 and 5.0 nm, respectively, thus corresponding to two and seven PtSe 2 layers. Both thin films were also verified through transmission electron microscopy to be high-quality samples 30 . Room-temperature spectroscopic ellipsometry spectra were recorded under incident angles of 60°, 65°, 70°, and 75° and over a spectral range of 0.73 to 6.42 eV by using an ellipsometer (J. A. Woollam Co. M-2000U). For temperature-dependent measurements between 4.5 and 500 K, the samples were placed in a Janis ST-400 ultrahigh-vacuum continuous-flow helium cryostat 31,32 . The optical constants were obtained through spectroscopic ellipsometry using the stacked layer model (sapphire substrate/thin film/surface roughness/air ambient structure) 32 . The parameters of the model used to fit the raw ellipsometry data are listed in Table 1. The values of the mean square error are 1.07 and 1.40 for bilayer and multilayer PtSe 2 thin films. The independently measured   Room-temperature micro-Raman scattering measurements were performed using a backscattering geometry with a laser excitation wavelength of 532 nm 31 . The linear polarized light was focused to a 3-μm-diameter spot on the sample surface. Subsequently, a SENTERRA spectrometer collected and dispersed the scattered light with a 1024-pixel-wide charge-coupled detector. The spectral resolution achieved using these instruments was generally less than 0.5 cm −1 . To avoid heating effects, the laser power was set to less than 0.5 mW. The sapphire substrate exhibited high thermal conductivity and evacuated heating well 33 . The samples were mounted in a continuous-flow helium cryostat and LINKAM heating stage, which enabled measurements in the temperature range of 10-500 K 31 . For both thin films, the room-temperature refractive index increased substantially with an increase in the wavelength in the spectral range from 193 to 700 nm for bilayer and from 193 to 1100 nm for multilayer thin films. It then approached one maximum, which corresponded with the anomalous dispersion regime 34 and finally decreased with the wavelength until the wavelength reached 1700 nm. With an increase in layer thickness, the value of refractive index increased. This phenomenon is consistent with previous reports of thickness-dependent optical constants 29 . Notably, multilayer PtSe 2 thin film exhibited large refractive index values (approximately 6.88 at a wavelength of 1070 nm). Bilayer PtSe 2 thin film exhibited a maximum refractive index of approximately 2.72  www.nature.com/scientificreports/ at a wavelength of 720 nm. The characteristics of high refractive indices of bilayer and multilayer PtSe 2 thin films indicated a large scattering cross-section inside the crystal 35 . Thus, these effects are highly favorable for light trapping in photonic 36 and optoelectronic 37 devices in the visible to near-infrared frequency range. With a decrease in temperature, the refractive index of bilayer PtSe 2 thin film decreased in the near-infrared region. This behavior is ascribed to the decreased electron-phonon interaction with a decrease in temperature, as observed for other semiconducting TMDs, such as monolayer MoS 2 , MoSe 2 , WS 2 , and WSe 2 32 . By contrast, this trend was reversed for multilayer PtSe 2 thin film, which could be associated with the enhanced electron-phonon interaction. The thermo-optic coefficients (∂n/∂T) for bilayer and multilayer PtSe 2 thin films were (4.31 ± 0.04) × 10 −4 /K and (− 9.20 ± 0.03) × 10 −4 /K, respectively, at a wavelength of 1200 nm. Bilayer PtSe 2 thin film exhibited a positive thermo-optic coefficient value, similar to the coefficient of other semiconducting materials such as silicon 38 . By contrast, multilayer PtSe 2 thin film had a negative value of thermo-optic coefficient that was similar to the coefficient of TiO 2 39 . The negative thermo-optic coefficient observed in multilayer PtSe 2 may arise from the enhanced electron-phonon interaction at low temperatures because of its semimetallic properties. The extinction coefficient spectra (Figs. 2 and 3) of two thin films were featureless above 1000 nm, but exhibited several absorption peaks below 1000 nm. These absorptions exhibited a blueshift trend with a decrease in temperature. A detailed analysis of temperature-dependent optical absorption is provided later. Figure 4 presents the temperature-dependent optical absorption coefficient spectra of two thin films. The absorption spectra were fitted using the Lorentzian-Gaussian function, as illustrated by the dashed lines in the inset of  www.nature.com/scientificreports/ between the hybridization of Pt 5d and Se 4p states at the valence and conduction band edges. Moreover, the first-principles calculations 20 predicted that the rapid decrease in band energy of conduction band states and increase in valence band states lead to metallization starting from trilayer PtSe 2 thin film. As a result, two absorption bands observed in multilayer PtSe 2 thin film exhibited a redshift as compared to those of bilayer PtSe 2 thin film. The band gap energy of bilayer and multilayer PtSe 2 thin films is depicted Fig. 5. The optical absorption coefficient, which includes contributions from both direct and indirect band gap transitions, was analyzed using the following expression 41 :

Results and discussion
where E g,dir and E g,ind are the magnitudes of direct and indirect band gaps, respectively; E ph is the emitted (absorbed) phonon energy, and A and B are constants. This model, which assumes a simple band shape, enables extraction of the direct band gap when (α·E) 2 is plotted as a function of photon energy and extraction of indirect band gap when (α·E) 1/2 is plotted as a function of photon energy. Figure 5 presents an indirect band gap of approximately 0.75 ± 0.01 eV at 300 K for bilayer PtSe 2 thin film, whereas multilayer PtSe 2 thin film exhibited semimetal behavior from 300 to 4.5 K (see Supplementary Fig. 5). Plotting (α·E) 2 as a function of photon energy for both thin films led to a negative value for the band gap. The results of our band gap analysis of bilayer PtSe 2 thin film were consistent with those of other experimental studies 29,41,42 . However, the results for multilayer PtSe 2 thin film differed from those of other reports of semiconducting behavior in films of a similar thickness 29,42,43 . One possibility that could account for these differences is due to different quality of thin films.
(1) www.nature.com/scientificreports/ Figure 6 displays the temperature dependence of the band gap of bilayer and multilayer PtSe 2 thin films. The band gap of bilayer PtSe 2 thin film increased with a decrease in temperature. The observed blueshift value of the band gap energy with decreasing temperature in semiconductors can be described using the Bose-Einstein model as follows 44 : where E g (0) represents the band gap at 0 K, a B is the strength of the electron-phonon interactions, and B is the average phonon temperature. Our fitting results indicated that the band gap energy toward 0 K was approximately 0.83 ± 0.01 eV. The strength of the electron-phonon interactions a B and the average phonon temperature Θ B were 66 meV and 288 K, respectively. These values are comparable to those obtained for other semiconducting materials such as ZnS 45 and ZnSe 46 . In contrast to bilayer PtSe 2 thin film, multilayer PtSe 2 thin film revealed a band gap energy that steadily increased with an increase in temperature from 310 to 500 K. This could induce semimetal to semiconducting transition and may be due to both the electron-phonon interaction and thermal expansion of the lattice 47 . The linearly fitted result indicated that the temperature coefficient was 1.75 × 10 −4 eV/K. This value is lower than those of other TMDs such as ReS 2 48 . Figures 7 and 8 illustrate the peak energy, damping, and normalized intensity of 2.22-and 3.75-eV optical transitions for bilayer PtSe 2 thin film and 1.51-and 3.39-eV optical transitions for multilayer PtSe 2 thin film as a function of temperature. The peak positions of all absorption bands shifted to higher photon energies, resonance damping narrowed, and normalized intensity increased with a decrease in temperature. Figure 9 depicts the room-temperature Raman scattering spectra of bilayer and multilayer PtSe 2 thin films. The spectra comprised three Raman phonon modes. We fitted these phonon peaks using a standard Lorentzian profile. The phonon frequency and assignment are summarized in Table 2. According to the results of factor group analysis, PtSe 2 had a 1 T-type hexagonal crystal structure (P-3m1) with one formula unit per primitive cell 27 . The irreducible representation of the phonon modes at the center of the Brillouin zone is expressed by Γ = A 1g + E g + 2A 2u + 2E u 27 . These modes are classified as Raman active (A 1g + E g ), infrared active (2A 2u ), and Raman and infrared active (2E u ). We observed two main peaks at approximately 179 and 207 cm −1 in bilayer PtSe 2 thin Figure 9. Raman scattering spectra of PtSe 2 thin films at room temperature. The inset illustrates vibrational modes of both PtSe 2 thin films 50 . www.nature.com/scientificreports/ film, which were associated with the zone center and first-order one-phonon emission for in-plane and out-ofplane with E g and A 1g symmetries , respectively. The peak frequencies (179 and 207 cm −1 ) reproduced previous Raman scattering measurements, indicating a bilayer signature 27 . Additionally, we observed one less-predominant peak at approximately 235 cm −1 , which corresponded to the longitudinal optical (LO) mode in bilayer PtSe 2 thin film. This mode is mainly separated into two vibrations that correspond to first-order two-phonon emissions for out-plane (A 2u ) and in-plane (E u ) motions of Pt and Se atoms. Similar phonon modes have been observed in CdI 2 as the same structure with PtSe 2 thin films 49 .
In the normalized condition of the intensity of the E g mode, two phonon modes (E g and LO) of PtSe 2 thin film shifted to lower frequency ranges (from 179 and 235 cm −1 [bilayer] to 178 and 232 cm −1 [multilayer], respectively) with an increase in the number of layers. Unlikely those two phonon modes, the frequency of the A 1g mode of bilayer PtSe 2 thin film was unchanged when the number of layers increased. This anomalous behavior is consistent with that of PtSe 2 thin film growth through molecular beam epitaxy 50 . Subsequently, we observed that the A 1g mode of multilayer PtSe 2 thin film exhibited higher intensity than that of bilayer PtSe 2 thin film because of stacking-induced structural changes and long-range Coulombic interlayer interactions 51 . The intensity of the LO mode decreased with an increase in thickness. This behavior could be associated with the enhanced interlayer coupling in multilayer PtSe 2 thin film 27 . Figure 10 displays the temperature dependence of the Raman scattering spectra of bilayer and multilayer PtSe 2 thin films. When the temperature decreased, the peak positions of all phonon modes shifted to higher frequencies, and their resonance linewidth decreased. The Raman scattering spectra exhibited sharp phonon modes at 10 K for both thin films. Four Lorentzian oscillators were used to represent the Raman scattering spectrum at 10 K (inset of Fig. 10), whereas the background was taken to be linear in these fits of the form Aω + B, where A and B are adjustable parameters. Figures 11 and 12 illustrate the frequency, linewidth, and normalized intensity of phonon modes as functions of temperature. The phonon modes changed continuously from temperatures of 500 to 10 K. In a normal anharmonic solid, a decrease in temperature causes an increase in phonon frequency but a decrease in linewidth. Anharmonic interactions are relevant to higher-order terms of atomic vibrations that are beyond traditional harmonic terms. The temperature-dependent phonon frequency and linewidth can be expressed as follows 52 : where ω 0 is the intrinsic frequency of the optical phonon mode, γ 0 is linewidth broadening due to defects, A and B are anharmonic coefficients, and Θ is the Debye temperature. The values of the fitting parameters are summarized in Table 3. Table 3 indicates that the high absolute A values of E g and A 1g modes in bilayer and multilayer PtSe 2 thin films revealed a dominant anharmonic interaction between Pt and Se atoms. These large values are crucial for reducing lattice thermal conductivity 53 . The relatively small absolute B values of E g and A 1g modes in bilayer and multilayer PtSe 2 thin films were associated with strong anharmonic phonon-phonon interactions. Thus, anharmonic phonon scattering with three-phonon process (Eqs. 3 and 4) is highly favorable for bilayer and multilayer PtSe 2 thin films. At a temperature of 10 K, as depicted in Fig. 10, the LO phonon mode of bilayer PtSe 2 thin film exhibited a peak position that split into two-phonon modes (A 2u and E u ) at approximately 235 and 239 cm −1 . By contrast, multilayer PtSe 2 thin film exhibited a broadening peak at approximately 236 cm −1 . Moreover, the A 2u and E u phonon modes of bilayer PtSe 2 thin film exhibited a blueshift and an increase in intensity in temperature with a decrease in temperature.
Summary. The temperature-dependent optical properties of bilayer and multilayer PtSe 2 thin films were investigated through spectroscopic ellipsometry and Raman scattering spectroscopy. Large value of the refractive index (approximately 6.88) in the near-infrared frequency range was obtained for multilayer PtSe 2 thin film. The thermo-optic coefficients of bilayer and multilayer PtSe 2 thin films were (4.31 ± 0.04) × 10 −4 /K and (-9.20 ± 0.03) × 10 −4 /K at a wavelength of 1200 nm. The room-temperature optical absorption spectra revealed

Data availability statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.