Objective Recently, two-dimensional materials, particularly transition metal sulfides, have attracted broad attention in the field of optoelectronics because of their unique properties. Platinum diselenide (PtSe₂) is a new type of transition metal sulfide material with unique features, such as adjustable bandgap and high carrier mobility, that has excellent potential for saturable absorbers, photodetectors, and photovoltaic cells. It is necessary to study the variation of PtSe₂ optical properties with the number of layers, which is essential for designing and optimizing related devices. Moreover, it is also valuable to study the change in the refractive index of PtSe₂ films with temperature in practical applications. In this work, PtSe₂ films with two, four, and six layers were grown on sapphire substrates using the chemical vapor deposition method. The optical properties of PtSe₂ with different thicknesses, including optical bandgap, refractive index, extinction coefficient, dielectric function, and thermo-optical coefficient, were investigated using the spectrophotometer and spectroscopic ellipsometry. This work can guide the design and optimization of PtSe₂-based optical modulation devices.

Methods The synthesis method of PtSe₂ films used in this work is the three-zone temperature-controlled chemical vapor deposition method (Fig.1). PtSe₂ films with two, four, and six layers were grown on sapphire substrates by controlling the growth time. The thickness and surface morphology of the samples were confirmed using atomic force microscopy. The Raman vibration patterns of samples with different layer numbers were investigated using Raman spectroscopy. The samples' absorption spectrum was obtained using the spectrophotometer, and the optical bandgap of the samples was obtained using the Tauc formula. The optical constants and dielectric functions of PtSe₂ with different layer numbers were obtained using spectroscopic ellipsometry. Three Tauc-Lorentz oscillators were used to describe the dielectric function of the PtSe₂ films during the analysis of elliptical polarization spectra. In addition, we studied the refractive index and extinction coefficient of PtSe₂ with increasing temperature using spectroscopic ellipsometry and a high-temperature thermal bench. The thermo-optical coefficients of four-layer and six-layer PtSe₂ films were calculated.

Results and Discussions The prepared PtSe₂ films have good homogeneity and the transmittance decreases as the number of layers increases (Fig.2). Raman spectra show that PtSe₂ has three main Raman vibrational modes, and the E_g and A_1g modes are red-shifted as the number of layers increases (Fig.3). This phenomenon can be attributed to the increase in interlayer coupling. The absorption spectra and Tauc formula calculations show that the optical absorption increases and the bandgap decrease as the number of sample layers increases (Fig.4). The bandgaps of the two-layer, four-layer, and six-layer PtSe₂ films are 1, 0.85, and 0.73 eV, respectively. The spectroscopic ellipsometry spectrum of PtSe₂ was modeled using three Tauc-Lorentz oscillators, and the optimum fitting parameters were obtained (Table 1). By fitting the ellipsometric parameters of the PtSe₂ films, the optical constants of the samples with different layers, including the refractive index, extinction coefficient, and the real and imaginary parts of the dielectric function, were obtained (Fig.6). The results show that the optical constants of PtSe₂ films are significantly correlated with both wavelength and thickness. In the wavelength range of 300-700 nm, the refractive index of PtSe₂ films increases with wavelength until it reaches a certain wavelength and then starts to decrease slowly. This transition wavelength is also red-shifted with the increase in the number of layers. This may be related to the increase in the interlayer coupling as the number of layers increases. Alternatively, as the number of layers increases, the peak position of the imaginary part of the dielectric function is also red-shifted, indicating that the electron leap energy between the conduction and valence bands is decreasing. In addition, the variation of the refractive index and extinction coefficient of PtSe₂ with temperature was obtained from variable-temperature spectroscopic ellipsometry measurements (Fig.7). The thermo-optical coefficient of PtSe₂ as a function of wavelength was obtained (Fig.8). As shown in Fig.8, the thermo-optical coefficient is around the zero-axis between the wavelength of 400-500 nm, indicating that the refractive index of PtSe₂ hardly changes with temperature in this band and has good thermo-optical stability.

In contrast, the thermo-optical coefficient is negative within the wavelength of 500-800nm, indicating that the refractive index decreases with an increase in temperature. It may be related to the semi-metallic properties exhibited in multilayer PtSe₂ films. Therefore, PtSe₂ films are more suitable for application within optoelectronic devices operating in the wavelength range of 400-500 nm.

Conclusions Continuous PtSe₂ films with two, four, and six layers were grown using chemical vapor deposition. Raman spectra indicated the existence of interlayer coupling in the samples. The bandgap, refractive index, extinction coefficient, and the dielectric function of the samples were characterized using the spectrophotometer and spectroscopic ellipsometry, and the results showed that the bandgap and optical constants of PtSe₂ were significantly correlated with the thickness. The effect of temperature on the optical constants of PtSe₂ was analyzed using variable temperature ellipsometric spectroscopy, and the thermo-optical coefficients at different wavelengths were obtained. The result shows that the thermo-optical coefficient is near the zero-axis between the wavelength of 400-500 nm. In contrast, the thermal-optical coefficient is negative in the wavelength range of 500-800 nm, which may be related to the semi-metallic nature of PtSe₂ multilayer films. This research can guide the design and optimization of PtSe₂-based light modulation devices.