Temperature-dependent optical constants of monolayer $${\text {MoS}}_2$$, $${\text {MoSe}}_2$$, $${\text {WS}}_2$$, and $${\text {WSe}}_2$$: spectroscopic ellipsometry and first-principles calculations
Hsiang‐Lin Liu, Teng Yang, Jyun-Han Chen, Hsiao‐Wen Chen, Huaihong Guo, Riichiro Saito, Mingyang Li, Lain‐Jong Li
Abstract
Abstract The temperature-dependent ( $$T = 4.5 \, \hbox {-} \, 500 \, \hbox {K}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>T</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4.5</mml:mn> <mml:mspace/> <mml:mtext>-</mml:mtext> <mml:mspace/> <mml:mn>500</mml:mn> <mml:mspace/> <mml:mtext>K</mml:mtext> </mml:mrow> </mml:math> ) optical constants of monolayer $${\text {MoS}}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>MoS</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:math> , $${\text {MoSe}}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>MoSe</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:math> , $${\text {WS}}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>WS</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:math> , and $${\text {WSe}}_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>WSe</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:math> were investigated through spectroscopic ellipsometry over the spectral range of 0.73–6.42 eV. At room temperature, the spectra of refractive index exhibited several anomalous dispersion features below 800 nm and approached a constant value of 3.5–4.0 in the near-infrared frequency range. With a decrease in temperature, the refractive indices decreased monotonically in the near-infrared region due to the temperature-dependent optical band gap. The thermo-optic coefficients at room temperature had values from $$6.1 \times 10^{-5}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>6.1</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> to $$2.6 \times 10^{-4} \, \hbox {K}^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2.6</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> <mml:mspace/> <mml:msup> <mml:mtext>K</mml:mtext> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> for monolayer transition metal dichalcogenides at a wavelength of 1200 nm below the optical band gap. The optical band gap increased with a decrease in temperature due to the suppression of electron–phonon interactions. On the basis of first-principles calculations, the observed optical excitations at 4.5 K were appropriately assigned. These results provide basic information for the technological development of monolayer transition metal dichalcogenides-based photonic devices at various temperatures.