Optical study of the structural change in ReS<sub>2</sub> single crystals using polarized thermoreflectance spectroscopy

Ching-Hwa Ho

doi:10.1364/OPEX.13.000008

Optics Express
Vol. 13,
Issue 1,
pp. 8-19
(2005)
•https://doi.org/10.1364/OPEX.13.000008

Optical study of the structural change in ReS₂ single crystals using polarized thermoreflectance spectroscopy

Ching-Hwa Ho

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Ching-Hwa Ho, "Optical study of the structural change in ReS₂ single crystals using polarized thermoreflectance spectroscopy," Opt. Express 13, 8-19 (2005)

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Abstract

In this report the optical properties of ReS₂ are characterized using polarized thermoreflectance (PTR) measurements in the temperature range between 25 and 300 K. Single crystals of ReS₂ were grown by chemical vapor transport method using Br₂ as a transport agent. Crystal morphologies of the as-grown rhenium disulfides were shown to possess two different kinds of the structural phases after crystallization. Observing in detail on the crystallized solids, the crystal phases can be essentially divided into two distinct types of normal triclinic layer and tetragonal structure. The PTR experiments were done with optical polarizations along and perpendicular to the crystals’ b-axis for both layer and tetragonal crystals. From the experimental analyses of PTR measurements the occurrence of structural change in ReS₂ is mostly probable caused by the atomic bonding deformation along b-axis, which is parallel to the Re₄ parallelogram consisted diamond chains. Temperature dependences of the band-edge transitions for the different structural phases of ReS₂ are analyzed. The parameters that describe temperature variations of the transition energies and broadening parameters for both layered and tetragonal ReS₂ are evaluated and discussed.

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Fig. 1. The crystal morphologies of the as-grown layer-type and tetragonal ReS₂ single crystals. The structural unit cells for both triclinic layer and tetragonal structure are included for comparison.

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Fig. 2. Polarized thermoreflectance spectra of (a) layer-type ReS₂ [denoted as ReS₂(L)] and (b) tetragonal ReS₂ [denoted as ReS2(T)] at 25K. The dashed lines are the experimental results and the solid curves are least-square fits to a derivative Lorentzian line-shape function which yield transition energies indicated by arrows.

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Fig. 3. Temperature-dependent PTR spectra of (a) ReS₂ (L) and (b) ReS2 (T) with E‖b and E⊥b polarizations at various temperatures between 25 and 300 K. The dashed lines and solid curves are respectively the experimental PTR spectra of E‖b and E⊥b polarizations while the hollow-circle lines are least-square fits to Eq. (1).

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Fig. 4. Temperature dependence of the transition energies of layered and tetragonal ReS2 with representative error bars. The dashed curves are least-squares fits to Eq. (2), the solid lines are least-squares fits to Eq. (3) and the hollow-square curves are least-squares fits to Eq. (4).

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Fig. 5. Temperature dependent spectral linewidths of the interband transitions

E_{1}^{ex}

E_{2}^{ex}

, E_d1, and E_d2 for ReS₂ (L) and ReS₂ (T). Representative error bars are shown. The full curves are least-squares fits to Eq. (5).

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Tables (3)

Table 1. Values of fitting parameters of Varshni equation and an expression proposed by O’Donnel & Chen which describe the temperature dependence of the transition energies for layer-type and tetragonal ReS₂ by PTR measurements. The values of fitting parameters for the temperature dependence of the indirect gap of layered ReS₂ are included for comparison.

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Table 2. Values of the Bose-Einstein type fitting parameters which describe the temperature dependence of the transition energies and band gaps of ReS₂(L), ReS₂(T), CdSe, GaAs, and InP.

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Table 3. Values of the parameters that describe the temperature dependence of the broadening function of the transition energies and band gaps of ReS₂(L), ReS₂(T), CdSe, GaAs, and InP.

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Equations (5)

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\frac{Δ R}{R} = Re [\sum_{i = 1}^{n} A_{i} e^{j ϕ_{i}} {(E - E_{i} + j Γ_{i})}^{- 2}],

E_{i} (T) = E_{i} (0) - \frac{α T^{2}}{(T + β)}

E_{i}^{oc} (T) = E_{i}^{oc} (0) - S 〈 ℏ Ω 〉 [\coth (〈 ℏ Ω 〉 ⁄ k T) - 1]

E_{i} (T) = E_{iB} - \frac{2 \cdot a_{iB}}{[\exp (\frac{Θ_{iB}}{T}) - 1]},

Γ_{i} (T) = Γ_{i 0} + \frac{Γ_{iLO}}{[\exp (Θ_{iLO} ⁄ T) - 1]},

Material type	Feature	$E_{i}^{oc}$ (0) (eV)	α(meV/K)	β(K)	S	<ħΩ>(meV)
ReS₂(L) ^a	$E_{1}^{ex}$	1.546±0.001	0.34±0.05	180±70	2.0±0.1	25±3
	$E_{2}^{ex}$	1.577±0.001	0.33±0.05	190±70	2.0±0.1	27±3
ReS₂(T) ^a	E_d1	1.711±0.001	1.2±0.2	1550±200	4.5±0.4	61±4
	E_d2	1.750±0.001	1.1±0.15	1590±200	4.0±0.4	59±4
ReS₂(L) ^b	$E_{g}^{ind}$	1.51±0.02	0.62 ± 0.05	115 ± 50	4.05±0.50	20±2

Feature	Materials	E_B (eV)	a_B (meV)	Θd (K)
$E_{1}^{ex}$	ReS₂(L) ^a	1.547±0.002	37±15	240±60
$E_{2}^{ex}$		1.578±0.002	35±14	240±60
E_d1	ReS₂(T) ^a	1.711±0.001	327±144	754±100
E_d2		1.750±0.001	235±107	688±100
$E_{g}^{d}$	CdSe ^b	1.830(5)	36(5)	179(40)
$E_{g}^{d}$	GaAs ^c	1.512±0.005	57±29	240±102
$E_{g}^{d}$	InP ^d	1.423±0.01	51±2	259±10

Feature	Materials	Γ₀ (meV)	Γ_LO (meV)	Θ_LO (K)
$E_{1}^{ex}$	ReS₂(L) ^a	9.5±0.5	36±15	326±100
$E_{2}^{ex}$		8.0±0.5	30±17	348±100
E_d1	ReS₂(T) ^a	73±2	40±12	250±60
Ed₂		73±2	46±15	350±60
$E_{g}^{d}$	CdSe ^b	2.3(3)	23(1)	300
$E_{g}^{d}$	GaAs ^c	2	20±1	417 ^d
E^ex	InP ^e	1.5±0.5	31±3.0	496 ^d

Material type	Feature	$E_{i}^{oc}$ (0) (eV)	α(meV/K)	β(K)	S	<ħΩ>(meV)
ReS₂(L) ^a	$E_{1}^{ex}$	1.546±0.001	0.34±0.05	180±70	2.0±0.1	25±3
	$E_{2}^{ex}$	1.577±0.001	0.33±0.05	190±70	2.0±0.1	27±3
ReS₂(T) ^a	E_d1	1.711±0.001	1.2±0.2	1550±200	4.5±0.4	61±4
	E_d2	1.750±0.001	1.1±0.15	1590±200	4.0±0.4	59±4
ReS₂(L) ^b	$E_{g}^{ind}$	1.51±0.02	0.62 ± 0.05	115 ± 50	4.05±0.50	20±2

Feature	Materials	E_B (eV)	a_B (meV)	Θd (K)
$E_{1}^{ex}$	ReS₂(L) ^a	1.547±0.002	37±15	240±60
$E_{2}^{ex}$		1.578±0.002	35±14	240±60
E_d1	ReS₂(T) ^a	1.711±0.001	327±144	754±100
E_d2		1.750±0.001	235±107	688±100
$E_{g}^{d}$	CdSe ^b	1.830(5)	36(5)	179(40)
$E_{g}^{d}$	GaAs ^c	1.512±0.005	57±29	240±102
$E_{g}^{d}$	InP ^d	1.423±0.01	51±2	259±10

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Tables (3)

Equations (5)

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