Direct observation of highly anisotropic electronic and optical nature in indium telluride

Geoffroy Kremer, Aymen Mahmoudi, Meryem Bouaziz, Cléophanie Brochard-Richard, Lama Khalil, Debora Pierucci, François Bertran, Patrick Le Fèvre, Mathieu G. Silly, Julien Chaste, Fabrice Oehler, Marco Pala, Federico Bisti, and Abdelkarim Ouerghi

Phys. Rev. Materials 7, 074601 – Published 11 July 2023

Abstract

Metal monochalcogenides $(M X,$ $M = Ga, In; X = S, Se, Te)$ offer a large variety of electronic properties depending on chemical composition, number of layers, and stacking order. InTe material has a one-dimensional chain structure, from which intriguing properties arise. Precise experimental determination of the electronic structure of InTe is needed for a better understanding of potential properties and device applications. In this study, by combining angle-resolved photoemission spectroscopy and density functional theory calculations, we demonstrate the stability of InTe in the tetragonal crystal structure, with a semiconducting character and an intrinsic $p$ -type doping. The valence band maximum results in being located at the high symmetric $M$ point with a high elliptical valley, manifesting a large effective mass close to the Fermi level. The longitudinal and transverse effective masses of the $M$ valley are measured as 0.2 $m_{0}$ and 2 $m_{0}$ , respectively. More specifically, we observe that the effective mass of the hole carriers is about ten times larger along the chain direction compared to the perpendicular one. Remarkably, the in-plane anisotropy of effective mass from the experiment and in theoretical calculations are in good agreement. These observations indicate a highly anisotropic character of the electronic band structure, making InTe of interest for electronic and thermoelectric applications.

Received 15 March 2023
Revised 4 June 2023
Accepted 14 June 2023

DOI:https://doi.org/10.1103/PhysRevMaterials.7.074601

Physics Subject Headings (PhySH)

Electronic structure

Density functional theory Photoemission spectroscopy Raman spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Geoffroy Kremer ^1,2, Aymen Mahmoudi ¹, Meryem Bouaziz¹, Cléophanie Brochard-Richard¹, Lama Khalil¹, Debora Pierucci ¹, François Bertran³, Patrick Le Fèvre³, Mathieu G. Silly ³, Julien Chaste¹, Fabrice Oehler ¹, Marco Pala¹, Federico Bisti⁴, and Abdelkarim Ouerghi^1,*

¹Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120 Palaiseau, Paris, France
²Institut Jean Lamour, UMR 7198, CNRS-Université de Lorraine, Campus ARTEM, 2 allée André Guinier, BP 50840, 54011 Nancy, France
³Synchrotron SOLEIL, L'Orme des Merisiers, Départementale 128, 91190 Saint-Aubin, France
⁴Dipartimento di Scienze Fisiche e Chimiche, Università dell’Aquila, Via Vetoio, 67100 L’Aquila, Italy

^*Corresponding author: abdelkarim.ouerghi@c2n.upsaclay.fr

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Issue

Vol. 7, Iss. 7 — July 2023

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Images

Figure 1
Crystal structure and structural properties of InTe: (a) Crystal structure of $I 4 / m c m$ tetragonal InTe crystal, showing to two inequivalent In atoms ( ${In}^{1 +}$ blue color, ${In}^{3 +}$ brown) and the preferential (110) cleavage plane (green color). (b) Local atomic arrangement of the (110) plane, displaying a strong structural anisotropy between the two in-plane directions, with infinite covalently-bounded chains along the $c$ axis and weak interaction along [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. (c) Polar-plot dependent Raman spectra of InTe with different in-plane orientation angle theta. For the $A_{1 g}$ mode, only Te atoms move in the $x y$ plane, whereas for the $E_{g}$ mode, ${In}^{3 +}$ and Te atoms vibrate along the $x y$ plane and $z$ direction, respectively. In both modes, the ${In}^{1 +}$ atoms do not exhibit any displacement. (d) Polar plot of the $A_{1 g}$ Raman line intensity against the in-plane angle theta. $Θ = 0$ and $90^{\circ}$ indicate the a- and $c$ -axis direction, respectively.
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Figure 2
Electronic band structure of InTe: (a) Brillouin zone of the body-centered-tetragonal unit cell of InTe. The high-symmetry points are indicated; (b) ARPES 3D mapping in the $M X P$ plane; (c) ARPES map of InTe along the ΜXΜ direction. (d) Comparison of experimental and DFT isoenergic ARPES maps of InTe at $E_{F}$ and −0.3 eV.
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Figure 3
Photon energy dependent ARPES measurements converted to $I$ ( $k_{z}$ , $k_{x}$ ) ARPES map ( $E - E_{F} = - 0.5$ eV) for InTe single crystal. The two dashed lines highlight the photon energies corresponding to the M-X-M high-symmetry direction.
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Figure 4
ARPES data of InTe measured in the vicinity of the $\bar{M} − \bar{X}$ - $\bar{M}$ high-symmetry direction compared with theoretical electronic band structure: (a) ARPES map of InTe along the $M X M$ high-symmetry directions ( $T = 50$ K and $hv = 55$ eV). (b),(c) Comparison between ARPES map and DFT calculations (PBE and HSE, respectively). The calculation was performed by considering an offset of 10% with respect to the $M X M$ high-symmetry direction. For this photon energy, VBM is located at the $M$ point.
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Figure 5
Anisotropic effective hole masses of InTe near the valence band maximum: (a) Isoenergic ARPES maps of InTe at −0.5 eV below $E_{F}$ . ARPES cut data along the in-plane momentum defined by the angle $θ$ [see colored lines in Fig. 4 for definition] for InTe. All the data sets are centered around the $M$ point at which VBM is located; (b),(c) ARPES cuts along and perpendicular to the ΜXΜ direction. The red lines indicate a quadratic function fitting the dispersions of the top-most bands. (d) Comparison of experimental and DFT polar plot of the effective mass against the in-plane angle theta. $Theta = 0$ and $90^{\circ}$ indicates the a- and $c$ -axis direction, respectively.
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