Crystal and electronic structure of a quasi-two-dimensional semiconductor Mg₃Si₂Te₆

Narrow-gap semiconductors (NGS) play an important role in optoelectronic and magnetic devices. Because of their unique advantages, the properties and applications of NGS have been widely studied for decades in a variety of fields, such as magnetic field sensors, photovoltaics, infrared photodetectors, lasers and so onElliott (1998); Maier and Hesse (1980); Stradling (1996); Xie et al. (2021); Zhang et al. (2017). Magnetic field sensors, including magnetoresistors and Hall sensors, are generally used in magnetic recording and magnetic measurement technologiesRipka and Janosek (2010); Heremans et al. (1993). Materials for magnetic field sensors are doped semiconductors with high electronic density of states and mobility, such as InSb and InAs which are extremely sensitive to magnetic fieldSolin et al. (2000); Berus et al. (2004); Mihajlović et al. (2005). Conventional photovoltaic materials mostly use wide-gap semiconductors that utilize photons in the ultraviolet and visible regions, limiting the conversion efficiency. Tuning the band gap is considered to be one of the effective solutionsCheng and Yang (2020). NGS-based photoelectrodes can absorb light at longer wavelengths and enhance the solar energy conversion efficiencyZheng et al. (2019). As a more widely used field, infrared photodetectors, such as the quantum dots-in-a-well photodetectors, have developed rapidly in recent yearsDowns and Vandervelde (2013); Martyniuk and Rogalski (2008); Chen et al. (2018). In addition, NGS lasers have attracted more and more attention due to their stability, tunability, simple structure, and many other advantagesTournie and Baranov (2012); Harman and Melngailis (1974).

One of the most important parameters for photoelectric materials is the value of the electronic band gap. Hg_1-xCd_xTe and Pb_1-xSn_xTe are among the hottest researched NGS systems in recent years, whose gaps can be tuned by compositions in a wide range, even close to zeroHarman and Melngailis (1974); Rogalski (2005); Lei et al. (2015); Piotrowski and Rogalski (2004). Alloying is also an effective method to modulate the band gap, which is beneficial for the application of the mid- and long-infrared photodetectorsYang et al. (2022). Although InSb and HgCdTe based detectors have been well available in commercial applications, their poor flexibility, instability of the material interface, complex manufacturing process, and low temperature working environment limit their further developmentPiotrowski and Rogalski (1998); Jiao et al. (2022); Yang et al. (2022). Therefore, it is crucial to search for more NGS that are suitable for manufacturing stable and efficient infrared detectors. Meanwhile, new NGS with excellent performance also have potential applications in laser, photovoltaics, and other magnetic devices.

In this work we report the successful synthesis of a Si-based nonmagnetic semiconductor Mg₃Si₂Te₆, whose structure is found to exhibit a quasi-two-dimensional (quasi-2D) layered configuration. Fittings using a direct and indirect band gap models to the ultraviolet-visible (UV-vis) absorption spectra result in a direct gap of 1.39 eV or an indirect gap of 0.6 eV, respectively. Electronic structure calculations using density functional theory (DFT) yield a direct band gap of 1.2 eV, close to the direct gap fitted from the UV-vis absorption spectra, revealing that Mg₃Si₂Te₆ is a direct gap semiconductor. The band gap is narrower than the energies of visible photons, allowing Mg₃Si₂Te₆ a potential candidate for infrared photoelectric material.

Single crystal samples of Mg₃Si₂Te₆ were grown by a self-flux methodYin et al. (2020); Sun et al. (2021); Li et al. (2021). Mg (99.99$\%$) robs, Si (99.99$\%$) powders, and Te blocks (99.99$\%$) were mixed in a molar ratio of $3:2:6$ after rough grinding, then sealed in an evacuated quartz ampoule. The ampoule was firstly heated to 600 ^∘C in 10 h and held for 15 h, then heated to 1050 ^∘C in 20 h and dwelled for 10 h, followed by a slow cooling to 750 ^∘C in 150 h before the furnace was shut down. Shiny plate-like single crystals were obtained. The samples are air sensitive and were stored in an argon-filled glove box to minimize the exposure to air.

Single-crystal x-ray diffraction (XRD) measurements on a single-crystal x-ray diffractometer (SuperNova, Rigaku), a scanning electron microscopy (SEM) photography, and an energy dispersive x-ray spectroscopy (EDS) (EVO, Zeiss) were employed to determine the crystal structure, morphology and composition. Resistivity was measured using the standard four-probe method on single crystals with a typical size of 3 $\times 1\times 0.5$ mm³ on a physical property measurement system (PPMS) (Quantum Design). UV-vis absorption spectroscopy measurements were conducted using an Ocean Optics DH-2000-BAL spectrometer. The sample was pre-peeled into thin flakes with right thickness and then loaded into a diamond anvil cell (DAC) to avoid oxidation. The outboard ring of the DAC is the T301 steel gasket, which was pre-indented and drilled a hole with a diameter of  150 $\mu$m to serve as the sample chamber. Each spectrum was collected for 2 seconds with wavelengthes ranged from 180 to 860 nm. The signal from background was obtained by shining the beam on a spot inside the sample chamber but away from the sample.

Electronic band structure was calculated using the DFT within the Perdew-Burke-Ernzerhof (PBE) exchange-correlation as implemented in the Vienna $Ab~{}initio$ Simulation Package (VASP) codePerdew et al. (1996); Vargas Hernández (2020). A plane wave energy cutoff of 600 eV and dense meshes of Monkhorst-Pack $k$-points were used to ensure that all calculations are well converged to 1 meV/atom.

The structure of Mg₃Si₂Te₆ is refined from XRD measurements on single crystals. The structural parameters are summarized in Table 1. Mg₃Si₂Te₆ crystalizes in the trigonal space group $P\overline{3}1c$ with $a$ = 7.0642(9) Å and $c$ = 14.464(2) Å at 253 K and exhibits a quasi-2D structure. The crystal structures viewed from different directions are illustrated in Fig. 1. The layer of the $ab$ plane constituting the formula as Mg₂Si₂Te₆ consists of edge shared MgTe₆ octahedra and Si-Si dimers. The Mg₂Si₂Te₆ layer is isomorphic to a widely studied 2D van der Waals ferromagnetic compound Cr₂Si₂Te₆Carteaux et al. (1995); Cai et al. (2020). The layers are linked by Mg2 that is half of Mg1, constituting Mg₃Si₂Te₆. Mg₃Si₂Te₆ is isostructural to Mn₃Si₂Te₆Vincent et al. (1986) and Mn₃Si₂Se₆May et al. (2020) which are quasi-2D semiconductors with enriched properties such as ferrimagnetism and large colossal magnetoresistanceNi et al. (2021); Seo et al. (2021).

To determine the composition of the samples, we performed EDS measurements on Mg₃Si₂Te₆ single crystals. Figure 2(a) is a zoomed-in view of the measured crystal in the $ab$ plane taken from SEM. It is obvious that the crystal is layered with some Te flux on the surface. By normalizing the content of Mg to be 3, the composition determined from EDS is Mg₃Si_1.87(4)Te_6.8(2). The ratio of Mg to Si ratio is close to expectation. The exceeding content of Te of 13% can be attributed to the excess Te flux on the surface.

Figure 3 shows the resistivity measured between 328 and 400 K. The resistivity below 328 K exceeding 10⁶ $\Omega$cm is beyond the measured range of the instrument. As shown in Fig. 3 (a), the resistivity exhibits an insulating behavior, and no obvious anomaly can be observed up to 400 K. Figure 3 (b) is a plot of the resistivity in $\ln\rho$ as a function of 1000/$T$. A fitting using the thermal activation-energy model $\rho$($T$) = $\rho$₀ exp($E$_a/$k$_B$T$) to the linear segment that corresponds to 350 to 400 K results in $E_{a}=0.378$ eV. In the model, $\rho$₀ is a prefactor, $k$_B is the Boltzmann constant, and $E_{a}$ is the thermal activation energy. The obtained activation energy of 0.378 eV indicates that the energy gap of Mg₃Si₂Te₆ may be narrower than that of visible light of $1.64\sim 3.19$ eV. We note the fitted thermal activation energy at $350\sim 400$ K may be much smaller than the band gap.

UV-vis absorption spectra were employed to study the electronic band gap of Mg₃Si₂Te₆. Five pieces of single crystals were measured separately. The absorption spectra are shown in Fig. 4 (a), yielding a typical semiconducting state with a strong absorption in the range of $700\sim 860$ nm, while the rest of the short wavelength data are removed because of relatively high noise. The band gap can be obtained by fitting the absorption spectra using the Tauc relation that is [$F$($R$_∞)$h$$\nu$]^1/n = $A$($h$$\nu$ - $E_{g}$), where $F$($R$_∞) is the Kubelka-Mubelka-Munk function, $h$ is the Planck constant, $\nu$ is the frequency, $A$ is a prefactor, and $E_{g}$ is the band gap energySarkar et al. (2017). For a direct band gap semiconductor, $n$ is 1/2; for an indirect band gap semiconductor, $n$ is 2. We plot the Tauc relations as a direct gap and indirect gap semiconductor in Figs. 4 (b) and 4 (c), respectively. The size of the band gap is extracted from the linear regression at the inflection point and the obtained $h\nu$-intercept value is taken as the band gap valueTauc et al. (1966). The measured absorption spectra could not distinguish the two models due to poor statistic. We fitted the linear parts of five sets of data by adopting the Tauc relation and $n=1/2$, resulting in the direct band gaps of 1.41, 1.43, 1.43, 1.37, and 1.31 eV. Thus, the direct gap is estimated to be 1.39(5) eV by averaging the fitted values. Following the same procedure and adopting $n=2$, an indirect band gap of 0.6(2) eV is obtained. The difference in the calculated energy gaps between different data sets can be attributed to the inconsistency of thicknesses of the samples, which causes calculation errors by affecting the transmittance and reflectivity of the samples to ultraviolet light.

In order to distinguish the direct gap and indirect gap from the fittings of the UV-vis absorption spectra, DFT calculations were performed to investigate the electronic band structure. Figure 5 displays the band structures along high symmetry directions in a Brillouin zone and partial density of states (PDOS) of Mg₃Si₂Te₆. The calculated data reveal a direct gap of $\sim$1.2 eV at the $\Gamma$ point, close to the fitting results from the UV-vis absorption spectra using the direct gap model. Thus, Mg₃Si₂Te₆ can be considered as a direct gap semiconductor with a gap size of $1.2\sim 1.39$ eV. This value is larger than the thermal activation energy of 0.378 eV fitted from the resistivity between 350 and 400 K. The outcomes may attribute to the fact that the activation energy is fitted from resistance change at high temperature, where thermal fluctuations increase the electron hopping capability, and the gap seems to be narrowed. The direct gap size of Mg₃Si₂Te₆ is smaller than the energies of visible light. Through doping, temperature, and pressure, the band gap of Mg₃Si₂Te₆ may be further decreased, allowing Mg₃Si₂Te₆ one of the potential candidates for infrared photoelectric materials.

In conclusion, we synthesized single crystals of Mg₃Si₂Te₆ by self-flux method, and characterized the structure, composition, resistivity, and electronic band gap. Mg₃Si₂Te₆ exhibits a quasi-2D structure constituted by Mg₂Si₂Te₆ layers (Mg1) that are linked by Mg2 atoms. The single crystals can be mechanically cleaved and are sensitive to air. By combining the UV-vis absorption spectra and DFT calculations, we demonstrate that Mg₃Si₂Te₆ is a direct band gap semiconductor with a gap size of $1.2\sim 1.39$ eV. This gap size is close to that of silicon, and may allow Mg₃Si₂Te₆ become one of the candidates for infrared photoelectric or other functional materials by tuning the energy level by rare earth ions doping. Moreover, the direct gap characteristics may provide higher photon absorption efficiency compared with traditional indirect-gap Si-based semiconductors. The absorption capacity and conversion efficiency require further investigations.

Work was supported by the National Natural Science Foundation of China (Grants No. 12174454, No. 11904414, No. 11904416, and No. 12104427), the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2021B1515120015), and National Key Research and Development Program of China (Grant No. 2019YFA0705702).