Effect of strain on the Curie temperature and band structure of low-dimensional SbSI Free

The exploration of optoelectronic properties of ferroelectric materials has led to a number of significant breakthroughs such as the discovery of giant above-bandgap open circuit voltages in BiFeO₃,¹ the possibility of developing ferroelectric photovoltaics above the Shockley-Queisser limit,² the realization of >8% photoferroelectric photovoltaics via the multiferroic material Bi₂FeCrO₆,³ and the utilization of BiFeO₃ photoactive properties in non-volatile memory devices.⁴ Most of these advances are based on complex oxide materials. Nevertheless, in spite of these successes, such transition metal oxides still present major disadvantages such as large bandgaps, poor carrier mobilities due to the localized d orbitals of the transition metals, and low quantum efficiencies. Thus, in order to compete with the state-of-the-art Si-based technology, it is critical to develop a semiconducting ferroelectric material with a proper bandgap and high carrier mobility.

Among all V-VI-VII materials (V: Sb, Bi, or As; VI: S, Se, Te, or O; VII: I, F, Cl, or Br),⁵ antimony sulpho-iodide (SbSI) is ferroelectric^6,7 close to room temperature and is expected to be a great solar absorber thanks to its proper bandgap and its potential of high electron/hole mobility.^8,9 In orthorhombic SbSI, double-chains of covalent bonds are formed along the c-axis,¹⁰ while only van der Waals interactions exist in the perpendicular direction. This makes SbSI a pseudo one-dimensional material, and indeed, most commonly observed morphologies of SbSI are randomly oriented needles.^11–15 It is documented that in the paraelectric phase (>287 K), SbSI has a $Pnam$ space group with lattice constants, $a=8.52 Å$⁠, $b=10.13 Å$⁠, and $c=4.10 Å$ [Fig. 1(a)].¹⁶ In the ferroelectric phase (<287 K), SbSI has a $Pna21$ space group with Sb and S atom shifting by $±0.20 Å$ and $±0.05 Å$ along the c-axis, respectively, compared to its paraelectric phase [Figs. 1(b) and 1(c)].^17,18 At 310 K (in paraelectric phase), SbSI has a 1.41 eV indirect bandgap between Z and U points in the Brillouin zone and a 1.82 eV direct bandgap at the U point; at 280 K (in the ferroelectric phase), SbSI has a 1.43 eV indirect bandgap between Z and R points and a 1.97 eV direct bandgap at U.^19,20 Despite the advantageous optical bandgap, SbSI has a very low Curie temperature, around 287–295 K,²¹ which makes the operation of the photoelectric device based on such a material at ambient conditions unrealistic. To increase SbSI Curie temperature, in this work, we introduce elastic strain and apply the concept of strain engineering for tuning the phase transition temperature.^22–24 

We grew low-dimensional SbSI crystals by the chemical vapor deposition method (CVD) with a home-made CVD system, and the furnace (Lindberg Blue M) was bought from Thermo Fisher Scientific, Inc. Sb₂S₃ and SbI₃ powders (Sigma Aldrich) were used as solid precursors. During a typical deposition process, Sb₂S₃ is placed at the furnace center with a temperature of around 650 K due to its higher melting point. SbI₃ is placed in the upper stream part, 10 cm away from the furnace center. Freshly cleaved muscovite mica substrates (SPI Grade V-5) are placed downstream for the growth. Prior to deposition, the base pressure of the system was pumped to 0.5 Torr after which a 30  sccm flow of argon was used to maintain the pressure at 100 Torr before deposition. The chamber temperature was raised from room temperature to deposition temperature rapidly in 7 min. The deposition process lasted 40 min. The furnace was cooled down naturally before the mica substrates were taken out. The SbSI low-dimensional crystals were, in most cases, found on the substrate about 8 cm away from the Sb₂S₃ precursor.

After growth, single low-dimensional crystals and clusters of SbSI low-dimensional crystals were found on the mica substrate [Fig. 1(d)], which are flatter as compared to the classical needle morphology of SbSI.^11,25,26 Morphology characterization was done with a Nikon Eclipse Ti–S inverted optical microscope and a scanning electron microscope (SEM). Optical microscopy was used to determine the size of the low-dimensional crystals. Low-dimensional crystals up to 100 μm long were observed, with widths of around 10 μm [Fig. 1(d) inset]. SEM images further reveal different morphologies and sizes of these low dimension crystals as shown in Fig. S1. Transmission electron microscopy (TEM) electron diffraction, which was done with a JEOL JEM-2010 transmission electron microscope, shows that the crystal grows along SbSI [001] [Fig. 1(e)] with the two side walls assigned to be SbSI (020) and (200). Based on our diffraction patterns, the lattice parameters of unstrained SbSI are a = 8.83 Å and c = 4.09 Å. X-ray diffraction (XRD) shows that the crystals synthesized are phase pure SbSI (Fig. S2).

Figure 2(a) shows the photoluminescence spectroscopy (PL) of SbSI at room temperature. Our PL system consists of a Thorlabs 4 Megapixel Monochrome Scientific CCD Camera, a Princeton Instruments SP-2358 spectrograph, a Nikon Ti-S optical microscope, and a Picoquant 405 nm excitation (pulsed) laser. A PL peak at 673 nm indicates an optical bandgap of around 1.84 eV. Based on Nako and Balkanski, SbSI has a direct bandgap of 1.82 eV and an indirect bandgap of around 1.41 eV at room temperature.²⁰ We anticipate that the observed PL peak represents the direct bandgap transition. The inset in Fig. 2(a) presents the time-resolved photoluminescence spectroscopy (TRPL) of SbSI done with a Picoquant PDM single photon detector at room temperature, indicating a carrier lifetime of around 260 ps with an excitation fluence of 79 pJ/pulse at 405 nm. Figure 2(b) presents the first Brillouin zone of SbSI, while the band structures of SbSI at 280 K and 310 K are given in Fig. 2(c).¹⁹ Both direct and indirect bandgaps of SbSI decrease when temperature is reduced from 310 K to 280 K.

The ferroelectric properties of SbSI were analyzed with temperature-dependent steady-state photoluminescence spectroscopy (TDPL) in an INSTEC HCS302 microscope cryostat, and the results for unstrained SbSI are shown in Fig. 2(d). As temperature decreases, the PL peak position continuously moves to higher energy until ∼300 K, where an abrupt jump of the PL peak towards lower energy occurs. Such optical transition carries the information associated with ferroelectric transition, e.g., Curie temperature for unstrained SbSI, which is consistent with the previous results by the absorption study.²¹ 

To increase the Curie temperature in SbSI, as a proof of concept, we introduce mechanical strain in the low-dimensional crystals as shown in Fig. 3(a). In our experiment, strain was generated through the traditional bending method. A polydimethylsiloxane (PDMS) stamp is pre-stretched and attached to mica. After transfer of the SbSI to the PDMS stamp, the previously induced stress on the stamp is removed, and therefore, SbSI is bent and strained by the restoring force of the PDMS stamp. Compressive and tensile strain distributes across the slab linearly, with a maximum strain of around 5%, which can be simply estimated by the curvature of low-dimensional crystals obtained from the optical microscopy image. The strain in our testing area is around 3% as the laser spot is a little bit away from the edge of the low-dimensional crystals. Figure 3(b) presents the TDPL results of strained SbSI, indicating a possibly increased Curie temperature of around 360 K, which is drastically increased compared to that of the material without strain (∼300 K). The experimentally observed effect of temperature on the optical bandgap of strained and unstrained SbSI is presented (dots) in Figs. 4(a) and 4(b), respectively.

To achieve a better understanding of the mechanisms responsible for the increase in Curie temperature with strain, Landau theory under single domain assumption was applied. In this framework, we can write the free energy of the crystal as a Taylor expansion of the polarization $P$ in the vicinity of the phase transition with an external electric field applied²⁷ 

where $F0$ is the free energy of the paraelectric phase and $α$⁠, $β$⁠, and $γ$ are the coefficients of the expansion series. Higher-order terms are neglected because $P$ is comparatively small.

Based on the study by Kikuchi et al., ferroelectric SbSI mainly polarizes along the c-axis.¹⁶ In our experiment, the strain can be approximated to be uniaxial strain along this axis. As a first order approximation, we can treat SbSI as a one-dimensional system. When an external stress $σ$ is added, the free energy is modified as^27,28

where $η$ is the strain, $K$ is the elastic constant, and $Q$ is the electrostrictive coefficient of SbSI.²⁸ At thermodynamic equilibrium, it is found that

Substituting Eq. (3) into Eq. (2),²⁷ we get

Via the Curie-Weiss law $χ=CT−T0′$ under the strained condition, it is found that

where $C$ is the Curie constant, and $T0′$ is a constant under the strained condition (⁠$T0$ of $χ=CT−T0$ is a constant under the unstrained condition). Combining the unstrained and strained cases, one gets

where $s$ is the elastic compliance of SbSI. Under the condition of $FFerroelectric=FParraelectric$⁠, one obtains

Here, $Tc′$ is the Curie temperature under the strained condition (⁠$Tc$ is the one under the unstrained condition). The change of Curie temperature can be obtained as

Equation (9) shows that the Curie temperature of SbSI linearly depends on the external tensile strain. To quantify the change of Curie temperature, parameters $η,Q,C,s,β, and γ$ would be needed.

The results from previous experiments give the following estimates for these parameters: $s$ ranges from $3×10−11 m2 N−1$ to $5×10−11 m2 N−1;$^29,30 $Q$ ranges from $0.011 m4 C−2$ to $0.23 m4 C−2;$^29,31–34 $C$ ranges from $1.3×105 K$ to $2.5×105 K.$^21,29,35,36 We can assume that $β$ and $γ$ are constant and independent of temperature since they are coefficients of high-order terms: $β=−3.02×108 V m5 C−3$ and $γ=6.99×109 V m9 C−5.$³⁵ Based on the above summary, reported values of $C, s, β$⁠, and $γ$ vary very little while reports on $Q$ differ significantly. Nevertheless, the blue surface in Fig. 4(c) shows the calculated values of $Tc′$ as a function of $Q$ and $η$ based on Eq. (9), and the yellow line and surface in Fig. 4(c) show the experimental result. The intersection of the Landau calculations with our experimental observation proves that our observation can be explained by Landau theory.

How does the optical phase transition correlate with the ferroelectric phase transition quantitatively in SbSI? Beyond the phase transition point, the bandgap of SbSI decreases with increasing temperature [Figs. 4(a) and 4(b)], which is consistent with the behavior of most semiconductors,³⁷ and can be qualitatively interpreted by the deformation potential theory.^37–39 Further, based on Kern's work,⁴⁰ in the SbSI crystal, at fixed temperature, it was found that the shift in the absorption edge was proportional to the square of the external field in the paraelectric phase.⁶ If considering both deformation and polarization factors, Kern found that

where $Eg0$ is a constant, $x$ is the strain, and $P$ is the polarization.^41,42$pp$ is the deformation potential constant, which is a linear approximation of deformation potential.^37–39 $βx$ is the polarization potential⁴³ and a positive coefficient illustrating the effect of crystal symmetry breaking on bandgap widening.

With first order approximation, it is found that

where $ax$ is the thermal expansion coefficient and the second term represents the polarization-induced lattice expansion. Further, it is found that

where $βx′≡(ppQ+βx)$ is a constant.

With Kern's formulation applied to our results, in the paraelectric phase $P=0$⁠, $Eg$ is linearly related to temperature. In the ferroelectric phase, polarization can be calculated based on Landau theory, and so, we have

Figures 4(a) and 4(b) show that Kern's theory (solid red lines) can explain our experimental observation to a great extent. It is shown that close to the Curie temperature at the ferroelectric phase, the plot of bandgap versus temperature (both experimental and theoretical results) in unstrained SbSI [Fig. 4(a)] shows a much larger curvature than the strained one [Fig. 4(b)]. This could be attributed to the reduction of polarization potential near Curie temperature for the strained crystal. Indeed, Choi et al. have found that the polarization potential of $BaTiO3$ decreased with external strain, in agreement with our results.²² 

In summary, low-dimensional crystals of SbSI were synthesized by the vapor deposition approach and its phase was confirmed by electron diffraction and optical characterization. Steady-state PL spectroscopy indicates an optical direct bandgap around 1.84 eV at room temperature, and TRPL shows the carrier lifetime at around 260 ps. TDPL experiments suggest a Curie temperature around 298 K for the unstrained crystal, as marked by an abrupt jump of the bandgap. Via mechanical strain, the Curie temperature of SbSI was increased by ∼60 K evidenced by our TDPL characterization. Landau theory and Kern formulation were used to analyze and quantify this effect. As a proof of concept, our results suggest a possible approach on engineering low bandgap photoferroelectric material's phase transition for technologically applicable purposes. In the future, epitaxially strained SbSI nanofilms could be a possible solution for the development of practical solar cells and memory.

See supplementary material for XRD spectra and SEM images of SbSI crystals.

This project was supported by NSF under Award Nos. CMMI 1635520 and CBET 1706815.

The authors declare no conflict of interest.