Photoferroelectric materials show great promise for developing alternative photovoltaics and photovoltaic-type non-volatile memories. However, the localized nature of the d orbital and large bandgap of most natural photoferroelectric materials lead to low electron/hole mobility and limit the realization of technologically practical devices. Antimony sulpho-iodide (SbSI) is a photoferroelectric material which is expected to have high electron/hole mobility in the ferroelectric state due to its non-local band dispersion and narrow bandgap. However, SbSI exhibits the paraelectric state close to room temperature. In this report, as a proof of concept, we explore the possibility to stabilize the SbSI ferroelectric phase above room temperature via mechanical strain engineering. We synthesized thin low-dimensional crystals of SbSI by chemical vapor deposition, confirmed its crystal structure with electron diffraction, studied its optical properties via photoluminescence spectroscopy and time-resolved photoluminescence spectroscopy, and probed its phase transition using temperature-dependent steady-state photoluminescence spectroscopy. We found that introducing external mechanical strain to these low-dimensional crystals may lead to an increase in their Curie temperature (by ∼60 K), derived by the strain-modified optical phase transition in SbSI and quantified by Kern formulation and Landau theory. The study suggests that strain engineering could be an effective way to stabilize the ferroelectric phase of SbSI at above room temperature, providing a solution enabling its application for technologically useful photoferroelectric devices.

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 ferroelectric6,7 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=8.52Å, b=10.13Å, and c=4.10Å [Fig. 1(a)].16 In the ferroelectric phase (<287 K), SbSI has a Pna21 space group with Sb and S atom shifting by ±0.20Å and ±0.05Å 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 

FIG. 1.

Crystal structure of SbSI and experimentally realized SbSI low-dimensional crystals. (a) and (b) Top and right hand views of paraelectric SbSI. The dashed circle highlights a double-chain of SbSI. (c) and (d) Right hand views of ferroelectric SbSI with up and down polarization, respectively. Atom shifts are exaggerated proportionally to each other for the presentation purpose. (e) Optical microscopy image of SbSI low-dimensional crystals on mica. The inset shows the magnified image of two single SbSI low-dimensional crystals. (f) TEM image of SbSI. Inset: TEM electron diffraction patterns of selected areas (from white circles).

FIG. 1.

Crystal structure of SbSI and experimentally realized SbSI low-dimensional crystals. (a) and (b) Top and right hand views of paraelectric SbSI. The dashed circle highlights a double-chain of SbSI. (c) and (d) Right hand views of ferroelectric SbSI with up and down polarization, respectively. Atom shifts are exaggerated proportionally to each other for the presentation purpose. (e) Optical microscopy image of SbSI low-dimensional crystals on mica. The inset shows the magnified image of two single SbSI low-dimensional crystals. (f) TEM image of SbSI. Inset: TEM electron diffraction patterns of selected areas (from white circles).

Close modal

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.

FIG. 2.

Optical properties of SbSI low-dimensional crystals. (a) Steady state PL of unstrained SbSI at room temperature. The PL peak at 673 nm indicates that SbSI has a direct bandgap of around 1.84 eV at room temperature. Inset: TRPL of unstrained SbSI at room temperature, which indicates a carrier lifetime of around 260 ps. (b) First Brillouin zone of unstrained SbSI. Adapted with permission from Physica B 371, 68–73 (2006). Copyright 2006 AIP Publishing.19 (c) Band structures of unstrained SbSI at 280 K (bottom graph) and 310 K (top graph). Adapted with permission from Physica B 371, 68–73 (2006). Copyright 2006 AIP Publishing.19 At 310 K, SbSI has a 1.82 eV direct bandgap at the U point of the Brillouin zone and a 1.41 eV indirect bandgap between Z and U points. At 280 K, SbSI has a 1.97 eV direct bandgap at U and a 1.43 eV indirect bandgap between Z and R points. (d) TDPL of unstrained SbSI. The PL peak position moves to higher energy continuously until ∼300 K, where an abrupt jump towards lower energy occurs and indicates the ferroelectric-paraelectric phase transition.

FIG. 2.

Optical properties of SbSI low-dimensional crystals. (a) Steady state PL of unstrained SbSI at room temperature. The PL peak at 673 nm indicates that SbSI has a direct bandgap of around 1.84 eV at room temperature. Inset: TRPL of unstrained SbSI at room temperature, which indicates a carrier lifetime of around 260 ps. (b) First Brillouin zone of unstrained SbSI. Adapted with permission from Physica B 371, 68–73 (2006). Copyright 2006 AIP Publishing.19 (c) Band structures of unstrained SbSI at 280 K (bottom graph) and 310 K (top graph). Adapted with permission from Physica B 371, 68–73 (2006). Copyright 2006 AIP Publishing.19 At 310 K, SbSI has a 1.82 eV direct bandgap at the U point of the Brillouin zone and a 1.41 eV indirect bandgap between Z and U points. At 280 K, SbSI has a 1.97 eV direct bandgap at U and a 1.43 eV indirect bandgap between Z and R points. (d) TDPL of unstrained SbSI. The PL peak position moves to higher energy continuously until ∼300 K, where an abrupt jump towards lower energy occurs and indicates the ferroelectric-paraelectric phase transition.

Close modal

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.

FIG. 3.

Strain-tuning of SbSI phase transition. (a) Schematic diagram of the curved region of the SbSI low-dimensional crystals, which is strained via a PDMS stamp. Inset: Optical image of strained SbSI. (b) TDPL of strained SbSI. The abrupt jump indicates a Curie temperature of around 360 K.

FIG. 3.

Strain-tuning of SbSI phase transition. (a) Schematic diagram of the curved region of the SbSI low-dimensional crystals, which is strained via a PDMS stamp. Inset: Optical image of strained SbSI. (b) TDPL of strained SbSI. The abrupt jump indicates a Curie temperature of around 360 K.

Close modal
FIG. 4.

Theoretical analysis of experimental results. (a) and (b) PL peak positions of unstrained and strained SbSI as a function of temperature, respectively. The jump towards lower energy with decreased temperature, highlighted by the colored rectangles, indicates the ferroelectric phase transition. (c) Landau theory prediction of the change of Curie temperature with strain (blue surface) and experimental results (yellow plane and yellow line). The yellow line indicates the Curie temperature without strain and the yellow plane indicates that with strain. The uncertainty of Q comes from the previous report,29,31–34 and we do not have that of our sample. The uncertainty of strain arises because it is not regardless of the size of our laser spot.

FIG. 4.

Theoretical analysis of experimental results. (a) and (b) PL peak positions of unstrained and strained SbSI as a function of temperature, respectively. The jump towards lower energy with decreased temperature, highlighted by the colored rectangles, indicates the ferroelectric phase transition. (c) Landau theory prediction of the change of Curie temperature with strain (blue surface) and experimental results (yellow plane and yellow line). The yellow line indicates the Curie temperature without strain and the yellow plane indicates that with strain. The uncertainty of Q comes from the previous report,29,31–34 and we do not have that of our sample. The uncertainty of strain arises because it is not regardless of the size of our laser spot.

Close modal

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 

F=F0+α2P2+β4P4+γ6P6EP,
(1)

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 as27,28

F=F+Fη,Fη=12Kη2KQηP2ση,
(2)

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

KηKQP2σ=0η=QP2+σK.
(3)

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

F=F+Fη=12α2σQP2+14β2Q2sP4+γ6P6.
(4)

Via the Curie-Weiss law χ=CTT0 under the strained condition, it is found that

α2σQ=TT0εoC,
(5)

where C is the Curie constant, and T0 is a constant under the strained condition (T0 of χ=CTT0 is a constant under the unstrained condition). Combining the unstrained and strained cases, one gets

T0=T0+2σQεoC=T0+2ηQεoCs,
(6)

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

Tc=T0+2ηQεoCs+316εoC(β2Q2s)2γ,
(7)
When T<Tc,P2=(β2Q2s)+(β2Q2s)24α2σQγ2γ.
(8)

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

TcTc=2ηQεoCs+316εoC(β2Q2s)2γ316εoCβ2γ.
(9)

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,andγ would be needed.

The results from previous experiments give the following estimates for these parameters: s ranges from 3×1011m2N1 to 5×1011m2N1;29,30Q ranges from 0.011m4C2 to 0.23m4C2;29,31–34C ranges from 1.3×105K to 2.5×105K.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=3.02×108Vm5C3 and γ=6.99×109Vm9C5.35 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

Eg=Eg0+ppx+βxP2,
(10)

where Eg0 is a constant, x is the strain, and P is the polarization.41,42pp 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

x=axT+QP2,
(11)

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

Eg=Eg0+ppaxT+βxP2,
(12)

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

Eg=Eg0+ppaxT+βxβ+β24TT0εoCγ2γ.
(13)

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.

1.
S. Y.
Yang
,
J.
Seidel
,
S. J.
Byrnes
,
P.
Shafer
,
C.-H.
Yang
,
M. D.
Rossell
,
P.
Yu
,
Y.-H.
Chu
,
J. F.
Scott
,
J. W.
Ager
,
L. W.
Martin
, and
R.
Ramesh
, “
Above-bandgap voltages from ferroelectric photovoltaic devices
,”
Nat. Nanotechnol.
5
,
143
147
(
2010
).
2.
J. E.
Spanier
,
V. M.
Fridkin
,
A. M.
Rappe
,
A. R.
Akbashev
,
A.
Polemi
,
Y.
Qi
,
Z.
Gu
,
S. M.
Young
,
C. J.
Hawley
,
D.
Imbrenda
,
G.
Xiao
,
A. L.
Bennett-Jackson
, and
C. L.
Johnson
, “
Power conversion efficiency exceeding the Shockley–Queisser limit in a ferroelectric insulator
,”
Nat. Photonics
10
,
611
616
(
2016
).
3.
R.
Nechache
,
C.
Harnagea
,
S.
Li
,
L.
Cardenas
,
W.
Huang
,
J.
Chakrabartty
, and
F.
Rosei
, “
Bandgap tuning of multiferroic oxide solar cells
,”
Nat. Photonics
9
,
61
67
(
2015
).
4.
R.
Guo
,
L.
You
,
Y.
Zhou
,
Z.
Shiuh Lim
,
X.
Zou
,
L.
Chen
,
R.
Ramesh
, and
J.
Wang
, “
Non-volatile memory based on the ferroelectric photovoltaic effect
,”
Nat. Commun.
4
,
1990
(
2013
).
5.
S.
Kvedaravicius
,
A.
Audzijonis
,
N.
Mykolaitiene
, and
J.
Grigas
, “
Soft mode and its electronic potential in SbSI-type mixed crystals
,”
Ferroelectrics
177
,
181
190
(
1996
).
6.
G.
Harbeke
, “
Absorption edge in ferroelectric SbSI under electric fields
,”
J. Phys. Chem. Solids
24
,
957
963
(
1963
).
7.
D.
Berlincourt
,
H.
Jaffe
,
W. J.
Merz
, and
R.
Nitsche
, “
Piezoelectric effect in the ferroelectric range in SbSI
,”
Appl. Phys. Lett.
4
,
61
63
(
1964
).
8.
A.
Audzijonis
,
R.
Žaltauskas
,
L.
Audzijonienė
,
I. V.
Vinokurova
,
O. V.
Farberovich
, and
R.
Šadžius
, “
Electronic band structure of ferroelectric semiconductor SbSi studied by empirical pseudopotential
,”
Ferroelectrics
211
,
111
126
(
1998
).
9.
K. R.
Rao
and
S. L.
Chaplot
, “
Dynamics of paraelectric and ferroelectric SbSI
,”
Phys. Status Solidi B
129
,
471
482
(
1985
).
10.
A.
Audzijonis
,
G.
Gaigalas
,
L.
Žigas
,
A.
Pauliukas
,
R.
Žaltauskas
,
A.
Čerškus
, and
J.
Narusis
, “
Theoretical investigation of the electronic structure of a ferroelectric SbSI cluster at a phase transition
,”
Cent. Eur. J. Phys.
3
,
382
394
(
2005
).
11.
K.
Nassau
,
J. W.
Shiever
, and
M.
Kowalchik
, “
The growth of large SbSI crystals: Control of needle morphology
,”
J. Cryst. Growth
7
,
237
245
(
1970
).
12.
S.
Kotru
,
W.
Liu
, and
R. K.
Pandey
, “
PLD growth of high vapor pressure antimony sulpho-iodide ferroelectric films for IR applications
,” in
ISAF 2000. Proceedings of the 2000 12th IEEE International Symposium on Applications of Ferroelectrics (IEEE Catalog No. 00CH37076)
(
2000
), Vol. 231, pp.
231
234
.
13.
M.
Tamilselvan
and
A. J.
Bhattacharyya
, “
Antimony sulphoiodide (SbSI), a narrow band-gap non-oxide ternary semiconductor with efficient photocatalytic activity
,”
RSC Adv.
6
,
105980
105987
(
2016
).
14.
P.
Szperlich
,
M.
Nowak
,
Ł.
Bober
,
J.
Szala
, and
D.
Stróż
, “
Ferroelectric properties of ultrasonochemically prepared SbSI ethanogel
,”
Ultrason. Sonochem.
16
,
398
401
(
2009
).
15.
N.
Solayappan
,
K. K.
Raina
,
R. K.
Pandey
, and
U.
Varshney
, “
Role of antimony sulfide buffer layers in the growth of ferroelectric antimony sulfo-iodide thin films
,”
J. Mater. Res.
12
,
825
832
(
1997
).
16.
A.
Kikuchi
,
Y.
Oka
, and
E.
Sawaguchi
, “
Crystal structure determination of SbSI
,”
J. Phys. Soc. Jpn.
23
,
337
354
(
1967
).
17.
K. T.
Butler
,
J. M.
Frost
, and
A.
Walsh
, “
Ferroelectric materials for solar energy conversion: Photoferroics revisited
,”
Energy Environ. Sci.
8
,
838
848
(
2015
).
18.
A.
Audzijonis
,
J.
Grigas
,
A.
Kajokas
,
S.
Kvedaravičius
, and
V.
Paulikas
, “
Origin of ferroelectricity in SbSI
,”
Ferroelectrics
219
,
37
45
(
1998
).
19.
A.
Audzijonis
,
R.
Žaltauskas
,
L.
Žigas
,
I. V.
Vinokurova
,
O. V.
Farberovich
,
A.
Pauliukas
, and
A.
Kvedaravičius
, “
Variation of the energy gap of the SbSI crystals at ferroelectric phase transition
,”
Physica B
371
,
68
73
(
2006
).
20.
K.
Nako
and
M.
Balkanski
, “
Electronic band structures of SbSI in the para- and ferroelectric phases
,”
Phys. Rev. B
8
,
5759
5780
(
1973
).
21.
E.
Fatuzzo
,
G.
Harbeke
,
W. J.
Merz
,
R.
Nitsche
,
H.
Roetschi
, and
W.
Ruppel
, “
Ferroelectricity in SbSI
,”
Phys. Rev.
127
,
2036
2037
(
1962
).
22.
K. J.
Choi
,
M.
Biegalski
,
Y. L.
Li
,
A.
Sharan
,
J.
Schubert
,
R.
Uecker
,
P.
Reiche
,
Y. B.
Chen
,
X. Q.
Pan
,
V.
Gopalan
,
L.-Q.
Chen
,
D. G.
Schlom
, and
C. B.
Eom
, “
Enhancement of ferroelectricity in strained BaTiO3 thin films
,”
Science
306
,
1005
1009
(
2004
).
23.
D. G.
Schlom
,
L.-Q.
Chen
,
C. J.
Fennie
,
V.
Gopalan
,
D. A.
Muller
,
X.
Pan
,
R.
Ramesh
, and
R.
Uecker
, “
Elastic strain engineering of ferroic oxides
,”
MRS Bull.
39
,
118
130
(
2014
).
24.
L. W.
Martin
and
A. M.
Rappe
, “
Thin-film ferroelectric materials and their applications
,”
Nat. Rev. Mater.
2
,
16087
(
2016
).
25.
J.
Manjaly Varghese
,
C.
O'Regan
,
N.
Deepak
,
R. W.
Whatmore
, and
J. D.
Holmes
, “
Surface roughness assisted growth of vertically oriented ferroelectric SbSI nanorods
,”
Chem. Mater.
24
,
3279
3284
(
2012
).
26.
A. S.
Bhalla
,
K. E.
Spear
, and
L. E.
Cross
, “
Crystal growth of antimony sulphur iodide
,”
Mater. Res. Bull.
14
,
423
429
(
1979
).
27.
P.
Chandra
and
P. B.
Littlewood
, “
A Landau primer for ferroelectrics
,” in
Physics of Ferroelectrics: A Modern Perspective
(
Springer
,
Berlin, Heidelberg
,
2007
), pp.
69
116
.
28.
L.-Q.
Chen
, “
APPENDIX A—Landau free-energy coefficients
,” in
Physics of Ferroelectrics: A Modern Perspective
(
Springer
,
Berlin, Heidelberg
,
2007
), pp.
363
372
.
29.
K.
Hamano
and
T.
Shinmi
, “
Electrostriction, piezoelectricity and elasticity in ferroelectric SbSI
,”
J. Phys. Soc. Jpn.
33
,
118
124
(
1972
).
30.
K.
Hamano
,
T.
Nakamura
,
Y.
Ishibashi
, and
T.
Ooyane
, “
Piezoelectric property of SbSl single crystal
,”
J. Phys. Soc. Jpn.
20
,
1886
1888
(
1965
).
31.
I.
Tatsuzaki
,
K.
Itoh
,
S.
Ueda
, and
Y.
Shindo
, “
Strain along c axis of SbSI caused by illumination in dc electric field
,”
Phys. Rev. Lett.
17
,
198
200
(
1966
).
32.
F.
Li
,
L.
Jin
,
Z.
Xu
, and
S.
Zhang
, “
Electrostrictive effect in ferroelectrics: An alternative approach to improve piezoelectricity
,”
Appl. Phys. Rev.
1
,
011103
(
2014
).
33.
S.
Ueda
,
I.
Tatsuzaki
, and
Y.
Shindo
, “
Change in the dielectric constant of SbSI caused by illumination
,”
Phys. Rev. Lett.
18
,
453
454
(
1967
).
34.
K.
Irie
, “
Dielectric properties of SbSI
,”
Ferroelectrics
21
,
395
397
(
1978
).
35.
K.
Toyoda
, “
Electrical properties of SbSI crystals in the vicinity of the ferroelectric curie point
,”
Ferroelectrics
69
,
201
215
(
1986
).
36.
A.
Starczewska
,
B.
Solecka
,
M.
Nowak
, and
P.
Szperlich
, “
Dielectric properties of SbSI in the temperature range of 292-475 K
,”
Acta Phys. Pol., A
126
,
1125
1127
(
2014
).
37.
Y.
Wang
,
L.
Seewald
,
Y.-Y.
Sun
,
P.
Keblinski
,
X.
Sun
,
S.
Zhang
,
T.-M.
Lu
,
J. M.
Johnson
,
J.
Hwang
, and
J.
Shi
, “
Nonlinear electron-lattice interactions in a wurtzite semiconductor enabled via strongly correlated oxide
,”
Adv. Mater.
28
,
8975
8982
(
2016
).
38.
S. L.
Chuang
and
C. S.
Chang
, “
k p method for strained wurtzite semiconductors
,”
Phys. Rev. B
54
,
2491
2504
(
1996
).
39.
K. P.
O'Donnell
and
X.
Chen
, “
Temperature dependence of semiconductor band gaps
,”
Appl. Phys. Lett.
58
,
2924
2926
(
1991
).
40.
R.
Kern
, “
An electro-optical and electromechanical effect in SbSI
,”
J. Phys. Chem. Solids
23
,
249
253
(
1962
).
41.
I.
Kenji
, “
Electric field effect on the absorption edge in SbSI
,”
Jpn. J. Appl. Phys.
19
,
1301
(
1980
).
42.
K.
Nakao
,
R.
Bennaceur
, and
M.
Balkanski
, “
On the electro-optic effects of the absorption edge of SbSI
,”
Phys. Lett. A
41
,
219
220
(
1972
).
43.
J. D.
Zook
and
T. N.
Casselman
, “
Electro-optic effects in paraelectric perovskites
,”
Phys. Rev. Lett.
17
,
960
962
(
1966
).

Supplementary Material