# Epitaxial growth and characterization of Bi1-xSbx thin films on (0001)
sapphire substrates

Yu-Sheng Huang  Saurav Islam<EMAIL_ADDRESS>Yongxi Ou  Department of
Physics, Pennsylvania State University, University Park, Pennsylvania 16802,
USA  Supriya Ghosh  Department of Chemical Engineering and Materials Science,
University of Minnesota, Minneapolis, Minnesota 55455, USA  Anthony
Richardella  Department of Physics and Materials Research Institute,
Pennsylvania State University, University Park, Pennsylvania 16802, USA  K.
Andre Mkhoyan  Department of Chemical Engineering and Materials Science,
University of Minnesota, Minneapolis, Minnesota 55455, USA  Nitin Samarth
<EMAIL_ADDRESS>Department of Physics, Department of Materials Science and
Engineering, and Materials Research Institute, Pennsylvania State University,
University Park, Pennsylvania 16802, USA

###### Abstract

We report the molecular beam epitaxy of $\mathrm{Bi_{1-x}Sb_{x}}$ thin films
($0\leq x\leq 1$) on sapphire (0001) substrates using a thin (Bi,Sb)2Te3
buffer layer. Characterization of the films using reflection high energy
diffraction, x-ray diffraction, atomic force microscopy, and scanning
transmission electron microscopy reveals epitaxial growth of films of
reasonable structural quality. This is further confirmed via x-ray diffraction
pole figures that determine the epitaxial registry between the thin film and
substrate. We further investigate the microscopic structure of thin films via
Raman spectroscopy, demonstrating how the vibrational modes vary as the
composition changes and discussing the implications for the crystal structure.
We also characterize the samples using electrical transport measurements.

††preprint: AIP/123-QED

##  I Introduction

Figure 1: (a) Schematic of the $\mathrm{Bi_{1-x}Sb_{x}}$ crystal structure
along the [100] direction and the [001], growth direction of the film. Violet
and dark yellow correspond to Bi and Sb atoms respectively. (b) RHEED patterns
of both the Bi0.59Sb0.41 layers and the (Bi0.95,Sb0.05)2Te3 buffer layer, the
electron beam is directed along the $10\bar{1}$ orientation of sapphire. (c)
AFM image of the Bi0.59Sb0.41 film over a 5$~{}\mu$m by 5 $\mu$m region.(d)
HAADF-STEM image of Bi0.84Sb0.16 on (Bi0.95,Sb0.05)2Te3 buffer layer grown on
sapphire substrate with the atomic structure of the film along the [100]
directions as seen in the model in (a), and with a $15-20^{\circ}$ in-plane
rotation in a different grain. Both show the atomically smooth interface and
epitaxial growth of the layers.

The $\mathrm{Bi_{1-x}Sb_{x}}$ alloy first garnered significant attention in
the field of semimetals and narrow bandgap semiconductors due to its electric,
magnetic, and thermal properties [1, 2, 3, 4, 5, 6]. While much of this past
work focused on the growth and properties of bulk single crystals, the use of
molecular beam epitaxy (MBE) had also been explored, demonstrating the growth
of $\mathrm{Bi_{1-x}Sb_{x}}$ thin films on BaF2 and CdTe substrates [7, 8]. It
has long been recognized that the energy bands of this alloy invert as a
function of composition leading to an unusual gapless state at the crossing
point [9, 10]. This was later understood to lead to topological surface states
that were first predicted by Kane and Mele [11] and then experimentally
realized in bulk single crystals [12, 13]. Recently, there has been renewed
interest in thin films of $\mathrm{Bi_{1-x}Sb_{x}}$ grown by both MBE [14, 15]
and sputtering [16], motivated by the prospect of exploiting the spin-momentum
correlation in the topological Dirac surface states for spin–orbit-torque
(SOT) devices. The high electrical conductivity of $\mathrm{Bi_{1-x}Sb_{x}}$
thin films coupled with a potentially large spin Hall angle makes them
attractive for realizing energy efficient SOT memory devices [17]. Large spin
Hall angle $\approx 52$ and magnetization switching at ultralow current
densities have been reported in $\mathrm{Bi_{1-x}Sb_{x}}$ films interfaced
with the metallic ferromagnet, MnGa [18], while interfacing with the
ferromagnetic semiconductor, (Ga,Mn)As, has shown giant unidirectional spin
Hall magnetoresistance [19]. These studies motivate the further exploration of
MBE growth of high-quality, single-crystal $\mathrm{Bi_{1-x}Sb_{x}}$ films on
different substrates. As mentioned above, attempts to grow high structural
quality $\mathrm{Bi_{1-x}Sb_{x}}$ thin films on BaF2 and CdTe (111) substrates
using MBE date back to the late 1990s [8]. More recent studies of MBE-grown
single crystal $\mathrm{Bi_{1-x}Sb_{x}}$ thin films have used GaAs (001) as a
substrate, yielding $\mathrm{Bi_{1-x}Sb_{x}}$ (012) growth of either
polycrystalline or textured nature, with limited structural characterization
details [18, 14, 15]. The renewed interest in $\mathrm{Bi_{1-x}Sb_{x}}$ thin
films for topological spintronics provides a strong motivation for exploring,
understanding, and improving the epitaxial growth of single crystal thin films
of this material on different substrates.

In this manuscript, we present a comprehensive study of a series of epitaxial
$\mathrm{Bi_{1-x}Sb_{x}}$ thin films grown by MBE on sapphire (0001)
substrates after the deposition of a thin (Bi0.95,Sb0.05)2Te3 buffer layer. We
explore the MBE growth of $\mathrm{Bi_{1-x}Sb_{x}}$ thin films over the entire
composition range, characterizing the microscopic structure, quality, and
composition of these films with a comprehensive suite of techniques, including
transmission electron microscopy (TEM), x-ray photoelectron spectroscopy
(XPS), x-ray diffraction (XRD), atomic force microscopy (AFM), electrical
transport, and Raman spectroscopy. The phonon modes in these thin films
observed using Raman spectroscopy provide insights into the effect of strain.
Our results demonstrate the growth of epitaxial $\mathrm{Bi_{1-x}Sb_{x}}$
films over the full range of composition; the controlled synthesis of such
films is relevant for the systematic exploration of spintronic devices based
upon spin-charge interconversion in this material [20].

Figure 2: (a) Out-of-plane $2\theta$-$\omega$ XRD measurements of 10 nm-thick
$\mathrm{Bi_{1-x}Sb_{x}}$ films of varying composition grown on sapphire
(0001) substrates (samples A-E, as described in Table I). Peaks from the
$\mathrm{Bi_{1-x}Sb_{x}}$ layer, (Bi0.95,Sb0.05)2Te3 buffer layer and the
substrate layer are detected. (b) A rocking curve of Bi0.84Sb0.16. (c) Lattice
constant $c$ extracted from the $2\theta$-$\omega$ XRD spectrum plotted
against composition. The dotted line indicates the trend suggested by Vegard’s
law. Figure 3: XRD pole figure measurements of the (012) peak in both the
substrate and sample layer in (a) Bi0.86Sb0.14, (b) Bi0.79Sb0.21, and (c) pure
Sb.

##  II Methods

We grow our samples on sapphire (0001) substrates using a Scienta Omicron
EVO50 MBE system. We first prepare the sapphire substrates by heating up to
1160 ∘C in air for 8 hours to produce an atomically ordered surface, dice it
from the back so it can be broken into smaller pieces for future use, and
clean it with a series of baths in acetone, isopropanol, DI water, Nanostrip
and then DI water again. Once pieces of the substrate are loaded into the MBE
system (base pressure $<10^{-10}$ mBar), they are outgassed at a substrate
heater temperature of 950 ∘C for 1 hour. We then proceed to grow 3 nm of
(Bi0.95,Sb0.05)2Te3 (in-plane lattice constant $0.437$ nm) as a buffer layer
by setting the flux ratio of Bi/Sb to 19 with an overabundance of Te flux. The
sample temperature is set to 170 ∘C (as measured by an infrared thermal
camera, substrate heater temperature $\approx 360~{}^{\circ}$C) at the start
and gradually increased to 200 ∘C. Finally, we grow 10 nm of
$\mathrm{Bi_{1-x}Sb_{x}}$ with different Bi/Sb compositions by adjusting the
flux ratio accordingly. A schematic of the crystal structure is shown in Fig.
1(a). $\mathrm{Bi_{1-x}Sb_{x}}$ has a trigonal crystal system and belongs to
R$\overline{3}$m space group, with lattice constants $a=b=0.433-0.455$ nm
(depending on composition), leading to $\approx 3$% mismatch. The sample
temperature is set at 160 ∘C (90 ∘C for Bi) during the growth. The lower
growth temperature for pure Bi is chosen based on previous work [17], which
show epitaxial growth of Bi at lower temperature. We use reflection high
energy electron diffraction (RHEED) to monitor the growth. A streaky
unreconstructed RHEED pattern is seen during the growth for both the buffer
layer and the sample layer (Fig. 1(b)), implying a relatively smooth surface
and good epitaxial growth.

Figure 4: (a) Schematic of the Ag vibrational mode of Bi-Sb crystal. (b) Raman
spectroscopy of $\mathrm{Bi_{1-x}Sb_{x}}$ films. (c) Peak location of
vibrational modes versus Sb composition. LR signified long-range metal like
vibration of Bi-Bi. Figure 5: Electrical transport measurements in three
$\mathrm{Bi_{1-x}Sb_{x}}$ films. Temperature dependence of the sheet
resistance for three compositions of Bi and Sb. (b) Normalized longitudinal
magnetoresistance, and (c) Transverse magnetoresistance for the same films.
The raw data for $R_{xx}$ and $R_{xy}$ have been symmetrized and
antisymmetrized, respectively.

We focus our discussion on five thin films with the same thickness ($\sim$10
nm) and different composition as determined by varying the Bi:Sb flux ratio;
the sample composition is verified post-growth using x-ray photoeelectron
spectroscopy (XPS) (Table 1). Unlike past work on $\mathrm{Bi_{1-x}Sb_{x}}$
thin films [7, 8, 15], we constrain our growth to very thin films since our
primary interest is to use these films eventually in SOT devices. The
thickness and surface topography of these samples are obtained using AFM, as
shown in Fig. 1(c). For films of $\sim$10 nm thickness, the RMS surface
roughness is $\sim 1-2$ nm. We note that this is still somewhat above the
requirements for SOT devices, but comparable to our recent work on TaAs thin
films, which show giant SOT efficiency [21]. We use high angle annular dark-
field (HAADF) scanning transmission electron microscopy (STEM) imaging to
study the film structure from similarly grown films. Figure 1(d) shows the
atomic structure of a $\mathrm{Bi_{1-x}Sb_{x}}$ film along the [100] direction
from different areas from the film, with the layered structure of the
(Bi0.95,Sb0.05)2Te3 buffer layer visible underneath. Further, the HAADF images
show an atomically smooth interface between the $\mathrm{Bi_{1-x}Sb_{x}}$ and
the buffer layer, confirming a good epitaxial growth between the two.

Sample | Growth Temperature (∘C) | Bi/Sb Flux Ratio | Bi% | Sb%
---|---|---|---|---
A | 90 | Pure Bi | 1 | 0
B | 160 | 3.4 | 0.84 | 016
C | 160 | 2.6 | 0.79 | 0.21
D | 160 | 0.97 | 0.59 | 0.41
E | 160 | Pure Sb | 0 | 1
Table 1: Details of sample growth

##  III Results

We first discuss the characterization of our samples using XRD measurements.
Figure 2 (a) shows out of plane $2\theta-\omega$ scans of all the five films.
We identify the (003) $\mathrm{Bi_{1-x}Sb_{x}}$ peaks at 22∘, (006) peaks at
45∘-46∘, and (009) peaks at 70∘-75∘. We can also identify the
(Bi0.95,Sb0.05)2Te3 (006) peak at around 18∘ and the (0 0 15) peak at around
52∘ for pure Bi and Sb films, but these peaks are absent in the alloy samples
(samples B,C, and D). The reason for this is not understood. We also confirm
good quality growth of our film from the rocking curve, an example of which is
shown in Fig. 2(b), showing full-width at half maxima of $0.22^{\circ}$ The
lattice constant $c$ determined from these XRD scans shows a linear
relationship with $x$ (the percentage of Sb) in Fig. 2(c), consistent with
Vegard’s law [22]. However, unlike past studies of much thicker films such as
$\mathrm{Bi_{1-x}Sb_{x}}$ films on (111) BaF2 [8], we find the alloys have a
lattice constant which is much closer together compared to their pure
counterparts. We will discuss this in more detail later in the manuscript. We
further investigate these films using XRD pole figure measurements to
understand the epitaxial behavior of the growth. Pole figure measurements can
be understood as multiple $\phi$-scans at different $\chi$ angles at a fixed
$2\theta-\omega$ angle. This allows us to focus on non-out-of-plane peaks in
different layers of the sample. This provides an understanding of how
different layers in the film are aligned with the substrate. Ideally, we want
to select reflections in all the layers with the same Miller indices, for
example, (012), (104), or (110). Amongst these, (012) has the strongest signal
for the $\mathrm{Bi_{1-x}Sb_{x}}$ layer. Thus, we measured the (012) peaks in
the substrate, (Bi0.95,Sb0.05)2Te3, and Bi1-xSbx layers (see Fig. 3).
Unsurprisingly, the signal from $3$ nm buffer layer was too weak to be
measured. Figure 3 shows that the $\mathrm{Bi_{1-x}Sb_{x}}$ film and the
substrate align on top of each other with a broader $\phi$ spread in the
sample layer. Twinning in the sample layer is observed only on the alloy
samples, as shown in Figs. 3(a) and (b), with sample peaks 60∘ apart, and is
not observed in the pure Sb sample (Fig. 3(c)). These pole figure scans
confirm that the samples are epitaxial and that the pure Bi and Sb films are
of higher quality than the alloyed $\mathrm{Bi_{1-x}Sb_{x}}$ films.

For further understanding of the lattice dynamics, we investigate the
vibrational modes of the films using Raman spectroscopy. Raman spectra of
single crystals of Bi1-xSbx were first investigated by Zitter and Watson [23].
Lannin further investigated sputtered $\mathrm{Bi_{1-x}Sb_{x}}$ thin films in
1979 [24]. Both results found five vibrational modes in
$\mathrm{Bi_{1-x}Sb_{x}}$ alloys: $A_{g}$ and $E_{g}$ mode of Sb-Sb vibration,
$A_{g}$ mode of Bi-Sb vibration, $A_{g}$ mode of Bi-Bi vibration, and long-
range metallic-like Bi-Bi vibration. The $A_{g}$ vibrational mode of the Bi-Sb
is shown schemtically in Fig. 4(a). The Raman spectra in our films are shown
in Fig. 4(b) and the wavenumber of different modes is plotted against
composition in Fig. 4(c). We identify the long-range metal-like Bi-Bi
vibration mode (blue diamonds) at $73.3$ cm-1 in the pure Bi sample and
$80-84$ cm-1 in $\mathrm{Bi_{1-x}Sb_{x}}$ alloy samples; this mode shifts to
higher wave number as Sb concentration increases. The $A_{g}$ mode of the Bi-
Bi vibration (blue triangles) is observed around $100$ cm-1 for all samples
except in the pure Sb sample; this mode remains constant as the Sb fraction
changes in the alloy samples (samples B, C, and D). The $A_{g}$ mode of the
Bi-Sb vibration (orange squares) is observed around $120$ cm-1 for all
$\mathrm{Bi_{1-x}Sb_{x}}$ alloy samples; this mode also remains at
approximately the same location as the composition is varied in the alloy
samples. The $E_{g}$ mode of the Sb-Sb vibration (black pentagon) is only
observed at $116.1$ cm-1 in pure Sb; this is most likely due to the lack of
enough Sb concentration in the alloy samples. The $A_{g}$ mode of the Sb-Sb
vibration (red circles) is observed at $152.8$ cm-1 in the pure Sb sample and
at $145$ cm-1 in $\mathrm{Bi_{1-x}Sb_{x}}$ alloy samples; this shows similar
behavior as the $A_{g}$ mode of the Bi-Bi vibration, and remains approximately
at the same position in samples B, C, D, with the mode in the pure Sb film
observed at higher wave number. Furthermore, we also identify an extra mode at
$66.9$ cm-1 (purple stars) in the pure Sb film. This mode does not correspond
to any mode previously observed in single crystal $\mathrm{Bi_{1-x}Sb_{x}}$
alloys. We believe this corresponds to the $A_{g}$ mode from Sb2Te3,
suggesting the interdiffusion of Te from the (Bi0.95,Sb0.05)2Te3 buffer layer.
In previous studies, the wave number of the $A_{g}$ modes had a linear
relationship with the composition of the Sb [23, 24]. In our study, we observe
these modes to be located at approximately the same wave number. Our alloy
films have a similar lattice constant $c$, as calculated from XRD measurements
(Fig. 2(b)). The $A_{g}$ mode vibrations are along the $c$ direction as shown
in the schematic in Fig. 4(a), and thus the wave number of the vibrations also
correspond to the lattice constant $c$. This can further be seen in Fig. 2(b),
where sample C(79:21) has a slightly larger lattice constant $c$ compared to
sample B(84:16) and similarly we also observe a slightly smaller wave number
of the $A_{g}$ in sample C compared to sample B. We believe this is because
presence of strain in our sample [25].

Finally, we investigate electrical transport in $\mathrm{Bi_{1-x}Sb_{x}}$ thin
films of varying composition grown under similar conditions. We carry out
these measurements using mechanically scratched Hall bars with channel
dimensions 1 mm $\times 500~{}\mu$m. The films show similar qualitative and
quantitative behavior. The sheet resistance ($R_{xx}$) vs. temperature ($T$)
in all samples shows metallic behavior (Figs. 5(a)). Longitudinal
magnetoresistance measurements at $T=4.2$ K shows a positive magnetoresistance
whose field-dependence is consistent with that expected from weak
antilocalization (Figs. 5(b). The carrier density ($n$) for all the samples is
extracted using Hall measurements (Figs. 5(c)). The samples are electron-doped
with $n\approx 10^{20}-10^{22}$ cm-3. The mobility is calculated using
$\mu=\frac{\sigma}{ne}$, where $\sigma$ is the conductivity and $e$ is the
electronic charge. The Fermi wavelength ($k_{f}$), calculated using
$k_{f}=(3\pi^{2}n)^{\frac{1}{3}}$ is $\approx 10^{-9}$ m-1 while the mean free
path ($l_{m}$), calculated using $l_{m}=\mu\hbar k_{f}/e$ varies between
$10^{-8}-10^{-9}$ m. $k_{f}l_{m}$ varies between $10-25$ in these films. The
parameters calculated from transport measurements are provided in Table II.
Note that the relatively low Hall mobilities extracted here can be attributed
to the thin nature of our films, where interfacial defects which act as
trapping-detrapping centers [26] and grain boundaries from twinning as
observed in XRD (Fig. 3), can lead to enhanced scattering compared to thicker
films: for example, the MBE growth of $\mathrm{Bi_{1-x}Sb_{x}}$ thin films of
about 60 nm thickness on GaAs substrates also shows Hall mobilities of order
100 cm2/(V.s) [15].

Sample |  $n$ (cm-3) |  $\mu$ (cm2/Vs) |  $k_{f}$ ($10^{9}$ m-1) |  $l_{m}$ (m) | $k_{f}l_{m}$
---|---|---|---|---|---
A | $-2.48\times 10^{21}$ | 1 | 9 | $5.2\times 10^{-10}$ | $4.7$
B | $-1.9\times 10^{21}$ | $12.7$ | $3.8$ | $3.2\times 10^{-9}$ | $12.3$
C | $-5.7\times 10^{20}$ | $67.7$ | $2.4$ | $1.07\times 10^{-9}$ | $25.8$
D | $-1.28\times 10^{22}$ | $2.2$ | $7.18$ | $1.04\times 10^{-9}$ | $7.5$
E | $-6.7\times 10^{20}$ | $51.4$ | $2.7$ | $9.1\times 10^{-9}$ | $24.8$
Table 2: Details of transport measurements

##  IV Conclusion

In conclusion, we used MBE to demonstrate the epitaxial growth of a series of
$\mathrm{Bi_{1-x}Sb_{x}}$ thin films over the entire alloy composition range
on sapphire (0001) substrates with a thin (Bi0.95,Sb0.05)2Te3 buffer layer.
Detailed structural characterization of the films via XRD and HR-TEM confirm
high-quality epitaxial registry with the substrate, while the composition of
these films was verified using XPS. We also probed the effect of strain (and
possible interdiffusion) using Raman spectroscopy and probed their electrical
properties using low temperature transport. Our growth protocol establishes
sapphire (0001) as an attractive substrate for MBE growth of
$\mathrm{Bi_{1-x}Sb_{x}}$ and provides a route for systematic studies of the
spin-charge conversion and SOT devices by interfacing such films with a
ferromagnetic overlayer [20].

###### Acknowledgements.

This project was supported by SMART, one of seven centers of nCORE, a
Semiconductor Research Corporation program, sponsored by the National
Institute of Standards and Technology (NIST) (YS, YO, NS, SG, KAM), NSF Grant
No. DMR-2309431 (SG, KAM), and by the Penn State Two-Dimensional Crystal
Consortium-Materials Innovation Platform (2DCC-MIP) under NSF Grant No.
DMR-2039351 (YO, SI, AR, NS). Parts of this work were carried out in the
Characterization Facility, University of Minnesota, which receives partial
support from the NSF through the MRSEC (Award Number DMR-2011401) and the NNCI
(Award Number ECCS-2025124) programs (SG, KAM).

## References

  * Mendez, Misu, and Dresselhaus [1981] E. Mendez, A. Misu, and M. Dresselhaus, “Pressure-dependent magnetoreflection studies of Bi and Bi1-xSbx alloys,” Phys. Rev. B 24, 639 (1981).
  * Brandt, Svistova, and Valeev [1969] N. Brandt, E. Svistova, and R. Valeev, “Investigation of the semiconductor-metal transition in the bismuth-antimony system in a magnetic field,” Sov. Phys. JETP 28, 245–254 (1969).
  * Brandt and Svistova [1970] N. Brandt and E. Svistova, “Electron transitions in strong magnetic fields,” J. of Low Temp. Phys. 2, 1–35 (1970).
  * Brandt, Svistova, and Semenov [1971] N. Brandt, E. Svistova, and M. Semenov, “Electron transitions in antimony-rich bismuth-antimony alloys in strong magnetic fields,” Sov. Phys. JETP 32, 238–243 (1971).
  * Hiruma  _et al._ [1980] K. Hiruma, G. Kido, K. Kawauchi, and N. Miura, “Shubnikov-de Haas effect and semimetal-semiconductor transition in bismuth-antimony alloys in high magnetic fields,” Solid State Commun. 33, 257–260 (1980).
  * Yim and Amith [1972] W. Yim and A. Amith, “Bi-sb alloys for magneto-thermoelectric and thermomagnetic cooling,” Solid-State Electronics 15, 1141–1165 (1972).
  * Morelli, Partin, and Heremans [1972] D. T. Morelli, D. L. Partin, and J. Heremans, “Galvanomagnetic properties of single-crystal bismuth-antimony thin films,” Semicon. Sci. Technol. 8, 369–420 (1972).
  * Cho  _et al._ [1999] S. Cho, A. DiVenere, G. K. Wong, J. B. Ketterson, and J. R. Meyer, “Molecular beam epitaxial growth and structural properties of BiSb alloy thin films on CdTe (111) substrates,” J. Vac. Sci. Tech. A 17, 9–13 (1999).
  * Brandt, Chudinov, and Karavaev [1972] N. Brandt, S. Chudinov, and V. Karavaev, “Investigation of gapless states in bismuth-antimony alloys under pressure,” Sov. Phys. JETP 34, 368–375 (1972).
  * Brandt, Ponomarev, and Chudinov [1990] N. Brandt, Y. G. Ponomarev, and S. Chudinov, “Investigation of the gapless state in bismuth-antimony alloys,” J. Low Temp. Phys. 5, S257 (1990).
  * Kane and Mele [2005] C. L. Kane and E. J. Mele, “Z 2 topological order and the quantum spin Hall effect,” Phys. Rev. Lett. 95, 146802 (2005).
  * Hsieh  _et al._ [2008] D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A topological Dirac insulator in a quantum spin Hall phase,” Nature (London) 452, 970–974 (2008).
  * Hsieh  _et al._ [2009] D. Hsieh, Y. Xia, L. Wray, D. Qian, A. Pal, J. Dil, J. Osterwalder, F. Meier, G. Bihlmayer, C. Kane, _et al._ , “Observation of unconventional quantum spin textures in topological insulators,” Science 323, 919–922 (2009).
  * Yao, Khang, and Hai [2019] K. Yao, N. H. D. Khang, and P. N. Hai, “Influence of crystal orientation and surface termination on the growth of BiSb thin films on GaAs substrates,” J. Cryst. Growth 511, 99–105 (2019).
  * Sadek  _et al._ [2022] D. Sadek, R. Daubriac, C. Durand, R. Monflier, Q. Gravelier, A. Proietti, F. Cristiano, A. Arnoult, and S. R. Plissard, “Structural and electrical characterizations of BiSb topological insulator layers epitaxially integrated on GaAs,” Crystal Growth & Design 22, 5081–5091 (2022).
  * Fan  _et al._ [2020] T. Fan, M. Tobah, T. Shirokura, N. H. D. Khang, and P. N. Hai, “Crystal growth and characterization of topological insulator BiSb thin films by sputtering deposition on sapphire substrates,” Jpn. J. Appl. Phys. 59, 063001 (2020).
  * Ueda  _et al._ [2017] Y. Ueda, N. H. Duy Khang, K. Yao, and P. N. Hai, “Epitaxial growth and characterization of Bi1-x Sbx spin Hall thin films on GaAs (111) A substrates,” Appl. Phys. Lett. 110, 062401 (2017).
  * Khang, Ueda, and Hai [2018] N. H. D. Khang, Y. Ueda, and P. N. Hai, “A conductive topological insulator with large spin hall effect for ultralow power spin–orbit torque switching,” Nat. Mater. 17, 808–813 (2018).
  * Duy Khang and Hai [2019] N. H. Duy Khang and P. N. Hai, “Giant unidirectional spin hall magnetoresistance in topological insulator–ferromagnetic semiconductor heterostructures,” J. Appl. Phys. 126, 233903 (2019).
  * Ou  _et al._ [2023] Y. Ou, W. Yanez, Y.-S. Huang, S. Ghosh, C. Sahin, M. Stanley, , S. Islam, S. Santhosh, A. Richardella, K. A. Mkhoyan, M. E. Flatte, and N. Samarth, “Spin Hall conductivity in $\mathrm{Bi_{1-x}Sb_{x}}$ as an experimental test of bulk-boundary correspondence,” arXiv , xxxx (2023).
  * Yanez  _et al._ [2022] W. Yanez, Y. Ou, R. Xiao, S. Ghosh, J. Dwivedi, E. Steinebronn, A. Richardella, K. A. Mkhoyan, and N. Samarth, “Giant dampinglike-torque efficiency in naturally oxidized polycrystalline $\mathrm{Ta}\mathrm{As}$ thin films,” Phys. Rev. Appl. 18, 054004 (2022).
  * Denton and Ashcroft [1991] A. R. Denton and N. W. Ashcroft, “Vegard’s law,” Phys. Rev. A 43, 3161 (1991).
  * Zitter and Watson [1974] R. Zitter and P. Watson, “Raman and x-ray spectra of single-crystal Bi-Sb alloys,” Physical Review B 10, 607 (1974).
  * Lannin [1979] J. S. Lannin, “First-order Raman scattering in Bi 1- x Sb x alloys,” Physical Review B 19, 2390 (1979).
  * Ni  _et al._ [2008] Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, “Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening,” ACS nano 2, 2301–2305 (2008).
  * [26] S. Islam, S. Shamim, and A. Ghosh, “Benchmarking noise and dephasing in emerging electrical materials for quantum technologies,” Advanced Materials 35, 2109671.