Band gap engineering of a soft inorganic compound PbI2 by incommensurate van der
Waals epitaxy
Yiping Wang, Yi-Yang Sun, Shengbai Zhang, Toh-Ming Lu, and Jian Shi
Citation: Applied Physics Letters 108, 013105 (2016); doi: 10.1063/1.4939269
View online: http://dx.doi.org/10.1063/1.4939269
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/108/1?ver=pdfcov
Published by the AIP Publishing
Articles you may be interested in
Layer specific optical band gap measurement at nanoscale in MoS2 and ReS2 van der Waals compounds by
high resolution electron energy loss spectroscopy
J. Appl. Phys. 119, 114309 (2016); 10.1063/1.4944431
Engineering 180° ferroelectric domains in epitaxial PbTiO3 thin films by varying the thickness of the underlying
(La,Sr)MnO3 layer
Appl. Phys. Lett. 105, 132903 (2014); 10.1063/1.4897144
Heterostructures based on inorganic and organic van der Waals systems
APL Mater. 2, 092511 (2014); 10.1063/1.4894435
Thermally-induced first-order phase transition in the (FC6H4C2H4NH3)2[PbI4] photoluminescent organicinorganic material
J. Appl. Phys. 111, 053521 (2012); 10.1063/1.3690920
Effects of stress on the optical properties of epitaxial Nd-doped Sr0.5Ba0.5Nb2O6 films
AIP Advances 1, 032172 (2011); 10.1063/1.3647516
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 128.113.37.4 On: Sat, 30 Jul 2016
18:17:54
APPLIED PHYSICS LETTERS 108, 013105 (2016)
Band gap engineering of a soft inorganic compound PbI2
by incommensurate van der Waals epitaxy
Yiping Wang,1 Yi-Yang Sun,2 Shengbai Zhang,2 Toh-Ming Lu,2 and Jian Shi1,a)
1
Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy,
New York 12180, USA
2
Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute,
Troy, New York 12180, USA
(Received 24 October 2015; accepted 18 December 2015; published online 5 January 2016)
Van der Waals epitaxial growth had been thought to have trivial contribution on inducing
substantial epitaxial strain in thin films due to its weak nature of van der Waals interfacial energy.
Due to this, electrical and optical structure engineering via van der Waals epitaxial strain has been
rarely studied. In this report, we show that significant band structure engineering could be achieved
in a soft thin film material PbI2 via van der Waals epitaxy. The thickness dependent
photoluminescence of single crystal PbI2 flakes was studied and attributed to the substrate-film coupling effect via incommensurate van der Waals epitaxy. It is proposed that the van der Waals strain
is resulted from the soft nature of PbI2 and large van der Waals interaction due to the involvement
of heavy elements. Such strain plays vital roles in modifying the band gap of PbI2. The deformation
potential theory is used to quantitatively unveil the correlation between thickness, strain, and band
gap change. Our hypothesis is confirmed by the subsequent mechanical bending test and Raman
C 2016 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4939269]
characterization. V
The upsurge in the popularity of two-dimensional (2D)
materials with the emergence of graphene1 in recent years
has at the same time rejuvenated van der Waals (VDW) epitaxy, a materials growth technique invented almost 30 years
ago,2 which could yield layered materials with great crystallinity. The relatively weak VDW interaction between the
film and substrate enables a broader choice of film candidates3 and easier film transfer process,4 making itself a good
complement to the conventional chemical epitaxy. However,
such weak interaction also limits the further exploration of
its substrate-film coupling effect, whereas in the case of
chemical epitaxy accomplished by various techniques
including hot wall vacuum methods,5,6 the strain resulting
from the registration of the film to the substrate could bring
about controllable modification in the film properties including the change of band gap,7,8 the adjustment of electronic
band structure,9,10 the enhancement of the electron/hole
mobility,11 the modification of catalytic activity and ionic
conductivity,12 thermodynamic ferroelectric/ferromagnetic
phase change,13,14 insulator-metal transition in strongly
correlated oxides,15 and even superconducting phase transition.16,17 For most of the 2D materials, such as graphene,
h-BN, and transition metal dichalcogenides currently
involved in the VDW epitaxy, the film itself usually has an
increasingly high Young’s modulus18–20 that leaves the
VDW interaction at the interface a negligible effect on
straining the film and modifying its electrical and optical
properties. However, given a material soft enough, will a signification strain engineering be possible via VDW interfacial
interaction? Lead iodide (PbI2), among other 2D materials, is
extremely soft (E ¼ 17 GPa),21 more than two orders lower
a)
Author to whom correspondence should be addressed. Electronic mail:
[email protected]
0003-6951/2016/108(1)/013105/5/$30.00
than that of graphene (E ¼ 2000 GPa).18 Meanwhile, heavy
atoms like Pb and I render an enhanced VDW interaction.
Both make it an ideal candidate to study VDW epitaxy on
strain engineering. Finally, PbI2 itself has potential application prospects as radiation detectors22 and lasers.23 A possible manipulation of its optical property via the VDW epitaxy
could be especially beneficial. Understanding the role of
VDW interaction on soft inorganic materials would help to
shed light on manipulating the electrical, magnetic, and optical properties of 2D materials in future.
Here, in this letter, we report the observation of the
VDW epitaxy induced remarkable photoluminescence (PL)
change in PbI2 flakes grown on muscovite mica substrates.
The as-grown flakes exhibit a blue shift of PL peak with
decreasing thickness and increasing substrate-film coupling
effect. The tunable PL is in good agreement with the proposed model on strain-induced band gap shifting. Further
bending test and Raman spectroscopy characterization are
conducted as sound evidence to our hypothesis. Our discovery shows that a weak VDW epitaxial interface could have
substantial impacts on the optical properties of the thin film
material which is soft enough.
The PbI2 flakes were synthesized via Chemical Vapor
Deposition (CVD) method through a single source evaporation process. Detailed growth conditions and characterization
setups could be found from the supplementary material.24
Figure 1(a) shows the morphology of the PbI2 flakes after
growth. They present themselves as well aligned triangles or
truncated triangles with the size of a tens of microns and
sharp edges, indicating good crystallinity. The two insets of
Figure 1(a) marked by red rectangles show two other regions
where the crystals are also aligned to one direction marked
by the dashed arrows. While the different shape of the crystal, as investigated by our previous study,25 is a sign of
108, 013105-1
C 2016 AIP Publishing LLC
V
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 128.113.37.4 On: Sat, 30 Jul 2016
18:17:54
013105-2
Wang et al.
Appl. Phys. Lett. 108, 013105 (2016)
FIG. 1. Morphology and structural characterization of as-grown PbI2 flakes. (a) PbI2 orientation on the muscovite mica (001) substrate. The dashed arrows
indicate the parallel alignment of the crystals and hence the VDW epitaxy. The red rectangles are two other regions that have a similar line up; (b)-(f) individual PbI2 flake with different thicknesses from 90 to 400 nm as marked in the images; (g) AFM image of the 180-nm-thick flake as shown in (e); (h) AFM image
of the pile-ups of the flakes with an overall thickness of 1 lm, resembling wedding-cake growth; (i) diffraction pattern of mica substrate with [001] as zone
axis; (j) low magnification TEM image of one PbI2 flake; (k) diffraction pattern of PbI2 with [0001] as zone axis [scale bar: (a) main figure and middle inset:
20 lm, bottom inset: 50 lm; (b)-(f) 20 lm; (g) and (h) 10 lm].
kinetics-driven growth instability; the uniform orientation
suggests the existence of VDW epitaxy. The thickness of the
flakes, which is more of interest in current study, is revealed
by the different colors as shown in Figures 1(b)–1(f) where
the color changes from light yellow (b) to blue ((c) and (d))
and red (e), and finally almost transparent (f) and so does the
thicknesses from 90 nm to 400 nm as marked in the images.
The thickness is confirmed by subsequent AFM characterization where the AFM image of the180 nm-thick flake was
shown in Figure 1(g). We may notice some layered feature is
present at the edge of the flake, which is consistent with the
optical image of Figure 1(e) and the nature of PbI2 crystal.
As the thickness continues to increase, the crystal adopts a
wedding-cake growth model17 where different flakes pile up
without the presence of screw dislocations, as shown in the
AFM image in Figure 1(h) where the overall thickness
reaches 1 lm. The structural information is further revealed
by TEM diffraction patterns. Figure 1(i) shows the diffraction pattern of the mica substrate with [001] as zone axis
(ZA), a pseudo hexagonal lattice26 with a lattice constant of
a ¼ 5.19 Å and b ¼ 9.04 Å. Figure 1(j) shows the low magnification TEM image of one PbI2 flake transferred onto a
TEM grid, whose diffraction pattern is shown in Figure 1(k).
The first set of patterns proves to be {3360} of PbI2 with ZA
[0001]. From the alignment of the TEM image and the diffraction pattern, the facets of the flakes prove to be {1010},
which is again in agreement with the surface free energy
argument. Crystallographic analysis by combining both optical images (by which we know the orientations of both mica
and film) and structural data (by which we conclude the respective parallel planes between mica and film) confirms the
epitaxial growth.
PL characterization was performed at room temperature
on the PbI2 flakes investigated in Figure 1. PbI2 is a direct
band gap material with a band gap between 2.3 and 2.4 eV
(Ref. 27) and a green luminescence. Figure 2(a) shows the
different PL spectra of the flakes with different thicknesses
shown in Figures 1(c)–1(f) as well as the powder precursor,
the latter of which has a PL peak centered at 541 nm, indicating a band gap of 2.28 eV. All the peaks are normalized at
the peak intensity to emphasize the changing of peak position. From the spectrum, we may clearly notice a uniform
trend in the blue shift of the PL peak from 541 nm to 508 nm
(2.28 to 2.43 eV) as the thickness decreases from bulk crystal
to 110 nm thin film. The spectra for the thinnest 90 nm film
are absent due to the laser beam damage on the sample. The
typical PL photoluminescence images of the flakes of a
thicker transparent flake and a thinner bluish flake are shown
in Figures 2(b) and 2(c), respectively.
As the film thickness far exceeds a few layers and taking
into consideration the single crystalline, high-temperature
growth features, we may well rule out the possibility of
quantum confinement, the grain size, and defected induced
PL shift. We propose that it is the VDW epitaxy and the resultant substrate-film coupling effect that dictates the shifting
of the PL peaks. According to Figure 1, we show the proposed epitaxial relationship with the blue sphere as the mica
(M) lattice and the green square as the PbI2 (P) lattice in
Figure 3(a). While we still use the conventional monoclinic
indexing for mica lattice, the pseudo hexagonal lattice on the
FIG. 2. PL spectra of as-grown PbI2 flakes. (a) PL spectrum of PbI2 flakes
with different thicknesses as shown in Figure 1. PL peaks have a uniform
trend of blue shift of about 0.15 eV as the thickness decreases from bulk
crystal to 110 nm; (b) and (c) optical images of thicker (b) and thinner (c)
luminescent flakes.
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 128.113.37.4 On: Sat, 30 Jul 2016
18:17:54
013105-3
Wang et al.
Appl. Phys. Lett. 108, 013105 (2016)
FIG. 3. Quantitative analysis of the PL shift via deformation potential theory. (a) Proposed epitaxial relationship of mica lattice (blue) and PbI2 (green) based
on their lattice types and lattice mismatch. The [10
10 of PbI2 lines up with [310] of mica with a small lattice mismatch as shown by the lower inscriptions; (b)
surface plot of the change of band gap with different biaxial strain according to the deformation potential theory. (c) Plot of change of band gap with the
inverse of the thickness of the film with different interaction energies from 0.1 to 1 eV. The experiment data are also marked on the plot that fall within the
modelling curve region. The yellow curve indicates the Matthews model where misfit dislocations are introduced.
(001) plane of mica fits the 6 fold symmetry of PbI2 in terms
of lattice type. Moreover, in the [310] direction of mica
(in terms of a hexagonal indexing, it would be [1120]) and
the [10
10] direction of PbI2, the two lattices have a good
lattice match of e ¼
d½32120M 2d½10
10P
2d½10
10P
¼ 0:011, hence creating
a biaxial compressive strain of ex ¼ ey ¼ 1:1%. Therefore,
the overall epitaxial relationship is proposed to be
PbI2[0001]jjMica[001] with offset angle ¼ 5 and
10]jj mica[310].
PbI2[10
To investigate quantitatively how the strain may manipulate the shift of band gap and thereafter the PL peak, deformation potential theory is applied. Shockley and Bardeen
proposed in 1950s28 a deformation potential theory that
related the hydrostatic strain with the change of band gap
through a coefficient named deformation potential.
According to them, the shift in band gap in a non-polar crystal would be a sum of the valence and conduction band shift
and could be approximated as
DEg ¼ jDEC j þ jDEV j ¼ ECij eij þ Evij eij ¼ Egij eij ;
(1)
where E1C and E1V are the deformation potentials of the
conduction and valence band, respectively, and E1g is the
potential of the band gap. The theory was first used for the
study of mobility of semiconductors and later applied with
fairly good success in the strain engineering of epitaxial film
with biaxial strain.29 The deformation potential parameter of
PbI2 has been studied earlier from its mobility data30 that
showed a value from 5 to 9 eV, which is in a great consistency with a recent first-principle simulation on monolayer
PbI2.31 Figure 3(b) shows the surface plot of the change of
band gap of PbI2 in terms of different values of ex and ey and
a deformation potential of 7 eV from Eq. (1). The Poisson
ratio of PbI2 is taken as 0.3 according to the previous literature.32 As expected, the compressive strain increases the
band gap which is consistent with the shifting direction of
PL peaks.
Thin film mechanics analysis is conducted to take into
account the quantitative effect of thickness on the straining
of PbI2. For conventional chemical epitaxy where commensurate growth is usually observed, van der Merwe and
Matthews33,34 successfully predicted the thickness dependent
strain in epitaxial film by considering the generation of misfit
dislocations. According to them, a critical thickness of the
film is reached when energetically it is more favored to generate dislocation at the interface to relax the misfit strain and
therefore the strain energy. Upon reaching the critical thickness, the relaxation of the strain is found to be33
Gint
b
h
ln
þ1 ;
(2)
e¼
Gf ilm 8pð1 þ tÞh
b
where Gint and Gf ilm denotes the shear modulus at the interface
and of the film, b is the Burgers vector of the misfit dislocation,
h is the film thickness, and t is the Poisson’s ratio of film.
Here, the absolute value of Gint reflects whether it is a strongly
covalent interface or a weakly bonded VDW interface. In the
case of PbI2, from the proposed lattice mismatch and the
Matthews criterion of critical thickness, such thickness value is
only a few nanometers and all the films observed previously
should fall into the region where strain is partially relaxed.
With combination of the deformation potential theory, we plot
the change of band gap with the inverse of thickness shown as
the yellow curve in Figure 3(c). The curve is plotted under the
condition that GGfintilm ¼ 1, which is certainly an overestimation
since the bonding strength at the interface should be lower
than that of the film. However, even with the overestimation,
the curve still deviates far away from the experimental data,
indicating a much higher strain level in the film.
According to above analysis, Matthews theory fails to
explain the observed phenomenon quantitatively. First, the
Matthews theory was developed originally to apply for an epitaxy with accurate lattice registration (commensurate growth).
But in the case of VDW epitaxy, such prerequisite is not necessarily satisfied and indeed incommensurate growth of ZnO
nanowires on mica has been recently observed,35 where a substantial strain of 1% is observed in ZnO. Second, Matthews
theory only deals with the thermodynamic case. However,
practically, nucleation and propagation barrier of misfit dislocation act as even more pronounced role in determining strain
and critical thickness of thin films. Such scenario is commonly observed in the literature where critical thickness far
exceeds the Matthews limit.36 By taking into account these
considerations and for a first-order approximation, in this
analysis, the pseudomorphic thickness of the epitaxial growth
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 128.113.37.4 On: Sat, 30 Jul 2016
18:17:54
013105-4
Wang et al.
Appl. Phys. Lett. 108, 013105 (2016)
is applied, which reaches maximum when the strain energy
completely balances out the energy gain from the substratefilm interaction. The strain energy per unit volume with a unit
of GPa is a function of the biaxial strain and varies as37
Ustrain ¼
1
ex ey ;
s11 þ s12
(3)
where s11 and s12 are the components of the compliance matrix that can be evaluated by their stiffness counterparts
available from the earlier study.32 The substrate-film interaction per unit area, which is VDW in nature, on the other
hand, can be approximated as
1
UVDW ¼ 6 Eint =A;
3
(4)
where Eint denotes the interaction between a pair of lattice
points at the substrate and film and A is the area of the basal
plane of the unit cell. Therefore, the pseudomorphic thickness can be estimated as
h0 ¼
UVDW
2Eint ðs11 þ s12 Þ
¼q
ðnmÞ;
Ustrain
A ex ey
(5)
where q ¼ 1:6 1019 is the charge of an electron and Eint
in eV. As the overall thickness of the film h exceeds h0 , we
approximate the strain relaxation process from the overall
energy consideration similar to what Matthews has done.
The strain e would vary with the thickness of the film h such
that the interfacial energy benefit always balances out the
total strain energy, i.e.,
e ¼ ½UVDW ðs11 þ s12 Þ=h1=2 ;
(6)
and therefore the strain would have a h0:5 dependence on
the overall thickness. Figure 3(c) plots the change of the band
gap as the inverse of film thickness varies from 10 to 600 nm
at three different Eint values: (1) 0.1 eV that is commonly
found to be the value of unstrained two VDW layers lacking
epitaxial registration,38 (2) 0.5 eV that is a typical value for
the adsorption energy of heavy metal atoms on VDW substrates,38 and (3) 1 eV resembling that of the weak chemical
bonds. The experimentally obtained data are also marked on
the graph. The plateaus in the three computed curves indicate
the threshold thickness when the maximum band gap change
is reached. From the plot, we may see that the experimental
data fall within the region of 0.5 eV < Eint < 1 eV, suggesting
a large VDW interaction. The two data points higher than the
“plateau” value may possibly suggest a higher deformation
potential value. In addition, the mismatch between the experimental data and Matthew theory suggests the growth may follow incommensurate VDW epitaxy rather than commensurate
VDW growth.
To further confirm the cause of the PL peak shift and the
existence of VDW strain, bending test and Raman characterization are carried out, respectively. Figure 4(a) shows schematically the setup of the bending test where a single PbI2
flake was transferred onto a thick polydimethylsiloxane
(PDMS) stamp (10 mm long and 1.5 mm thick). Part of the
stamp close to the PbI2 flake was clamped, while a micromanipulation probe was controlled manually to press and lift
the other free end so as to create a uniaxial tensile (compressive) strain. All the manipulation was done on the optical
microscope where the PL change caused by the strain can be
recorded. Under such setup, the maximum strain exerted on the
flake, with its lateral size and thickness neglected, would be39
emax ¼
3b
tanðhÞ;
2l
(7)
where b and l are the thickness and length of the beam and h is
the bending angle just close to the clamped side. Figure 4(b)
shows the PL spectrum of a thick PbI2 flake (approximate
thickness 400 nm) under different stress states, where the compressive state has a bending angle of around 10 and the tensile
one 5 equivalent to a strain of 3.97% and 1.96%. In the
FIG. 4. Bending test and Raman characterization of the PbI2 flakes. (a)
Schematic showing the setup of the
bending test. (b) PL spectrum of the
same flake under compressive (black),
neutral (red), and tensile (blue) strain
states. (c) Comparison of the data
obtained in (b) with deformation
potential approximation; (d) Raman
spectrum of 110-nm-thick (black),
400-nm-thick (red) PbI2 flakes, and the
powder precursor (black). A visible
red shift at the first peak is shown as
the thickness decreases.
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 128.113.37.4 On: Sat, 30 Jul 2016
18:17:54
013105-5
Wang et al.
neutral state, the PL peak positions at 536 nm, with some red
shift compared with the one in Figure 2(a) with similar thickness. This very likely implies that when the film is transferred,
the VDW strain is more or less relaxed that makes the band
gap shift towards the original value. The compressive and tensile strains, on the other hand, also have the effect consistent
with the previous deformation potential theory, with the compressive increasing the band gap (536 to 529 nm) and vice
versa (536 to 550 nm). The PL spectra for the tensile strain
show an additional “shoulder” to the left of the main peak and
we attribute it to the possible delamination and damage to the
film when stretched. The result of the bending test is further
quantitatively studied as shown in Figure 4(c) where the modelling curve and the experimental data are present. We may
see that while both data points fit qualitatively the theoretical
value, the tensile strain matches pretty well and the compressive strain deviates quite far away. We believe that, in the case
of a large compressive strain, PbI2 may buckle up and do not
follow completely the curvature of the PDMS stamp and thus
experiencing a much smaller strain. Both the buckling in the
compressive state and the delamination in the tensile state are
consistent with the “soft nature” of the material itself. Also, at
relatively large strain value, the deformation potential theory
may be less accurate, since the theory is a linear approximation
for a small amount of strain at the vicinity of the original band
gap. Finally, to confirm the existence of compressive strain of
the VDW epitaxial PbI2 flake, Raman characterization was
performed. Figure 4(d) shows the Raman spectrum of the thinner (110 nm) and thicker (400 nm) flakes and also the powder
precursor, all of which show two peaks at Raman shifts at
around 167 cm1 and 213 cm1. The first peak is assigned to
the 2Eg vibration mode while the second one to the 4Eu peak
according to the previous study,40 with the former one being
more of interest to the present study since it is related directly
with the shearing motion of the I-Pb-I bonds.41 The spectrum
shows as visible red shift from 165 cm1 to 169 cm1 as the
thickness decreases, which implies a more rigid vibration and
hence shorter I-Pb-I bond length and a possible compressive
strain. The second peak, the 4Eu mode is associated with the
motion of the two iodide atoms in the z axis compared with
the Pb atom,41 which from the spectrum has very slight change
that is also consistent with our hypothesis.
In conclusion, by studying single crystalline soft PbI2
crystal through VDW epitaxy, we demonstrate that through
the deformation potential theory that linearly (when perturbation is small) correlates the strain and the shift of band
gap, thickness-dependent VDW epitaxial strain can be significant (as high as 1.1%) and substantially influence the
photoluminescence properties of the hosted film with a low
Young’s modulus and heavy atomic masses. Our results suggest a possible approach to modifying the electrical, optical,
and possibly magnetic properties of 2D thin films grown by
VDW epitaxy.
Appl. Phys. Lett. 108, 013105 (2016)
J. S. and Y. W. were supported by J.S.’s start-up fund
from Rensselaer Polytechnic Institute and National Science
Foundation under Grant No. CMMI 1550941.
1
K. S. Novoselov, A. K. Geim, S. Morozov, D. Jiang, Y. Zhang, S. A.
Dubonos, I. Grigorieva, and A. Firsov, Science 306, 666 (2004).
2
A. Koma, K. Sunouchi, and T. Miyajima, Microelectron. Eng. 2, 129 (1984).
3
A. Koma, K. Ueno, and K. Saiki, J. Cryst. Growth 111, 1029 (1991).
4
A. Geim and I. Grigorieva, Nature 499, 419 (2013).
5
D. Pathak, R. Bedi, and D. Kaur, Optoelectron. Adv. Mater. 4, 657 (2010).
6
D. Pathak, R. Bedi, D. Kaur, and R. Kumar, Chalcogenide Lett. 8, 213 (2011).
7
R. People, Phys. Rev. B 32, 1405 (1985).
8
K. Zhang, V. Lazarov, T. D. Veal, F. Oropeza, C. F. McConville, R.
Egdell, and A. Walsh, J. Phys.: Condens. Matter 23, 334211 (2011).
9
E. Yablonovitch and E. Kane, J. Lightwave Technol. 6, 1292 (1988).
10
A. Adams, Electron. Lett. 22, 249 (1986).
11
M. V. Fischetti and S. E. Laux, J. Appl. Phys. 80, 2234 (1996).
12
B. Yildiz, MRS Bull. 39, 147 (2014).
13
J. H. Lee, L. Fang, E. Vlahos, X. Ke, Y. W. Jung, L. F. Kourkoutis, J.-W.
Kim, P. J. Ryan, T. Heeg, and M. Roeckerath, Nature 466, 954 (2010).
14
D. G. Schlom, L.-Q. Chen, C.-B. Eom, K. M. Rabe, S. K. Streiffer, and
J.-M. Triscone, Annu. Rev. Mater. Res. 37, 589 (2007).
15
A. J. Hauser, E. Mikheev, N. E. Moreno, J. Hwang, J. Y. Zhang, and S.
Stemmer, Appl. Phys. Lett. 106, 092104 (2015).
16
E. Tang and L. Fu, Nat. Phys. 10, 964 (2014).
17
I. Bozovic, G. Logvenov, I. Belca, B. Narimbetov, and I. Sveklo, Phys.
Rev. Lett. 89, 107001 (2002).
18
J.-U. Lee, D. Yoon, and H. Cheong, Nano Lett. 12, 4444 (2012).
19
A. Castellanos-Gomez, M. Poot, G. A. Steele, H. S. van der Zant, N.
Agra€ıt, and G. Rubio-Bollinger, Adv. Mater. 24, 772 (2012).
20
Q. Peng, W. Ji, and S. De, Comput. Mater. Sci. 56, 11 (2012).
21
W. Veiga and C. M. Lepienski, Mater. Sci. Eng., A 335, 6 (2002).
22
K. Shah, F. Olschner, L. Moy, P. Bennett, M. Misra, J. Zhang, M. R.
Squillante, and J. C. Lund, Nucl. Instrum. Methods Phys. Res., Sect. A
380, 266 (1996).
23
X. Liu, S. T. Ha, Q. Zhang, M. de la Mata, C. Magen, J. Arbiol, T. C.
Sum, and Q. Xiong, ACS Nano 9, 687 (2015).
24
See supplementary material at http://dx.doi.org/10.1063/1.4939269 for the
description of the van der Waals epitaxy growth and characterization of
the PbI2 flakes.
25
Y. Wang, Y. Shi, G. Xin, J. Lian, and J. Shi, Cryst. Growth Des. 15, 4741
(2015).
26
E. Radoslovich, Acta Crystallogr. 13, 919 (1960).
27
A. F. Da Silva, N. Veissid, C. An, I. Pepe, N. B. De Oliveira, and A. B. Da
Silva, Appl. Phys. Lett. 69, 1980 (1996).
28
J. Bardeen and W. Shockley, Phys. Rev. 80, 72 (1950).
29
J. Liu, D. D. Cannon, K. Wada, Y. Ishikawa, D. T. Danielson, S.
Jongthammanurak, J. Michel, and L. C. Kimerling, Phys. Rev. B 70, 155309
(2004).
30
P. Bloch, J. Hodby, T. Jenkins, D. Stacey, G. Lang, F. Levy, and C.
Schwab, J. Phys. C 11, 4997 (1978).
31
M. Zhou, W. Duan, Y. Chen, and A. Du, Nanoscale 7, 15168 (2015).
32
B. Dorner, R. Ghosh, and G. Harbeke, Phys. Status Solidi B 73, 655 (1976).
33
J. Matthews, D. Jackson, and A. Chambers, Thin Solid Films 26, 129
(1975).
34
J. van der Merwe, Philos. Mag. 7, 1433 (1962).
35
M. I. B. Utama, F. J. Belarre, C. Magen, B. Peng, J. Arbiol, and Q. Xiong,
Nano Lett. 12, 2146 (2012).
36
A. Fiory, J. Bean, L. Feldman, and I. Robinson, J. Appl. Phys. 56, 1227 (1984).
37
J. Shen, S. Johnston, S. Shang, and T. Anderson, J. Cryst. Growth 240, 6
(2002).
38
K. T. Chan, J. Neaton, and M. L. Cohen, Phys. Rev. B 77, 235430 (2008).
39
C. Sun, J. Shi, and X. Wang, J. Appl. Phys. 108, 034309 (2010).
40
W. M. Sears, M. Klein, and J. Morrison, Phys. Rev. B 19, 2305 (1979).
41
L. Pedesseau, J. Even, C. Katan, F. Raouafi, Y. Wei, E. Deleporte, and
J.-M. Jancu, Thin Solid Films 541, 9 (2013).
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 128.113.37.4 On: Sat, 30 Jul 2016
18:17:54