Supplementary Materials
Mechanically controlling the reversible phase transformation from zinc blende to wurtzite
in AlN
Zhen Lia,b, Satyesh K. Yadavc, Youxing Chena, Nan Lia,f*, Xiang-Yang Liuc, Jian Wangd*,
Shixiong Zhangb, J. Kevin Baldwina, Amit Misrae, Nathan Maraa,f
a Center for Integrated Nanotechnologies, MPA-CINT, Los Alamos National Laboratory, Los
Alamos, NM 87545, USA
b Department of Physics, Indiana University, Bloomington, IN 47405, USA
c Materials Science and Technology Division, MST-8, Los Alamos National Laboratory, Los
Alamos, NM 87545, USA
d Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588,
USA
e Department of Materials Science, University of Michigan, Ann Arbor, MI, 48109, USA
f Institute for Materials Science, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Zhen Li: Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos,
NM 87545, USA, and
Department of Physics, Indiana University, Bloomington, IN 47405, USA
E-mail: [email protected]; Tel.: 812-856-1360
Satyesh Yadav: Materials Science and Technology Division, MST-8, Los Alamos National
Laboratory, Los Alamos, NM 87545, USA
E-mail: [email protected]; Tel.: 505-665-5960
Youxing Chen: Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los
Alamos, NM 87545, USA
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E-mail: [email protected]; Tel.: 505-665-6859
Nan Li: Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos,
NM 87545, USA, and
Institute for Materials Science, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
E-mail: [email protected]; Tel.: 505-665-1857
Xiang-Yang Liu: Materials Science and Technology Division, MST-8, Los Alamos National
Laboratory, Los Alamos, NM 87545, USA
E-mail: [email protected]; Tel.: 505-667-6260
Jian Wang: Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln,
NE 68588, USA
E-mail: [email protected]; Tel.: 402-472-1514
Shixiong Zhang: Department of Physics, Indiana University, Bloomington, IN 47405, USA
E-mail: [email protected]; Tel.: 812-856-1360
Jon Kevin Baldwin: Center for Integrated Nanotechnologies, Los Alamos National Laboratory,
Los Alamos, NM 87545, USA
E-mail: [email protected]; Tel.: 505-665-7359
Amit Misra: Department of Materials Science and Engineering, University of Michigan, Ann
Arbor, Michigan 48109, USA
E-mail: [email protected]; Tel.: 734-763-2445
Nathan Mara: Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los
Alamos, NM 87545, USA, and
Institute for Materials Science, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
E-mail: [email protected]; Tel.: 505-667-8665
2
* Corresponding authors: Nan Li, Email: [email protected]; Jian Wang, Email: [email protected].
Methods
Synthesis: The multilayers composed of alternating Al and AlN individual layers were deposited
by reactive direct current magnetron sputtering on Si (111) substrates. It is noted that the
substrate orientation may influence the texture and the strain state of the thin film. The
deposition was performed at room temperature. The vacuum pumping system was consisted of a
turbomolecular pump backed by a mechanical pump, which provided a base pressure lower than
10-6 mTorr, while the process pressure was kept at 6 mTorr for both Al and AlN layer deposition.
Argon and nitrogen gases were introduced into the chamber by separated mass flow controllers.
Only argon flow was introduced at 40 sccm during the deposition of the Al layers. For the
deposition of the AlN layers, the argon flow was set to 25 sccm and nitrogen flow was
simultaneously introduced at 15 sccm.
Characterization and in situ nanoindentation: Both the microstructural characterization and
the in situ mechanical tests were conducted inside an FEI Tecnai G(2) F30 S-Twin 300 kV
transmission electron microscope equipped with a Nanofactory TEM-STM platform. An etched
W tip with minimum diameter of 100 nm was on one end of the TEM-STM platform, and the
TEM foil was attached to a piezo-operated STM probe by silver paste on the other end. The
videos during the indentation test were recorded by a CCD camera at 3 frames/second. The
HRTEM images were taken along zb-AlN [110] or wz-AlN[211 0¿ direction after phase
transformation. The hexagonal Wurtzite structure is fourfold coordinated but with an ababab…
stacking sequence along the [0001] axis. On the other hand, the stacking of zinc blende AlN
along its [111] axis is abcabc…
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Density functional theory calculations: Our DFT calculations were performed using the
Vienna Ab initio Simulation Package (VASP) [1, 2]. The DFT calculations employed the
Perdew, Burke, and Ernzerhof (PBE) [3] generalized gradient approximation (GGA) exchange-
correlation functional and the projector-augmented wave (PAW) method [4]. For all calculations,
a plane wave cutoff of 500 eV for the plane wave expansion of the wave functions was used to
obtain highly accurate forces. 12x12x12, and 3x3x3 Monkhorst-pack mesh for k-point sampling
are required to calculate the elastic constants of Al and AlN, respectively. All structures are
considered to be converged when each component of the force on every atom is smaller than
0.02 eV/Å. The numbers of valence electrons (states) of the psedudo-potentials are 3 (2s22p1) for
Al, and 5 (2s22p3) for N. In order to make direct comparison of the cohesive energies of
supercells containing AlN which is sandwiched between Al, in zinc blende or wurtzite structure,
supercells containing 3 or 6 layers of AlN with varying number of Al layers were created. For
the supercell containing 6 layers of AlN, it is periodically repeating at the interface plane, and in
the direction perpendicular to the interface plane. Fig. S1 shows such supercell and the resultant
electron localization function (ELF) contours due to the electron density distributions. For
supercells containing 3 layers of AlN, it is periodically repeating at the interface plane as well.
However, it is not possible to have a periodically repeating supercell in the direction
perpendicular the interface plane if the supercell with sandwiched zinc blende AlN and the
supercell with sandwiched wurtzite AlN have the same number of Al atoms. This is due to the
ABC stacking of Al atoms in zb-AlN and ABA stacking of Al atoms in wz-AlN. Thus, to have
same number of Al atoms, a supercell slab with vacuum of more than 12 Å normal to the
interface plane is created. The supercells are allowed to relax until all stresses vanish in all
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directions. A 15x9x1 Monkhorst-Pack mesh for k-point sampling is used for all calculations
involving interfaces, with 1 k-point along the largest length in the supercells.
For the chosen number of Al layers, the relative formation energy is calculated as the difference
in formation energy of the slab with AlN in zinc blende phase bersus the wurtzite phase. Relative
interface formation energy is calculated as difference in interface formation energy of slab
containing zb-AlN and wz-AlN. There are two types of interfaces that form between Al and AlN,
and they are inseparable. Here the average of the interface energies of two types of interfaces are
calculated. The relative interface related energy term is calculated as,
Ezbint−Ewz
int=E zb
supercell−nE zbAlN−mEzb
Al
2 A−
Ewzsupercell−nEwz
AlN−mEwzAl
2 A (S.1)
where Esupercell is the total energy of the supercell; EAlN and EAl are cohesive energies of AlN and
Al biaxially strained to the in-plane lattice parameter of the relaxed supercell; n and m are the
total numbers of AlN functional units and Al atoms in the supercell, respectively; A is the
interface area. Computing the average of the interface energies is not an issue since we expect
the experimental structures should also have both types of interfaces at the same ratios. So it
does not affect the free energy model in this paper.
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Figure S1. Schematic of Al/AlN supercells containing 6 layers of AlN in (a) zb-AlN, and (b) wz-
AlN and the resultant electron localization function (ELF) contours due to the electron density
distributions.
Strain Analysis method. The strain analysis is operated through two steps, (1) Identify the
position of each atomic-column in a HRTEM image with Peak Pairs Analysis (PPA) software [5]
and (2) Calculate strains at the position of each atomic-column. Using a lattice image that is
composed of a set of points in a plane, the three local strain components in rectilinear
coordinates, 11, 22, and 12, at any point surrounded by 8 neighbors, define the radial strain in the
direction of the th neighbor, , according to the coordinate transformation law [6]
, (1)
with l and m as direction cosines of the th neighbor in a perfect (undeformed) lattice in 2D,
and higher order terms in strain have been neglected as they are assumed small. In strain space,
Eq. (1) is an ellipse. Thus there are N equations of this form for each lattice point, and the left
side of each equation is known since
(2)
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where r and R are the distances to the th neighbor in the deformed and perfect lattices,
respectively. Referring to Ref [6], the set of N equations enable the determination of the ij
components in a least squares sense giving the strains expressed as a column vector
, (3)
where the matrix N and column vector Q are given by
and (4)
and the sums are over all neighbors. The least squares determination of the strain components,
leading to Eq. (3), is necessitated by various uncertainties in the positions of the various lattice
points extracted from the HRTEM image [7, 8].
Meanwhile, the TEM foil is assumed to be under the condition of plane stress. This assumption
is reasonable since the thickness of TEM foil along the e-beam direction is ~ 50 nm and the
loading is parallel to the TEM foil. Corresponding to plane-stress condition, the stress along the
e-beam direction is equal to zero. The strain along the e-beam can be calculated using the
measured in-plane strains.
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In situ nanoscale mechanical testing setup.
Figure S2. In situ TEM setup. Both TEM foil and chemical etched W tip are loaded into the
Nanofactory TEM-STM platform. And the cross-sectional TEM micrograph of the Al/AlN
multilayered thin film in contact with the W tip inside the TEM column during the in situ
nanoindenation experiments is presented.
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The atomic configuration of the region immediately preceding the formation of wz-AlN,
and the corresponding strain distribution.
Figure S3. Strain analysis. (a) The atomic configuration of the region immediately before the
formation of wurtzite AlN. (b)-(d) The strain εxx, εxy, and εyy distributions with an average value
of 2%, 1.6%, and -7%, respectively.
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Transformation of stiffness tensor under a transformation of the coordinate system. The
transformation of stiffness tensor under a different coordinate system has been calculated
according to ref [9]. The old and new Cartesian coordinate systems are denoted by x, y, z and x’,
y’, z’ respectively. The crystallographic directions of x’, y’, z’ are [-112], [1-11] and [110]
respectively. The position of the new system with respect to the old system x, y, z, is determined
by Table 1 of direction cosines.
Table 1. Direction cosines
x y zx' -1/√6 1/√6 2/√6y' √3/3 -√3/3 √3/3z' √2/2 √2/2 0
The stiffness tensor in old system is
Cij = ,
and the stiffness tensor in new coordinate system is
Ci'j' = .
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Calculation of the free energy associated with the phase transformation.
E free=Einteraction+E self+∆ Ecohesive+∆ Einterface−W applied stress,
According to Hirth and Lothe [10], the interaction energy between dislocations is
Einteraction=−μave(b ∙ξ )(−b ∙ ξ)
2πln R
Ra−
μave (b × ξ)(−b × ξ)2 π (1−υ)
ln RRa
−μave
2 π (1−υ) R2 [ (b×ξ )∙ R][(−b ×ξ )∙ R] .
Here μave is the average shear modulus of Al/AlN multilayered composite, the calculation of
which follows the rule of mixture. Wherein phase transformation occurs, the ratio of the layer
thickness of Al to that of AlN is ~ 6, thus 1/μave = 6/7 μAl + 1/7 μAlN = 32GPa. As presented in
Fig. 4a, Shockley partials b1 and b2 are nucleated and remained on side of the new wurtzite
phase. Here b is the sum of the Shockley partials b1 and b2. R is the length of the new phase
along x' direction. Ra is the core cutoff and equals to the length of one partial dislocation, since
the stacking fault energies of both Al and AlN are high. ν is the Poisson’s ratio (0.24 here).
E self=Eelastic +Emisfit.
Here Eelastic is the elastic strain energy stored in the two half crystals, Eelastic=μave b2
4 π (1−ν )ln r
2ζ ,
where r equals to the length of one full dislocation and ζ =d AlN (111)
2(1−ν).Emisfit is associated with the
distorted bonds across the plane, Emisfit=μave b2
4 π (1−ν ).
∆ Ecohesive=Ewurtzite phase−E zincblende phase. The phase energy is calculated from DFT. Meanwhile, the
strain energy has been considered in this term [11].
∆ E interface=Ewurtzite /Alinterface−E zincblende/ Al interface
. The interfacial energy is obtained from DFT as well.
W applied stress=σx ' y ' ∙ b ∙ R. The calculation of σ x ' y' is followed by the assumption that the TEM foil is
under the condition of plane stress and the value is estimated to be ~ -0.8 GPa.
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The attractive force between two Shockley dipoles.
Figure S4. The attractive force between two Shockley dipoles as a function of the distance
between Shockley partial dipoles
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The corresponding strain environment of the region immediately preceding the reverse
phase transformation from wurtzite to zinc blende.
Figure S5. Strain analysis. (a)-(c) The strain εxx, εyy, and εxy distributions with an average value of
1.5%, -3%, and 0.2%, respectively.
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Reference
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