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: zl23@umail.iu.edu; Tel.: 812-856-1360

Satyesh Yadav: Materials Science and Technology Division, MST-8, Los Alamos National

Laboratory, Los Alamos, NM 87545, USA

E-mail: syadav@lanl.gov; 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: youxing@lanl.gov; 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: nanli@lanl.gov; 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: xyliu@lanl.gov; Tel.: 505-667-6260

Jian Wang: Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln,

NE 68588, USA

E-mail: jianwang@unl.edu; Tel.: 402-472-1514

Shixiong Zhang: Department of Physics, Indiana University, Bloomington, IN 47405, USA

E-mail: sxzhang@indiana.edu; Tel.: 812-856-1360

Jon Kevin Baldwin: Center for Integrated Nanotechnologies, Los Alamos National Laboratory,

Los Alamos, NM 87545, USA

E-mail: jkbal@lanl.gov; Tel.: 505-665-7359

Amit Misra: Department of Materials Science and Engineering, University of Michigan, Ann

Arbor, Michigan 48109, USA

E-mail: amitmis@umich.edu; 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: namara@lanl.gov; Tel.: 505-667-8665

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* Corresponding authors: Nan Li, Email: nanli@lanl.gov; Jian Wang, Email: jianwang@unl.edu.

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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