Microstructure and surface morphology of InAsSbBi grown by molecular beam epitaxy

High performance infrared photodetectors and emitters are desired for many applications, including navigation, night vision, launch detection, communications, imaging, and spectroscopy.¹ The III-V-bismide alloys are an emerging class of materials for mid and long wave infrared applications. Bismuth incorporation in InAs reduces the room-temperature bandgap energy of InAs by 51 meV/% Bi,² which is a much greater rate than Sb at 9.3 meV/% Sb.³ In particular, the quaternary alloy InAsSbBi lattice-matched to commercially available GaSb substrates spans bandgap energies from 0.32 to 0.10 eV (4–12 μm) at low temperature and from 0.27 to 0.042 eV (5–30 μm) at room temperature. The InAsSbBi material system offers independent control of strain and bandgap energy by independently adjusting the Sb and Bi mole fractions. The bandgap energy of InAsSbBi is bound above by InAsSb and below by InAsBi and further examined in a companion paper.⁴ 

InAsSbBi is a highly mismatched alloy with isoelectronic group-V elements of different sizes, ionicities, and electronegativities. These types of alloys can have miscibility gaps⁵ over certain composition ranges that make them challenging to grow. The microstructure and surface morphology have been reported for GaAsBi,^6–8 GaSbBi,^9,10 InAsBi,¹¹ and (In,Ga)AsN.¹² However, the microstructural properties of InAsSbBi have received scant attention. The investigation of the microstructural properties of the InAsSbBi alloy system is essential as feedback to optimize growth conditions and optical performance of this emerging infrared material system.

This work examines four InAs_1−x−ySb_yBi_x samples grown by solid-source molecular beam epitaxy⁴ at a rate of 15 nm/min on GaSb (100) oriented substrates. The sample cross section is shown in Fig. 1 and consists of a 500 nm GaSb buffer, a 10 nm InAs/10 nm AlSb partially strain balanced barrier, the InAsSbBi active region, and a terminating 10 nm AlSb/10 nm InAs barrier/cap layer. The GaSb buffer layer is grown at 500 °C except for the last 70 nm where the substrate temperature is reduced by 70–100 °C in preparation for the growth of the InAsSbBi active layer. The InAsSbBi layers are grown at temperatures from 400 to 430 °C, using V/In flux ratios 0.120 for Sb/In, 0.050 and 0.100 for Bi/In, and 0.911 and 0.940 for As/In. The temperatures and V/In flux ratios used during growth and the in-plane biaxial strain of the InAsSbBi bulk layers are provided for each sample in Table I. Droplets are observed on the two samples grown with the smallest As flux.

All growths are performed at a constant In flux of 4.4 × 10¹⁴ cm⁻² s⁻¹ corresponding to an InAsSbBi on a GaSb growth rate of about 15 nm/min. The As/In and Sb/In fluxes are calibrated prior to each growth by growing InAs on InAs and InSb on InSb and slowly lowering the V/In flux ratio until the transition from a group-V to a group-III rich surface reconstruction is observed using reflection high energy electron diffraction. This procedure accurately and repeatably calibrates the one-to-one group-V to In flux ratios for As and Sb, from which existing ion gauge measurements of the As and Sb fluxes as a function of valve position are employed to set the flux with a precision better than 1%. The Bi flux is calibrated using scanning electron microscope measurements of the thickness of 190 nm of elemental Bi deposited on GaAs at 100 °C. The substrate temperature is measured using an IrconModline 3 (model 3G-10C05) pyrometer.

All growths are performed under group-V rich surface reconstructions where all of the incident In flux incorporates at these growth temperatures. The individual group-V fluxes are set in terms of excess elemental overpressure, defined as the difference between the incident flux for a given element (specified by the V/In flux ratio for that element) and the fraction of the incident flux incorporated (specified by the elemental mole fraction). In particular, the As overpressure, set at either 1% or 4% for the InAsSbBi growths examined here, is found to strongly influence Bi incorporation and surface morphology.

The chemical composition of the InAsSbBi layers is examined using Rutherford backscattering (RBS), high-resolution X-ray diffraction (XRD), and transmission electron microscopy (TEM) with dark-field imaging. The RBS measurements are carried out using a 1.7 MV General IonexTandetron accelerator with 2 MeV doubly ionized He atoms and measured using a passivated implanted planar silicon detector. The samples are mounted on a two-axis goniometer that enables polar and azimuthal rotations in a vacuum chamber at a pressure of 10⁻⁶ Torr. The ion beam is incident on the sample 8° from the normal and the sample is rocked about the normal through an angular range of 5° at a rate of about one round cycle every 2 h. The backscattered ion yield for the various elements is simulated using commercial software.¹³ The XRD patterns are measured using a PANalyticalX’Pert Pro materials Research X-ray diffractometer with an instrumental resolution of 12 arcsec and Cu Kα₁ radiation with a 1.54 Å wavelength. Simulations of diffraction patterns are carried out using the PANalyticalX’Pert Epitaxy¹⁴ dynamical diffraction modeling software.

The microstructural properties of InAsSbBi films are investigated using transmission electron microscopy. Cross sectional TEM samples are prepared in the $[011]$ and $[011¯]$ projections using wedge polishing followed by Ar-ion milling at liquid nitrogen temperature. TEM imaging and energy dispersive X-ray (EDX) analysis is carried out using a Philips CM 200 microscope operating at 200 kV, with an interpretable resolution of 2.5 Å. Scanning TEM imaging and energy dispersive X-ray spectroscopy is carried out using an aberration-corrected JEOL ARM 200F operated at an acceleration voltage of 200 kV, with a spatial resolution of 0.8 Å.

The surface morphology is examined using Nomarski optical microscopy and atomic force microscopy (AFM). Nomarski optical images are acquired using an Olympus MX50 optical microscope with Nomarski prism, analyzer, and polarizer components. The AFM measurements are performed using a Brucker multimode 8 with a lateral scan range of 100 μm and vertical scan range of 5.5 μm.

The RBS measurements and simulations of the InAsSbBi samples are shown in Fig. 2. The experimental measurements are shown as solid blue curves. The simulated profile shown as the red solid curve is the sum of simulated ion yields for each element shown as solid curves. Although the In, As, Sb, and Bi signals arise from the same InAsSbBi layer, the backscattered ion yield for these increasingly heavier elements occurs at progressively larger backscattered ion energies. As the element with the largest atomic mass, Bi yields a high energy shoulder from 1.765 to 1.858 MeV in the backscattering spectrum that is typically sensitive to small 0.1% variations in the Bi mole fraction of bulk layers.¹⁵ Nevertheless, the analysis overestimates the Bi mole fraction in InAsSbBi samples that have Bi-rich surface features, due to a large backscattering signal from the surface. This is evident from the backscattered ion yield in Fig. 2(a) (sample A), where the elemental Bi signal is not what is expected from a uniform bulk layer. The fact that the Bi signal exhibits a nonuniform peak at the highest energies indicates the presence of Bi-rich regions near and at the sample surface. This particular Bi signal is reproduced in the simulation by using a model with multiple Bi containing layers that comprises 160 nm of InAs_0.919Sb_0.055Bi_0.026, 50 nm of InAs_0.923Sb_0.039Bi_0.038, 10 nm of AlSb_0.955Bi_0.045, and 10 nm of InAs_0.950Bi_0.050. This indicates approximately 5% Bi coverage on or near the sample surface that is a consequence of the accumulation of unincorporated Bi on the growth surface that does not evaporate with the other group-V elements As and Sb. The simulated Bi mole fractions are 0.1% and 0.4% for samples B and C that do not have Bi-rich surfaces and 2.6% and 1.1% for samples A and D that have Bi-rich surfaces (see Fig. 2).

Measurements and simulations of (400) ω-2θ coupled XRD scans from the four samples are shown in Fig. 3. The measured diffraction patterns are given by the solid black curves and the simulations by the solid red curves. The InAsSbBi layers are coherently strained with in-plane compressive strains from −0.061% to −0.142%. The lattice mismatch is sufficiently small that the critical thicknesses (240–630 nm) exceed that of the 210 nm thick InAsSbBi layers grown. The simulated epilayer thicknesses are 180 nm (A), 210 nm (B), 210 nm (C), and 194 nm (D). A lower than expected intensity for the InAsSbBi layer peak and Pendellösung fringes in samples A and D indicates diminished interface quality, due to the presence of Bi-rich surface features that permeate InAsSbBi layer and barriers. Broadening of the InAsSbBi layer peak in samples C and D indicates fluctuations in the material composition within the layer. In addition to the compressively-strained InAsSbBi layer peak, a tensile peak is observed near the GaSb substrate peak that is due to the unintentional incorporation of As in the GaSb buffer. The dilute As mole fractions range from 0.17% to 0.48% and are insufficient to induce relaxation in the 500 nm buffer as the critical thicknesses are greater than 1.2 μm for all samples. The unintentional As originates from the As background pressure in the growth chamber.

The XRD analysis provides the in-plane strain values reported in Table I. The Bi and Sb mole fractions of strained InAsSbBi are linearly related in the analysis,^4,16 a result of the linear relationship between the constituent binary lattice constants assumed in Vegard’s law. In the limit with no Bi, the in-plane strain establishes maximum Sb and minimum As mole fraction limits for the InAsSbBi layers, which are reported in the XRD section of Table II. The RBS analysis has a limited sensitivity to the Sb mole fraction because the Sb signal overlaps the much larger In signal from the InAsSbBi layer. Likewise, the As signal overlaps the much larger Sb signal from the GaSb buffer layer. When fit independently, the RBS simulated Sb mole fractions exceed the maximum possible mole fraction given by XRD by about 0.01 for the droplet-free samples and by about 0.2 for the droplet covered samples. Therefore, the Sb and As mole fractions used in the RBS simulations are the limits provided by XRD.

The Bi mole fraction, x, provided by the RBS simulations in Fig. 2 is reported in the RBS section of Table II. The Sb mole fraction, y, given by its relationship to Bi mole fraction and layer strain is reported in the RBS + XRD section of Table II for the droplet-free samples B and C. For completeness, the As mole fractions are reported as $1−x−y$⁠. Since the RBS measurements of the droplet covered samples do not provide the Bi mole fraction of the InAsSbBi layer, it is not possible to determine the Sb mole fraction for samples A and D using RBS and XRD. The mole fractions obtained directly from TEM dark-field images of the InAsSbBi layers are reported in the TEM + XRD section of Table II. The results are provided in Sec. III B.

The composition distribution of the InAsSbBi layers is examined using cross-sectional TEM, 200 dark-field imaging, high-angle annular-dark-field imaging, and STEM energy-dispersive X-ray spectroscopy. Low magnification bright-field TEM micrographs from the four InAsSbBi samples are presented in Fig. 4. These results show the overall microstructure of the bulk material and indicate that the 210-nm-thick InAsSbBi layers are pseudomorphic with no visible defects over large lateral distances. Furthermore, contrast modulation due to inhomogeneous composition¹⁷ is observed in samples B, C, and D shown in Figs. 4(b)–4(d), respectively. As the growth temperature decreases, the Bi mole fraction increases, and the lateral composition modulation becomes more pronounced.

A contrast-enhanced TEM cross-sectional image of sample C is shown in Fig. 5 and illustrates that columns of heavy element-rich (dark regions) and heavy element-deficient (light regions) form spontaneously with a period of approximately 30 nm as the growth progresses from the bottom to the top of the image.

The 200 dark-field imaging is a chemically sensitive technique in zinc blende alloys that provides local chemical information and has been employed to study composition modulation in InAs/AlAs and InAs/InAsSb superlattices,¹⁸ GaAsBi,⁶ and GaSbBi⁹ alloys. The contrast arises primarily from difference in atomic scattering factors between the group-III and group-V constituent elements and qualitatively reflects the content of different atomic constituents in the alloy.¹⁹ Dark-field TEM micrographs from samples C and D are shown in Fig. 6, where intensity line profiles across the areas marked show lateral quasiperiodic composition modulations with a period of approximately 30 nm. The contrast is chemically sensitive to the elemental content of the layer imaged in these micrographs. The bright areas likely correspond to Bi-rich regions, and the dark areas correspond to Bi-deficient regions similar to that observed in GaAsBi⁷ and InAsBi.¹¹These features are consistent with the broadening of the InAsSbBi peak in the XRD patterns shown in Figs. 3(c) and 3(d) and the low magnification transmission electron micrographs shown in Figs. 4(c) and 4(d).

The Bi mole fraction is estimated from the (200) dark-field images using a method proposed by Bithell and Stobbs.¹⁹ This method of composition analysis is applicable to the InAsSbBi samples as the atomic scattering factors of each element differ significantly, the material is not highly strained, and the specimen thickness is much less than the 1.7 μm extinction distance. The samples have a thickness of approximately 80 nm and a biaxial strain that is less than 0.15%. The diffraction pattern satisfies the Bragg condition and is absent of double diffraction. The samples imaged at an under focus condition where spherical aberrations are minimal and contrast reversals are not present.

In this method, according to kinematical approximation, the intensity of the dark-field reflection, $I200,InAsSbBi$⁠, is proportional to the square of the specimen thickness d and the square of the structure factor for the (200) reflection that satisfies the selection rule $h+k+l=4n+2$⁠. This relation is expressed in terms of the atomic scattering factors²⁰ and atomic mole fractions as

Thus, by considering the ratio of intensity scattered by InAsSbBi into the 200 reflection to that scattered by AlSb at same specimen thickness, the constant of proportionality and the specimen thickness are eliminated, and the ratio of the intensities is given as

Using this relationship, the Bi mole fraction is expressed in terms of the scattering factors, the Sb mole fraction, and the ratio of the intensities, with

The atomic scattering factors $fAl$⁠, $fIn$⁠, $fAs$⁠, $fSb$⁠, and $fBi$ for Al, In, As, Sb, and Bi used in the analysis are provided in Table III. These scattering factors are determined from Doyle and Turner²⁰ by linearly interpolating their tabulated values to the relevant scattering angle parameter $s=1/aInAsSbBi⊥$⁠, where $aInAsSbBi⊥$ is the out-of-plane lattice constant of the InAsSbBi layer.

The Sb mole fraction $y(x,aInAsSbBi)$ is a function of the Bi mole fraction x and the unstrained InAsSbBi lattice constant $aInAsSbBi$ provided by the XRD analysis. The lattice constant of the coherently strained InAsSbBi layer is distorted in the growth direction and matched to the substrate lattice in the growth plane and is given as²⁹ 

where $ε⊥$ is the tetragonal distortion of the unit cell, $aGaSb$ is the GaSb substrate lattice constant, and $νInAsSbBi$ is Poisson’s ratio that is estimated using a linear interpolation of the binary values $νInAs=0.3521$⁠,^25,$νInSb=0.3530$⁠,²⁵ and $νInBi=0.3503$⁠.¹⁵ For the InAsSbBi compositions examined, its value varies by less than 1 part in 1000 from 0.35213 to 0.35219 and is assumed to be constant with $νInAsSbBi=0.3522$⁠. This simplifies the relation in Eq. (4) as a given tetragonal distortion corresponds to a unique lattice constant, regardless of the mole fraction distribution. The out-of-plane lattice constant²⁹ is $aInAsSbBi⊥=[ε⊥+1]aGaSb$⁠, and the in-plane lattice constant is $aInAsSbBi∥=aGaSb$⁠.

Assuming Vegard’s law,²¹ the InAs_1−x−ySb_yBi_x lattice constant is given as a linear combination of the known binary lattice constants $aInAs=6.0583Å$⁠, $aInSb=6.4794Å$⁠, and $aInBi=6.611Å$ for InAs,²⁵ InSb,²⁵ and InBi.¹⁵ From Vegard’s law, the Sb mole fraction in terms of the InAsSbBi lattice constant and the Bi mole fraction is

This relationship provides a family of Sb and Bi mole fractions for a given InAsSbBi lattice constant with $dy/dx=(aInBi−aInAs)/(aInSb−aInAs)=1.3120$⁠. The in-plane biaxial strain is defined as $εxx=εyy=aGaSb/aInAsSbBi−1$ and is reported in Table I. The resulting out-of-plane uniaxial strain is $εzz=aInAsSbBi⊥/aInAsSbBi−1=−εxx2νInAsSbBi/(1−νInAsSbBi)$⁠, and the tetragonal distortion in terms of the in-plane and out-of-plane strains is $ε⊥=(εzz−εxx)/(1+εxx)$⁠.

The subsequent lateral profiles in the Bi mole fraction are shown in Fig. 7 for all samples. The values shown are averages over the approximately 80 nm thick specimen cross section. The lateral Bi mole fraction varies from 0.13% to 0.16% with an average of 0.14% in sample A, from 0.35% to 0.38% with an average of 0.36% in sample B, from 0.43% to 0.58% with an average of 0.52% in sample C, and from 0.73% to 0.83% with an average of 0.78% in sample D. In comparison, the RBS measurements specify an average Bi value of 0.1% for sample B and 0.4% for sample C that have little or no excess Bi on a smooth surface, and 2.6% for sample A and 1.1% for sample D that have excess Bi on a droplet covered surface. The Sb mole fractions specified by the dark field and XRD measurements are 10.80%, 9.61%, 9.13%, and 9.52%, for samples A through D, respectively.

High angle annular dark-field scanning transmission electron micrographs from samples C and D are shown in Figs. 8(a) and 8(b), respectively. These images, commonly referred to as Z-contrast images,²² provide mass thickness contrast that is primarily dependent on atomic number and are particularly well suited for detecting heavier elements such as Bi, and confirming the presence of lateral composition modulation. Energy dispersive X-ray (EDX) spectrum maps from samples C and D are shown in Fig. 8 to the right of the Z-contrast images. These images provide spatial maps of the elemental distribution of In, As, and Sb, where the signal for each corresponds to the L electron shell transition with energies at 3.29 keV, 1.29 keV, and 3.60 keV, respectively. These maps show that these elements are essentially homogeneous in the lateral direction. The decrease in signal observed from the lower to upper AlSb markers is due to a decrease in the sample thickness. The X-ray signal from the comparatively dilute Bi mole fractions is insufficient to map. The EDX analysis indicates that the observed lateral composition modulation is not due to variations in the In, As, or Sb mole fractions.

The Bi-rich columns originate during the early stages of bulk layer growth and become more pronounced as growth proceeds. The diffusivity of Bi plays a role in the formation of these Bi-rich columns; therefore, kinetic factors such as growth temperature influence the development of these features. The composition modulation period is approximately the same in the samples although the layer strain varies (see Table I), indicating that strain plays little to no role in the development of these nanocolumns.⁸ Similar Bi-rich nanostructures have been reported for GaAsBi bulk layers⁶ and quantum wells.²³ The phase separation and surface segregation of Bi likely occur because of a preferential attraction of Bi atoms toward Bi-rich areas.

Nomarski optical microscopy images of the surface of InAsSbBi samples A through D, labeled (a) through (d), are shown in Fig. 9. The images are 200 μm wide by 150 μm high and the significant growth conditions are shown for each. Figures 9(b) and 9(c) show that samples B and C are optically smooth. While sample A [Fig. 9(a)] exhibits droplet features with 1.5 μm diameters and 3 × 10⁶ cm⁻² densities, sample D [Fig. 9(d)] exhibits droplet features with 3 μm diameters and 0.5 × 10⁶ cm⁻² densities.

Atomic force microscopy images of the surface morphology of the InAsSbBi samples A through D, labeled (a) through (d), are shown in Fig. 10. The images are 100 μm by 100 μm on the left with a zoomed in 5 μm by 5 μm measurement on the right. The root mean square (RMS) roughness over the entire area imaged is shown for each and summarized in Table IV. The optically smooth samples B and C are remarkably flat on the 5 μm length scale with a RMS roughness less than 1 nm; however, these samples display long scale ∼100 μm waves in the surface morphology with roughness on the order of 10 nm. The droplet-covered samples A and D are rough on 100 μm length scale with droplets over 100 nm high and a RMS roughness around 40 nm. When zoomed in between the large droplet features of sample D, it is observed to be relatively smooth on the 5 μm length scale with a RMS roughness less than 1 nm. While a second set of much smaller and higher density droplets is observed between the large droplets on sample A. The droplets are isotropic, indicating the absence of a preferential direction in diffusion of the Bi atoms.

The droplet sizes and densities are summarized in Table V. Samples A and D both have large droplet features, and sample A has a second set of much higher density (2.3 × 10¹⁰ cm⁻²) of much smaller droplets between the large droplets. The small droplet diameters range from 30 to 100 nm with an average of 70 nm. An estimation of the fraction of the surface covered by the droplets and the average droplet volume per unit area are reported in Table V. The volume of each droplet set is roughly 5% of the InAsSbBi layer volume. Sample A grown with the largest Bi flux and at the highest temperature has the largest surface droplet coverage.

To aid the incorporation of Bi during the growth of InAsSbBi at these temperatures,⁴ small excess As overpressures are used. Since the samples contain about 90% As, about 1% of the 0.911 incident As/In flux is not incorporated and desorbs from the surface of the droplet covered surfaces, and about 4% of a larger 0.940 incident As/In flux is not incorporated and desorbs from the smooth surfaces. This indicates that the Bi-As interaction on the surface plays an important role in the incorporation and desorption of Bi adatoms from the total group-V surface reservoir. Under a larger As flux, the Bi-Bi interaction and the surface diffusion of Bi may be suppressed, while the Bi-As interaction leads to enhanced Bi desorption. For the rough, feature covered, samples A and D, some of the excess Bi remains on the surface and segregates, diffuses, and coalesces to form macroscopic droplets. Since this does not occur in the optically smooth samples B and C, the excess Bi desorbs from these surfaces along with the other excess group-V elements.

The small droplet imaged in Fig. 4(a) is further examined using high resolution transmission electron microscopy. The results are presented in Fig. 11, with a high-resolution micrograph in (a), a fast Fourier transform (FFT) of the high-resolution atomic image of the droplet in (b), and the InAs cap in (c), and the EDX spectrum in (d). The droplet is crystalline and 75 nm wide by 20 nm high, and the results indicate that the droplet has a misoriented zinc blende structure and is primarily composed of In, Sb, and Bi.

The lattice constant, a, of the droplet feature is determined by the separation, $rhkl$⁠, between the FFT pattern spot $(h,k,l)$ and the origin $(0,0,0)$ with

where $λ$ is the wavelength of electron, L is the distance between the sample and the screen, and the camera constant $λL$ is 121.2 Å, as determined using the indexed FFT from the InAs cap layer with known InAs lattice constant $aInAs=6.0583$⁠. Nevertheless, the droplet lattice constant can be expressed in terms of the known InAs lattice constant as

The separations in units of pixels are $r022,InAs=40.02±0.26$ and $r111,InAs=24.47±0.28$ from Fig. 11(c) and $r022,droplet$$=36.99±0.14$ and $r111,droplet=22.72±0.21$ from Fig. 11(b). From these values, the droplet lattice constant is found to be 6.553 ± 0.042 Å using the (022) spots and 6.525 ± 0.073 Å using the (111) spots for the analysis. The uncertainties provided for each value are reported as the standard deviation²⁴ in 10 separate measurements of separations in each diffraction spot set. Since each set of diffraction spots provides a slightly different value, the best estimate of the lattice constant is reported as a weighted mean and uncertainty of the two values, which is 6.543 ± 0.038 Å and lies between that of InSb and InBi. The weighting is inversely proportional to the standard deviation of each value, and the uncertainty is reported as the standard deviation of the weighted mean.

Reports on the synthetization of other III-V Bi containing materials also indicate the formation of similar crystalline features attributed to difficulties in Bi incorporation, including Bi-rich zinc blende Ga(As,Bi) clusters in GaAsBi after annealing,^26,27 InBi clusters with a distorted PbO structure in InAsBi,²⁸ and Bi-rich surface droplets with distorted zinc blende structures with a 80° tilt in InAsBi.¹¹ 

The chemical and structural properties of InAsSbBi layers grown by molecular beam epitaxy on GaSb at 400, 420, and 430 °C are examined. The layers are 210 nm thick, coherently-strained, with sharp interfaces, and contain dilute Bi mole fractions. Lateral modulation of the Bi mole fraction is observed in the InAsSbBi layers and is particularly pronounced in the two samples grown at the lowest 400 °C temperature where more Bi is incorporated. The two growths with As overpressures around 1% resulted in the formation of Bi-rich surface droplet features with diameters much larger than the InAsSbBi layer thickness and a volume per unit area of about 5% of the InAsSbBi layer. The two growths with As flux overpressures around 4% resulted in droplet-free surfaces, indicating that the presence of excess surface As plays a role in the desorption of excess Bi from the surface. The sample grown at the highest 430 °C temperature and the largest 0.10 Bi/In flux ratio also contains a much larger surface density of much smaller microscopic crystalline droplets with a misoriented zinc-blende crystal structure primarily composed of In, Sb, and Bi, and a lattice constant of 6.543 ± 0.038 Å that is between that of InSb and InBi.

The authors gratefully acknowledge financial support from Sandia National Laboratories and the National Science Foundation (NSF) (Award No. DMR-1410393) and the use of facilities in the Eyring Materials Center at Arizona State University.