Atomic-Scale Phase Transition of Epitaxial GaN on NanostructuredSi(001): Activation and BeyondS. C. Lee,*,† Y.-B. Jiang,‡ M. T. Durniak,§ T. Detchprohm,∥ C. Wetzel,§,∥ and S. R. J. Brueck†

†Department of Electrical and Computer Engineering and Center for High Technology Materials and ‡Department of Earth andPlanetary Sciences, University of New Mexico, Albuquerque, New Mexico 87106, United States§Department of Materials Science and Engineering and ∥Department of Physics, Applied Physics, and Astronomy, RensselaerPolytechnic Institute, Troy, New York 12180, United States

ABSTRACT: An atomic-scale phase transition in heterophase epitaxy (HPE) ofGaN on a 900 nm-wide v-grooved Si(001) substrate is reported. Two differentincorporation mechanisms of adatoms sequentially occur for the hexagonal (h-) tocubic (c-) phase transition: orientation- and phase-dependent incorporation (ODIand PDI). Epitaxy begins with ODI that results in preferential growth of h-GaNindividually aligned to opposing Si(111) facets inside a v-groove but incurs astructural instability by crystallographic mismatch at the groove bottom. Thisinstability is relieved by an abrupt transition to c-phase, initiating from single ormultiple atomic sites uniquely arranged atop the mismatch along the groove.Epitaxy proceeds with PDI that allows μm-scale c-GaN extended from these siteswhile suppressing growth of h-GaN. An important condition for HPE and thestability of c-GaN in further growth is derived from equilibrium crystal shape.

■ INTRODUCTION

III−N compound semiconductors are polytype with stablehexagonal (h-) and metastable cubic (c-) phases.1 Epitaxy ofIII−N materials on Si addresses fundamental issues insemiconductor heteroepitaxy including lattice and phasemismatches. While Si(001) has been a less popular substrateorientation than Si(111) particularly for III−N nanowireepitaxy,2 it dominates silicon microelectronics by unmatchedwafer sizes and crystalline perfection. The c-phase is energeti-cally unstable but has a major advantage over the h-phase forscaling of nonpolar-facet light emission with reduced efficiencydroop.3 Epitaxy of c-III-N on Si(001) is therefore a challengingissue with both scientific and technological implications.Traditional large-area planar epitaxy has not provided an

effective route to device quality c-GaN. Previously, we havereported phase-modulated growth of GaN on a (111)-facetedv-groove array fabricated into a Si(001) substrate,4,5 where nm-scale, defect-free c-phase is separated from h-phase through theh- to c-phase transition (h-c transition) activated at the regionspredefined by the topography of the substrate surface. A similarresult was reported by other research group.6 We refer to thisgrowth as heterophase epitaxy (HPE). Recently, we haveextended the lateral dimension of the c-phase up to ∼1 μm thatis acceptable for the fabrication of multiple nanoscale devices,and successfully demonstrated green light emitting diodes withc-InxGa1−xN/GaN quantum well (QW) structures from HPE.7,8

These results show the potential of HPE for c-III-N on Si(001),as in situ direct single-step epitaxy compatible with Si CMOS.In spite of this progress, however, the mechanism of HPE

that leads to a defect-less c-III-N over Si(001) is still unknown.HPE involves several complex processes resulting from the

crystallographic collision that is forced by the groove geometry.Figure 1 shows the structure of a GaN epilayer grown by HPE.While the groove in this figure is filled with dual phase GaN, itretains a clear phase separation with (111)-(0001) phaseboundary up to the top surface, implying that h-phase coversthe v-groove first and then c-phase fills the space inside the h-GaN. This means HPE is a sequential process driven by the h-ctransition that allows a different phase for groove filling. Weobserve that the nucleation of c-phase occurs exclusively atatomic sites on the line along a groove, passing point T in thecross section of Figure 1. Under the suppression of h-phasegrowth, the c-GaN grows up from these seed sites until thefilling is completed. To understand HPE, we concentrate onthis unusual filling process, a unique characteristic of HPE thatis directly related to the activation of the phase transition.In HPE, as discussed below, growth of each phase is assisted

by different adatom incorporation mechanisms: orientation-dependent incorporation (ODI) for nucleation on Si(111)preferentially with h-phase and phase-dependent incorporation(PDI) for fill-up inside the h-GaN exclusively with c-phase.Their results are illustrated in Figure 1. In contrast to ODI, PDIincludes an energetic penalty associated with the volumeincrease of the metastable c-phase. Eventually, PDI is a limitedprocess that is effective until the groove filling is completed.Different epitaxy conditions are required for subsequent c-phasegrowth after the groove filling.

Received: December 31, 2015Revised: February 20, 2016Published: March 24, 2016

Article

pubs.acs.org/crystal

© 2016 American Chemical Society 2183 DOI: 10.1021/acs.cgd.5b01845Cryst. Growth Des. 2016, 16, 2183−2189

In this work, we elucidate these complicated processesqualitatively and find that they are consistently explained withinequilibrium crystal shape (ECS) which governs both ODI andPDI with the minimization of total crystal energy.6 On the basisof ECS, we extract a condition for the compensation that drivesthe groove filling with PDI, from the reduction in the surfacefree energy of the h-GaN even while both the surface andvolume energies of the c-GaN are increased. HPE is radicallydifferent from other approaches for III−N on Si,10−12 and iscrucial to versatile applications of c-III-N on Si(001). We focuson the activation of the h-c transition and the underlyinggrowth mechanisms that trigger it. We also report the conditionfor the stability of the c-phase beyond the phase transition thatis important for larger scale epitaxy.

■ RESULTS AND DISCUSSIONIn Figure 1, a secondary v-groove bounded by the top (0001)surfaces of h-GaN is defined as groove g with junction d. Thestarting point of junction d is point F where the two h-GaNepilayers meet first. As epitaxy proceeds, junction d extendsupward and terminates at point T where the c-GaN is nucleatedand HPE begins. Here, points F and T (groove g and junctiond) on the cross sectional view correspond to a single row(plane) of atomic sites along a v-groove. The right column ofFigure 2 is a schematic flow of the evolution of HPE observedin this work. On both (111) facets inside a v-groove (Stage 1),epitaxy begins in the h-phase with ODI (Stage 2) that is relatedwith the strain relief of the h-GaN depending on Siorientation.4,8 Growth continues with generating point F but

ultimately achieves the lattice configuration required for the h-ctransition by producing groove g with point T at the bottom(Stage 3). The detailed conditions are discussed below. AtStage 4, the most critical h-c transition occurs exclusively at arow of points T, not on the whole plane defining groove g. Itsonset from an atomic site localized at point T is a fundamentalcharacteristic of HPE that can minimize the activation energy.Then, from these sites, c-GaN grows upward with a single(001) top facet identically aligned to that of the substrate, untilgroove g is completely filled (Stage 5). This is analogous to afluid fill of a trough and is basically different from the groove

Figure 1. A schematic illustration of a section of a v-grooved Si(00l)substrate with h- and c-GaN formed by the phase transition in HPE. Adisassembly of the rear part (a dotted outline part at the bottom)clearly reveals the c-GaN by PDI (top) and the h-GaN by ODI(middle) over the Si(00l) substrate. Dashed red and orange linescorrespond to junction d from the two colliding h-GaNs and groove grepresenting a (111)-(0001) phase interface at the cross section. Thefacet orientations in this and other figures are collective notations forsimplicity.

Figure 2. A schematic illustration of the major steps in the h-ctransition of HPE. The right column from Stages 1−6 shows theepitaxy that begins with a (111)-faceted, rounded bottom v-groovefabricated into a Si(001) substrate at the top. The Stage 6 is identicalto the bottom of Figure 1. The panels in the left column correspond tothe cases forbidden or not observed in the experiment.

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filling observed in the homophase epitaxy conformallyproceeding with finite incorporation on every facet.13 Duringthe groove filling (Stages 3−5), further growth on any facet ofthe h-GaN along the groove is suppressed. Particularly, nomore h-phase growth is allowed inside the groove. This is PDIdefined earlier that drives HPE with the h-c transition. Foridentical incoming flux on the Si(001) substrate, therefore h-and c-GaN are sequentially grown with ODI and PDI in a singlelayer, respectively. Stage 6 evolving to Figure 1 reveals thecrystal shape evolution after the groove filling, when there iscompeting growth on all exposed h-GaN and c-GaN facets.This work concentrates on Stages 3−6 to confirm the validity

of ECS on HPE from local atomic sites to microscale materialssuitable for device applications. Three different epilayers (N1,N2, and N3) were prepared by metal−organic vapor-phaseepitaxy (MOVPE) on a v-groove array fabricated into a Si(001)substrate with KOH-based anisotropic wet etching. The grooveperiods are 4.2 μm (N1) and 1.8 μm (N2, N3), while the widthof the v-groove top opening was kept to ∼900 nm for bothsamples. For this purpose, interferometric lithogrpahy wasemployed with Cr films prepared by electron-beam evaporationfor etch masks. This groove width is small enough to allowfacet-to-facet migration of adatoms encouraging ODI and PDI.Deposition amount was controlled to observe the c-GaN atStages 3−4 (N1) and Stages 5−6 (N2, N3) over the v-grooves.N1 was grown until the initial formation of groove g and theearly stages of the transition to c-GaN. For N2, the growth wascontinued so that c-GaN mostly filled groove g. Afterconfirming groove filling, further epitaxy with five InxGa1−xNlayers (x ≈ 0.2) as markers was performed for N3. Thesubstrates were treated by HF immediately before loading intothe reactor to remove native oxide. The epitaxy began with athin AlN buffer to promote the nucleation of GaN on the Sisurfaces. The deposition temperature was set to ∼1100−1150°C. Triethylgallium (TEG) and NH3 were used for group IIIand V sources in GaN growth. The details of v-groovefabrication and growth conditions were reported elsewhere.4−6

Figure 3 is a scanning electron microscopy (SEM) image ofsample N1 where the growth was terminated corresponding toStages 3−4 of Figure 2. In Figure 3a,d,e, h-GaN layers aremainly bounded by (0001), (0001 ) - parallel to Si(111), and,(11 01)-, and (11 01)-type edge facets with a tiny volume of c-GaN inhomogeneously formed at the bottom of groove g thatreveals an early stage of HPE. As a result of ODI, the apparentincorporation rate of adatoms, estimated from the thicknessdifference of the h-GaN on the various Si facets, is higher onSi(111) (∼210 ± 10 nm) than on Si(001) (∼105 ± 15 nm). Itshould be noted that this partial ODI was achieved in spite oflarge separation of grooves (>1 μm for N1) and the AlN buffer.As seen later, it does not affect the conclusion of this work.In Figure 3d,e, the epitaxy on the (11 01) and (11 01 ) facets

at the edge of the v-groove (blue arrows with blue dashedreference lines) shows a large thickness fluctuation ranging∼1× to 3× that on (0001) inside the v-groove (black arrowsfrom yellow dashed lines). However, the growth on the (0001 )facets (white arrows from the same reference) laterally evolvingover each Si(001) facet between v-grooves is not very differentfrom that on the (0001) facets inside the v-grooves. Evidently,the growth rates of h-GaN on (0001) and (0001 ) are similarand lower than those on (11 01).14−16In Figure 3, the growth of h-GaN inside the groove stops

with the initiation of the c-GaN formation by PDI, as confirmedlater. Qualitatively, each groove in Figure 3c can be categorized

into two regions depending on the amount of c-GaN at thegroove bottom: region A with significant amounts of c-GaN andregion B with much smaller amounts of c-GaN. A gap withoutany c-GaN indicated by an arrow is observed in the middle ofregion B. Figure 4a,b shows scanning tunneling electronmicroscopy (STEM) images corresponding to the highdeposition (A) and low deposition (B) regions, respectively.Figure 4a belonging to region A has a c-GaN cross section areawhich is ∼100× larger than that of Figure 4b matching region B

Figure 3. SEM images of N1 in (a) cross sectional and (b) top-downview. The insets in (b) reveal the formation of c-GaN near the bottomof groove g in individual v-grooves. (c) A magnification of the top-down view with c-GaN categorized into regions A and B by its amountat the bottom of groove g. (d, e) Cross sectional SEM imagescorresponding to regions A and B in (c) respectively. The yellow(blue) dashed lines in each figure are GaN/Si(111) interface stretchedbeyond h-GaN [initial locations of (11 01)-type facets conjecturedfrom the crystal shape of h-GaN]. The length of individual straightarrows indicates the distance of corresponding facets that are assumedto grow from yellow dashed lines [(0001): black, (0001 ): white], bluedashed lines [(11 01)-type: blue], and point T [(001): green]. Theinsets in (d) and (e) correspond to a birdʼs eye view of (d) and amagnification of a white box in (e). Note that (d) and (e) reveal therelation between the amount of c-GaN and the presence of voids nearthe bottom of a v-groove on the cross section. A white scale bar atlower left of each figure is 1 μm.

Figure 4. STEM images of N1 corresponding to regions (a) A and (b)B indicated in Figure 3c. The insets correspond to the magnification ofthe blue box with TEM in (a) and the red box with STEM mode in(b). Junction d in the inset of (a) follows the line revealing contrastchange and may have a little difference from the actual junction of h-GaN.

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in Figure 3c. Thus, some regions of the v-groove presentfavorable nuclei for the h-c transition, which does not proceedevenly along the bottom of groove g at the very early stage of c-GaN unlike Stage 4 of Figure 2, but rather fills in by lateralextension along each groove to result in a relatively uniformgrowth once the transition is activated at any points in regionA. All of the top c-GaN facets in Figures 3 and 4 are (001)independent of the A, B classification.Only a single void (A1) at the groove bottom is evident in

Figure 4a, while the h-GaN in Figure 4b includes at least fourvoids labeled B1 through B4 along the junction d. As Figures 3and 4 show, fewer and smaller voids along junction d arecorrelated with a larger growth of c-GaN, and the h-c transitionis directly affected by the void formation. In the inset of Figure4a, void A1 is highly symmetrical compared with void B1 ofFigure 4b which is more amorphous in shape. Also, the as-fabricated groove bottom is more rounded and thus isenergetically too unstable for adatoms to incorporate. VoidsA1 and B1 are due to the first contact of the two h-GaNepilayers on the opposing Si(111) faces over the roundedgroove bottom. They correspond to a channel passing throughthe bottom of each groove rather than to localized voids. Acertain degree of local shape fluctuation in the groove bottom isinevitable and can induce an off-center first contact that canresult in void B1. Another possible reason for the void shape(or channel cross section) fluctuation is the nucleation mode ofh-GaN on Si(111) that begins in a Stranski−Krastanov (S−K)mode.17 The resulting roughness indicated in Figure 4 is curedwith subsequent growth of GaN. Depending on the coverage orlocal coalescence status of h-GaN islands on each Si(111) facetnear its junction to the rounded bottom, piecewise first contactlikely happens along the groove. The epitaxy achieving firstcontact at the bottom can fill up the gap in Figure 3c withlateral growth that eventually extends all along the bottom ofgroove g. This is analogous to epitaxial lateral overgrowth butcould result in mosaicity (e.g., antiphase domains) of the c-GaN. Therefore, the S−K epitaxial mode on a nonuniform,variably rounded bottom of a v-groove is a major reason foruncertainty in the control of the h-c transition.Voids B2 through B4 in Figure 4b, which are enclosed by h-

GaN have a different physical origin from the initial voids A1and B1. The lattice structure of h-GaN near junction d is highlydeformed as the contact is forced by the groove geometry.Adatoms likely migrate away from the area to find lower energylattice sites for incorporation. Thus, the lateral dimension of thevoids ∼40 nm in Figure 4b can be regarded as the range of h-phase deformation by the engineered orientation mismatch.Several reports have discussed voids artificially generated inpatterned epitaxy at the μm-scale for stress reduction.18,19 It isevident that the nanovoids in Figure 4b provide stress reliefduring growth. From the comparison with Figure 3 and thesingle void A1 in Figure 4a, multiple voids along junction d inregion B could be inherently related to the structure of theinitial void B1 that is not highly symmetric in cross sectionalshape and as a result in stress distribution. This emphasizes thesignificance of the first contact for h-c transition. Conclusively,region B is not suitably aligned for the h-c transition.As seen in Figure 3b matching with Figure 3a, the h-c

transition is triggered simultaneously across the whole sample.This means that the deposition amount is also a criticalparameter. This requirement is related to the strain relief of theh-GaN over the Si(111). It has been reported that theestimated misfit between h- and c-GaN, f, is ∼0.002 at the phase

interface, small enough to avoid even electronic defect states atthe interface, and the h-GaN on Si(111) facets inside the v-grooves is close to total relaxation whereas both the c-GaN on itand the h-GaN on Si(001) facets between grooves are undertensile stress.5,8,20 Thus, strain relief of the h-GaN inside a v-groove can favorably reduce the instability of the phaseinterface. This is an important prerequisite for the h-c transitionand therefore provides a partial answer to ODI. The absence ofnanovoids above void A1 in Figure 4a means the latticedeformation around region A is limited to at most a few latticesites, favorable for the h-c transition. This could be partlyrelated to nearby regions B where local stress relief occurs. Thestrain relief of h-GaN inside the v-groove and the resultingsmall f are important conditions for the activation of the h-ctransition.Figure 5a is a schematic illustration of the atomistic

arrangement near the starting point of HPE. In this figure,

the details of the surface reconstruction are omitted, and onlyquadruple layers of h-GaN over the v-groove are considered.Here, a layer means a Ga−N single molecular unit in crosssection along (110). As discussed above, a Ga-terminated(gallided) surface is assumed at the top of the h-GaN in Figure5a.16 In Figure 5a, the two top layers of h-GaN that wereseparately grown from opposing Si(111) facets meet each otherat junction d. They are equivalent to a single h-GaN layersymmetrically deflected by 54.7° with respect to the molecularunit at the center. It is known that both h- and c-GaN havesimilar bonding length and angle, very close to the angle∼109.4° made by deflection in Figure 5a.1 Particularly, themolecular unit in the lower semicircle and its nearest neighborsin the circle of Figure 5a form a bonding structure very close toc-GaN by this deflection, while they still individually belong totheir respective h-phase regions. Moreover, the density of thedangling bonds becomes higher at the bottom of groove g.Then, the incorporation of another molecular unit at the uppersemicircle can lower the surface free energy most effectively andas a result terminate the lattice disorder originated from point F(dashed rectangle in Figure 5a). This incorporation is thestarting point of c-GaN and the circle becomes point T. HPEfrom the h-c transition therefore begins at a single atomic sitewith the lowest activation energy. This is highly probable at

Figure 5. (a) A cross sectional, atomistic illustration with a large(small) sphere for a Ga (N) atoms in [110]. A circle in the middlecorrespond to point T in Figure 1. The atoms inside the dashed linebelow the circle means entangled arrangement of the atoms nearjunction d. (b) A high resolution cross sectional TEM of region Afrom N1 around point T of Figure 4a. Every line corresponds to aGaN monolayer. Inset: A magnification revealing the starting site of h-ctransition pointed at by an arrow. This or its nearest neighbor sitescould correspond to the atoms in the circle of (a) or point T in Figures1 and 2.

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region A of Figure 3c. Ideally, the molecular unit at point Twould form a seed row by homogeneous occupation along thegroove, as illustrated in Figure 2. Experimentally, HPE locallyproceeds from a multiplicity of available atomic sites in regionA. At all other sites on groove g, the resulting c-GaN is simply achange of the stacking order across the (0001)-(111) interfaceof GaN by the extremely small f. Figure 5b from N1 and itsinset reveal junction d and point T in the cross sectioncorresponding to region A in Figure 4a.Figure 6 shows an annotated cross sectional STEM image of

sample N3 corresponding to Stage 5−6 in Figure 2 that is

directly related to the stability of the h-c transition beyondgroove filling. First of all, PDI is confirmed by the comparablephysical dimensions of the h-GaN of N1 in Figure 3d,e and N3in Figure 6. The growth of h-GaN was suppressed during thedeposition of the c-GaN. In Figure 6, the slight contrastdifference along the orange lines corresponds to the h-c phaseinterface. Near the top surface, the five white lines are ∼3 nm-thick InxGa1−xN QW layers that serve as markers in STEM,revealing the evolution of the front surface faceting duringcontinued growth after the groove filling confirmed with N2(the region below the first InxGa1−xN layer).8 In Figure 6,groove g is roughly the orange line in the cross section belowfirst InxGa1−xN layer. The top growth surface consists of threemajor regions: nonpolar (001) of c-GaN in the middle and{11 01} [or simply (11 01) as denoted in Figure 6] and (0001 )of h-GaN at both edges.The inset in Figure 6 is a magnification of the region inside

the white bold solid box revealing the details of the crystalshape evolution. Additional (11 00)-type facets (green arrows)from h-GaN exist at both edges for the first three QW growths.This facet is annihilated as the growth proceeds to the last twoQW layers. In the growth from N2 to N3, therefore the fourorientations compete with very different growth rates resultingin layer-to-layer thickness variation and leading to a dynamicevolution of the crystal shape. From the first GaN spacer

(above the first InxGa1−xN QW layer) to the cap layer, thenominal deposition thickness is 100 nm. The actual depositionthicknesses on each facet are

= ∼ ∼ ∼

∼ t t t t: : : 23nm: 83nm: 107nm

: 230nm000 1 1 1 01 001 1 1 00

(1)

where tX refers to the deposition thickness atop the facet X.21

Then, the growth rates relative to (0001 ) are approximatelygiven as r11 01: r001: r11 00 = ∼3.6: ∼4.7: ∼10, with rX representingthe relative growth rate of facet X normalized to that of (0001 ).Equation 1 and rX’s are consistent with Figure 3, both (0001)and (0001 ) facets have a similar growth rate between ∼1/3 to 1of that on (11 01).16 Also, as reported previously, r11 01 ∼ r001suggests that the crystal shape can be retained with the currenttop surface after the groove filling.4,8 In ECS, the decreasingorder of growth rate is roughly proportional to the energeticstability of the given facets. Then, eq 1 can be rewritten withinequalities as

σ σ σ σ< ≲ < 000 1 1 1 01 001 1 1 00 (2)

where σX means the surface free energy per unit area oforientation X. Volumetrically, c-GaN has a higher energy thanh-GaN by ∼10 meV/atom.1,22 Specifically, the condition ofσ0001 ≈ σ0001 < σ001 in eq 2 and r0001 ≈ r0001 in Figure 3,obtained from nanoscale facet competition under identicalgrowth condition in a single epilayer is important evidencesupporting the metastability of c-GaN suggested by theoreticalcalculations.1

The h-c transition suppresses further instability in h-phasebeyond point T. However, the c-phase material accumulatesextra volume energy. Immediately after the onset of the h-cphase transition, there are several possible growth scenarios forthe epitaxy from Stage 3 as illustrated in Figure 2: alternativeStages F4−1; F4−2; and F4−3; as well as the experimentallyobserved Stage 4. In Stage F4−1, the growth of c-GaN becomesnegligible and the initial h-GaN grows again along the v-groove;For Stage F4−2, the c-GaN extends conformally across grooveg, and for Stage F4−3, the c-GaN evolves with <111> facets.Each of these alternatives requires an additional energy for theactivation but Stage 4, observed experimentally, is definitely thelowest energy path for the epitaxy under the experimentalgrowth conditions. Taking δE as the difference of the totalcrystal energy of a GaN epilayer in Stage 4 for time interval δt,it can be written as

δ δ δ≅ +E E Ev s (3)

where δEv and δEs are the change of the total volumetric energyby the h-c transition in the additional growth for δt and thechange of the total surface free energy determined by the areaand free energy of the individual facets associated with thevolume change for δt, respectively. Here, the change of strainenergy by the tensile stress of c-GaN is included in δEv, and theenergy at the h-c interface is taken to be negligible as a result ofthe small f.20,23,25 No facet changes are observed during thegroove filling by PDI and therefore neither additional change intotal energy due to the creation/annihilation of any facets northe kinks associated with their junctions/intersections need tobe considered in eq 3. Stages F4-1 to F4-3 were not observedand as a result do not correspond to the lowest total energyalternatives. HPE proceeds to Stage 4 which corresponds to theminimization of the total energy associated with continuedgrowth.

Figure 6. A cross sectional STEM image of the as-grown N3. The fivewhite lines near the top surface correspond to InxGa1−xN layers usedfor markers. Thus, N2 corresponds to the region below the firstInxGa1−xN layers. An orange dashed line, equivalent to the same colorline Figure 1 (groove g), follows the phase boundary and c-phase isabove this boundary. Note the color code of the arrows foridentification of material/facet orientation. Inset: Magnification ofthe area defined by the white bold solid square at upper left corner.Note InxGa1−xN markers on (0001 ) in the inset that reveals extremelyslow but nonzero growth rate of this orientation.

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Both the GaN volume and surface area depend on growthtime, t, starting from the onset of the h-c transition. Inhomophase epitaxy δEv ≅ 0. In the HPE of this work, it ispositive. To keep δE < 0 despite δEv > 0, δEs has to benegative.25 This necessary condition is possible since the groovefilling reduces the total surface area by the extension of a single(001) facet of c-GaN at the expense of two (0001) facets of h-GaN inside the groove g. The geometry inside a v-groovebefore complete groove filling is illustrated in Figure 7. At time

t, the height of c-GaN from point T, is given as H. From Figure3, the growth on all facets of h-GaN comes to a halt untilgroove g is filled by c-GaN. Then, the surface area of the (100)facet of c-GaN at the top per unit length along a groove, Ac, is2H/tan θ with θ = 54.7° indicated in Figure 7. If the change ofH for δt is δH, the corresponding change in Ac, δAc, is increasedwith growth and can be written as 2δH/tan θ. But theconsumption of the surface area of the (0001) facets of h-GaNopposing to each other inside the groove means that the h-GaNsurface area, Ah, is reduced by −2δH/sin θ, as denoted inFigure 7. If δEs is the change of surface energy from thesevariations for δt, it can be written as

δ σ δ σ δ

σ δ θ σ δ θ

= +

= −

E A A

H H2 /tan 2 /sins c h001 0001

001 0001 (4)

where σ001 and σ0001 are the unit area surface free energies of(001) of c-GaN and (0001) of h-GaN respectively, as definedearlier. To avoid δEs ≥ 0, σ001 must be less than σ0001/cos(54.7°) in eq 4. This does not contradict eq 2 and allows awindow for σ001. From Figure 3, r0001 is comparable to r0001,meaning σ0001 < σ001 at the given growth condition in eq 2.16

Then,

σ σ σ< < 1.730001 001 0001 (5)

for δEs < 0 corresponding to Stage 4 in Figure 2. The rightinequality of eq 5 is derived from eq 4 by the condition of δEs <0. It should be noted that the change of total crystal energy, δE,

given in eq 3 includes the change due to the volume energy,δEv, for the same deposition but does not count it so far in thecondition for δE < 0. This is because we do not have sufficientanalysis of its contributions; δEv is based on theoreticalcalculations that need to be confirmed in experiments andincludes the change of strain energy due to the tensile stress inc-GaN which requires rigorous theoretical and experimentalapproaches.If σ001 < σ0001 were the case, the h-c transition would still be

available with δEs < 0 but could induce a typical conformalfilling or another type of groove fill-up depending on themagnitude of σ111, as illustrated at Stages F4-2 or F4-3 in Figure2. But, these are not observed under the present growthconditions.26 Equation 4 therefore provides a window of σ001for unidirectional HPE from the bottom of groove g with (001)at the top. For δE < 0, or the lowest δE, the window in eq 4should be narrower, implying further requirements on σ001relative to σ0001.In Figure 6, the top surface of the c-phase is already flat and

parallel to the Si substrate, and wide enough for multipledevices, a very important result for the integration of III−Nwith Si microelectronics. However, the c-GaN is in tensilestress.5,8 Moreover, δE definitely changes to positive aftergroove filling since the reduction in surface area is no longeravailable. As seen in Figure 6, continual HPE is not driven byPDI anymore but is still governed by ECS as long as there issufficient adatom surface mobility. Then, further extension of c-phase becomes energetically uncertain. From Stage 5 to 6 inFigure 2, one of the (11 01) and (11 01) facets annihilates withthe extension of the other, as confirmed from the inset ofFigure 6. Since they are physically identical, this processeffectively results in the extension of (0001 ) that has the lowestsurface free energy in eq 2. In this process, (11 00) facets inFigure 6 are temporarily formed to accelerate the extension of(0001 ). This allows the kink to move toward the edge andeventually disappear. The alternative case illustrated at Stage F6in Figure 2 was not observed. This is because it accompaniesthe expansion of c-GaN that must result in positive δEv with theδEs less sufficient than Stage 6 (or Figure 6) in compensationby eq 2, and violates ECS. This provides an important insight topredict HPE beyond groove filling. In order to maximize thelateral dimension of c-GaN, the growth conditions must becontrolled so that σ001 remains comparable to σ11 01, for exampleby varying the N/III flux ratio and growth temperature.27−29

Finally, the groove dimensions should be less than orcomparable to the adatom migration length to allow the h-ctransition. In Figure 3, groove g was prepared for the transitionwith two well-defined and unstrained (0001) facets. This ispossible because their lateral scale is comparable to or less thanthe adatom migration length. Otherwise, the adatoms thatarrive around junction d would not be able to migrate out to anadjacent (11 01) facet even though they might successfullyescape from this unstable region. Then, they would nucleatesomewhere above the bottom of the v-groove. This couldroughen the (0001) facets by uneven incorporation andinterfere the h-c transition by retriggering the growth of h-phase inside the groove. The largest lateral dimension of c-GaNfrom h-c transition is therefore correlated to an adatommigration length under the given growth conditions (typicallyμm-scale in MOVPE as confirmed in this work) that limits theavailable groove width with the energetic conditions discussedabove.

Figure 7. A schematic cross section corresponding to Stage 4 in Figure2. It shows the variation of surface areas of individual facets inside a v-groove by epitaxy for t to t+ δt. The dashed chevrons on both ends ofh-GaN correspond to its areal extension identical to the areal increaseof c-GaN in cross section for δt under the assumption of zero growrate of (0001)-type facets in- and outside groove for the case ofincomplete groove filling, as illustrated in Stage F4−1 in Figure 2. Ayellow dashed line is equivalent to those in Figure 2d,e.

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■ CONCLUSIONHPE of a microscale engineered material arising from the h-ctransition induced in a v-grooved Si(001) substrate has beendemonstrated and analyzed with ECS. While c-III-N isinherently metastable and difficult to grow, this workdefinitively shows the feasibility of growing large areas. LocalHPE would possibly allow integration of GaN devices with Sielectronics, if compatible processing sequences could bedeveloped. The mechanisms that lead to the formation of amacroscopic volume of c-III-N include (1) ODI of h-GaN onthe starting Si(111) faces of a v-groove; (2) Strain relief of h-GaN for lattice match to Si; (3) an atomically induced phasetransition to c-GaN; followed by (4) the growth of the c-GaNwith PDI until groove filling; (5) further evolution of the dualphase material once the groove has filled. For minimalmosaicity of the c-phase, it would be advantageous to startwith an incompletely formed, flat-bottom groove, for the stressrelief, providing an artificial homogeneous channel replacingvoid A.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: slee@unm.edu. Phone: 1-5052727800. Fax: 1-505-272-7801.FundingThis work was supported primarily by the EngineeringResearch Centers Program (ERC) of the National ScienceFoundation under NSF Cooperative Agreement No. EEC-0812056 and in part by New York State under NYSTARContract No. C090145.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe fabrication of the groove pattern used for sample N1 wasassisted by A. Chaudhuri.

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