Atomic-Scale Phase Transition of Epitaxial GaN on Nanostructured Si

Mar 24, 2016 - for the stability of the c-phase beyond the phase transition that is important for larger ..... nanovoids above void A1 in Figure 4a me...
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Atomic-Scale Phase Transition of Epitaxial GaN on Nanostructured Si(001): Activation and Beyond S. 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 and Planetary 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, Rensselaer Polytechnic Institute, Troy, New York 12180, United States ABSTRACT: An atomic-scale phase transition in heterophase epitaxy (HPE) of GaN on a 900 nm-wide v-grooved Si(001) substrate is reported. Two different incorporation mechanisms of adatoms sequentially occur for the hexagonal (h-) to cubic (c-) phase transition: orientation- and phase-dependent incorporation (ODI and PDI). Epitaxy begins with ODI that results in preferential growth of h-GaN individually aligned to opposing Si(111) facets inside a v-groove but incurs a structural instability by crystallographic mismatch at the groove bottom. This instability is relieved by an abrupt transition to c-phase, initiating from single or multiple atomic sites uniquely arranged atop the mismatch along the groove. Epitaxy proceeds with PDI that allows μm-scale c-GaN extended from these sites while suppressing growth of h-GaN. An important condition for HPE and the stability of c-GaN in further growth is derived from equilibrium crystal shape.

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INTRODUCTION III−N compound semiconductors are polytype with stable hexagonal (h-) and metastable cubic (c-) phases.1 Epitaxy of III−N materials on Si addresses fundamental issues in semiconductor heteroepitaxy including lattice and phase mismatches. While Si(001) has been a less popular substrate orientation than Si(111) particularly for III−N nanowire epitaxy,2 it dominates silicon microelectronics by unmatched wafer sizes and crystalline perfection. The c-phase is energetically unstable but has a major advantage over the h-phase for scaling of nonpolar-facet light emission with reduced efficiency droop.3 Epitaxy of c-III-N on Si(001) is therefore a challenging issue with both scientific and technological implications. Traditional large-area planar epitaxy has not provided an effective route to device quality c-GaN. Previously, we have reported phase-modulated growth of GaN on a (111)-faceted v-groove array fabricated into a Si(001) substrate,4,5 where nmscale, defect-free c-phase is separated from h-phase through the h- to c-phase transition (h-c transition) activated at the regions predefined by the topography of the substrate surface. A similar result was reported by other research group.6 We refer to this growth as heterophase epitaxy (HPE). Recently, we have extended the lateral dimension of the c-phase up to ∼1 μm that is acceptable for the fabrication of multiple nanoscale devices, and successfully demonstrated green light emitting diodes with c-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 © XXXX American Chemical Society

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, it retains a clear phase separation with (111)-(0001) phase boundary up to the top surface, implying that h-phase covers the v-groove first and then c-phase fills the space inside the hGaN. This means HPE is a sequential process driven by the h-c transition that allows a different phase for groove filling. We observe that the nucleation of c-phase occurs exclusively at atomic sites on the line along a groove, passing point T in the cross section of Figure 1. Under the suppression of h-phase growth, the c-GaN grows up from these seed sites until the filling is completed. To understand HPE, we concentrate on this unusual filling process, a unique characteristic of HPE that is 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: orientationdependent 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, PDI includes an energetic penalty associated with the volume increase of the metastable c-phase. Eventually, PDI is a limited process that is effective until the groove filling is completed. Different epitaxy conditions are required for subsequent c-phase growth after the groove filling. Received: December 31, 2015 Revised: February 20, 2016

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DOI: 10.1021/acs.cgd.5b01845 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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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. A disassembly 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 lines correspond to junction d from the two colliding h-GaNs and groove g representing a (111)-(0001) phase interface at the cross section. The facet orientations in this and other figures are collective notations for simplicity.

In this work, we elucidate these complicated processes qualitatively and find that they are consistently explained within equilibrium crystal shape (ECS) which governs both ODI and PDI with the minimization of total crystal energy.6 On the basis of ECS, we extract a condition for the compensation that drives the groove filling with PDI, from the reduction in the surface free energy of the h-GaN even while both the surface and volume energies of the c-GaN are increased. HPE is radically different from other approaches for III−N on Si,10−12 and is crucial to versatile applications of c-III-N on Si(001). We focus on the activation of the h-c transition and the underlying growth mechanisms that trigger it. We also report the condition for the stability of the c-phase beyond the phase transition that is important for larger scale epitaxy.

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

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RESULTS AND DISCUSSION In Figure 1, a secondary v-groove bounded by the top (0001) surfaces of h-GaN is defined as groove g with junction d. The starting point of junction d is point F where the two h-GaN epilayers meet first. As epitaxy proceeds, junction d extends upward and terminates at point T where the c-GaN is nucleated and HPE begins. Here, points F and T (groove g and junction d) on the cross sectional view correspond to a single row (plane) of atomic sites along a v-groove. The right column of Figure 2 is a schematic flow of the evolution of HPE observed in this work. On both (111) facets inside a v-groove (Stage 1), epitaxy begins in the h-phase with ODI (Stage 2) that is related with the strain relief of the h-GaN depending on Si orientation.4,8 Growth continues with generating point F but

ultimately achieves the lattice configuration required for the h-c transition by producing groove g with point T at the bottom (Stage 3). The detailed conditions are discussed below. At Stage 4, the most critical h-c transition occurs exclusively at a row of points T, not on the whole plane defining groove g. Its onset from an atomic site localized at point T is a fundamental characteristic 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, until groove g is completely filled (Stage 5). This is analogous to a fluid fill of a trough and is basically different from the groove B

DOI: 10.1021/acs.cgd.5b01845 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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filling observed in the homophase epitaxy conformally proceeding with finite incorporation on every facet.13 During the groove filling (Stages 3−5), further growth on any facet of the h-GaN along the groove is suppressed. Particularly, no more h-phase growth is allowed inside the groove. This is PDI defined earlier that drives HPE with the h-c transition. For identical incoming flux on the Si(001) substrate, therefore hand c-GaN are sequentially grown with ODI and PDI in a single layer, respectively. Stage 6 evolving to Figure 1 reveals the crystal shape evolution after the groove filling, when there is competing 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 materials suitable for device applications. Three different epilayers (N1, N2, and N3) were prepared by metal−organic vapor-phase epitaxy (MOVPE) on a v-groove array fabricated into a Si(001) substrate with KOH-based anisotropic wet etching. The groove periods are 4.2 μm (N1) and 1.8 μm (N2, N3), while the width of the v-groove top opening was kept to ∼900 nm for both samples. For this purpose, interferometric lithogrpahy was employed with Cr films prepared by electron-beam evaporation for etch masks. This groove width is small enough to allow facet-to-facet migration of adatoms encouraging ODI and PDI. Deposition amount was controlled to observe the c-GaN at Stages 3−4 (N1) and Stages 5−6 (N2, N3) over the v-grooves. N1 was grown until the initial formation of groove g and the early stages of the transition to c-GaN. For N2, the growth was continued so that c-GaN mostly filled groove g. After confirming groove filling, further epitaxy with five InxGa1−xN layers (x ≈ 0.2) as markers was performed for N3. The substrates were treated by HF immediately before loading into the reactor to remove native oxide. The epitaxy began with a thin AlN buffer to promote the nucleation of GaN on the Si surfaces. The deposition temperature was set to ∼1100−1150 °C. Triethylgallium (TEG) and NH3 were used for group III and V sources in GaN growth. The details of v-groove fabrication and growth conditions were reported elsewhere.4−6 Figure 3 is a scanning electron microscopy (SEM) image of sample N1 where the growth was terminated corresponding to Stages 3−4 of Figure 2. In Figure 3a,d,e, h-GaN layers are mainly bounded by (0001), (0001̅) - parallel to Si(111), and, (11̅01)-, and (11̅01̅)-type edge facets with a tiny volume of cGaN inhomogeneously formed at the bottom of groove g that reveals an early stage of HPE. As a result of ODI, the apparent incorporation rate of adatoms, estimated from the thickness difference of the h-GaN on the various Si facets, is higher on Si(111) (∼210 ± 10 nm) than on Si(001) (∼105 ± 15 nm). It should be noted that this partial ODI was achieved in spite of large 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 (11̅01) and (11̅01̅) facets at the edge of the v-groove (blue arrows with blue dashed reference lines) shows a large thickness fluctuation ranging ∼1× to 3× that on (0001) inside the v-groove (black arrows from yellow dashed lines). However, the growth on the (0001̅) facets (white arrows from the same reference) laterally evolving over each Si(001) facet between v-grooves is not very different from that on the (0001) facets inside the v-grooves. Evidently, the growth rates of h-GaN on (0001) and (0001̅) are similar and lower than those on (110̅ 1).14−16 In Figure 3, the growth of h-GaN inside the groove stops with the initiation of the c-GaN formation by PDI, as confirmed later. Qualitatively, each groove in Figure 3c can be categorized

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

into two regions depending on the amount of c-GaN at the groove bottom: region A with significant amounts of c-GaN and region B with much smaller amounts of c-GaN. A gap without any c-GaN indicated by an arrow is observed in the middle of region B. Figure 4a,b shows scanning tunneling electron microscopy (STEM) images corresponding to the high deposition (A) and low deposition (B) regions, respectively. Figure 4a belonging to region A has a c-GaN cross section area which is ∼100× larger than that of Figure 4b matching region B

Figure 4. STEM images of N1 corresponding to regions (a) A and (b) B indicated in Figure 3c. The insets correspond to the magnification of the 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 contrast change and may have a little difference from the actual junction of hGaN. C

DOI: 10.1021/acs.cgd.5b01845 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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interface, small enough to avoid even electronic defect states at the interface, and the h-GaN on Si(111) facets inside the vgrooves is close to total relaxation whereas both the c-GaN on it and the h-GaN on Si(001) facets between grooves are under tensile stress.5,8,20 Thus, strain relief of the h-GaN inside a vgroove can favorably reduce the instability of the phase interface. This is an important prerequisite for the h-c transition and therefore provides a partial answer to ODI. The absence of nanovoids above void A1 in Figure 4a means the lattice deformation around region A is limited to at most a few lattice sites, favorable for the h-c transition. This could be partly related to nearby regions B where local stress relief occurs. The strain relief of h-GaN inside the v-groove and the resulting small f are important conditions for the activation of the h-c transition. Figure 5a is a schematic illustration of the atomistic arrangement near the starting point of HPE. In this figure,

in Figure 3c. Thus, some regions of the v-groove present favorable nuclei for the h-c transition, which does not proceed evenly along the bottom of groove g at the very early stage of cGaN unlike Stage 4 of Figure 2, but rather fills in by lateral extension along each groove to result in a relatively uniform growth once the transition is activated at any points in region A. 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 four voids labeled B1 through B4 along the junction d. As Figures 3 and 4 show, fewer and smaller voids along junction d are correlated with a larger growth of c-GaN, and the h-c transition is directly affected by the void formation. In the inset of Figure 4a, void A1 is highly symmetrical compared with void B1 of Figure 4b which is more amorphous in shape. Also, the asfabricated groove bottom is more rounded and thus is energetically too unstable for adatoms to incorporate. Voids A1 and B1 are due to the first contact of the two h-GaN epilayers on the opposing Si(111) faces over the rounded groove bottom. They correspond to a channel passing through the bottom of each groove rather than to localized voids. A certain degree of local shape fluctuation in the groove bottom is inevitable and can induce an off-center first contact that can result in void B1. Another possible reason for the void shape (or channel cross section) fluctuation is the nucleation mode of h-GaN on Si(111) that begins in a Stranski−Krastanov (S−K) mode.17 The resulting roughness indicated in Figure 4 is cured with subsequent growth of GaN. Depending on the coverage or local coalescence status of h-GaN islands on each Si(111) facet near its junction to the rounded bottom, piecewise first contact likely happens along the groove. The epitaxy achieving first contact at the bottom can fill up the gap in Figure 3c with lateral growth that eventually extends all along the bottom of groove g. This is analogous to epitaxial lateral overgrowth but could result in mosaicity (e.g., antiphase domains) of the cGaN. Therefore, the S−K epitaxial mode on a nonuniform, variably rounded bottom of a v-groove is a major reason for uncertainty in the control of the h-c transition. Voids B2 through B4 in Figure 4b, which are enclosed by hGaN have a different physical origin from the initial voids A1 and B1. The lattice structure of h-GaN near junction d is highly deformed as the contact is forced by the groove geometry. Adatoms likely migrate away from the area to find lower energy lattice sites for incorporation. Thus, the lateral dimension of the voids ∼40 nm in Figure 4b can be regarded as the range of hphase deformation by the engineered orientation mismatch. Several reports have discussed voids artificially generated in patterned epitaxy at the μm-scale for stress reduction.18,19 It is evident that the nanovoids in Figure 4b provide stress relief during growth. From the comparison with Figure 3 and the single void A1 in Figure 4a, multiple voids along junction d in region B could be inherently related to the structure of the initial void B1 that is not highly symmetric in cross sectional shape and as a result in stress distribution. This emphasizes the significance 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 critical parameter. This requirement is related to the strain relief of the h-GaN over the Si(111). It has been reported that the estimated misfit between h- and c-GaN, f, is ∼0.002 at the phase

Figure 5. (a) A cross sectional, atomistic illustration with a large (small) sphere for a Ga (N) atoms in [110]. A circle in the middle correspond to point T in Figure 1. The atoms inside the dashed line below the circle means entangled arrangement of the atoms near junction d. (b) A high resolution cross sectional TEM of region A from N1 around point T of Figure 4a. Every line corresponds to a GaN monolayer. Inset: A magnification revealing the starting site of h-c transition pointed at by an arrow. This or its nearest neighbor sites could correspond to the atoms in the circle of (a) or point T in Figures 1 and 2.

the details of the surface reconstruction are omitted, and only quadruple layers of h-GaN over the v-groove are considered. Here, a layer means a Ga−N single molecular unit in cross section along (110). As discussed above, a Ga-terminated (gallided) surface is assumed at the top of the h-GaN in Figure 5a.16 In Figure 5a, the two top layers of h-GaN that were separately grown from opposing Si(111) facets meet each other at junction d. They are equivalent to a single h-GaN layer symmetrically deflected by 54.7° with respect to the molecular unit at the center. It is known that both h- and c-GaN have similar bonding length and angle, very close to the angle ∼109.4° made by deflection in Figure 5a.1 Particularly, the molecular unit in the lower semicircle and its nearest neighbors in the circle of Figure 5a form a bonding structure very close to c-GaN by this deflection, while they still individually belong to their respective h-phase regions. Moreover, the density of the dangling bonds becomes higher at the bottom of groove g. Then, the incorporation of another molecular unit at the upper semicircle can lower the surface free energy most effectively and as a result terminate the lattice disorder originated from point F (dashed rectangle in Figure 5a). This incorporation is the starting point of c-GaN and the circle becomes point T. HPE from the h-c transition therefore begins at a single atomic site with the lowest activation energy. This is highly probable at D

DOI: 10.1021/acs.cgd.5b01845 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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

region A of Figure 3c. Ideally, the molecular unit at point T would form a seed row by homogeneous occupation along the groove, as illustrated in Figure 2. Experimentally, HPE locally proceeds from a multiplicity of available atomic sites in region A. At all other sites on groove g, the resulting c-GaN is simply a change of the stacking order across the (0001)-(111) interface of GaN by the extremely small f. Figure 5b from N1 and its inset reveal junction d and point T in the cross section corresponding 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

t000 1̅ : t1 1̅ 01: t001: t1 1̅ 00 = ∼23nm: ∼83nm: ∼107nm : ∼230nm

(1)

where tX refers to the deposition thickness atop the facet X.21 Then, the growth rates relative to (0001̅) are approximately given as r11̅01: r001: r11̅00 = ∼3.6: ∼4.7: ∼10, with rX representing the relative growth rate of facet X normalized to that of (0001̅). Equation 1 and rX’s are consistent with Figure 3, both (0001) and (0001̅) facets have a similar growth rate between ∼1/3 to 1 of that on (11̅01).16 Also, as reported previously, r11̅01 ∼ r001 suggests that the crystal shape can be retained with the current top surface after the groove filling.4,8 In ECS, the decreasing order of growth rate is roughly proportional to the energetic stability of the given facets. Then, eq 1 can be rewritten with inequalities as σ000 1̅ < σ1 1̅ 01 ≲ σ001 < σ1 1̅ 00

(2)

where σX means the surface free energy per unit area of orientation X. Volumetrically, c-GaN has a higher energy than h-GaN by ∼10 meV/atom.1,22 Specifically, the condition of σ0001 ≈ σ0001̅ < σ001 in eq 2 and r0001 ≈ r0001̅ in Figure 3, obtained from nanoscale facet competition under identical growth condition in a single epilayer is important evidence supporting the metastability of c-GaN suggested by theoretical calculations.1 The h-c transition suppresses further instability in h-phase beyond point T. However, the c-phase material accumulates extra volume energy. Immediately after the onset of the h-c phase transition, there are several possible growth scenarios for the epitaxy from Stage 3 as illustrated in Figure 2: alternative Stages F4−1; F4−2; and F4−3; as well as the experimentally observed Stage 4. In Stage F4−1, the growth of c-GaN becomes negligible and the initial h-GaN grows again along the v-groove; For Stage F4−2, the c-GaN extends conformally across groove g, and for Stage F4−3, the c-GaN evolves with facets. Each of these alternatives requires an additional energy for the activation but Stage 4, observed experimentally, is definitely the lowest energy path for the epitaxy under the experimental growth conditions. Taking δE as the difference of the total crystal energy of a GaN epilayer in Stage 4 for time interval δt, it can be written as

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

directly related to the stability of the h-c transition beyond groove filling. First of all, PDI is confirmed by the comparable physical dimensions of the h-GaN of N1 in Figure 3d,e and N3 in Figure 6. The growth of h-GaN was suppressed during the deposition of the c-GaN. In Figure 6, the slight contrast difference along the orange lines corresponds to the h-c phase interface. Near the top surface, the five white lines are ∼3 nmthick InxGa1−xN QW layers that serve as markers in STEM, revealing the evolution of the front surface faceting during continued 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 below first InxGa1−xN layer. The top growth surface consists of three major regions: nonpolar (001) of c-GaN in the middle and {11̅01} [or simply (11̅01) as denoted in Figure 6] and (0001̅) 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 crystal shape evolution. Additional (11̅00)-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 two QW layers. In the growth from N2 to N3, therefore the four orientations compete with very different growth rates resulting in layer-to-layer thickness variation and leading to a dynamic evolution of the crystal shape. From the first GaN spacer

δE ≅ δEv + δEs

(3)

where δEv and δEs are the change of the total volumetric energy by the h-c transition in the additional growth for δt and the change of the total surface free energy determined by the area and free energy of the individual facets associated with the volume change for δt, respectively. Here, the change of strain energy by the tensile stress of c-GaN is included in δEv, and the energy at the h-c interface is taken to be negligible as a result of the small f.20,23,25 No facet changes are observed during the groove filling by PDI and therefore neither additional change in total energy due to the creation/annihilation of any facets nor the kinks associated with their junctions/intersections need to be considered in eq 3. Stages F4-1 to F4-3 were not observed and as a result do not correspond to the lowest total energy alternatives. HPE proceeds to Stage 4 which corresponds to the minimization of the total energy associated with continued growth. E

DOI: 10.1021/acs.cgd.5b01845 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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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 the condition for δE < 0. This is because we do not have sufficient analysis of its contributions; δEv is based on theoretical calculations that need to be confirmed in experiments and includes the change of strain energy due to the tensile stress in c-GaN which requires rigorous theoretical and experimental approaches. If σ001 < σ0001 were the case, the h-c transition would still be available with δEs < 0 but could induce a typical conformal filling or another type of groove fill-up depending on the magnitude of σ111, as illustrated at Stages F4-2 or F4-3 in Figure 2. But, these are not observed under the present growth conditions.26 Equation 4 therefore provides a window of σ001 for unidirectional HPE from the bottom of groove g with (001) at the top. For δE < 0, or the lowest δE, the window in eq 4 should be narrower, implying further requirements on σ001 relative 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 multiple devices, a very important result for the integration of III−N with Si microelectronics. However, the c-GaN is in tensile stress.5,8 Moreover, δE definitely changes to positive after groove filling since the reduction in surface area is no longer available. As seen in Figure 6, continual HPE is not driven by PDI anymore but is still governed by ECS as long as there is sufficient adatom surface mobility. Then, further extension of cphase becomes energetically uncertain. From Stage 5 to 6 in Figure 2, one of the (11̅01̅) and (11̅01) facets annihilates with the extension of the other, as confirmed from the inset of Figure 6. Since they are physically identical, this process effectively results in the extension of (0001)̅ that has the lowest surface free energy in eq 2. In this process, (11̅00) facets in Figure 6 are temporarily formed to accelerate the extension of (0001̅). This allows the kink to move toward the edge and eventually disappear. The alternative case illustrated at Stage F6 in Figure 2 was not observed. This is because it accompanies the expansion of c-GaN that must result in positive δEv with the δEs less sufficient than Stage 6 (or Figure 6) in compensation by eq 2, and violates ECS. This provides an important insight to predict HPE beyond groove filling. In order to maximize the lateral dimension of c-GaN, the growth conditions must be controlled so that σ001 remains comparable to σ11̅01, for example by varying the N/III flux ratio and growth temperature.27−29 Finally, the groove dimensions should be less than or comparable to the adatom migration length to allow the h-c transition. In Figure 3, groove g was prepared for the transition with two well-defined and unstrained (0001) facets. This is possible because their lateral scale is comparable to or less than the adatom migration length. Otherwise, the adatoms that arrive around junction d would not be able to migrate out to an adjacent (11̅01) facet even though they might successfully escape from this unstable region. Then, they would nucleate somewhere above the bottom of the v-groove. This could roughen the (0001) facets by uneven incorporation and interfere the h-c transition by retriggering the growth of hphase inside the groove. The largest lateral dimension of c-GaN from h-c transition is therefore correlated to an adatom migration length under the given growth conditions (typically μm-scale in MOVPE as confirmed in this work) that limits the available groove width with the energetic conditions discussed above.

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

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

t, the height of c-GaN from point T, is given as H. From Figure 3, the growth on all facets of h-GaN comes to a halt until groove 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, is 2H/tan θ with θ = 54.7° indicated in Figure 7. If the change of H for δt is δH, the corresponding change in Ac, δAc, is increased with growth and can be written as 2δH/tan θ. But the consumption of the surface area of the (0001) facets of h-GaN opposing to each other inside the groove means that the h-GaN surface area, Ah, is reduced by −2δH/sin θ, as denoted in Figure 7. If δEs is the change of surface energy from these variations for δt, it can be written as δEs = σ001δAc + σ0001δAh = σ0012δH /tan θ − σ00012δH /sin θ

(4)

where σ001 and σ0001 are the unit area surface free energies of (001) of c-GaN and (0001) of h-GaN respectively, as defined earlier. To avoid δEs ≥ 0, σ001 must be less than σ0001/cos (54.7°) in eq 4. This does not contradict eq 2 and allows a window for σ001. From Figure 3, r0001 is comparable to r0001̅, meaning σ0001 < σ001 at the given growth condition in eq 2.16 Then, σ0001 < σ001 < 1.73σ0001 (5) for δEs < 0 corresponding to Stage 4 in Figure 2. The right inequality 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, F

DOI: 10.1021/acs.cgd.5b01845 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

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Article

(13) Kapon, E.; Simhony, S.; Bhat, R.; Hwang, D. M. Appl. Phys. Lett. 1989, 55, 2715−2717. (14) Yeh, T.-W.; Lin, Y.-T.; Ahn, B.; Stewart, L. S.; Dapkus, P. D.; Nutt, S. R. Appl. Phys. Lett. 2012, 100, 033119. (15) Held, R.; Nowak, G.; Ishaug, B. E.; Seutter, S. M.; Parkhomovsky, A.; Dabiran, A. M.; Cohen, P. I.; Grzegory, I.; Porowski, S. J. Appl. Phys. 1999, 85, 7697−7704. (16) The classification of (0001) and (0001̅) requires further study because they likely have similar growth rates in Figure 3d,e and Figure 6 seen later. This does not agree with the results of ref 14 where in growth rate (0001) is higher than any other facets of the h-GaN observed in the figures. The stability of this facet is critical to the h-c transition. It must compete with the surface roughening from the local fluctuation of adatom incorporation due to the presence of junction d. On the basis of its low growth rate, the facet classified to (0001) is stable enough to assume that it is not very different from (0001̅) in terminating atoms and surface reconstruction at the given growth condition. As seen later, this is a very important assumption for this work. From ref 15, both could be a Ga-terminated (gallided) surface energetically more stable than a N-terminated (nitrided) surface and therefore have identically lowered growth rate. (17) Daudin, B.; Widmann, F.; Feuillet, G.; Samson, Y.; Arlery, M.; Rouvière, J. L. Phys. Rev. B: Condens. Matter Mater. Phys. 1997, 56, R7069−R7072. (18) Frajtag, P.; El-Masry, N. A.; Nepal, N.; Bedair, S. M. Appl. Phys. Lett. 2011, 98, 023115. (19) Mitsunari, T.; Tanikawa, T.; Honda, Y.; Yamaguchi, M.; Amano, H. Phys. Stat. Solidi C 2012, 9, 480−483. (20) Northrup, J. E.; Ihm, J.; Cohen, M. L. Phys. Rev. B: Condens. Matter Mater. Phys. 1980, 22, 2060−2065. (21) In eq 1 t11̅00 is estimated with the deposition thickness from the first three pairs of a h-GaN barrier and an h-InxGa1‑xN well layer since the (11̅00) facet is no longer available in growth of the later InxGa1‑xN QW layers. (22) Stampfl, C.; Van de Walle, C. G. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 5521−5535. (23) Ueno, M.; Yoshida, M.; Onodera, O.; Shimomura, O.; Takemura, K. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 49, 14−21. (24) Serrano, J.; Rubio, A.; Hernandez, E.; Munoz, A.; Mujica, A. Phys. Rev. B: Condens. Matter Mater. Phys. 2000, 62, 16612−16623. (25) In ODI, δEv in eq 3 should include the energy enhancement due to junction d and the h-GaN/Si(111) interface instead of the change of the volume energy from the phase transition. Then, δEv is still positive during growth and the condition of δEs < 0 is also a necessary condition for ODI. Ultimately, both ODI and PDI are governed by ECS, as mention earlier. (26) In Stages F4−2 and F4−3 in Figure 2 shown as examples, (111)-type facets of c-GaN accompany additional facets or kinks that cause complexity in crystal shape and are unlikely available, as confirmed in the experiment. (27) Bryant, B. N.; Hirai, A.; Young, E. C.; Nakamura, S.; Speck, J. S. J. Cryst. Growth 2013, 369, 14−20. (28) Dreyer, C. E.; Janotti, A.; Van de Walle, C. G. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 081305. (29) Li, H.; Geelhaar, L.; Riechert, H.; Draxl, C. Phys. Rev. Lett. 2015, 115, 085503.

CONCLUSION HPE of a microscale engineered material arising from the h-c transition induced in a v-grooved Si(001) substrate has been demonstrated and analyzed with ECS. While c-III-N is inherently metastable and difficult to grow, this work definitively shows the feasibility of growing large areas. Local HPE would possibly allow integration of GaN devices with Si electronics, if compatible processing sequences could be developed. The mechanisms that lead to the formation of a macroscopic volume of c-III-N include (1) ODI of h-GaN on the starting Si(111) faces of a v-groove; (2) Strain relief of hGaN for lattice match to Si; (3) an atomically induced phase transition to c-GaN; followed by (4) the growth of the c-GaN with PDI until groove filling; (5) further evolution of the dual phase material once the groove has filled. For minimal mosaicity of the c-phase, it would be advantageous to start with an incompletely formed, flat-bottom groove, for the stress relief, providing an artificial homogeneous channel replacing void A.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 1-5052727800. Fax: 1-505272-7801. Funding

This work was supported primarily by the Engineering Research Centers Program (ERC) of the National Science Foundation under NSF Cooperative Agreement No. EEC0812056 and in part by New York State under NYSTAR Contract No. C090145. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The fabrication of the groove pattern used for sample N1 was assisted by A. Chaudhuri. REFERENCES

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DOI: 10.1021/acs.cgd.5b01845 Cryst. Growth Des. XXXX, XXX, XXX−XXX