Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Classification of the Morphologies and Related Crystal Phases of III− V Nanowires Based on the Surface Energy Analysis Vladimir G. Dubrovskii,*,†,‡ Nickolay V. Sibirev,† Nripendra N. Halder,§ and Dan Ritter§ †
ITMO University, Kronverkskiy pr. 49, 197101 St. Petersburg, Russia Ioffe Physical Technical Institute RAS, Politekhnicheskaya 26, 194021 St. Petersburg, Russia § Electrical Engineering Faculty, Technion Israel Institute of Technology, Haifa 32000, Israel
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‡
ABSTRACT: Zincblende-wurtzite polytypism in III−V nanowires has been of great interest for a long time. However, full understanding and control over the crystal phase is still lacking. Here, we propose a model for the morphologies and related crystal phases of vapor−liquid− solid III−V nanowires by considering the minimum surface energies of different side wall facets as a function of the droplet contact angle. On the basis of the recent experimental data and earlier theoretical calculations of the surface energies, a simple classification of the possible growth modes is presented. It shows that the wurtzite phase forms in vertical nanowires at intermediate contact angles whereas the zincblende phase is predominant for vertical or inverse-tapered nanowires with a truncated top at larger contact angles. The small stable contact angle corresponds to faulted wurtzite−zincblende intermix. Pure zincblende phase is possible for even smaller contact angles only in the kinetic growth regimes. The wurtzite and zincblende domains are highly sensitive to surface energetics. Using the model, we explain why most gold-catalyzed GaAs nanowires are wurtzite whereas most gallium-catalyzed GaAs nanowires are zincblende and why it is more difficult to obtain pure wurtzite GaP nanowires. We present experimental data on such GaP NWs grown by gold-catalyzed metal organic molecular beam epitaxy and interpret them within the model. Overall, the proposed picture gives a clear route for the crystal phase engineering in III−V nanowires.
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grow gallium-catalyzed WZ GaAs NWs13 (whose structure is often believed to be almost exclusively ZB14). Very important results in this direction have been obtained using in situ growth monitoring of III−V NWs inside a transmission electron microscope (TEM).2,15,16 In ref 15, it has been demonstrated that gold-catalyzed GaP NWs exhibit nonplanar growth interface with the truncated facets, whose amount of truncation oscillates with supersaturation of the catalyst. It has been shown later that the morphology of goldcatalyzed GaAs NWs depends on the contact angle of the catalyst droplet, with the growth front being planar at smaller and truncated at larger contact angles.16 According to Tersoff et al.,15,16 if all facets are truncated and the truncation is present at the beginning of each monolayer growth cycle, the crystal phase should be pure ZB. This is related to the stability of the truncated facet such that new islands nucleate at the liquid−solid interface rather than at the triple phase line where the vapor, liquid, and solid phases meet. Nucleation at the triple phase line is indeed the necessary condition for the WZ phase formation according to Glas et al.4 Dubrovskii et al.14 noticed that breaking the energetic condition for the triple phase line nucleation is actually equivalent to wetting of vertical NW side walls by the catalyst droplet. Hence, it becomes unclear how such ZB NWs can grow at all unless the
INTRODUCTION
Polytypism in III−V nanowires (NWs) offers the otherwise unattainable tool for crystal phase engineering in these materials (see, for example, refs 1−3 for a review). According to the early models of Glas et al.,3−6 the wurtzite (WZ) phase formation is possible due to a lower surface energy of the relevant vertical facets of hexahedral WZ NWs relative to their zincblende (ZB) counterparts. This explains why the effect is specific for (111)-oriented NWs and is rarely observed in other geometries. According to refs 7−9, the lowest energy facets are the (11̅00) ones in the WZ phase and the (110) ones in the ZB phase. The kinetic condition for the WZ phase formation was related to chemical potential (or supersaturation) of a liquid alloy in the droplet promoting the vapor−liquid−solid (VLS) NW growth,4−6 where higher chemical potentials favor the WZ phase. All of these considerations were originally developed for vertical facets and planar liquid−solid interfaces, which seemed to be the natural geometry of VLS NWs. This model has been used for controlling the crystal phase switching in III−V NWs by growth parameter tuning (see, for example, ref 3 for a review). Some questions, however, require a deeper understanding; for example, why it is difficult to obtain pure WZ GaP NWs (see ref 10 and references therein); why InSb NWs are predominantly ZB whereas InAs NWs grown under very similar conditions are usually WZ (see ref 11 and references therein); why gallium-rich Au−Ga droplets yield pure ZB phase of GaAs NWs,12 and whether it is possible to © XXXX American Chemical Society
Received: May 27, 2019 Revised: July 4, 2019 Published: July 9, 2019 A
DOI: 10.1021/acs.jpcc.9b05028 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C droplet acquires a nonspherical configuration,14 which has not been confirmed experimentally. In the first approximation, the current understanding of the crystal phase selection in III−V NWs is such that planar growth interface usually favors the WZ phase, whereas the truncated facets yield a pure ZB phase. This view is based on the surface energy analysis including the key role of the contact angle, which can easily be tuned by the V/ III flux ratio. In this work, we try to give a simple classification of the growth morphologies of III−V NWs and the related crystal phases by developing the approach of ref 17. We consider effective surface energies of forming III−V NWs terminated by different facets in different crystal phases (ZB or WZ), using a simplified angular-symmetric NW geometry. On the basis of the available theoretical values for the surface energetics of solid−vapor interfaces and experimental data on the stable contact angles of gallium-catalyzed GaAs18 and GaP19 NWs, we plot the relevant surface energies as functions of the droplet contact angle. This naturally leads to the structural diagrams, where the preferred crystal phase is determined by the minimum surface energy among the possible NW facets (vertical, tapered, or with a truncated top) for a given contact angle. We then present a comparative analysis of the morphologies and related crystal phases of GaAs versus GaP NWs and show why the WZ phase is much more difficult to achieve in GaP material. We analyze pure WZ GaP NWs grown by gold-assisted metal organic molecular beam epitaxy (MOMBE)10 and explain why the desired phase purity is achieved for these NWs at small contact angles of the droplet under optimized V/III flux ratios.
To calculate the surface energies of forming different facets, we study the VLS system at a fixed volume of liquid droplet, VL = const, as in refs 17 and 20. This is different from considering instantaneous addition of monolayers;3,5 however, the leading terms in the surface energy differences of interest appear identical in both approaches (see ref 17 for more details). Treating the VLS growth at a fixed volume of the droplet is well justified when the facets are much higher than the monolayer, and hence their formation involves continuous droplet refill from vapor.17 We use the well-known expressions for the volume (V) and surface area (S) of a spherical cap seated on a NW with the top radius R and contact angle β given by V=
(1 − cos β)(2 + cos β ) πR3 f (β), f (β) = 3 (1 + cos β)sin β
(1)
S=
2πR2 1 + cos β
(2)
From eq 1 for f(β), it is easy to derive df 3 = dβ (1 + cos β)2
(3)
In the nonwetting (nw) case, the droplet volume equals the volume of the spherical cap, VL = V. Using eqs 1 to 3, it is easy to calculate the change of surface area of the droplet at a fixed volume. Differentiating eq 1 for V, using eq 3 and putting dV = 0, we get dβ = −sin β(2 + cos β)dR/R, showing that β increases when R decreases and vice versa. Now, eq 2 contains only one independent variable, because dβ and dR are linked by the above condition. Taking the differential of eq 2 and using the obtained relationship between dβ and dR, after some simple manipulations, we obtain dS|dV=0 = 2πR cos β dR. For an inclined facet, dR = −dH tan θ from geometrical considerations, with dH as the facet height. The surface energy for forming the nonwetted segment of height dH is given by ÅÄÅ γ (θ ) ÑÉÑ Å Ñ − γSL(π /2)tan θ ÑÑÑÑ2πR dH + γLV dS Gnw (θ ) = ÅÅÅÅ SV ÅÅÇ cos θ ÑÑÖ
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MODEL Using the approach of ref 17, we consider the NW geometries illustrated in Figure 1. The NWs can form in (i) tapered
Figure 1. Nonwetted (a) narrowing (θn > 0) and (b) widening (θw < 0) facets, yielding an increasing or decreasing contact angle β, respectively. (c) Truncated wetted facet having the angle θtr to the vertical, growing to a finite length. These configurations are compared to the standard VLS growth geometry with a planar liquid−solid interface and vertical side walls, shown in (d). Note that in the wetting case, we define the contact angle of the droplet with respect to the horizontal, as shown in (c).
(4)
Here, the first term stands for the newly formed solid−vapor interface and the second describes the corresponding change of the surface area of the horizontal solid−liquid interface. The last term is related to the change of the droplet surface area5 and equals −γLV cos β tan θ × 2πR dH. Using this in eq 4 and introducing the excess surface energy (per unit area) with respect to the vertical nonwetted facet [Gnw(0)] by definition ΔΓnw = [Gnw(θ) − Gnw(0)]/(2πR dH), we obtain
geometry with nonwetted narrowing facets making a positive angle θn with respect to the vertical [Figure 1a], (ii) inversetapered geometry with nonwetted widening facets inclined at a negative angle θw with respect to the vertical [Figure 1b], (iii) truncated wetted growth interface at an angle θtr with respect to the vertical, which will grow only to a finite length according to ref 15 [Figure 1c], or (iv) the standard VLS geometry with nonwetted vertical facets and planar growth interface [Figure 1d]. The surface energies of interest include those of the solid−vapor interfaces at the NW side walls [γSV(θ)], solid− liquid interfaces [γSL(θ), including horizontal interface at θ = π/2], and liquid−vapor interface at the droplet surface (γLV), as shown in Figure 1.
ΔΓnw =
γSV(θ ) cos θ
− γSV(0) − [γSL(π /2) + γLV cos β)]tan θ (5)
Here, θ = θn for the narrowing and θ = θw for the widening facet. In the wetting case (w), the liquid volume equals VL = V − πR2H, with V given by eq 1 and H as the total height of the wetted facet. Here, we neglect the “corner” term that gives a correction on the order of H/R. From the condition dVL = 0, we get B
DOI: 10.1021/acs.jpcc.9b05028 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C R dβ (1 + cos β)2
dH =
morphology and related crystal phase should now be determined by the minimum surface energy among the possible facets in the ZB or WZ stacking for a given contact angle β. If the zero energy level corresponds to vertical (110) facets of ZB NWs, the negative surface energy difference between vertical (11̅00) WZ facets and (110) ZB facets is described by a horizontal line below zero. GaAs Nanowires. For GaAs NWs, we use the calculated surface energies of (11̅00) WZ and (110) ZB vertical facets of ref 7, which are very close to those given in ref 8. The widening facet should be the low energy (111)B ZB facet (θw = −19.5°), for which we use the surface energy calculated in ref 21. The surface energy of liquid gallium γLV equals 0.671 J/m2 at a typical growth temperature of 620 °C according to ref 23. In situ growth monitoring of gallium-catalyzed growth of GaAs NWs in TEM (at a low temperature of 420 °C) revealed that the narrowing ZB facet is the (110) one (θn = 54.7°) (Panciera et al., manuscript in preparation). This readily gives the surface energy of the narrowing facet, which is the same as that for vertical (110) ZB facets. Furthermore, the truncated facet of GaAs NWs also belongs to the (110) family; hence, θtr = θn = 54.7°. It is interesting to note that the (110) wetted facets were also observed by ex situ measurements of ref 23 after stopping gallium-catalyzed growth of GaAs NWs and appeared to be more stable than the (111)A facets. With these data, the two unknowns remaining in eqs 5 and 10 are the solid−liquid surface energies γSL(π/2) (for the horizontal facet) and γSL(θtr) (for the truncated facet). To estimate these unknowns, we use the data of ref 18 for the two stable contact angles of gallium droplets on top of GaAs NWs. The large stable contact angle, around 130°, corresponds to NW growth with radial extension, in the pure ZB phase, occurring under gallium-rich conditions. The small contact angle, in the range from 95 to 100°, is observed in the stage of the NW radius shrinking under gallium-poor conditions, with a faulted WZ/ZB structure (predominantly in the WZ phase). A similar contact angle of approximately 100° corresponded to the start of NW tapering in the kinetic growth regime. Using eqs 5 for narrowing (110) and widening (111)B facets, a value of γSL(π/2) = 0.598 J/m2 gives the two stable contact angles at 100 and 128°, as shown in Figure 2. The truncation starts to develop at approximately 125° (for T = 420 °C). Using this critical contact angle for the WZ-ZB phase transition also at 620 °C, the truncation curve given by eq 10 is fitted with a value of γSL(θtr) = 0.588 J/m2. The full set of parameters for GaAs NWs is given in Table 1, along with the corresponding references. The graphs presented in Figure 2 lead to the following general classification of the VLS growth scenarios for GaAs NWs. The small stable contact angle of the catalyst droplet (∼100°) at point 1 corresponds to inward-tapered NW morphology and faulted WZ/ZB structure. Clearly, this stable contact angle corresponds to nonstationary growth regimes with gradually diminishing volume of the droplet by shrinking the NW top radius, as in ref 18. Any decrease of the contact angle below point 1 will be compensated by introduction of a narrowing facet, retaining the VLS system back to point 1. The large stable contact angle (∼128°) yields a pure ZB phase, because point 3 is separated from the WZ region. This stable contact angle is maintained in nonstationary growth regimes with gradually increasing volume of the droplet by extending the NW top radius, as in ref 24. The truncated part of the NW for β larger than the critical contact angle of 125° should be ZB
(6)
On the other hand, the increase of the droplet surface area equals dS =
2πR2 sin β dβ (1 + cos β)2
(7)
from eq 2 at a constant R. Now, the droplet surrounds the truncated part of the NW, which is why the droplet surface area increases for larger H by increasing its contact angle even at a fixed volume of liquid. The particular case of this process for vertical NW side walls was considered earlier in ref 14. Excluding dβ from eqs 6 and 7, we get dS = 2πR sin β dH
(8)
The surface energy for forming a wetted truncated segment of height dH at the angle θtr is given by ÅÄÅ γ (θ ) ÑÉÑ Å Ñ tr − γSL(π /2)tan θtr ÑÑÑÑ2πR dH + γLV dS Gw (θtr) = ÅÅÅÅ SL ÅÅÇ cos θtr ÑÑÖ (9)
Here, the first term stands for the newly formed solid−liquid interface, the second term describes the corresponding change of the surface area of horizontal solid−liquid interface, and the third term gives the increase of the droplet surface energy, similar to eq 4. Using eq 8 in eq 9 and introducing the excess surface energy with respect to the vertical nonwetted facet by definition ΔΓw = [Gw(θtr) − Gnw(0)]/(2πR dH), we arrive at the result of ref 16 ΔΓw =
γSL(θtr) cos θtr
− γSV(0) − γSL(π /2)tan θtr + γLV sin β (10)
Any inward-tapered facet cannot grow infinitely because the growth of tapered (or truncated) NW takes less material from the supersaturated phase compared with NW with vertical (or less tapered) facets. Rather, such tapered NW sections acquire an energetically preferred height, below which the NW is restricted by the vertical or less tapered facets. This observation of ref 15 in fact applies to any facet type, not necessarily the wetted truncation on top of vertical NW.
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RESULTS AND DISCUSSION Generalizing the approach of ref 17 for III−V NWs that may form in either ZB or WZ phase, we use eqs 5 and 10 for classification of the morphologies and crystal phases of III−V NWs under the following assumptions (i) Solid−liquid surface energies γSL are independent of the crystal phase (WZ or ZB)4 for any θ; (ii) Inward-tapered III−V NWs with a planar growth interface form in the ZB phase (Panciera et al., manuscript in preparation); hence, γSV(θn) = γZB(θn); (iii) Surface energy of an Au−Ga liquid alloy in the droplet is given by that of liquid gallium, which is accumulated at the droplet surface due to its lower energy. Under assumption (iii), the surface energetics of goldcatalyzed and gallium-catalyzed III−V NWs is identical, with any possible difference arising only due to different growth kinetics determining how the contact angle changes under varying group III and V fluxes. The energetically preferred NW C
DOI: 10.1021/acs.jpcc.9b05028 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C
Let us now discuss why most gallium-catalyzed GaAs NWs exhibit a pure ZB phase (see, for example, refs 3, 13, 14, 18, 24, 29), except the very tip that forms in the cool-down step after stopping the gallium flux.24 Leaving aside the stage of droplet shrinking, as in ref 18, the standard gallium-catalyzed VLS growth employs effectively gallium-rich conditions (including surface diffusion of gallium adatoms from the NW side walls to the top); otherwise, the droplet would soon be consumed by the excessive arsenic flux.30 According to the diagram in Figure 2, such a regime corresponds to the large stable contact angle and radial growth of GaAs NWs (until saturation) in the pure ZB phase. Since most gallium-catalyzed GaAs NWs are obtained in the regime of radial growth at the large stable contact angle, their phase is very predominantly ZB. However, decreasing the contact angle by increasing the V/III ratio allows one to achieve pure WZ gallium-catalyzed GaAs NWs. According to theoretical results of ref 27, GaAs and other III−V NWs grown by gold-catalyzed VLS method are not expected to continuously shrink or extend their top radius. This is related to the fact that there is always a stationary solution to the kinetic equations for the group III and V concentrations in the droplet, with a time-independent droplet volume. In other words, the droplet size is stabilized by the presence of gold. Therefore, gold-catalyzed GaAs NWs should normally be untapered, either with a planar or truncated growth interface. Of course, the contact angle of the droplet can still be tuned between point 1 and 3 by changing the V/III flux ratio. This explains predominantly the WZ crystal phase of gold-catalyzed GaAs NWs (see, for example, refs 3 and 29 for a review). According to Figure 2, very high V/III flux ratios can only render the droplet contact angle close to point 1, where the crystal phase is polytypic. Decreasing the V/III flux ratio results in a pure WZ phase in a wide range of contact angles from 100 to 125°, corresponding to gallium and arsenic fluxes typically employed in the growth experiments. Conversely, a pure ZB phase can only be achieved in a narrow range of contact angles (from 125 to 128°), corresponding to very low V/III ratios. These conclusions are fully consistent with the earlier experimental observations given, for example, in ref 31, for gold-catalyzed GaAs NWs whose structure was ZB for large and WZ for small contact angles, regulated by the V/III flux ratio. GaP Nanowires. We now consider the less known case of GaP NWs, for which no in situ monitoring of the morphology and crystal phase versus the contact angle was reported to date to our knowledge (apart from pure ZB GaP NWs with truncated tips of ref 15). We use the calculated surface energies of (110) and (111) ZB facets of ref 32. Applying the method of ref 9, calculating the density of dangling bonds on the (11̅00) plane and using the (110) and (111) surface energies as the reference values, we estimate the γSV(0) for the lowest energy WZ facet. As for GaAs NWs, we assume that the widening facet is the low energy (111)B ZB facet, for which we use the surface energy calculated in ref 32. However, we take the
Figure 2. Surface energies of different facets of GaAs NWs relative to ZB NWs with vertical (110) facets (the zero level) versus the contact angle of the catalyst droplet, at a temperature of 620 °C. The parameters used in eqs 5 and 10 are summarized in Table 1. The blue horizontal line at −0.098 J/m2 corresponds to the lower surface energy of vertical (11̅00) WZ side walls. The small stable contact angle, approximately 100° (point 1) corresponds to inward-tapered NWs with a planar liquid−solid interface and a faulted WZ/ZB structure in the kinetic regime of droplet shrinking (until the top NW radius stabilizes at a certain stationary one). The large stable contact angle, approximately 128° (point 3) corresponds to inverse-tapered NWs and pure ZB structure in the regime of droplet swelling. These two regimes are entirely possible for gallium-catalyzed GaAs NWs growth but unlikely for gold-catalyzed GaAs NWs. The WZ phase forms in vertical GaAs NWs for intermediate contact angles between ∼100° (point 1) and ∼125° (point 2), after which truncated facets are introduced at the NW top. The broad WZ region is shown in pink. The narrow range between ∼125° (point 2) and ∼128° (point 3), shown in green, corresponds to ZB GaAs NWs with vertical (110) side walls. This structural diagram is not considerably different from the one at 420 °C (Panciera et al., manuscript in preparation), showing a relatively small effect of the growth temperature.
according to ref 15, and it determines the ZB phase of the nonwetted stem. The facet type of the nonwetted NW part should now change from truncated wetted to the minimum energy nonwetted in the ZB phase, which is the vertical (110) facet. Kinetic regimes with tapering or inverse tapering of GaAs NWs are usually observed during self-catalyzed VLS growth, where the droplet serves as a nonstationary reservoir of gallium.18,24−27 Tapering with the small stable contact angle occurs under high V/III flux ratios, whereasinverse tapering with the large stable contact angle requires low V/III ratios.13,18,27 Subsequent radial growth may retain cylindrical NW geometry, which is why many gallium-catalyzed GaAs NWs show a uniform radius from base to top, increasing with time.13,18,24 However, inverse-tapered gallium-catalyzed GaAs NWs have also been reported.13,28 After some time, the NW radius should self-equilibrate to a certain stationary one, as predicted theoretically in refs 24, 25 and demonstrated experimentally in ref 26.
Table 1. Parameters of GaAs and GaP NWs Used in Calculationsa material GaAs GaP
θn (deg)
θw (deg)
−19.5a 54.7a 19.5 (Asmp) −19.5 (Asmp)
θtr (deg) 54.7a 54.7 (Asmp)
γZB SV (0) (J/m2)
γWZ SV (0) (J/m2)
γZB SV (θn) (J/m2)
γZB SV (θw) (J/m2)
γLV (J/m2)
γSL(π/2) (J/m2)
0.7987 0.86033
0.7007 0.7509,33
0.7987 0.87533
0.69022 0.77033
0.67123 0.67123
0.598 (fit) 0.540 (fit)
γSL(θtr) (J/m2) 0.588 (fit) 0.481 (Asmp)
a
Panciera et al., manuscript in preparation. D
DOI: 10.1021/acs.jpcc.9b05028 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C symmetrical (111)A narrowing facet (θn = −θw = 19.5°) for GaP NWs, because its effective surface energy γSV(θn)/cos θn is lower than that of the (110) facet.33 Next, we use the data of ref 19, showing that the contact angle of the droplets on top of gallium-catalyzed, pure ZB GaP NWs is close to 123° for any NW geometry (vertical, tapered, or inverse-tapered) within a wide range of V/III flux ratios from 1 to 6. This leads to an estimate for γSL(π/2) at 0.540 J/m2. Finally, we assume that the truncated facet is of the (110) family, as for GaAs NWs (θtr = 54.7°), with a surface energy of 0.484 J/m2, to fit the experimental data presented below. These model parameters are summarized in Table 1 (where “Asmp” stands for “Assumption”) and yield the structural diagram shown in Figure 3.
the critical value of 105° (corresponding to the WZ-to-ZB phase transition) yields a pure ZB phase. There is only a narrow range of contact angles, approximately between 122 and 126°, where GaP NWs are vertical. This is strongly reminiscent of the Nebol’sin-Shchetinin contact angle obtained in ref 20 from different considerations, which corresponds to stable NW growth with vertical side wall facets. Galliumcatalyzed GaP NWs grown at high V/III ratios should taper and increase the contact angle of gallium droplets to ∼122°, whereas GaP NWs grown at low V/III ratios should inversetaper and decrease the contact angle to ∼126°, which is consistent with the observations of ref 19. Figure 4 shows the possible structural diagrams that yield pure ZB or almost pure WZ phases of III−V NWs. Assuming the narrowing and widening curves being similar to those of GaAs (Figure 2), we define the contact angles β1, β2, and β3 corresponding to points 1, 2, and 3, respectively. β1 is the small stable contact angle at which the narrowing facet has the same surface energy as the vertical WZ facet, the β3 is the large contact angle at which the surface energy of vertical ZB facet equals that of the widening ZB facet, whereas β2 is the critical contact angle at which the surface energy of the vertical WZ facet equals that of the truncated ZB facet. When β2 < β1, or in the extreme case where the low truncated curve does not cross the one of the vertical WZ facet, as in Figure 4a, the WZ phase cannot form at all. Indeed, the ZB-to-WZ transition at point 1 will not occur because the growth interface is already truncated. Rather, tapered ZB NW will reach point 4 by increasing the contact angle due to tapering, where the side wall facets become vertical. Further increase of the contact angle by decreasing the V/III ratio will bring the system to the stable point 3, after which the droplet will grow by increasing the NW top radius at a fixed β3. When β2 > β3, as in Figure 4b, any contact angle between points 1 and 2 yields the pure WZ phase. Inflating the droplet by decreasing the V/III ratio introduces truncation at point 2, after which the wetted part of the NW becomes ZB. However, the lowest energy ZB facet of the nonwetted lower part of the same NW is widening. Introduction of widening facets decreases the contact angle to the stable value β3, after which the side wall facets should become vertical. At this contact angle, the WZ vertical facets are preferred to the ZB ones, without truncation of the growth interface. This leads to the return to the WZ phase. If the droplet continues to grow, the whole loop is periodically repeated, most probably leading to the WZ/ZB superlattice with vertical WZ and inversetapered ZB sections. No pure ZB NWs can form in this case. We now present the supporting experimental data on the morphology of pure GaP NWs. Gold-catalyzed GaP NWs were grown in circular openings in a 15 nm thick SiNx mask on GaP (111)B substrates, following the selective area VLS method. The details of growth and the multistep process of mask patterning and positioning of the gold catalyst on the GaP substrate are reported earlier.10,35,36 For these experiments, VISTEC EBPG 5200+ electron beam lithography system was operated at 100 kV to keep the catalyst diameter within 20 nm at a periodic pattern consisted of circular holes with a pitch of 1 μm. The NWs were grown in a compact MOMBE system37 for 50 min using triethylgallium (TEG) and thermally cracked phosphine (PH3) as precursors, at a temperature of 620 °C. The TEG flow rate was kept fixed and corresponded to a planar growth rate of 0.084 μm/h for In0.53Ga0.47As on
Figure 3. Surface energies of different facets of GaP NWs relative to ZB NWs with vertical (110) facets (the zero level) versus the contact angle of the catalyst droplet, at a temperature of 620 °C. The parameters used in eqs 5 and 10 are summarized in Table 1. The blue horizontal line at −0.110 J/m2 corresponds to the lower surface energy of vertical (11̅00) WZ side walls. The small stable contact angle, approximately 95° (point 1) corresponds to inward-tapered NWs with a planar liquid−solid interface and a faulted WZ/ZB structure. The truncated curve crosses the (11̅00) WZ line at approximately 105° (point 2). The narrow range of contact angles between points 1 and 2 yields WZ GaP NWs (the pink region), with vertical side walls and a planar liquid−solid interface. After developing the truncation, NWs become ZB and continue to taper until the narrow range 3 (between ∼122 and 126°), where the preferred structure is ZB NWs with vertical side walls and a truncated tip. Very low V/III flux ratios yield inverse-tapered GaP NWs. Unlike in GaAs system, pure ZB GaP NWs form in a wide range of V/III ratios and the corresponding contact angles (the green region), stabilizing to 122−126° by either inward (at higher V/III ratios) or outward (at low V/III ratios) tapering.
The gap between the surface energies of (110) ZB and (11̅00) WZ facets for GaP is almost the same as that for GaAs. However, due to the differences in surface energies of other interfaces, the predicted growth morphologies and structural trends of GaP NWs change drastically. According to Figure 3, the small stable contact angle around 95° should correspond to a mixture of the WZ and ZB phases. The range of contact angles from ∼95 to ∼105° yields the WZ phase of GaP NWs and is considerably reduced with respect to GaAs NWs. Therefore, it is more difficult to find the appropriate range of the V/III flux ratios corresponding to this narrow range, which explains why pure WZ GaP NWs are rarely achieved. Clearly, small contact angles corresponding to the pure WZ phase require relatively high V/III flux ratios to empty the droplets with their gallium. The morphology of ZB GaP NWs is also very different from that of GaAs NWs. Any contact angle above E
DOI: 10.1021/acs.jpcc.9b05028 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C
Figure 4. Illustrations of surface energy landscapes yielding (a) pure ZB and (b) almost pure WZ phases of III−V NWs in the entire ranges of contact angles, regulated by the V/III flux ratio. The arrows show evolution of the VLS system as the droplet is inflated by decreasing the V/III flux ratio. When the truncated curve is low, as in (a), there is no ZB-to-WZ transition at point 1, because the growth interface is already truncated. Rather, tapered ZB NW will reach point 4 and become vertical with the truncated tip. Point 3 remains stable in the ZB phase; any further decrease of the V/III flux ratio will lead to inverse tapering with this stable contact angle. Hence, no WZ phase can form in this case. When the truncated curve is high, as in (b), stable point 1 corresponds to a faulted WZ/ZB structure. Further decrease of the V/III flux ratio leads to increasing the droplet contact angle without changing the top NW radius, in the pure WZ phase. At point 2, truncated facets are introduced and the phase switches to ZB. However, nonwetted ZB NW stem must inverse-taper. This decreases the contact angle and retains the system to point 3, where the WZ phase is preferred again due to the absence of truncation. If the droplet continues to inflate, this loop is repeated and leads to the WZ/ZB superlattice with vertical WZ and inverse-tapered ZB sections, as shown in the insert. No pure ZB phase is possible in this case.
Figure 5. High-resolution TEM micrographs of three different regions along the NW grown at a PH3 flow of 3 sccm at (a) top, (b) neck, and (c) middle regions recorded along the [11̅0]/[112̅0] zone axis at an accelerating voltage of 200 kV. Fast Fourier transform of the neck and middle region are in (d) and (e), respectively. The measured contact angles β are within 95 to 105° for any PH3 flux involved in the MOMBE process.
InP(001) substrate at an AsH3 flow of 2 sccm and at a growth temperature of 500 °C. For the NWs shown in Figure 5, the PH3 flow was maintained at 3 sccm throughout the experiment. The magnified top, neck, and middle sections of a representative NW are shown in Figure 5a,c and confirm pure WZ crystal structures with no stacking faults. Therefore, the particular growth conditions followed here are capable of producing pure WZ phase of GaP NWs. For the NWs shown in Figure 6, after growing the NWs for 40 min following the previous growth protocol, the PH3 flow was increased abruptly to 9 sccm for 10 min. As explained previously,35 this type of growth is performed to notice any stacking fault introduced due to the abrupt change in the phosphorous supply. The three sections shown in Figure 6 represent the microstructure originating from different growth conditions. Figure 6a shows the top section of a NW grown at a PH3 flow of 9 sccm and reveals the pure WZ structure obtained for higher phosphorous supply. Figure 6b shows a representative image of the section where the abrupt change of PH3 was made. As it is very hard to detect the particular point
at which the switching from axial to radial growth mode took place, we explored around 300 nm from the catalyst and did not observe any stacking fault in that region. Figure 6c shows the portion that was grown at a lower PH3 flow of 3 sccm. As discussed earlier, this PH3 flow produces a pure WZ phase of GaP NWs. We can thus conclude that the entire range of PH3 flows from 3 to 9 sccm employed in these MOMBE experiments leads to the WZ crystal phase. The absence of stacking faults or ZB insertions in the transition region reveals the exceptional stability of GaP NWs in the WZ structure. Most importantly for our analysis, the measured contact angles of all our GaP NWs after growth appeared to be within the range from 95 to 105° for any PH3 flow between 3 and 9 sccm. Of course, the growth stop occurred under phosphorous flux, which is why the droplet volume gradually decreased. This nonstationary process should be responsible for the formation of a tapered neck under the droplet, clearly seen in Figures 5 and 6. According to the structural diagram of GaP NWs shown in Figure 3, the contact angle of the droplet seated on top of tapered GaP NWs should equal 95°. The WZ section of the F
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Figure 6. High-resolution TEM micrographs of three different regions along the NW grown with the abrupt change of PH3 flow from 3 to 9 sccm at (a) top section grown at 9 sccm PH3 flow, (b) transition section, and (c) middle section grown at 3 sccm PH3 flow, recorded along the [11̅0]/ [112̅0] zone axis at an accelerating voltage of 200 kV. Fast Fourier transform of the corresponding images are shown in (d) to (f).
each of the six equivalent facets can be treated separately in an effectively one-dimensional case. Second, the truncated facets were assumed as being single crystal plane and not a combination of higher index facets. Although (110) truncated facets are supported by the results of in situ growth monitoring of GaAs NWs,19 more complex geometries cannot be excluded in the general case. Third, oscillations of truncation15,16 were not considered. This is justified if the amount of truncation never shrinks to zero, as in ref 15, because our analysis of the crystal phase assumed the suppression of WZ whenever the truncated growth interface is preferred to the planar one on surface energetic grounds (validity of this view will be studied elsewhere). Then, neglect of oscillations is natural in studying the VLS system at a fixed liquid volume, which necessarily implies averaging over a period of time much longer than the monolayer growth cycle. Fourth, and most important, our considerations were based entirely on the surface energetics of ZB or WZ NWs in different morphologies and ignored the influence of chemical potential on the crystal phase switching.3−6 In this simplified picture, the preferred crystal phase is controlled by the sole parameter, the droplet contact angle, which is supported by experimental data. Although including the chemical potential considerations may refine the picture, our analysis strongly suggests that phase transitions in NWs occur quite abruptly whenever allowed by surface energetics. In other words, chemical potential near the transition points quickly exceeds the energy of stacking fault, which is required for switching
diagram corresponds exactly to the measured contact angles from 95 to 105°. Although a cool-down under a phosphorous flux involves kinetic factors that cannot be described within the frame of our equilibrium model for the surface energetics, the observed trend is remarkable. It strongly suggests that pure WZ phase of GaP NWs presented here is explained by the small contact angles of Au−Ga droplets, achieved through the high effective V/III flux ratios. Transition from the pure WZ phase to faulted WZ/ZB structure for tapered NWs at the small stable contact angle requires a certain period of time. This time is needed to surpass the activation energy for the phase transition and may be much longer than the duration of the cool-down process. Therefore, the top part of the NWs immediately below the droplet remains WZ. A similar trend was observed in ref 18 for gallium-catalyzed GaAs NWs in the stage of droplet shrinking, where the transition region was predominantly WZ.
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CONCLUSIONS
Our theoretical analysis relied upon several assumptions and simplifications. First, we used the angular-symmetric cylindrical NW geometry and spherical cap geometry for the droplet, whereas real NWs are hexahedral and the droplet becomes slightly asymmetric to cover the hexagonal top facet of the NW.33 Equations 5 and 10 can be derived in a rigorous manner only for cylindrical NW geometry (another possibility is considering one-dimensional geometry, as in refs 15, 16, 34, leading to the same results). We do not anticipate any significant errors originating from this simplification, because G
DOI: 10.1021/acs.jpcc.9b05028 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C from the ZB to WZ phase4 and does not significantly affect the critical contact angles for the transition. In summary, the presented approach provides a solid ground for the analysis of polytypism and crystal phase engineering in III−V NWs by tuning the contact angle of the catalyst droplet by material fluxes. It combines the main ingredients of prior works, such as the preference of narrowing, widening, and vertical side wall facets under different conditions15−17,34 and the lower surface energy of vertical WZ side wall facets with respect to their ZB counterparts.3−9 The model allows one to map out the preferred morphology and crystal phase as a function of the contact angle. In particular, the pure WZ phase of MOMBE-grown, gold-catalyzed GaP NWs has been explained by the correct choice of the PH3 flows, leading to the small contact angles within a narrow WZ range in the structural diagram. Allowing for different surface energies of WZ and ZB NWs in vertical geometry considerably refines the earlier results of ref 16. The minimum energy landscape appears highly sensitive to the surface energy values for different side facets of ZB and WZ NWs, which are only obtainable through the first principle calculations. This shows once again the importance of such calculations for different III−V materials. Estimation of the unknown surface energies of solid−liquid interfaces requires some additional data. We now plan to consider InAs, InSb, and other III−V material systems, possibly including elemental Si and Ge NWs, within the same model to understand the crystal phase trends imposed by surface energetics of these materials in combination with different catalysts. Another interesting possibility is using surfactants, which may significantly modify the surface energies and the corresponding structural trends in III−V NWs.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: dubrovskii@ioffe.mail.ru. ORCID
Vladimir G. Dubrovskii: 0000-0003-2088-7158 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS V.G.D. and N.V.S. acknowledge the Russian Science Foundation for financial support under the Grant 19-72-30004. REFERENCES
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