Coherent Twinning Phenomena: Towards Twinning Superlattices in III

Department of Physics, Department of Materials Science and Engineering, Material Research Institute, The ..... The Journal of Physical Chemistry C 0 (...
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NANO LETTERS

Coherent Twinning Phenomena: Towards Twinning Superlattices in III−V Semiconducting Nanowires

2006 Vol. 6, No. 12 2736-2742

Qihua Xiong,†,‡,| J. Wang,§ and P. C. Eklund*,†,‡,§ Department of Physics, Department of Materials Science and Engineering, Material Research Institute, The PennsylVania State UniVersity, UniVersity Park, PennsylVania 16802 Received July 21, 2006

ABSTRACT We report evidence in GaP and InP nanowires for a coherent modulation of the structure along the wire axis. By using electron diffraction, we have observed an additional series of diffraction peaks consistent with a quasiperiodic placement of twinning boundaries along the wire. This observation is indeed unexpected, as the vapor−liquid−solid growth conditions used to produce the nanowires were not modulated. The averaged repeat distance of the structure, i.e., the distance between twin boundaries, has been found to depend on the temperature gradient imposed in the growth zone. Future control of the twinning superlattice period should allow significant design possibilities for electronic, thermoelectric, thermal and electro-optic applications of semiconducting nanowires.

A superlattice is a term given to a periodic modulation of a crystal structure along a specific direction. Implicit in the definition is a hierarchy of order. One can imagine the stacking of fundamental A and B units along the superlattice direction to yield, for example, the structure AABBAABB... with the superlattice unit cell containing two A and two B units. The difference between A and B might be the local crystalline structure (e.g., cubic zinc blende phase versus hexagonal wurtzite phase, yet each has the same chemical composition; this type of superlattice even occurs naturally in SiC and ZnS crystals1) or it can be a compositional difference (e.g., A ) AlxGa1-xAs, B ) AlyGa1-yAs (x * y)), where both A and B exhibit the same local structure). A third possibility is that A and B exhibit the same local structure and composition, while they differ only by a relative 180° rotation of the crystal orientation. In this case, A and B are “twins” and the lattice is called a twinning superlattice (TSL). Different from compositional or structural superlattices, a TSL is perfectly lattice-matched across the twinning boundary. Nevertheless, the TSL has a nontrivial consequence on the electronic and phonon properties of the materials. Conventional continuum models for superlattice properties, such as the effective mass model, are not applicable to TSLs because neither the potential nor the * Corresponding author. E-mail: [email protected]. † Department of Physics. ‡ Department of Materials Science and Engineering. § Material Research Institute. | Present address: Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138. 10.1021/nl0616983 CCC: $33.50 Published on Web 11/16/2006

© 2006 American Chemical Society

effective mass changes across the twinning boundaries.2 Theoretical calculations indicate that TSLs in diamond and zinc-blende structures can have very different properties compared to their bulk semiconductor counterparts such as zero-energy gap, miniband gaps,3 or direct optical transitions for otherwise indirect bulk semiconductors.4 A few examples of twinning superlattices have been reported in the literature for epitaxial Si films5 grown by periodically introducing boron to produce the twin boundaries. As dimensionally confined systems, compositionalmodulated heterostructure superlattices have been grown in GaAs/GaP6 and InAs/InP7 nanowires. Interesting electronic and photonic properties have also been demonstrated in these systems, e.g., polarized single-wire photoluminescence6 and single-electron transistors.8 Recently, a report of high-density twinning in ZnSe (wurtzite) nanowires has appeared.9 The twinning periodicity was shown to be related to the diameter, and the occurrence of twinning is suggested to be driven by the elastic energy.9 Most recently, a periodic twinned structure has been observed in ZnS nanowires.10 The origin of this “automatic” twinning in nanowires has been discussed in a very recent paper in the context of nucleation,11 however, the factor that controls the periodicity of twinning is still unknown. Here we report the observation of coherent twinning in GaP and InP nanowires. The coherence is observed over lengths at least as long as 500 nm, and the modulated structure forms spontaneously without modulation of feedstock or growth parameters. Our observation and other previous reports9-12 may suggest the possibility of a control-

Figure 1. Schematic diagram of coherent twinning formation mechanism, PLV apparatus, and temperature profiles. (a) Proposed twinning formation mechanism. At a certain undercooling, twinned nuclei formation at the three-phase boundary is thermodynamically favorable. The nucleation rate increases exponentially with increasing of temperature and increasing of undercooling. A twinning boundary is formed when the axial growth of single crystalline nanowire is interrupted by the twinned nuclei nucleation at the threephase boundary. (b) Our PLV apparatus. (c) Temperature profiles (for GaP) inside the inner quartz tube, without offsets (no. 1) and with offset (no. 2). The top arrow indicates the approximate time that gas flows from the target, estimated from the tube cross-section area and the gas flow rate. The shadow indicates the TSL growth zone.

lable growth of periodic twinning superlattices in semiconducting nanowires (SNWs). In the vapor-liquid-solid (VLS) growth of SNWs, a small metal particle (e.g., Au) is chosen so that at elevated temperature it binds and dissolves semiconductor atoms (e.g., Ga and P) present in the vapor phase above the particle. A liquid pseudobinary system forms (e.g., Au-GaP),13 and in the steady state, semiconductor atoms are thought to rapidly diffuse through the liquid droplet to the base of the nanowire growing from the liquid particle surface. This process is shown schematically in Figure 1a. Many of the details of VLS growth are still not understood. In fact, the very idea that VLS growth automatically applies to all SNWs found with a metal particle at one end has been challenged recently.14 As commonly accepted, the VLS growth consists Nano Lett., Vol. 6, No. 12, 2006

of four important aspects:15,16 (1) chemical reaction at the vapor-liquid particle interface, (2) mass transport of the semiconductor atoms across the vapor-liquid droplet interface, (3) dissolution of these atoms and mass transport through the liquid droplet, and (4) precipitation of these atoms and growth of the nanowire at the liquid-solid interface. The liquid-phase droplet plays a crucial role in the VLS process: (1) it should have a high accommodation coefficient (i.e., high probability that an impinging atom or molecule will be incorporated into the droplet) compared with the nanowire solid phase, and (2) it should reduce the activation energy of nucleation at the liquid-solid (nanowire) interface.16 In some cases, e.g., chemical vapor source VLS growth of Si and Ge from SiH4 and GeH4, the GibbsThomson effect seems to determine the critical (minimum) diameter of the nanowires,16 while other reports support the idea that the diameter of the metal nanoparticle largely determines the nanowire diameter.17 Below, we demonstrate the production of coherent twinning in GaP and InP nanowires grown by pulsed laser vaporization (PLV) of Au:GaP and Au:InP targets. The apparatus is shown schematically in Figure 1b.18 Pulses from a Nd:YAG laser were focused onto the target and scanned under computer control across the surface. Au particles/ clusters form in the vapor phase near the target (point A) and drift down the furnace entrained in an inert gas flow (Figure 1b). The particles form a liquid pseudobinary alloy droplet in the furnace between the position of the GaP(InP) target and middle point M. After passing M, the Au semiconductor alloy droplet becomes saturated with semiconductor and nanowire growth starts. The nanowires grow as the particle drifts down the furnace entrained in the inert gas and are collected on a cooler region of the quartz wall near point B (inner tube). They were harvested from there after the furnace had cooled to room temperature. Given the inert gas flow (100 sccm) and the inner tube diameter (∼25 mm), we estimate that it takes ∼3 min for the particles/SNWs to drift down the central quartz tube to point B. Of particular importance to this work is that, as the particle/ SNW drifts slowly down the inner quartz tube, it experiences a variation in the local growth temperature and temperature gradient. The character of nanowire and the coherent twinning produced under these local growth conditions is “frozen” into the nanowire and can be inspected later (after harvest) by transmission electron microscopy (TEM). In this paper, we have considered the effect on the twinning growth in GaP and InP resulting from two different temperature profiles: one profile has a “flat mid-zone” and the other has a “gradient mid-zone” profile. The exact profile for GaP growth is plotted in Figure 1c; similar shaped profiles, but slightly cooler, were used for InP (see Supporting Information). In our comparative study, all other experimental PLV parameters were fixed (e.g., Ar flow rate, laser pulse energy, and repetition rate, total reactor pressure, etc.); only the effects of the temperature profile on the coherent twinning were investigated. In Figure 2, we show bright-field TEM images of a typical GaP nanowire grown in the “flat mid-zone” profile (Figure 2737

Figure 2. TEM and HRTEM images of GaP nanowires grown under different temperature profiles. (a) TEM image of an individual GaP nanowire with a diameter of ∼80 nm and a length of ∼20 µm grown with temperature profile no. 1 (Figure 1c). Three magnified images show the structure associated with early growth (Figure 2a-1), the transition region from early single-crystal growth to the onset of the coherent twinning (Figure 2a-2, hollow arrow) and the late growth near the nanoparticle (Figure 2a-3). Solid arrows highlight some of the twinning boundaries. (b) TEM image of an individual GaP nanowire with a diameter of ∼40 nm and a length of ∼18 µm grown with temperature profile no. 2 (Figure 1c). Three magnified views show the quasiperiodic twinning superlattice along the whole nanowire. No transition from single crystal to coherent twinning is observed.

2a) and in the “gradient mid-zone” (Figure 2b) profile. A composite TEM image of the entire length of SNW is shown. The image is actually a composite of many individual highresolution segments collected over several tens of microns along the wire length. The late wire growth appears, of course, in the region next to the dark nanoparticle appearing at the bottom of the figure. For each nanowire, we also present three magnified images that show more clearly the contrast changes associated with the coherent twinning 2738

structure. We discuss the results for GaP nanowires grown using the flat mid-zone profile first. Figure 2a-1 indicates that this wire starts growing as a single crystal (i.e., no twinning band contrast is observed). Figure 2a-2 shows the region of the nanowire where the transition from singlecrystal growth to coherent twinning growth occurs (see the arrow marked “onset”). Finally, Figure 2a-3 shows the coherent twinning structure during late growth. A series of arrows have been added to indicate the positions of some of Nano Lett., Vol. 6, No. 12, 2006

Figure 3. TEM and HRTEM images of single crystalline GaP/InP nanowire and TSLs in GaP/InP nanowires. (a) HRTEM image of an early grown single crystalline segment GaP nanowire as shown in Figure 2a-1. The lattice fringes are resolved with [111] growth direction and the spacing between adjacent planes is 0.314 nm. The inset shows a SAD pattern indexed by a 2-fold [1h10] pattern showing [111] as the growth direction. (b) TEM image of coherent twinning in GaP nanowires. (c) HRTEM image of the edge of the coherent twinning in the GaP nanowire specifically shown in Figure 3b. Several twinning boundaries are shown. (d) HRTEM image of an early grown InP nanowire grown along [111] direction with plane spacing of 0.340 nm. Single crystallinity was identified with lattice fringes. (e) HRTEM image of TSL in InP nanowires. Long-range superlattice periodicity is clearly identified. (f) Fourier-filtered HRTEM image of the TSL (dashed line box) shown in Figure 3e. The inset is a space-filling model of the twinning boundary. All the out surfaces are {111} surfaces.

the twinning boundaries that are obvious under this low magnification. A low-magnification image of a typical GaP wire grown with the gradient mid-zone profile is shown in Figure 2b. The magnified images from early, middle, and late growth are shown in Figure 2b-1, 2b-2, and 2b-3, respectively. In contrast to the GaP wire produced in the flat mid-zone profile, quasiperiodic coherent twinning is observed at the beginning of growth, as shown in the magnified image (Figure 2b-1). Parts 2b-2 and 2b-3 of Figure 2 are magnified images of the coherent twinning structure at intermediate and late growth, where larger period coherent twinning is observed. Nano Lett., Vol. 6, No. 12, 2006

In Figure 3 we show high-resolution TEM (HRTEM) images revealing the local order of GaP and InP grown with the flat mid-zone profile. Both of these wires start as single crystals and evolve to coherent twinning. They are observed to grow along the [111] direction (zinc-blende structure) under these conditions. In Figure 3a, the HRTEM image is from early GaP growth. The wire exhibits single-crystal growth. The inset to Figure 3a is a selected area diffraction (SAD) pattern from this region indexed as a 2-fold symmetric [1h10] pattern. The 〈111〉 lattice fringes in Figure 3a exhibit a spacing of 0.314 nm, the same as in the bulk.19 In Figure 3b, we display a lower magnification image of the same GaP wire in the middle of the coherent twinning region. Figure 2739

Figure 4. SAD patterns of TSLs in GaP and InP nanowires. (a) SAD pattern from the TSL in individual GaP nanowire shown in Figure 3b. The pattern shows rotational twins with [111] direction as a twin axis. (b) A magnified view of the SAD pattern indicated by the white box in Figure 3d. The white arrows indicate some of the spots diffracted from the twinning superlattice. (c) SAD pattern of the TSL in InP nanowire shown in Figure 3e. This pattern also shows rotational twins with [111] direction as a twin axis. (d) A magnified view of the SAD pattern indicated by the white box in Figure 4c. The white arrows highlight some of the spots diffracted from the twinning superlattice. The periodicity of superlattice in InP nanowires has a narrower distribution than that in GaP nanowires. So the SAD pattern shows more spots with more uniform intensity and distance (arrows) compared with the SAD shown in Figure 3e.

3c is a magnified view of several consecutive GaP quasiperiodic superlattice unit cells displayed at lower magnification than that shown in Figure 3b. Parts d-f of Figure 3 refer to InP growth with a flat midzone profile. In Figure 3d, we display an HRTEM image of early InP growth, where the single-crystal character is evident. Figure 3e refers to the same InP wire, but later in its growth where the coherent twinning occurs. A short period structural modification is evident in this figure. The dashed lines in the image (Figure 3e) indicate the boundaries inside of which we have carried out Fourier filtering to enhance the image quality. Results of this filtering are shown in Figure 3f, and the inset to Figure 3f shows a space-filling model of a twinning boundary along the [111] direction. The twinning boundary is perfectly perpendicular to the axial direction [111]. The 112h direction is in the plane of the figure; this vector flips by 180° as one crosses a twinning boundary. In Figure 4a and c, respectively, we show the selective area diffraction (SAD) patterns associated with coherent twinning in GaP and InP wires identified with diffraction from a ∼0.5-1.0 µm long segment of the wire that appear in Figure 3b,e. Both the SAD patterns (Figure 4a,c) can be indexed as a typical rotational twinning pattern with [111] as the twin axis.18,20 Unlike the SAD for single crystalline material (inset to Figure 3a), these two SAD patterns show the unambiguous character of a long-range twinning coherence (quasiperiodic twinning superlattice), i.e., they exhibit a series of additional distinct diffraction spots superimposed onto the [111] rotational twinning pattern. The diffraction structure associated with the coherent twinning is best seen by expanding the fine structure in the SAD pattern inside the white-outlined boxes, as shown in Figure 4b,d. The arrows highlight the superlattice diffraction spots. Their spacing leads to a superlattice unit cell length of ∼18.8 nm 2740

Figure 5. HRTEM images of the faceted nanowire twnning surfaces. (a) HRTEM image of twinning superlattice surface of GaP nanowires showing zigzag facets indicated by white lines. (b) HRTEM image of twinning superlattice surface of InP nanowires showing zigzag facets indicated by white lines. These planes highlighted in Figure 5a and b are identified to be {111} planes.

for the local twinning coherence in GaP (Figure 4a,b) and ∼11.0 nm for the TSL in InP (Figure 4c,d); these unit cell lengths are consistent with statistics on twin boundary spacings obtained by the careful study of many HRTEM images taken along the wire axis. It should be noted that the superlattice unit cell parameter is twice the distance between adjacent twin boundaries. The perfection of the local periodicity of the TSL in InP nanowires is better than observed for GaP nanowires, so the SAD pattern (Figure 4d) shows a larger series of better-defined diffraction spots. Interesting faceting of the wire surface is also observed and may be connected with the coherent twinning. This faceting correlates with the location of the twin boundaries, as can be seen in the HRTEM images for GaP (Figure 5a) and InP (Figure 5b). The white lines added to these images highlight the profile of the faceted surfaces, which are identified as {111} surfaces. It is well-known that the {111} surfaces of the zinc-blende structure have the lowest free energy compared with that of other surfaces. The cross section of our GaP and InP nanowires during TSL growth is therefore not cylindrical, and the modulation of the wire cross section during TSL growth region is defined by the family of {111} planes. It is worth mentioning here that periodic surface roughness in SNWs has been associated with the Raman activity of particular q-vector surface optic (SO) modes,21,22 and furthermore, in single-crystal nanowires, the dominant diameter modulation mechanism has been reported to be the instability of the diameter of the liquid droplet during growth.16,22 It is very interesting to examine the evolution of the local TSL period ξ along the wire length, where the local value of the period ξ is taken to be twice the distance d between adjacent twin boundaries (i.e., ξ ) 2d). Interestingly, we find that the evolution of ξ along the wire axis depends on the temperature profile in the growth zone. After a careful analysis of the TEM images of the two GaP nanowires shown in Figure 2, we located all of the twin boundaries and measured their spacing d. We can then plot the local value of the twin boundary density (1/d) vs the distance (L) of the twin boundary to the nanoparticle at the base of the nanowire. Our results are shown in Figure 6 for GaP nanowires grown Nano Lett., Vol. 6, No. 12, 2006

Figure 6. Statistics of twinning density in GaP nanowires, plotted as 1/d versus position (L in µm) of the twinning along the wire with respect to the grow tip. Top panel: wire (Figure 2a) grown with temperature profile no. 1. Bottom panel: wire (Figure 2b) grown with temperature profile no. 2. Thicker blue curves represent 10-point smoothing results. The dashed blue curves are the linear trends from a least-square fitting.

in the flat mid-zone profile (bottom panel) and gradient midzone profile (top panel). The data appear at first glance to be scattered about a linear trend whose slope depends on the temperature profile. However, this fluctuation in 1/d may not be random scatter. Further insight into this speculation may be obtained by carrying out a modest 10-point cubic smoothing of the data, i.e., a cubic spline, or Savitsky-Golay smoothing of the data.23 The outcome of this cubic spline is shown as the thicker blue curve superimposed over the raw data. The average linear trends are shown as dashed blue lines in the figures. As can be seen in the top and bottom panels of Figure 6, the linear trend and period of the oscillations depend on the nature of the mid-zone temperature profile; e.g., the slope of the trend and the average period of the smoothed oscillations in 1/d are both much larger for the nanowires grown in the gradient mid-zone profile. Our observations are consistent with recent statistics on microtwins in GaP nanowires, suggesting that thicker twinning bands form at lower temperature.11 Twinning has been carefully studied in the growth of large single crystals.24 For example, studies of Czochralski growth of III-V crystals concluded that the formation of twinned nuclei are thermodynamically favored at the three-phase boundary (for the VLS analog, see Figure 1a) when the undercooling (∆T ) Tm - T) was sufficiently high, where Tm is the melting temperature and T is the local temperature Nano Lett., Vol. 6, No. 12, 2006

at the liquid-solid interface.24 Thermodynamic models for this twinning have been explored.24 The result is that a thermal barrier is present and random thermal events are necessary that allow twin formation. However, in the present case (VLS growth of quasiperiodic twinning superlattice nanowires), we observe a coherent modulation of the structure over 500-1000 nm, as evidenced by superlattice diffraction. Thus, we are not observing the product of a random thermal process. Rather, we are observing a quasiperiodic oscillation of the 112h direction with time or distance down the nanowire. It seems to us that this structural modulation signals the presence of an oscillation in an important physical parameter in the droplet subsystem, at the phase liquid-solid boundary, or at the three-phase boundary (Figure 1a). A critical parameter to suspect in the twinning formation is the concentration Cs of the semiconductor in the liquid droplet. An oscillation of Cs, as determined by the relative rates of supply and depletion of semiconductor from the liquid droplet, may occur. A time-dependent value for Cs should be dependent on at least five factors: (1) the concentration of semiconductor in the vapor phase, (2) the sticking coefficient to the particle surface, and (3) the diffusion rate within the particle, (4) the intradroplet diffusion, and (5) the diffusion of semiconductor atoms across the liquid-solid boundary. If (4) and (5) are slow, then Cs increases. Factors (1, 2, 3) are on the supply side, i.e., a decrease in vapor pressure (1), sticking coefficient (2), or intraparticle diffusion tends to decrease Cs. Thus, depending on the balance and competing rates (dCs/dt) set up by factors (1-5), Cs can oscillate. The amount of metal in the droplet is assumed to be more or less fixed. Thus, the diameter of the liquid droplet also depends on Cs, and we therefore expect that the diameter of the particle can also oscillate. We speculate that it is the Cs-driven oscillation of the diameter of the Au semiconductor droplet that drives the flipping of the 112h vector in the nanowire and the twinning. In effect, the droplet may act like a regenerative oscillator, whose frequency depends on the details of the concentration dependence of the supply and depletion rates of semiconductor to the alloy droplet. A recent work on periodic twinning in ZnS nanowires also suggested that the periodicity is due to the intrinsic self-oscillating nature of VLS growth.10 On the other hand, the faceting may drive the twinning and the faceting may be driven by surface energetics.25 A periodic modulation in the diameter of Si whiskers along their growth axis was also observed and discussed by Givargizov many years ago. He noted that a microscopic mechanism of the VLS instability was needed that could, in general, generate positive feedback.26 They proposed that the driving force behind the diameter modulation was the supersaturation of the droplet.26 Recently, results of elegant in situ TEM studies of VLS growth of Si nanowires were presented.25 In this work, Ross et al. observed periodic faceting of the Si nanowires under carefully controlled conditions. However, they did not report twinning associated with the intersection of these facets. In their work, they stated that the driving force for the faceting was the surface 2741

energetics of the nanowire. In principle, they argued that any nanowire system with lower energy surfaces inclined to the growth direction could form periodic facets, such as we have observed in our III-V GaP and InP nanowires. It might also be concluded from our work, in conjunction with theirs,25 that periodic faceting is the phenomenon that drives the formation of coherent twinning (quasiperiodic twinning superlattice) in III-V nanowires and that the energy barrier for the twin boundary to form is much lower in the III-Vs than in the elemental semiconductor Si. In summary, we have observed coherent twinning phenomena in GaP and InP nanowires grown by vapor-liquidsolid mechanism. The coherence takes place over distances along the wire axis of ∼0.5-1 micron. We have observed that the twinning correlates with [111] faceting on the surface of the nanowires. The quasiperiodic structural modulation along the wire axis may be connected with a regenerative oscillation of the concentration Cs of the semiconductor in the alloy droplet as the result of competition between factors that tend to accumulate and deplete semiconductor in the droplet. It is not yet known how to connect faceting with the high-density twin formation, i.e., it may be the result of twinning, or it may be the cause. Further work, both theoretical and experimental, will be needed to provide the microscopic details necessary to explain the formation of coherent twinning by the VLS process. Our work, together with other recent works, suggests the possibility of future control over the period of the twinning superlattices. Acknowledgment. This work was supported by NFSNIRT (Nanotechnology and Interdisciplinary Research Initiative), grant DMR-0304178. We thank Mr. Y. Tang for producing the figure of the twin boundary. Supporting Information Available: Nanowire synthesis and transmission electron microscopy methods. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Sorrel, C. A.; Sandstorm, G. F. The Rocks and Minerals of the World; Collins: London, 1977. (2) Ikonic, Z.; Srivastava, G. P.; Inkson, J. C. Phys. ReV. B 1993, 48, 17181.

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NL0616983

Nano Lett., Vol. 6, No. 12, 2006