Diameter control of gallium nitride nanowires

JOURNAL OF APPLIED PHYSICS 101, 094305 共2007兲

Diameter control of gallium nitride nanowires B. S. Simpkinsa兲 and P. E. Pehrsson Chemistry Division, Naval Research Laboratory, Washington, D.C. 20375

M. L. Taheri Chemistry, Materials, and Life Sciences, Lawrence Livermore National Laboratory, Livermore, California 94550

R. M. Stroud Materials Science and Technology Division, Naval Research Laboratory, Washington, D.C. 20375

共Received 6 November 2006; accepted 9 March 2007; published online 7 May 2007兲 Gallium nitride 共GaN兲 nanowires are grown with controlled diameter and position by combining electron-beam lithography and naturally occurring surface tension forces. Lithographically defined particle diameters were held constant while only the film thickness was varied. Annealing drives as-deposited metal disks toward hemispheres according to conservation of volume constraints, resulting in well-controlled catalyst particles with radii smaller than those of the as-deposited particles. Transmission electron microscopy and electron diffraction confirm that the nanowires are highly crystalline wurtzite GaN. The ability to structurally control the GaN nanowire size yields effective modulation of NW-FET conductivity. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2728782兴 I. INTRODUCTION

Structural and position control of semiconductor nanowires 共NWs兲 is becoming increasingly important as researchers fabricate nanowire-based electrical1,2 and optical3,4 structures and propose to investigate size-dependent quantum phenomena.5 Typically, metal catalyst particles are used to initiate NW growth through a vapor-liquid-solid6 共VLS兲 or vapor-solid-solid7,8 共VSS兲 mechanism, with catalyst particle size determining the final diameter of the nanowire.9 Although size-controlled nanoscale Au and Ag colloids are commercially available, the exclusive use of these particular metals limits the variety of NW materials that may be grown. For instance, some researchers have found Au to be an ineffective catalyst for the growth of gallium nitride 共GaN兲 NWs.10 Such NWs are strong candidates for optical applications in the high-visible and UV. The formation of discrete Ni particles by annealing a continuous Ni film occurs through a controllable thermally activated surface diffusion process.11 However, this approach does not result in controlled catalyst particle placement, which is one approach to overcoming the task of NW integration.12 It is therefore of great scientific and technological importance to develop a method for controlling catalyst particle size and position while retaining the freedom to use a wide variety of metals. Electron-beam lithography 共EBL兲 has previously been used to control the position of solution-based9 and solid catalysts12 but this technique has not yet been fully explored for controlling NW size. The current work describes a technique to control both catalyst placement and size by combining EBL with naturally occurring surface tension forces. The interfacial enera兲

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gies utilized in the previously described approach,11 in which discrete Ni particles form from continuous films, will be used to drive EBL-defined metal disks toward hemispheres of the same volume. The lower limit for reproducible feature size defined by EBL is tens of nanometers; however, evaporated film thicknesses can be controlled to ⬍1 nm, enabling very accurate control of the total catalyst particle volume. Thus, by varying deposited film thickness, one may control the final radii of the catalyst particles, and therefore, the final nanowire size. The size and microstructure of grown NWs will be evaluated, compared to analytical prediction, and their impact on electrical response determined. II. METHODOLOGY

Catalyst particles were deposited on SiO2 / Si substrates using electron-beam lithography 共EBL兲 and electron-beam metal evaporation. The catalyst metal 共permalloy; 80:20 Ni:Fe兲 was chosen as part of a separate study in which incorporation of Fe from the catalyst particle was evaluated as a compensator for the unintentional n-type doping typically found in GaN. This issue is still under investigation and will not be addressed in the current manuscript. Square arrays of permalloy catalyst dots were fabricated at dot separations of 2, 4, and 8 ␮m. The radius of the dots was fixed at ⬃50 nm while the evaporated metal thickness was varied from 5–43 nm. The initial catalyst particle height and radius were characterized with a Dimension 3100 atomic force microscope 共AFM兲 and a field emission LEO scanning electron microscope 共SEM兲, respectively. GaN nanowires were synthesized by placing solid Ga metal and the patterned SiO2 / Si substrates in a quartz tube furnace with the Ga located 100 mm upstream from the growth substrate. Growths were performed at 940 °C under 20 sccm NH3 at atmospheric pressure for 20 min. NW size and microstructure were evaluated with SEM and transmission electron microscopy 共TEM兲 with

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selected area electron diffraction 共SAED兲. As described elsewhere,13 wires were harvested and assembled into fieldeffect transistor 共FET兲 structures for electrical characterization. These devices were fabricated on 100 nm SiO2 on n+-Si, the latter of which served as a global back gate. The specific diameter control methodology is now described. Upon heating, thermally activated diffusion processes become substantial and surface energy provides a driving force for the as-deposited catalyst disks to form lower surface/volume structures. This mechanism has previously been used to form discrete Ni particles from continuous films11 and to “soften” the shape of triangular Ag particles prepared using nanosphere lithography for plasmonic applications.14 It is important to note that in Ref. 11 faceted Ni particles were formed from a thin film after only several minutes of annealing at 500 °C. Although the Ni was solid throughout this referenced procedure, solid-phase diffusion was sufficient to enable the morphology change. Our growth procedure includes a ramp to growth temperature 共50 °C/ min兲, where samples spend ⬃10 min at or above 500 °C, ensuring adequate time for particle shape evolution. Surface energy diminishes as a disk evolves into a hemisphere, but whether full transition to a sphere occurs depends on the relative energies of the particle-vapor and particle-substrate interfaces and the system kinetics. Both cases can be treated analytically and will be considered in comparison to experimental observations. The size of subsequently grown NWs will be determined by the final particle radius, R, and may be related to the initial disk radius and thickness through conservation of volume. If one assumes the final geometry to be a hemisphere, and ignores N incorporation due to its negligible solubility in Ni under these conditions,15 the final particle radius may be written as R=

冋冉 冊 冉

3 ⌾Ga ␳Ga hr2 1 + 2 ⌾NiFe ␳NiFe

冊册

1/3

,

共1兲

where h is the as-deposited disk thickness and r the initial disk radius, ⌾ is the molar fraction of the subscripted component in the alloy, and ␳ is the molar density of the subscripted component in units of cm3 / mol. If a spherical final geometry is assumed, the same functionality would be followed with the fraction 3/2 replaced by 3/4. Therefore, final catalyst particle size may be manipulated through control of the deposited film thickness. This approach may even enable the production of discrete nanoscale particles below the ultimate size limit of EBL features. III. RESULTS AND DISCUSSION

Catalyst particle preparation and evolution are illustrated in Fig. 1. A micrograph of as-deposited catalysts is presented in Fig. 1共a兲. Square arrays of catalyst particles were fabricated with dot pitches of 2, 4, and 8 ␮m, with full arrays measuring 100⫻ 100 ␮m2. The as-deposited particles 关inset of Fig. 1共a兲兴 had average measured radii of 50 nm. As illustrated in Fig. 1共b兲, each as-deposited catalyst particle is initially a disk with radius and thickness determined by the EBL exposure parameters and the deposited metal thickness, respectively. Upon heating, the catalyst particle evolves to-

FIG. 1. 共a兲 Array of as-deposited catalyst particles with inset showing an individual particle with ⬃50 nm radius. 共b兲 Schematic of particle evolution illustrating the effect of surface energies driving particle toward hemispherical shape.

ward a low surface/volume shape, such as the hemisphere pictured. Reactants are introduced into the chamber, leading to wire nucleation and growth. Substrates were prepared with catalyst disk thicknesses of 5, 8, 12, 24, and 43 nm, while the disk radius was fixed at 50 nm. SEM images of typical growth products for catalyst dot spacings of 2, 4, and 8 ␮m are shown in Figs. 2共a兲 and 2共b兲 and Figs. 2共c兲 and 2共d兲, respectively. GaN NW growth was strictly confined to the EBL-defined grids and so accomplished the first goal of this study: predictable management of NW position. Nanowire density was also effectively controlled through manipulation of catalyst particle density, further demonstrating the value of EBL for catalyst preparation. NWs were ⬃10 ␮m long and showed no tapering. There was no regular orientation of the wires with respect to the substrate due to the lack of epitaxial registry between the crystalline NWs and the amorphous SiO2 substrate. The random orientation of the NWs obfuscates the square array pattern of the catalyst particles. For this reason, and to clearly illustrate control of NW position, several catalyst particle locations have been marked with circles in Fig. 2共d兲 as an aid to the eye. Wires originate from these locations but grow in random directions. The critical role of the catalyst particle in initiating NW growth is confirmed by the inset of Fig. 2共c兲, which shows a metal catalyst particle at the end of a GaN NW. The aerial density of NWs was calculated from SEM images such as those shown in Fig. 2, and yielded a simple 1:1 ratio between lithographically defined catalyst particles and resulting NWs. This clearly demonstrated that EBL can be used to initiate the growth of single NWs with precise positional control. Catalyst shape and wire crystallography were investi-

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FIG. 3. 共a兲 TEM image of wire tip with hemispherical catalyst and 共inset兲 SAED pattern indexed to wurtzite GaN. 共b兲 High-resolution TEM image of lattice fringes indicating high crystalline quality.

of the film thicknesses studied. Measurements were taken from SEM images. Figure 4 shows average measured radii for wires grown from as-deposited catalyst disks with initial thicknesses of 5, 8, 12, 24, and 43 nm with error bars reflecting the standard deviations. These results establish that NW radius can be controlled, and that increased catalyst disk thickness yielded increased NW radius. We can now examine the possible mechanisms directing catalyst evolution and NW growth. The binary Ni-Ga phase diagram16 predicts the formation of a solid+ liquid alloy at 50 at % Ga and a complete liquid alloy at ⬃70 at % Ga at our growth temperatures. Although many researchers invoke the VLS growth FIG. 2. SEM images of typical GaN NWs grown from catalyst arrays with 共a兲 2, 共b兲 4, and 共c兲,共d兲 8 ␮m spacing. Inset of 共c兲 shows metallic catalyst particle at NW tip. Circles included in 共d兲 aid recognition of square array pattern which is obscured by random NW direction.

gated with TEM and electron diffraction. As shown in Fig. 3共a兲, the catalyst particles were hemispherical and confirmed that the catalyst disks do indeed undergo a shape transformation which reduces surface energy. The SAED pattern shown in the inset of Fig. 3共a兲 was taken at a position in the bulk of the wire and has been indexed to wurtzite GaN. SAED patterns recorded at several positions along single wires verified that the wires were single crystals with some wires exhibiting twinning defects. Figure 3共b兲 is a high-resolution TEM image taken from the bulk of a NW. Clearly visible lattice fringes revealed the excellent crystalline quality of these NWs. Detailed analysis of wire size distributions was carried out by measuring the radii of ⬃100 NWs grown from each

FIG. 4. Plot of NW radius vs as-deposited catalyst disk thickness. Error bars reflect standard deviation from ⬎100 measured NWs for each point. Following Eq. 共1兲, relationships for spherical final particle shape with no Ga content 共simple dashed兲, hemispherical final particle shape with no Ga 共solid兲, and 70 at % Ga content 共dash-dotted兲 are plotted.

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mechanism, several groups have identified a NW growth mechanism mediated by solid catalyst particles.7,8 Therefore, the functional relationship between as-deposited disk thickness and final particle radius, as described earlier in Eq. 共1兲, was plotted in Fig. 4 for three cases: spherical final particle shape with no Ga incorporation 共simple dashed兲, hemispherical final particle shape with no Ga incorporation 共solid兲, and hemispherical final particle shape with 70 at % Ga incorporation 共dash-dotted兲. There is strong agreement between the experimental data and the hemispherical model with no Ga incorporation. It is important to note that no fitting was done for this curve. The analytical relationship described in Eq. 共1兲 was directly plotted in Fig. 4 with the only input parameters being the initial disk radius as determined from SEM imaging and XGa = 0, i.e., assuming no Ga incorporation. The measured wire radii were slightly larger than this prediction, which was likely the result of increased catalyst particle size due to reactant incorporation. If one assumes a fully liquid catalyst particle occurring at the 70 at % Ga predicted by the bulk phase diagram, predicted wire sizes 共dash-dotted兲 are well above the experimental observations. Given the poor agreement between this model and the experimental results, it appears that either NW growth occurred through a solid catalyst mechanism or the catalyst particles experienced a melting point depression significantly larger than that predicted by the Gibbs-Thomson17 treatment 共⬃5% for our system兲. Significant deviation from the Gibbs-Thomson prediction has been reported elsewhere in the literature.18 The analytical expression describing a spherical final particle also shows poor agreement with experimental results. These results demonstrate that, not only can the final wire size be manipulated, but that this behavior follows a well-defined and predictable functional relationship. The agreement between the experimental data and the hemispherical model, as well as the TEM image in Fig. 3共a兲, strongly suggests that particle evolution stops at a hemisphere rather than continuing to a full sphere. This can be understood by considering that there will always be a decrease in surface energy as a particle changes from a disk to a hemisphere; however, whether additional energy is saved by forming a full sphere will depend on the relative surface energies of the particle-vapor and particle-substrate interfaces. The particle-substrate interfacial energy will depend on the local chemical and structural details which are not well-known and thus render a complete analytical treatment difficult. The current experimental evidence, however, consisting of direct TEM and SEM imaging and the clear agreement between experimental data and the hemispherical model, provide strong indication that the as-deposited disks evolve into a final hemispherical shape. Wire diameter affects a number of important optical and electrical properties. For instance, gate-induced depletion is significantly reduced with increasing wire radius due to the rapid increase in total charge and the small capacitance associated with this cylinder-plane system, as discussed elsewhere.13,19 The impact of NW diameter on gate-induced conductivity modulation is demonstrated in Fig. 5, which shows normalized conductivity as a function of gate bias for three NW-FETs. These results were normalized to the re-

FIG. 5. Plot of conductivity vs gate bias, Vg, for three NW-FETs fabricated from NWs with diameters of 115, 80, and 30 nm. Conductivity was recorded at Vsd = 1 V and normalized to maximum value, enabling direct comparison of depletion behavior.

sponse at Vg = + 40 V to facilitate direct comparison of conductivity modulation between the devices, since the raw source-drain conductivity of a thicker NW will be much higher due to the factors discussed above. All devices showed a reduction of current under negative gate bias, indicating that the majority carriers were electrons. The largest NW showed only ⬃4% conductivity modulation while the conductivity of the 80 nm NW was reduced by 30%. This is nearly an order of magnitude difference in conductivity modulation over the range of diameter control demonstrated earlier in this article. To further establish this point, Fig. 5 includes data for a 30 nm NW which showed nearly a 75% reduction in conductivity over the same gate bias range. The significant conductivity modulation of the smallest NW allowed extraction of the carrier density by fitting a line through the linear portion of this curve.20 This line was extended to zero conductivity to extract a threshold voltage of Vth = −58 V. Using established procedures relating Vth to carrier density,21 a carrier concentration of n ⬃ 4 ⫻ 1019 cm−3 was determined. Larger NWs generally show decreased modulation over the same gate bias range due to the greater amount of total charge within the wire. This result demonstrates the impact of NW diameter on the ability to effectively modulate NW conductivity, and also has implications for the ultimate utility of NW-FETs with similar carrier densities. In particular, the conductivity of NW-FETs based on thicker NW elements with high carrier densities may require excessively large turn-off voltages and will be less sensitive to surface chemical reaction, functionalization, and structural changes.22 IV. CONCLUSIONS

The growth of GaN NWs with both diameter and position control was established. Naturally occurring interfacial energy driving forces transformed as-deposited catalyst disks into hemispheres of the same volume. These acted as catalyst particles for the growth of GaN NWs. By varying the initial disk thickness, the particle volume, and hence the final particle size, was controlled. The size distribution of the resulting NWs corresponded very well to an analytical treatment

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assuming a hemispherical final particle shape. TEM results confirmed the presence of hemispherical catalyst particles and indicated that the NWs were high-quality single-crystal wurtzite GaN. NW size significantly affected the function of NW-FET devices. In particular, the ability to modulate NWFET conductivity was severely reduced for larger wires and may limit the ultimate usefulness of larger NWs with high carrier densities. These results highlight the critical need for NW diameter control if large-scale implementation of NWbased FET or other conductivity modulation-based devices such as chemical or biological sensors is to be developed. ACKNOWLEDGMENTS

This work was supported by the Naval Research Laboratory and the Office of Naval Research. This research was performed while B.S. Simpkins and M.L. Taheri held National Research Council Research Associateship Awards at the Naval Research Laboratory. Portions of this work were performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory, under Contract No. W-7405–Eng-48. 1

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