(Color online) Schematic diagrams of droplets formed for growth of XmYn (for example, XmYn ≡ GaN with X = Ga, Y = N, and m = n = 1) nanowires by the (a) vapor-solid-liquid (VLS) mechanism, (b) oxide-assisted growth (OAG) mechanism, (c) self-catalytic growth (SCG) mechanism, and (d) vapor-quasiliquid-solid or vapor-quasisolid-solid or vapor-semiliquid-solid or vapor-semisolid-solid (VQS) mechanism. For the OAG, X-oxide is actually Ga2O3 and oxygenated X droplet is the Ga droplet with a high concentration of oxygen atoms into it. The ZNS-substrate is generally silicon or sapphire substrate. For VLS nanowires, the angle θ between the droplet/nanowire interface and the droplet surface is smaller than 90°. For the OAG and the SCG nanowires, it is ∼90°. For the VQS nanowires it is smaller than 90°, but larger than that for the VLS nanowires. As depicted by arrows, a thin layer of interface states may exist between the droplet and the nanowire tip in the VLS and the VQS nanowires. This layer may actually be quasi-crystalline in which atoms may be reorganized (rearranged) without changes in the original crystal structure. This allows the nanowire to exhibit a certain growth direction. Even if the temperature of this layer is lower than the FECA/X eutectic temperature TE, it may still exist due to the interface melting effect. Unlike other nanowires, the OAG nanowires have almost always oxide sheath. The quality of these nanowires hinges on how effectively the oxide is segregated from the core to the peripheral surface of the droplet during growth.
(Color online) Variation of carrier mobility μ disl with the nanowire diameter dNW for various dislocation densities in Ge nanowires grown by the Au/Ge-mediated VLS mechanism.
(Color online) Variations of carrier mobilities μ ion, μ disl, μ dsin, μ dsac, and μ dsacin in Ge nanowires grown by the Au/Ge-mediated VLS mechanism as functions of (a) doping concentration and (b) temperature. Increase in mobility with increasing nanowire diameter was taken into consideration to model the carrier mobilities. Such an increase for mobility due to acoustic phonon scattering resulted from quantum confinement of electrons enlarging the electron-phonon deformation potential scattering. The nanowire diameter dNW = 10 nm used for the calculations was too large to have quantum confinement effect and dielectric confinement effect.
Some representative nanowires available in the literature (Refs. 74, 89, 91, and 92): (a) self-aligned InAs nanowires grown by the FECA ≡ Au mediated VLS mechanism on InAs (111)B substrate (reproduced with permission from L. E. Jensen, M. T. Bjork, S. Jeppesen, A. I. Persson, B. J. Ohlsson, and L. Samuelson, Nano Lett. 4, 1961 (2004). © 2004, American Chemical Society); (b) InP nanowires grown by VQS mechanism on Si (111) substrate employing X ≡ In (reproduced with permission L. Gao, R. L. Woo, B. Liang, M. Pozuelo, S. Prikhodko, M. Jackson, N. Goel, M. K. Hudait, D. L. Huffaker, M. S. Goorsky, S. Kodambaka, and R. F. Hicks, Nano Lett. 9, 2223 (2009). © 2009, American Chemical Society), (c) self-aligned InGaAs nanowires grown by the SCG mechanism on InP(111)B substrate employing X ≡ In (reproduced with permissions from J. Motohisa, J. Noborisaka, J. Takeda, M. Inari, and T. Fukui, J. Cryst. Growth 272, 180 (2004). © 2004, Elsevier), and (d) self-aligned InP nanowires grown by the SCG mechanism on InP(111)A substrate employing X ≡ In (reproduced with permissions from P. Mohan, J. Motohisa, and T. Fukui, Nanotechnology 16, 2903 (2005). © 2005, IOP Publishing Ltd.).
(Color online) Variation of minimum radius rmin of a Au/Ge droplet with the X at. % in it: (a) ξ is included in the formulation and (b) ξ is excluded from the formulation (e.g., Nx = Nx0, ξ = Nx/Nx0 = 1 and log(ξ) = 0). The droplets were not always the eutectic droplets. So, temperature corresponding to each Ge atomic % in Au/Ge droplet did not follow the binary phase diagram. At a temperature T, the effective chemical potential increases, and the minimum Au/Ge droplet dimension decreases, if the instantaneous Ge content in it exceeds the equilibrium Ge content of it. The radius rmin0 and hence rmin are smaller at higher T. Equation (B8) for rmin often erroneously makes use of the Boltzmann constant kB instead of the gas constant R.
(Color online) Variations of the adatom-induced growth rate GNWI of silicon nanowires with nanowire radius rD. (a) Au-mediated VLS growth; (b) self-catalytic growth. Size-dependent melting point depression (see Eq. (C1)) was taken into account for the calculations. The calculations made use of the surface energies σLS = 1.402 J/m2 for Au and σLS = 1.362 J/m2 for Si; the molar latent heat of melting Hseed = 36.96 kJ/mol for Au and Hseed = 50.55 kJ/mol for Si; the molar volume Ωseed = 13.6 cm3/mol for Au and Ωseed = 12.06 cm3/mol for Si; diameter of the spherical seed particle dseed = 2.92 Å for Au and dseed = 2.54 Å for Si; and seed density ρseed = 19.32 gm/cm3 for Au and ρseed = 2.33 gm/cm3 for Si. Increase in TB leads to higher increase in the self-catalyzed peak growth rate than in the VLS peak growth rate.
(Color online) Variations of the diffusion-induced growth rate GNWW of silicon nanowires with nanowire radius rD. (a) Au-mediated VLS growth; (b) self-catalytic growth. Size-dependent melting point depression (see Eq. (C7)) was taken into account for the calculations. The calculations made use of the surface energies σLS = 1.402 J/m2 for Au and σLS = 1.362 J/m2 for Si; the molar latent heat of melting Hseed = 36.96 kJ/mol for Au and Hseed = 50.55 kJ/mol for Si; the molar volume Ωseed = 13.6 cm3/mol for Au and Ωseed = 12.06 cm3/mol for Si; diameter of the spherical seed particle dseed = 2.92 Å for Au and dseed = 2.54 Å for Si; and seed density ρseed = 19.32 gm/cm3 for Au and ρseed = 2.33 gm/cm3 for Si. Increase in TB leads to an increase in the peak growth rate, but at higher temperature.
(Color online) Variations of (a) the droplet electrostatic field EL (at the Rayleigh limit) and (b) the droplet charge QL (at the Rayleigh limit) with the minimum radius rmin of the Au/Ge droplet. For calculations, both the FECA-mediated and FECA-free droplets were assumed to be spherical. Large curvature of these spherical droplets gives rise to large excess pressure driven by the surface tension. Even ionization of 1 in each 18 atoms on the droplet surface yields an electric field as high as 20 V/nm. The surface energy σLS and the dielectric constant ɛL of the Au/Ge droplet were obtained from Table II and Eqs. (1) and (4), respectively.
(Color online) Variation of Young’s modulus EMOD with diameter dNW of GaN nanowires. Various parameters used for the calculations are density of bulk GaN ρ NW = 6.16 g/cm−3, BNW = 1.875, and nanowire length LNW = 3 μm. (a) Defect-independent variation; (b) defect-dependent variation. Atomic coordination and cohesion are poor at the surface than at the bulk. Because of this, increase in the surface-to-volume ratio with decreasing dNW may also have contributed to decrease in EMOD with decreasing dNW. It may though be small as nanowires from hard metals (W, Ni) also show similar trend.
(Color online) Variation of Young’s modulus EMOD with external diameter dNT1 of GaN nanotubes. Various parameters used for the calculations are density of bulk GaN ρ NT = ρ NW = 6.16 g/cm−3, BNT = BNW = 1.875, and nanotube length LNT = 3 μm. Defect-dependent variations based on the formula (a) , (b) . Experiments indicate that presence of pinhole defects significantly reduces the elasticity of carbon nanotubes, and this reduction is higher for larger number of pinhole defects. The Young’s modulus also decreases with increasing surface-to-volume ratio indicating that both defect density and surface-atom cohesion dictate EMOD.
(Color online) Schematic diagrams of large arrays of seeds formed on the substrate surface for nanowire growths. (a) Arrays of seeds for adatom-induced growth; the arrows indicate the landing of the RS species on the tips of the seeds. (b) Arrays of seeds for diffusion-induced growth; the arrows indicate the impingement of the RS species on the substrate surface inside the collection region of each seed. Only five seeds of the arrays have been shown.
(Color online) Variation of self-aligned silicon nanowire growth rate GNWI by the adatom-induced process as a function of the seed-to-seed distance δ ss for three different values of (a) nanowire radius rD, (b) temperature T. The seeds constitute large arrays. Calculated GNWI decreases with increasing rD because the adatom adsorption coefficient α acoef on the droplet surface employed for the calculations was not designed to provide the RS atoms per nm2 as much for thick nanowire growth as for thin nanowire growth. If this is corrected, the calculated nanowire growth rate can also increase with increasing rD. Borgstrom et al. showed that depending on the availability of the RS species, the nanowire growth rate could indeed increase or decrease.
(Color online) Variation of self-aligned silicon nanowire growth rate GNWW by the diffusion-induced process as a function of the seed collection area radius δ ca for three different values of (a) nanowire radius rD, (b) temperature T. The seeds constitute large arrays. Calculated GNWW decreases with increasing rD because the adatom impingement rate on the substrate surface employed for the calculations was not designed to provide the RS atoms per nm2 as much for thick nanowire growth as for thin nanowire growth. If this is corrected, the calculated nanowire growth rate can also increase with increasing rD. Experiments show, depending on growth parameters, both increase and decrease in GNWW with increasing rD.
(Color online) Schematic diagrams of the (a) wurtzite and (b) zincblende structures in the lateral direction (reproduced with permission from M. Paladugu, J. Zou, Y. N. Guo, X. Zhang, H. J. Joyce, Q. Gao, H. H. Tan, C. Jagadish, and Y. Kim, Nanoscale Res. Lett. 4, 84 (2009). © 2009, Springer).
(Color online) Schematic diagrams of the cross-sectional surface of some representative seeds made of component seeds (CSDs): (a) seed with FECA/X CSDs at the peripheral surface and FECA CSDs at the core; (b) seed comprising FECA/X CSDs, but having domains of clustered-FECA CSDs; (c) seed comprising FECA/X CSDs at the peripheral surface, FECA CSDs at the core, and X-nanoparticle CSDs in between the core and the shell; (d) seed comprising FECA/X CSDs, clustered-FECA CSDs, and X-nanopaarticle CSDs; (e) seed comprising X-nanoparticle CSDs; and (f) seed comprising X-nanoparticle CSDs and oxygenated nanoparticle CSDs. CODs are the molten CSDs. These CODs may merge together to create a droplet.
(Color online) Schematic diagrams of six different wurtzite/zincblende structures: (a) core/shell structure with zincblende core and wurtzite shell; (b) purely wurtzite or zincblende structure; (c) planar zincblende defects in wurtzite nanowire running parallel to the nanowire length; (d) planar wurtzite defects in zincblende nanowire running parallel to the nanowire length; (e) wurtzite/zincblende superlattice structure vertically one above the other between the nanowire tip and the nanowire base; and (f) wurtzite/zincblende superlattice structure concentric with one another between the nanowire tip and the nanowire base.
Calculated variation of weighted vapor pressure ps/ps0 with the V/III ratio ξ rto for InAs nanowire during switch-on and switch-off of the RS ≡ In flow (flux) maintaining all other parameters, including the RS ≡ As flow (flux), unaltered.
(Color online) Calculated variation of weighted vapor pressure ps/ps0 with the V/III ratio ξ rto for InAs nanowire for (a) three different temperatures and (b) three different nanowire diameters. For all the curves, ξ rtopt = 100; ξ rto ≤ ξ rtopt. Also γsurf0 = 0.641 J/m2, M = 189.7396 gm/mol, ρseed = 5.68 gm/cm3, T0 = 300°C, ξ rto = 7, dseed = 50 nm, and d0 = 166 nm. With second term on the right hand side of Eq. (15) deleted, as in the Thompson equation, the variation of ps/ps0 with ξ rto becomes almost temperature independent. For example, with ξ rto = 100, ps/ps0 = 130, 125, and 121 for T = 300, 400, and 500°C, respectively.
(Color online) InAs nanowires grown on InAs seed. Variation of the weighted vapor pressure ps/ps0 with the seed diameter dseed for three different values of the surface energy γ surf0 of InAs seed. Various parameters used for the calculations are T = 400 °C, T0 = 300 °C, d0 = 166 nm, ξ rto = 5, M = 189.7396 g/mol, and ρ seed = 5.68 g/cm3.
Comparison of full-width-at-half-maximum (FWHM) of the most prominent photoluminescence peaks from some representative nanowires grown by various mechanisms.
List of various parameters used for the calculations.
List of various parameters used for the present calculations of nanowires growth rate and growth temperature.
Surface energy and melting point of some selected elements.
Values of the weighted vapor pressure ps/ps0 as functions of the parameters d0 and V/III ratio for different values of the seed diameter dseed. T = 400°C; γsurf0 = 0.641 J/m2.
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