^{1,a),b)}

### Abstract

Nanowires are grown by a variety of mechanisms, including vapor-liquid-solid, vapor-quasiliquid-solid or vapor-quasisolid-solid, oxide-assisted growth, and self-catalytic growth (SCG) mechanisms. A critical analysis of the suitability of self-catalyzed nanowires, as compared to other nanowires, for next-generation technology development has been carried out. Basic causes of superiority of self-catalyzed (SCG) nanowires over other nanowires have been described. Polytypism in nanowires has been studied, and a model for polytypism has been proposed. The model predicts polytypism in good agreement with available experiments. This model, together with various evidences, demonstrates lower defects, dislocations, and stacking faults in SCG nanowires, as compared to those in other nanowires. Calculations of carrier mobility due to dislocation scattering, ionized impurity scattering, and acoustic phonon scattering explain the impact of defects, dislocations, and stacking faults on carrier transports in SCG and other nanowires. Analyses of growth mechanisms for nanowiregrowth directions indicate SCG nanowires to exhibit the most controlled growth directions. In-depth investigation uncovers the fundamental physics underlying the control of growth direction by the SCG mechanism. Self-organization of nanowires in large hierarchical arrays is crucial for ultra large-scale integration (ULSI). Unique features and advantages of self-organized SCG nanowires, unlike other nanowires, for this ULSI have been discussed. Investigations of nanowire dimension indicate self-catalyzed nanowires to have better control of dimension, higher stability, and higher probability, even for thinner structures. Theoretical calculations show that self-catalyzed nanowires, unlike catalyst-mediated nanowires, can have higher growth rate and lower growth temperature. Nanowire and nanotube characteristics have been found also to dictate the performance of nanoelectromechanical systems. Defects, such as stacking faults, dislocations, and nanopipes, which are common in catalyst-mediated nanowires and nanotubes, adversely affect the efficiency of nanowire (nanotube) nanoelectro-mechanical devices. The influence of seed-to-seed distance and collection area radius on the self-catalyzed, self-aligned nanowiregrowths in large arrays of seeds has been examined. A hypothesis has been presented for this. The present results are in good agreement with experiments. These results suggest that the SCG nanowires are perhaps the best vehicles for revolutionary advancement of tomorrow’s nanotechnology.

The author wishes to thank the anonymous referee of the paper for constructive comments, criticisms, and suggestions. He is grateful to Albert Davydov, Arif Khan, Chip Eddy, Ron Carter, David Hernandez, and Pratul Ajmera for help. Crucial role of Maoqi He in the discovery of self-catalyzed nanowires in our laboratory is greatly acknowledged.

I. INTRODUCTION

II. NANOWIRE CHARACTERISTICS

A. Background

B. Basic causes of superiority of SCG nanowires over other nanowires

C. Lower defects, dislocations, and stacking faults in SCG nanowires

III. CONTROL OF GROWTH DIRECTION

A. Background

B. Inability of VLS and OAG nanowires to exhibit correct growth direction

C. Uniqueness of growth direction of the SCG nanowires

IV. CONTROL OF NANOWIRE POSITION

A. Background

B. Substrate characteristics for nanowire self-organization

C. Basic science underlying SCG nanowire self-organization

D. Advantages of self-organized SCG nanowires

V. CONTROL OF NANOWIRE DIMENSION

VI. NANOWIREGROWTH RATE AND GROWTH TEMPERATURE

VII. SELF-CATALYZED DROPLETS ARE MORE STABLE THAN FECA-MEDIATED DROPLETS

VIII. NANOELECTROMECHANICAL PROPERTIES

IX. SELF-ALIGNMENT OF LARGE-SCALE VERTICAL NANOWIRE ARRAYS

A. Guideline and hypothesis for adatom-induced growth

B. Guideline and hypothesis for diffusion-induced growth

C. Demonstration for adatom-induced growth

D. Demonstration for diffusion-induced growth

X. OSTWALD RIPENING

XI. NANOWIREHETEROSTRUCTURES

XII. POLYTYPISM

A. Background

B. Basic principles dictating polytypism

C. Creation of high-surface-energy, moderate-surface-energy, and low-surface-energy regions in seed

D. Ground rule

E. Creation of modulated structures

F. Experimental evidences of structural inhomogeneity of seeds

G. Evidential demonstration of polytypism

H. Diameter dependence of polytypism

XIII. DISCUSSIONS

XIV. CONCLUSIONS

### Key Topics

- Nanowires
- 547.0
- Fluid drops
- 163.0
- III-V semiconductors
- 81.0
- Chemical vapor deposition
- 63.0
- Semiconductor growth
- 55.0

## Figures

(Color online) Schematic diagrams of droplets formed for growth of X_{m}Y_{n} (for example, X_{m}Y_{n} ≡ 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 Ga_{2}O_{3} 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 T_{E}, 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) Schematic diagrams of droplets formed for growth of X_{m}Y_{n} (for example, X_{m}Y_{n} ≡ 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 Ga_{2}O_{3} 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 T_{E}, 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 d_{NW} for various dislocation densities in Ge nanowires grown by the Au/Ge-mediated VLS mechanism.

(Color online) Variation of carrier mobility *μ* _{disl} with the nanowire diameter d_{NW} 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 d_{NW} = 10 nm used for the calculations was too large to have quantum confinement effect and dielectric confinement effect.

(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 d_{NW} = 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.).

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 r_{min} 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., N_{x} = N_{x0}, ξ = N_{x}/N_{x0} = 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 r_{min0} and hence r_{min} are smaller at higher T. Equation (B8) for r_{min} often erroneously makes use of the Boltzmann constant k_{B} instead of the gas constant R.

(Color online) Variation of minimum radius r_{min} 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., N_{x} = N_{x0}, ξ = N_{x}/N_{x0} = 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 r_{min0} and hence r_{min} are smaller at higher T. Equation (B8) for r_{min} often erroneously makes use of the Boltzmann constant k_{B} instead of the gas constant R.

(Color online) Variations of the adatom-induced growth rate G_{NWI} of silicon nanowires with nanowire radius r_{D}. (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 σ_{LS} = 1.402 J/m^{2} for Au and σ_{LS} = 1.362 J/m^{2} for Si; the molar latent heat of melting H_{seed} = 36.96 kJ/mol for Au and H_{seed} = 50.55 kJ/mol for Si; the molar volume Ω_{seed} = 13.6 cm^{3}/mol for Au and Ω_{seed} = 12.06 cm^{3}/mol for Si; diameter of the spherical seed particle d_{seed} = 2.92 Å for Au and d_{seed} = 2.54 Å for Si; and seed density ρ_{seed} = 19.32 gm/cm^{3} for Au and ρ_{seed} = 2.33 gm/cm^{3} for Si. Increase in T_{B} leads to higher increase in the self-catalyzed peak growth rate than in the VLS peak growth rate.

(Color online) Variations of the adatom-induced growth rate G_{NWI} of silicon nanowires with nanowire radius r_{D}. (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 σ_{LS} = 1.402 J/m^{2} for Au and σ_{LS} = 1.362 J/m^{2} for Si; the molar latent heat of melting H_{seed} = 36.96 kJ/mol for Au and H_{seed} = 50.55 kJ/mol for Si; the molar volume Ω_{seed} = 13.6 cm^{3}/mol for Au and Ω_{seed} = 12.06 cm^{3}/mol for Si; diameter of the spherical seed particle d_{seed} = 2.92 Å for Au and d_{seed} = 2.54 Å for Si; and seed density ρ_{seed} = 19.32 gm/cm^{3} for Au and ρ_{seed} = 2.33 gm/cm^{3} for Si. Increase in T_{B} 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 G_{NWW} of silicon nanowires with nanowire radius r_{D}. (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 σ_{LS} = 1.402 J/m^{2} for Au and σ_{LS} = 1.362 J/m^{2} for Si; the molar latent heat of melting H_{seed} = 36.96 kJ/mol for Au and H_{seed} = 50.55 kJ/mol for Si; the molar volume Ω_{seed} = 13.6 cm^{3}/mol for Au and Ω_{seed} = 12.06 cm^{3}/mol for Si; diameter of the spherical seed particle d_{seed} = 2.92 Å for Au and d_{seed} = 2.54 Å for Si; and seed density ρ_{seed} = 19.32 gm/cm^{3} for Au and ρ_{seed} = 2.33 gm/cm^{3} for Si. Increase in T_{B} leads to an increase in the peak growth rate, but at higher temperature.

(Color online) Variations of the diffusion-induced growth rate G_{NWW} of silicon nanowires with nanowire radius r_{D}. (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 σ_{LS} = 1.402 J/m^{2} for Au and σ_{LS} = 1.362 J/m^{2} for Si; the molar latent heat of melting H_{seed} = 36.96 kJ/mol for Au and H_{seed} = 50.55 kJ/mol for Si; the molar volume Ω_{seed} = 13.6 cm^{3}/mol for Au and Ω_{seed} = 12.06 cm^{3}/mol for Si; diameter of the spherical seed particle d_{seed} = 2.92 Å for Au and d_{seed} = 2.54 Å for Si; and seed density ρ_{seed} = 19.32 gm/cm^{3} for Au and ρ_{seed} = 2.33 gm/cm^{3} for Si. Increase in T_{B} leads to an increase in the peak growth rate, but at higher temperature.

(Color online) Variations of (a) the droplet electrostatic field E_{L} (at the Rayleigh limit) and (b) the droplet charge Q_{L} (at the Rayleigh limit) with the minimum radius r_{min} 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 σ_{LS} and the dielectric constant ɛ_{L} of the Au/Ge droplet were obtained from Table II and Eqs. (1) and (4), respectively.

(Color online) Variations of (a) the droplet electrostatic field E_{L} (at the Rayleigh limit) and (b) the droplet charge Q_{L} (at the Rayleigh limit) with the minimum radius r_{min} 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 σ_{LS} and the dielectric constant ɛ_{L} of the Au/Ge droplet were obtained from Table II and Eqs. (1) and (4), respectively.

(Color online) Variation of Young’s modulus E_{MOD} with diameter d_{NW} of GaN nanowires. Various parameters used for the calculations are density of bulk GaN *ρ* _{NW} = 6.16 g/cm^{−3}, B_{NW} = 1.875, and nanowire length L_{NW} = 3 *μ*m. (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 d_{NW} may also have contributed to decrease in E_{MOD} with decreasing d_{NW}. It may though be small as nanowires from hard metals (W, Ni) also show similar trend.

(Color online) Variation of Young’s modulus E_{MOD} with diameter d_{NW} of GaN nanowires. Various parameters used for the calculations are density of bulk GaN *ρ* _{NW} = 6.16 g/cm^{−3}, B_{NW} = 1.875, and nanowire length L_{NW} = 3 *μ*m. (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 d_{NW} may also have contributed to decrease in E_{MOD} with decreasing d_{NW}. It may though be small as nanowires from hard metals (W, Ni) also show similar trend.

(Color online) Variation of Young’s modulus E_{MOD} with external diameter d_{NT1} of GaN nanotubes. Various parameters used for the calculations are density of bulk GaN *ρ* _{NT} = *ρ* _{NW} = 6.16 g/cm^{−3}, B_{NT} = B_{NW} = 1.875, and nanotube length L_{NT} = 3 *μ*m. 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 E_{MOD}.

(Color online) Variation of Young’s modulus E_{MOD} with external diameter d_{NT1} of GaN nanotubes. Various parameters used for the calculations are density of bulk GaN *ρ* _{NT} = *ρ* _{NW} = 6.16 g/cm^{−3}, B_{NT} = B_{NW} = 1.875, and nanotube length L_{NT} = 3 *μ*m. 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 E_{MOD}.

(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 R_{S} species on the tips of the seeds. (b) Arrays of seeds for diffusion-induced growth; the arrows indicate the impingement of the R_{S} species on the substrate surface inside the collection region of each seed. Only five seeds of the arrays have been shown.

(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 R_{S} species on the tips of the seeds. (b) Arrays of seeds for diffusion-induced growth; the arrows indicate the impingement of the R_{S} 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 G_{NWI} by the adatom-induced process as a function of the seed-to-seed distance *δ* _{ss} for three different values of (a) nanowire radius r_{D}, (b) temperature T. The seeds constitute large arrays. Calculated G_{NWI} decreases with increasing r_{D} because the adatom adsorption coefficient *α* _{acoef} on the droplet surface employed for the calculations was not designed to provide the R_{S} atoms per nm^{2} 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 r_{D}. Borgstrom *et al.* showed that depending on the availability of the R_{S} species, the nanowire growth rate could indeed increase or decrease.

(Color online) Variation of self-aligned silicon nanowire growth rate G_{NWI} by the adatom-induced process as a function of the seed-to-seed distance *δ* _{ss} for three different values of (a) nanowire radius r_{D}, (b) temperature T. The seeds constitute large arrays. Calculated G_{NWI} decreases with increasing r_{D} because the adatom adsorption coefficient *α* _{acoef} on the droplet surface employed for the calculations was not designed to provide the R_{S} atoms per nm^{2} 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 r_{D}. Borgstrom *et al.* showed that depending on the availability of the R_{S} species, the nanowire growth rate could indeed increase or decrease.

(Color online) Variation of self-aligned silicon nanowire growth rate G_{NWW} by the diffusion-induced process as a function of the seed collection area radius *δ* _{ca} for three different values of (a) nanowire radius r_{D}, (b) temperature T. The seeds constitute large arrays. Calculated G_{NWW} decreases with increasing r_{D} because the adatom impingement rate on the substrate surface employed for the calculations was not designed to provide the R_{S} atoms per nm^{2} 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 r_{D}. Experiments show, depending on growth parameters, both increase and decrease in G_{NWW} with increasing r_{D}.

(Color online) Variation of self-aligned silicon nanowire growth rate G_{NWW} by the diffusion-induced process as a function of the seed collection area radius *δ* _{ca} for three different values of (a) nanowire radius r_{D}, (b) temperature T. The seeds constitute large arrays. Calculated G_{NWW} decreases with increasing r_{D} because the adatom impingement rate on the substrate surface employed for the calculations was not designed to provide the R_{S} atoms per nm^{2} 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 r_{D}. Experiments show, depending on growth parameters, both increase and decrease in G_{NWW} with increasing r_{D}.

(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 (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 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.

(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 p_{s}/p_{s0} with the V/III ratio *ξ* _{rto} for InAs nanowire during switch-on and switch-off of the R_{S} ≡ In flow (flux) maintaining all other parameters, including the R_{S} ≡ As flow (flux), unaltered.

Calculated variation of weighted vapor pressure p_{s}/p_{s0} with the V/III ratio *ξ* _{rto} for InAs nanowire during switch-on and switch-off of the R_{S} ≡ In flow (flux) maintaining all other parameters, including the R_{S} ≡ As flow (flux), unaltered.

(Color online) Calculated variation of weighted vapor pressure p_{s}/p_{s0} 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 γ_{surf0} = 0.641 J/m^{2}, M = 189.7396 gm/mol, ρ_{seed} = 5.68 gm/cm^{3}, T_{0} = 300°C, *ξ* _{rto} = 7, d_{seed} = 50 nm, and d_{0} = 166 nm. With second term on the right hand side of Eq. (15) deleted, as in the Thompson equation, the variation of p_{s}/p_{s0} with *ξ* _{rto} becomes almost temperature independent. For example, with *ξ* _{rto} = 100, p_{s}/p_{s0} = 130, 125, and 121 for T = 300, 400, and 500°C, respectively.

(Color online) Calculated variation of weighted vapor pressure p_{s}/p_{s0} 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 γ_{surf0} = 0.641 J/m^{2}, M = 189.7396 gm/mol, ρ_{seed} = 5.68 gm/cm^{3}, T_{0} = 300°C, *ξ* _{rto} = 7, d_{seed} = 50 nm, and d_{0} = 166 nm. With second term on the right hand side of Eq. (15) deleted, as in the Thompson equation, the variation of p_{s}/p_{s0} with *ξ* _{rto} becomes almost temperature independent. For example, with *ξ* _{rto} = 100, p_{s}/p_{s0} = 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 p_{s}/p_{s0} with the seed diameter d_{seed} for three different values of the surface energy *γ* _{surf0} of InAs seed. Various parameters used for the calculations are T = 400 °C, T_{0} = 300 °C, d_{0} = 166 nm, *ξ* _{rto} = 5, M = 189.7396 g/mol, and *ρ* _{seed} = 5.68 g/cm^{3}.

(Color online) InAs nanowires grown on InAs seed. Variation of the weighted vapor pressure p_{s}/p_{s0} with the seed diameter d_{seed} for three different values of the surface energy *γ* _{surf0} of InAs seed. Various parameters used for the calculations are T = 400 °C, T_{0} = 300 °C, d_{0} = 166 nm, *ξ* _{rto} = 5, M = 189.7396 g/mol, and *ρ* _{seed} = 5.68 g/cm^{3}.

## Tables

Comparison of full-width-at-half-maximum (FWHM) of the most prominent photoluminescence peaks from some representative nanowires grown by various mechanisms.

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 calculations.

List of various parameters used for the present calculations of nanowires growth rate and growth temperature.

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.

Surface energy and melting point of some selected elements.

Values of the weighted vapor pressure p_{s}/p_{s0} as functions of the parameters d_{0} and V/III ratio for different values of the seed diameter d_{seed}. T = 400°C; γ_{surf0} = 0.641 J/m^{2}.

Values of the weighted vapor pressure p_{s}/p_{s0} as functions of the parameters d_{0} and V/III ratio for different values of the seed diameter d_{seed}. T = 400°C; γ_{surf0} = 0.641 J/m^{2}.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content