Vapor–liquid–solid method

• Greatly lowered reaction energy compared to normal vapor-solid growth.
• Wires grow only in the areas activated by the metal catalysts and the size and position of the wires are determined by that of the metal catalysts.
• This growth mechanism can also produce highly anisotropic nanowire arrays from a variety of material.

The requirements for catalysts are:[3]

• It must form a liquid solution with the crystalline material to be grown at the nanowire growth temperature.
• The solid solubility of the catalyzing agent is low in the solid and liquid phases of the substrate material.
• The equilibrium vapor pressure of the catalyst over the liquid alloy must be small so that the droplet does not vaporize, shrink in volume (and therefore radius), and decrease the radius of the growing wire until, ultimately, growth is terminated.
• The catalyst must be inert (non-reacting) to the reaction products (during CVD nanowire growth).
• The vapor–solid, vapor–liquid, and liquid–solid interfacial energies play a key role in the shape of the droplets and therefore must be examined before choosing a suitable catalyst; small contact angles between the droplet and solid are more suitable for large area growth, while large contact angles result in the formation of smaller (decreased radius) whiskers.
• The solid-liquid interface must be well-defined crystallographically in order to produce highly directional growth of nanowires. It is also important to point out that the solid-liquid interface cannot, however, be completely smooth. Furthermore, if the solid liquid interface was atomically smooth, atoms near the interface trying to attach to the solid would have no place to attach to until a new island nucleates (atoms attach at step ledges), leading to an extremely slow growth process. Therefore, “rough” solid surfaces, or surfaces containing a large number of surface atomic steps (ideally 1 atom wide, for large growth rates) are needed for deposited atoms to attach and nanowire growth to proceed.

Figure 4: Schematic illustration of metal-alloy catalyzed whisker growth depicting the catalyst droplet formation during the early stages of whisker growth.

The materials system used, as well as the cleanliness of the vacuum system and therefore the amount of contamination and/or the presence of oxide layers at the droplet and wafer surface during the experiment, both greatly influence the absolute magnitude of the forces present at the droplet/surface interface and, in turn, determine the shape of the droplets. The shape of the droplet, i.e. the contact angle (β₀, see Figure 4) can, be modeled mathematically, however, the actual forces present during growth are extremely difficult to measure experimentally. Nevertheless, the shape of a catalyst particle at the surface of a crystalline substrate is determined by a balance of the forces of surface tension and the liquid–solid interface tension. The radius of the droplet varies with the contact angle as:

${\displaystyle R={\frac {r_{\mathrm {o} }}{\sin(\beta _{\mathrm {o} })}},}$

where r₀ is the radius of the contact area and β₀ is defined by a modified Young’s equation:

${\displaystyle \sigma _{\mathrm {1} }\cos(\beta _{\mathrm {o} })=\sigma _{\mathrm {s} }-\sigma _{\mathrm {ls} }-{\frac {\tau }{r_{\mathrm {o} }}}}$,

It is dependent on the surface (σ_s) and liquid–solid interface (σ_ls) tensions, as well as an additional line tension (τ) which comes into effect when the initial radius of the droplet is small (nanosized). As a nanowire begins to grow, its height increases by an amount dh and the radius of the contact area decreases by an amount dr (see Figure 4). As the growth continues, the inclination angle at the base of the nanowires (α, set as zero before whisker growth) increases, as does β₀:

${\displaystyle \sigma _{\mathrm {1} }\cos(\beta _{\mathrm {o} })=\sigma _{\mathrm {s} }\cos(\alpha )-\sigma _{\mathrm {ls} }-{\frac {\tau }{r_{\mathrm {o} }}}}$.

The line tension therefore greatly influences the catalyst contact area. The most import result from this conclusion is that different line tensions will result in different growth modes. If the line tensions are too large, nanohillock growth will result and thus stop the growth.

The diameter of the nanowire which is grown depends upon the properties of the alloy droplet. The growth of nano-sized wires requires nano-size droplets to be prepared on the substrate. In an equilibrium situation this is not possible as the minimum radius of a metal droplet is given by[4]

${\displaystyle R_{\mathrm {min} }={\frac {2V_{l}}{RTln(s)}}\sigma _{lv}\,}$

where V_l is the molar volume of the droplet, σ_lv the liquid-vapor surface energy, and s is the degree of supersaturation[5] of the vapor. This equations restricts the minimum diameter of the droplet, and of any crystals which can be grown from it, under typically conditions to well above the nanometer level. Several techniques to generate smaller droplets have been developed, including the use of monodispersed nanoparticles spread in low dilution on the substrate, and the laser ablation of a substrate-catalyst mixture so to form a plasma which allows well-separated nanoclusters of the catalyst to form as the systems cools.[6]

During VLS whisker growth, the rate at which whiskers grow is dependent on the whisker diameter: the larger the whisker diameter, the faster the nanowire grows axially. This is because the supersaturation of the metal-alloy catalyst (${\displaystyle \Delta \mu }$) is the main driving force for nanowhisker growth and decreases with decreasing whisker diameter (also known as the Gibbs-Thomson effect):

${\displaystyle \Delta \mu =\Delta \mu _{\mathrm {o} }-{\frac {4\alpha \Omega }{d}}}$.

Again, Δµ is the main driving force for nanowhisker growth (the supersaturation of the metal droplet). More specifically, Δµ₀ is the difference between the chemical potential of the depositing species (Si in the above example) in the vapor and solid whisker phase. Δµ₀ is the initial difference proceeding whisker growth (when ${\displaystyle d\rightarrow \infty }$), while ${\displaystyle \Omega }$ is the atomic volume of Si and ${\displaystyle \alpha }$ the specific free energy of the wire surface. Examination of the above equation, indeed reveals that small diameters (${\displaystyle <}$100 nm) exhibit small driving forces for whisker growth while large wire diameters exhibit large driving forces.

Figure 6:One possible configuration of a PLD deposition chamber.

Involves the removal of material from metal-containing solid targets by irradiating the surface with high-powered (~100 mJ/pulse) short (10 Hz) laser pulses, usually with wavelengths in the ultraviolet (UV) region of the light spectrum. When such a laser pulse is adsorbed by a solid target, material from the surface region of the target absorbs the laser energy and either (a) evaporates or sublimates from the surface or is (b) converted into a plasma (see laser ablation). These particles are easily transferred to the substrate where they can nucleate and grow into nanowires. The laser-assisted growth technique is particularly useful for growing nanowires with high melting temperatures, multicomponent or doped nanowires, as well as nanowires with extremely high crystalline quality. The high intensity of the laser pulse incident at the target allows the deposition of high melting point materials, without having to try to evaporate the material using extremely high temperature resistive or electron bombardment heating. Furthermore, targets can simply be made from a mixture of materials or even a liquid. Finally, the plasma formed during the laser absorption process allows for the deposition of charged particles as well as a catalytic means to lower the activation barrier of reactions between target constituents.

Some very interesting nanowires microstructures can be obtained by simply thermally evaporating solid materials. This technique can be carried out in a relatively simple setup composed of a dual-zone vacuum furnace. The hot end of the furnace contains the evaporating source material, while the evaporated particles are carrier downstream, (by way of a carrier gas) to the colder end of the furnace where they can absorb, nucleate, and grow on a desired substrate.

Molecular beam epitaxy (MBE) has been used since 2000 to create high-quality semiconductor wires based on the VLS growth mechanism. However, in metal-catalyzed MBE the metal particles do not catalyze a reaction between precursors but rather adsorb vapor phase particles. This is because the chemical potential of the vapor can be drastically lowered by entering the liquid phase.

MBE is carried out under ultra-high vacuum (UHV) conditions where the mean-free-path (distance between collisions) of source atoms or molecules is on the order of meters. Therefore, evaporated source atoms (from, say, an effusion cell) act as a beam of particles directed towards the substrate. The growth rate of the process is very slow, the deposition conditions are very clean, and as a result four superior capabilities arise, when compared to other deposition methods:

• UHV conditions minimize the amount of oxidation/contamination of the growing structures
• Relatively low growth temperatures prevent interdiffusion (mixing) of nano-sized heterostructures
• Very thin-film analysis techniques can be used in-situ (during growth), such as reflection high energy electron diffraction (RHEED) to monitor the microstructure at the surface of the substrate as well as the chemical composition, using Auger electron spectroscopy.