page_title: Vapor–liquid–solid method
section_title: Catalyst droplet formation
hierarchical_section_title: Vapor–liquid–solid method / Growth mechanism / Catalyst droplet formation
caption_attribution_description: English: Figure 4: Schematic illustration of metal-alloy catalyzed whisker growth depicting the catalyst droplet formation during the early stages of whisker growth. Русский: Figure 4: Schematic illustration of metal-alloy catalyzed whisker growth depicting the catalyst droplet formation during the early stages of whisker growth.
context_page_description: The vapor–liquid–solid method is a mechanism for the growth of one-dimensional structures, such as nanowires, from chemical vapor deposition. The growth of a crystal through direct adsorption of a gas phase on to a solid surface is generally very slow. The VLS mechanism circumvents this by introducing a catalytic liquid alloy phase which can rapidly adsorb a vapor to supersaturation levels, and from which crystal growth can subsequently occur from nucleated seeds at the liquid–solid interface. The physical characteristics of nanowires grown in this manner depend, in a controllable way, upon the size and physical properties of the liquid alloy.
context_section_description: 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:
   
  where r₀ is the radius of the contact area and β₀ is defined by a modified Young’s equation:
  ,
  It is dependent on the surface (σₛ) and liquid–solid interface (σₗₛ) 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:
  .
  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.
caption: Figure 4: Schematic illustration of metal-alloy catalyzed whisker growth depicting the catalyst droplet formation during the early stages of whisker growth.
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