## Thermodynamics of Chemical Reactions: Growing Si Nanowires

One of the cool things that an understanding of reaction equilibrium allows us to do is to manipulate the chemical potential of one of the species by controlling that of the other species that participate in a reaction. For example, when this reaction,

$\nu_{A}A + \nu_{B}B = \nu_{C} C \;,$

reaches equilibrium, the following condition holds:

$\nu_C \mu_C - \nu_A \mu_A - \nu_B \mu_B = 0 \, .$

This allows us to control the chemical potential of A, say, by controlling those of B and C; one of the reasons why the latter might be easy is that B and C might be gaseous species, and controlling their chemical potentials is through controlling the temperature, pressure and gas composition in the reaction chamber.

This principle is used in growth of Si nanowires through a process called Vapor-Liquid-Solid (VLS) method (see the Wikipedia entry), in which Si gets into fine (nano!) gold droplets from the gas phase, and makes its way down the droplet to join the Si substrate that lies just underneath the droplet.

In the vapor phase, the reaction is the following:

$\textrm{SiCl}_{2} + 2 \textrm{H}_{2} \rightarrow \textrm{Si} + 4 \textrm{HCL}$

All except Si are in their gaseous state. By controlling the gas composition, one controls $\mu_{Si}$ to a value well above that required for solubility of Si, allowing Si to enter the droplets, making them supersaturated solutions of Si in gold. The second part — diffusion of Si through the droplet to reach the Si underneath — is straight-forward.

I think it’s a great example of Clarke’s third law:

Any sufficiently advanced technology is indistinguishable from magic.

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Check out this paper by Guo et al on InGaAs nanowires grown using a similar method.