# Kris's Research Notes

## September 15, 2011

### Nanowires, Part 4: Mixing

Filed under: Nanowire — Kris Reyes @ 6:16 am

Recall in the previous post, we observed a significant amount of mixing of the solid phase as the nanowire grew. This mixing is mostly a result of liquid B atoms diffusing through the A material quickly. This is probably not physical and hence we wish to control the amount of atom-atom exchanges within the solid. In this note, we describe how to do this and its effect on the growth of the nanowire. We also study how deposition rate and droplet size changes the growth mode.

The relevant parameter that controls exchanges in the bulk of the solid is $\gamma_{HH}$, which serves a penalty term for atom-atom exchanges not inside a liquid neighborhood. The more negative it is, the harder it is for atoms to exchange. As described in the previous post, fixing all other energies $\gamma_{AA}, \gamma_{AB}, \gamma_{BB}, \lambda_S, \lambda_D$, varying $\gamma_{HH}$ is equivalent to varying $\epsilon_I$ by the equation:

$\gamma_{HH} = 3\gamma_{AB} - \gamma_{AA} - \gamma_{BB} - \lambda_D - \epsilon_I$.

Therefore if we wish to discourage mixing by making $\gamma_{HH}$ more negative, we equivalently increase $\epsilon_I$. This implies a slower nucleation rate at the liquid/solid interface. This is entirely artificial. This is due to how we define a liquid neighborhood. Those atoms (both A and B atoms) at the liquid/solid interface are not considered within a liquid neighborhood. (More on this in later posts.)

## Deposition rate 1 monolayer/second

We simulate nanowire growth with energy parameters $\gamma_{AA} = 0.5$ eV, $\gamma_{BB} = 0.4$ eV, $\gamma_{AB} = 0.35$ eV, and liquid barriers $\lambda_D = \lambda_S = 0.7$ eV (i.e. $\epsilon_D = \epsilon_S = 0$). Initially, a droplet of material B of radius 16 atoms sits on a substrate of material A. Then, A atoms are deposited at a rate of 1 monolayer/second at 600K. The desorption potential of A atoms is set to 0.045 eV so that there is an equilibrium between solid and vapor phases of A.

We then vary $\gamma_{HH} = -0.55, -0.65, ..., -0.95$ eV (equiv. $\epsilon_I = 0.0, 0.1, 0.2, 0.3, 0.4$). For each choice of $\gamma_{HH}$, we run 16 independent trials. Here are results (deposited A material is colored as a function of time):

### $\gamma_{HH} = -0.95$ eV

Note: as $\gamma_{HH}$ becomes more negative, we do indeed see less mixing in the A material. For $\gamma_{HH}$ small in absolute value (e.g. $\gamma_{HH} = -0.55$ eV), nanowires grow perpendicular to the substrate. But as $\gamma_{HH}$ decreases, the simulated nanowires tilt until they grow laterally along the substrate. (Note, due to periodic boundary conditions, those nanowires growing along the substrate eventually intersect themselves.)

## Deposition rate 0.1 monolayers/second

We repeat the above experiment, but deposit A at a rate of 0.1 monolayer/second. In order to maintain an equilibrium between solid and vapor phases, we set $\mu_A = 0.165$ eV. Here are the results as we vary $\gamma_{HH}$:

### $\gamma_{HH} = -0.95$ eV

Interestingly, we do not see nanowire growth for $\gamma_{HH} = -0.55$ eV. At $\gamma_{HH} = -0.65, -0.75$ eV, we do see some nanowires which attempt to grow oblique from the substrate. For more negative $\gamma_{HH}$, we again see lateral growth. For a better understanding of what occurs when $\gamma_{HH} = -0.55$ eV to prevent nanowire formation, we examine one simulation run:

We see the mixing causes the deposited A material to diffuse sufficiently away from the droplet that a base can never form. Indeed, we see a more moderate version of this phenomenon in the large-flux case when we compare the base of a nanowire in the $\gamma_{HH} = -0.55$ eV case to that of a nanowire when $\gamma_{HH} = -0.65$ eV. We observe a more diffuse, broader base in the former case. When the deposition rate is reduced to 0.1 monolayer/second, this diffusion is amplified, preventing the formation of nanowires when atom-atom mixing is high.

As stated above, $\gamma_{HH}$ affect both nucleation rate at the droplet/solid interface as well as diffusion of B atoms within solid A (and hence solid-solid mixing). The effect on nucleation rate at the droplet/solid interface is artificial: we deemed those atoms on this interface NOT in a liquid neighborhood. We can remove this effect, which we study in a later post. This should tell us whether it is solid-solid mixing or nucleation speed that affects the growth mode of a nanowire.