Kris's Research Notes

September 4, 2012

VLS Nanowire Simulations — Exchange barrier

Filed under: KMC, Nanowire — Kris Reyes @ 6:10 pm

In this note, we continue to study the effect of energy parameters have on the growth modes observed in VLS nanowire growth. Here we consider the energy \epsilon, the additive barrier for exchanges at solid/liquid interface. This governs the attachment and detachment kinetics of solid material to and from the interface, and hence roughly measures the mobility of the interface.

We repeat the experiments described in previous posts. To reiterate, the following bond energies were used:

\displaystyle \gamma(A,A) = \gamma(A,B) = \gamma(A,C) = 0.10 eV,

\displaystyle \gamma(B,B) = 0.4 eV, \gamma(B,C) = 0.35 eV.

\displaystyle  \gamma(C,C) = 0.50 eV.

The following desorption barriers were used:

\displaystyle  \mu(A) = 0.5 eV, \mu(B) = \mu(C) = \infty.

The following reaction barriers for the reaction A \rightarrow C were used:

\displaystyle \rho_(A,C) = 1.50 eV, \rho_{liquid}(A,C) = 0.5 eV.

All other reaction barriers (including the ones for the reverse reaction C \rightarrow A) were set to \infty.
The exchange barrier in the liquid was set at \epsilon_{liquid} - 0.7 eV. Bulk events were not allowed. The exchange barrier away from liquid and bulk neighborhoods \epsilon was varied as:

\displaystyle \epsilon \in \left\{ 0.80, 0.90, ... , 1.20\right\} eV.

Material A was deposited at a rate of 0.5 ML/sec at 623 seconds until 512 ML material was deposited. Here are the results for the different values of \epsilon.

\epsilon = 0.80

\epsilon = 0.90

\epsilon = 1.00

\epsilon = 1.10

\epsilon = 1.20

\epsilon = 1.30

\epsilon = 1.40

We see that as \epsilon increases, the tendency of the nanowire to bend increases. Recall that \epsilon measures the mobility of the interface, in the sense that atoms on the interface that wish to diffuse along that interface must over come the barrier of \epsilon in addition to the change in energy E(X) - E(X\wedge Y) calculated by bond-counting. As \epsilon increases, diffusion along the interface slows down, and hence the relaxation time for the interface grows. If this relaxation time is sufficiently larger than the time scale of nanowire growth, then we expect the nanowire to grow in the direction of the facet that occurs in the unrelaxed interface. If we assume this growth is initiated from the triple-junction, then it is reasonable to assume that new facets can grow, and hence determine the direction of the nanowire.

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