Calculating the Stability of Different Surfaces of GaAsxP1-x Mixed-Crystals using the Virtual Crystal Approximation

Abstract

The theoretical treatment of mixed-crystals is very demanding. A straight-forward approach to attack this problem is using a super cell method (SCM). Another one is the Virtual Crystal Approximation (VCA), which is a feature of the Vienna Ab initio Simulation Package (VASP). For comparison we use both methods to calculate the total energy (Etot) and the density of states (DOS) of bulk GaAsxP1-x. We then apply VCA to compute the stability of different surfaces using an extended version of the surface formation energy Omega. Our calculations show, on one hand, a working VCA implementation with its flaws (overestimation of Etot) and strengths (well modelling of DOS). On other hand, a further result is that bulk of the slab of a mixed-crystal has a minor influence on the configuration of the surface.

Figures (4)

• Figure 1: Total energy (per atom) of a mixed-crystal $GaAs_{x}P_{1-x}$ vs. concentration $x$. The circles are the results given by the super-cell method and the $\times$-symbols are for the Virtual Crystal Approximation. The differences increase for $x$ towards $\frac{1}{2}$ and vanish at the edges. The dashed lines are just to guide the eye.
• Figure 2: Density of states of a mixed-crystal $GaAs_{x}P_{1-x}$ for different concentrations $x$. The gray solid line is for the super-cell method (SCM) and the black dashed lines for the Virtual Crystal Approximation (VCA). Besides the fact that neither method produces the exact solution -- VCA uses weighted virtual atoms, SCM suffers mainly from the periodic boundary conditions -- the over all similarity encourages us to consider the implementation of VCA as reliable.
• Figure 3: Surface formation energy $\Omega$ versus concentration $x$, with $x$= 0, 0.25, 0.5, 0.75, 1. Circles and diamonds are for pure phosphorous surfaces whereas +-symbols and triangles are for surfaces with the same $x$ as in the bulk. The lines are just to guide the eye. The insets display the situations at the edges of the $x$-interval in more detail. The (2$\times$2)-2D-2H $P$-coated geometry is over nearly the whole $x$-range energetically favored. The change to the $\beta2(2\times4)$ reconstruction seems to happen at rather large $x$.
• Figure 4: Density of states (DOS) of (2$\times$2)-2D-2H with $x=0.5$ and only $P$ in the surface for a random configuration and the Virtual Crystal Approximation (VCA). The gray solid line is for the random configuration and the black dashed line is for the VCA. The result is that both curves have approximately the same shape. Due to the kind of comparison, one should not stress the differences.