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Aiding nitride growth with accurate surface energies

Calculations offer insights into nitride growth conditions for different planes.

The surface structure and the energy of different facets that are present during semiconductor growth significantly influences the morphology of films, bulk crystals and nanostructures. State-of-the-art calculations of surfaces can provide insight into the effects of growth conditions such as temperature (T) andpressure (p). Image Credit: Cyrus Dreyer, UCSB

Growers of nitrideshave been held back by a lack of knowledge of this material’s surface energies, which determine how stable particular planes are and how fast growth will occur on them. But this weakness has now been addressed by calculations by Chris Van de Walle’s team from the University of California, Santa Barbara.

One of the key findings of this work is that the non-polar a-and m-planes have similar stability, and thus growth rates, even when the deposition conditions are changed substantially. However, when it comes to polar planes, growth rates vary a great deal with growth conditions.

These findings have implications for selective MOCVD re-growth. This often involves the growth of stripes in the c-direction for lateral overgrowth, in order to then obtain low-defect-density material in the wings − that is used to make lasers. To succeed with this technique, lateral overgrowth taking place on the non-polar planes must occur at a faster rate than the vertical growth.

“According to our calculations, you would want to grow under more nitrogen-rich conditions, with lower pressure and higher temperature,” explains Van de Walle. “Alternatively, if you are trying to grow nanowires, you would like faster growth on the c-plane and slower on the non-polar planes. For that purpose, our calculations suggest higher pressure, lower temperature, and more gallium-rich conditions.”

The West-coast team says that accurate values for nitride surface energies have been hard to come by, due to: the absolute energies for polar or semi-polar planes being fundamentally ill-defined for crystals with low symmetry, such as the wurtzite crystal structure of GaN; and limitations in the computational methods used by previous research groups. Van de Walle’s team addresses the flaws associated with low crystal symmetry by calculating values for a zinc blende structure, which differs only in its stacking sequence from a wurtzite structure. “You have to move three atoms below the surface before you see any difference between wurtzite and zinc blende,” arguesVan de Walle, “and since surface energies depend on properties such as bonding between atoms that are very local in nature, we expect the results to be very similar between the two polytypes.”

The researchers also improve the methods used to calculate the surface energies, by switching from traditional variants of density functional theory − such as the local density approximation or the generalised gradient approximation − to the use of a ‘hybrid functional’ form.

According to Van de Walle, although the local density approximation and the generalised gradient approximation do a “good job” for structural properties, they fail to predict the bandgap correctly. “In some cases, this also affects energies: for instance, surface energy depends on the position of surface states within the bandgap, and if the bandgap is wrong, the surface energy will be affected.”

The West-coast team normally employs periodic boundary conditions, because this allows the use of computational approaches, such as fast Fourier transforms, that speed up calculations.However, for the recent work on surface energies, they had to consider a surface. Ideally, they would perform calculations for a semi-infinite solid, but this is not a periodic structure. So instead they look at a slab − a layer of finite thickness, surrounded by a vacuum on both sides.

“If the layer of vacuum is wide enough, interactions between the surfaces across the vacuum layer are negligible,” explains Van de Walle, who adds that by making the slab sufficiently thick, surfaces on either side do not interact with each other.

Plans for future work include modelling the surface energy of III-nitride semi-polar planes and investigating other materials, such as complex oxides.

Ref: C. Dreyer et. al.
Phys. Rev. B 89081305R (2014)
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