Compound semiconductor heterostructures containing ternary, quaternary or even more complex alloys are inevitably subject to alloy fluctuations. The apparent atomistic nature of such effects makes a realistic description within simulations highly challenging due to the demand of both atomistic accuracy and large simulation cells. While alloy clustering or a graded alloy profile are often considered in the simulation of the electronic and optical properties of semiconductor heterostructures, random alloy fluctuations are rarely taken into account. In the latter case the assumption is that the material can be described as a homogenous alloy and local fluctuations in content are of secondary importance. For many III-V semiconductor alloys, e.g. (In,Ga)As, this approximation is largely sufficient to achieve an accurate description of their electronic and optical properties. However, III-N alloys, e.g. (In,Ga)N, strongly deviate from this simple assumption.
Electron (red) and hole (blue) ground state charge density for the case of maximum and minimum exciton binding energy observed throughout 200 simulations with randomized, fluctuating In content in the active layer for three selected model systems, along with the reference data of the respective systems assuming a homogeneous alloy without any fluctuations. The corresponding exciton binding energies are provided as numbers and the bottom row shows the statistical distribution of exciton binding energies observed for each model system.
We have systematically investigated to which extent random alloy fluctuations can be described within a continuum framework, e.g. the widespread employed k·p formalism. To do so the electronic properties of planar InxGa1-xN layers (quantum wells) in GaN have been computed using a modified eight-band k·p model implemented within the SPHInX library compared with results from atomistic tight-binding approach operating on the same underlying random alloy configuration in the layer. We found a very good agreement between both models, even if we reduce the resolution of the simulation cell of the continuum model to grid discretisations that facilitate simulations of larger, more realistic heterostructures.
Encouraged by this comparison, we have performed a statistical analysis of the impact of random alloy fluctuations on the electronic properties of axial InxGa1-xN/GaN nanowire heterostructures of realistic dimensions. Given that excitonic effects will play an important role in electron- and hole-confinement in these systems, we have compared the ground-state exciton binding energy computed using a Hartree approach for a set of characteristic properties such as mean In content and thickness of the active layer as well as the overall wire diameter. We find that the influence of random alloy fluctuations alone can induce a scattering of exciton binding energies by several tens of meV in comparison to reference systems assuming a homogeneous alloy composition. However, we also note that random alloy fluctuations play a less pronounced role when reducing the nanowire diameter, as the large potentials of the nanowire side facets govern charge confinement here.
Funding acknowledgement This work was funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC2046: MATH+ Berlin Mathematics Research Center (project IN-7) and Science Foundation Ireland (grant numbers 17/CDA/4789 and 12/RC/2276 P2).
NUSOD Blog 