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Register a new userDetermination of the carrier diffusion length in GaN from cathodoluminescence maps around threading dislocations: fallacies and opportunities
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We investigate, both theoretically and experimentally, the drift, diffusion, and recombination of excitons in the strain field of an edge threading dislocation intersecting the GaN{0001} surface. We calculate and measure hyperspectral cathodoluminescence maps around the dislocation outcrop for temperatures between 10 to 200 K. Contrary to common belief, the cathodoluminescence intensity contrast is only weakly affected by exciton diffusion, but is caused primarily by exciton dissociation in the piezoelectric field at the dislocation outcrop. Hence, the extension of the dark spots around dislocations in the luminescence maps cannot be used to determine the exciton diffusion length. However, the cathodoluminescence energy contrast, reflecting the local bandgap variation in the dislocation strain field, does sensitively depend on the exciton diffusion length and hence enables its experimental determination.
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We investigate the impact of threading dislocations with an edge component (a or a+c-type) on carrier recombination and diffusion in GaN(0001) layers close to the surface as well as in the bulk. To this end, we utilize cathodoluminescence imaging of the top surface of a GaN(0001) layer with a deeply buried (In,Ga)N quantum well. Varying the acceleration voltage of the primary electrons and comparing the signal from the layer and the quantum well enables us to probe carrier recombination at depths ranging from the close vicinity of the surface to the position of the quantum well. Our experiments are accompanied by fully three-dimensional Monte Carlo simulations of carrier drift, diffusion, and recombination in the presence of the surface, the quantum well, and the dislocation, taking into account the dislocation strain field and the resulting piezoelectric field at the dislocation outcrop. Near the surface, this field establishes an exciton dead zone around the dislocation, the extent of which is not related to the carrier diffusion length. However, reliable values of the carrier diffusion length can be extracted from the dipole-like energy shift observed in hyperspectral cathodoluminescence maps recorded around the dislocation outcrop at low acceleration voltages. For high acceleration voltages, allowing us to probe a depth where carrier recombination is unaffected by surface effects, we observe a much stronger contrast than expected from the piezoelectric field alone. This finding provides unambiguous experimental evidence for the strong nonradiative activity of edge threading dislocations in bulk GaN and hence also in buried heterostructures.
The strain field of a dislocation emerging at a free surface is partially relaxed to ensure stress free boundary conditions. We show that this relaxation strain at the outcrop of edge threading dislocations in GaN{0001} gives rise to a piezoelectric volume charge. The electric field produced by this charge distribution is strong enough to dissociate free excitons at distances over 100 nm from the dislocation line. We evaluate the impact of this effect on cathodoluminescence images of dislocations.
We determine the diffusion length of excess carriers in GaN by spatially resolved cathodoluminescence spectroscopy utilizing a single quantum well as carrier collector or carrier sink. Monochromatic intensity profiles across the quantum well are recorded for temperatures between 10 and 300 K. A classical diffusion model accounts for the profiles acquired between 120 and 300 K, while for temperatures lower than 120 K, a quantum capture process has to be taken into account in addition. Combining the diffusion length extracted from these profiles and the effective carrier lifetime measured by time-resolved photoluminescence experiments, we deduce the carrier diffusivity as a function of temperature. The experimental values are found to be close to theoretical ones for the ambipolar diffusivity of free carriers limited only by intrinsic phonon scattering. This agreement is shown to be fortuitous. The high diffusivity at low temperatures instead originates from an increasing participation of excitons in the diffusion process.
The determination of the carrier diffusion length of semiconductors such as GaN and GaAs by cathodoluminescence imaging requires accurate knowledge about the spatial distribution of generated carriers. To obtain the lateral distribution of generated carriers for sample temperatures between 10 and 300 K, we utilize cathodoluminescence intensity profiles measured across single quantum wells embedded in thick GaN and GaAs layers. Thin (Al,Ga)N and (Al,Ga)As barriers, respectively, prevent carriers diffusing in the GaN and GaAs layers to reach the well, which would broaden the profiles. The experimental CL profiles are found to be systematically wider than the energy loss distributions calculated by means of the Monte Carlo program CASINO, with the width monotonically increasing with decreasing temperature. This effect is observed for both GaN and GaAs and becomes more pronounced for higher acceleration voltages. We discuss this phenomenon in terms of the electron-phonon interaction controlling the energy relaxation of hot carriers, and of the non-equilibrium phonon population created by this relaxation process. Finally, we present a phenomenological approach to simulate the carrier generation volume that can be used for the investigation of the temperature dependence of carrier diffusion.
We analyze the lineshape of x-ray diffraction profiles of GaN epitaxial layers with large densities of randomly distributed threading dislocations. The peaks are Gaussian only in the central, most intense part of the peak, while the tails obey a power law. The $q^{-3}$ decay typical for random dislocations is observed in double-crystal rocking curves. The entire profile is well fitted by a restricted random dislocation distribution. The densities of both edge and screw threading dislocations and the ranges of dislocation correlations are obtained.
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