Combatting Droop In Ultraviolet LEDs
Gradual variation in quantum well composition promises to slash Auger rates in AlN/GaN LEDs
Eight-band calculations reveal the dependence of Auger and radiative recombination on the electric field strength in quantum wells of differing thickness. The inset details the plummeting internal quantum efficiency with increasing field strength.
UltravioletLEDs, like their visible cousins, suffer from droop, a decline in efficiency with increasing current density. But it should be possible to combat this unwanted phenomena in conventional, polar LEDs by turning to active regions with a gradual variation in quantum well composition. This modification compensates for the effect of the electric field acting on the holes.
This opportunity for improvement is one outcome of a theoretical study by an international partnership that has revealed how the polarization field in an AlN/GaN LED magnifies Auger recombination, and also edges up radiative recombination.
“We present an intuitive explanation of why such an enhancement should occur, and we support it with calculations," says Roman Vaxenburg from Technion, who has carried out this work as part of a team that includes university colleague Efrat Lifshitz, Anna Rodina from Ioffe Physical-Technical Institute and Alexander Efros from the Naval Research Laboratory.
The multi-national team has also considered non-polar LEDs: Their latest calculations indicate that Auger-induced droop should be present in InGaN/GaN LEDs, but not in their GaN/AlN cousins. “These two materials have different energy gaps, which strongly affects the efficiency of the Auger process in the non-polar case," explains Vaxenburg.
He and his co-workers argue that in all forms of LED, the probability of non-radiative Auger recombination – a process involving the excitation of charge carriers to continuum states – is governed by the overlap between the wavefunction of the localised initial state and that of delocalised carriers.
Due to strong polarization fields in the quantum well, polar LEDs feature sharp corner-like features and a tilted shape of the confining potential. This creates high Fourier components in the localised carrier wavefunctions that match the momentum of the excited carrier,
leading to high rates of Auger recombination.
According to Vaxenburg, the team’s calculations are rather difficult to do: “All the steps, from the theory construction to the actual coding, are very involved. Fortunately, we ended up with a very efficient code, which allowed us to collect all the data within a few weeks, running several powerful computers."
Even such complex calculations can fail to accurately describe every aspect of the LED. The team’s current eight-band model ignores contributions from higher energy bands and neglects screening effects created by free carriers, which could modify the electric fields in the structure.
“However, the general effect of the Auger enhancement by the electric field should persist, because the sharp features in the potential profile will be there in any case," argues Vaxenburg.
Calculations considered quantum well widths of 2 nm, 2.5 nm and 3 nm, electric fields from 0 to 4 MV cm-1 and an injection current of
200 A cm-2. Radiative rates in all wells decrease at higher fields, due to decreasing electron-hole overlap.
This impact is greatest in the widest wells, where carrier separation is more pronounced (see Figure). Meanwhile, the Auger rate increases by one-to-three orders of magnitude with increasing field strength.
One upshot of the changes in Auger rate and radiative rate is a strong reduction in internal quantum efficiency with increasing electric field. Note that when this field is zero, however – which is the case for a non-polar AlN/GaN LED – the radiative rate is far higher than the Auger rate.
The latter finding suggests that in polar AlN/GaN LEDs, the Auger rate, which is governed by a hole-hole-electron process, could be suppressed by restoring a rectangular confining potential for the holes. This is possible by gradually varying the quantum well layer composition to create a gradual increase in bulk energy gap.
Goals for the team include an extension of the calculation beyond the standard eight-band model. “We will add a more realistic self-consistent profile, which will depend on the carrier concentration and will reflect the screening effects," explains Vaxenburg.
R. Vaxenburg et. al.
Appl. Phys. Lett. 103 221111 (2013)