research review Accounting for droop with Auger
recombination and polarization fields Minimizing polarization fields in LEDs fails to enhance quantum efficiency
A US team has constructed a model that offers new insights into the interplay of Auger recombination, polarization fields and two of the biggest weaknesses of the GaN LED: Droop, the decline in efficiency at higher drive currents; and the ‘green- gap’, which is the decline in efficiency at longer wavelengths.
Calculations by the team from the University of California, Santa Barbara (UCSB), and the University of Michigan, account for reductions in droop that can result from a switch from conventional, polar LEDs to non-polar equivalents. According to the researchers, this switch does not, in itself, lead to a higher internal quantum efficiency in the device. Instead, the light output is higher for the nonpolar device because the reduction in polarization fields enhances the radiative recombination rate. This reduction also allows for the introduction of wider wells, which reduce carrier concentrations and non-radiative Auger recombination.
The researchers blame polarization fields for the green gap. To increase the wavelength of LEDs, engineers add more indium to the InGaN quantum well. This increases the strength of the polarization field and cuts electron-hole overlap, leading to a decline in radiative recombination.
The team of theorists, headed by Chris Van de Walle from UCSB, have previously performed first-principles calculations for bulk InGaN. Extending this to the modelling of real devices is not feasible, according to Van de Walle, so this time they are performing Schrödinger-Poisson calculations with the SimuLED package produced by STR Group of St. Petersburg, Russia.
Van de Walle and his colleagues model a relatively simple LED structure: A 200 nm thick n-type, silicon-doped layer; a 3 nm- thick InGaN quantum well; a 10 nm thick GaN barrier; a 10 nm-thick Al0.2
Ga0.8 N
electron-blocking layer; and a 200 nm- thick, p-type GaN layer. Their background in first-principles calculations has come in useful, because in addition to providing quantitative information, it has equipped
Van de Walle and his co-workers have studied droop in polar and non-polar LEDs by considering how the radiative and non- radiative rates vary with polarization fields.
A radiative process takes place in LEDs (right),with electrons and holes recombining to emit a photon. In a defect-assisted nonradiative process (bottom left),an electron is trapped by a defect (here a nitrogen vacancy, represented by a dark wave function). In Auger recombination,another type of nonradiative process (top left),an electron and hole recombine (assisted by lattice vibrations) but the energy is transferred to a third carrier which is excited to a higher-energy state. Credit: Qimin Yan,UCSB.§
them with insights into the mechanisms that come into play in InGaN. “By looking at what the main contributions are to the Auger recombination process, we were able to gain more confidence that the numbers that we were calculating for the bulk are also very relevant for the quantum well,” explains Van de Walle.
Previous efforts determined that the dominant Auger process in bulk InGaN is one that involves interplay with phonons.
“What we found by analysing the contributions to the Auger rate is that it is the phonons with large momentum that are playing the dominant role in the Auger process.”
Large momenta correspond to small spatial distances, which are on a scale of a few atomic bond lengths. The width of the well is more than ten times this, implying that the calculations for Auger processes in bulk material also give reliable rates for this non-radiative mechanism in quantum wells.
The radiative rate has been calculated before by others, and is known to depend on the square of the overlap of electrons and holes. The formula for the non- radiative rate, however, had to be determined by the team, and they were surprised by what they found. “It turns out that the Auger process and the Shockley- Read-Hall, defect-related process depend on the overlap in exactly the same way – the square of the overlap between electrons and holes.”
What this means is that the radiative and non-radiative rates scale in the same manner, so in terms of quantum efficiency, there is no benefit in switching from polar to non-polar material. So is there any benefit associated with non-polar material?
“Of course,” says Van de Walle. “The radiated power at a given carrier concentration is higher for nonpolar wells because the electron-hole overlap is larger, which enhances the radiative recombination rate. In addition, you can have wider wells.” The far weaker polarization fields allow this, and it enables lower carrier concentrations, which in turn reduce the strength of the non-radiative Auger process.
Switching to non-polar material is not the only route to reducing polarization fields. Fred Schubert’s team from Rensselear Polytechnic Institute in Troy, NY, have previously shown that it is possible to reduce polarization fields by modifying the composition of the quantum barrier, an approach that is claimed to trim electron leakage from the active region.
“An additional reason may be the reduced polarization charges at the quantum well- barrier interfaces, which enhance the electron-hole overlap in polarization- matched structures,” write the UCSB- Michigan team in its paper.
E. Kioupakis et. al. Appl. Phys . Lett. 101 231107 (2012)
January / February 2013
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