Calculations by Chris Van de Walle’s team from the University of California, Santa Barbara, (UCSB) expose two forms of indirect Auger recombination as the primary causes of LED droop

 

THE many researchers intensely debating the cause of LED droop, the decline in device efficiency at high drive currents, can be divided into two camps: those that believe Auger is the culprit, and those with alternative theories.

Within the Auger fraternity, there is a lively discussion regarding the exact form of Auger recombination responsible for droop. Chris Van De Walle’s team from UCSB are now claiming that they have uncovered the true cause: indirect Auger recombination, mediated by electron phonon scattering and alloy scattering.

Their efforts follow in the footsteps of the first claim for Auger recombination’s dominant role in LED droop, which came from researchers at Philips Lumileds in late 2007, who argued their case based on the results of photoluminescence measurements. But a theoretical team led by Joerg Hader from the University of Arizona poured doubt on this claim in early 2009 when they calculated that the standard Auger process – direct intraband Auger recombination – was far too weak to account for droop.

Later that year, Van de Walle’s group showed that interband transitions to the second conduction band play a significant role in LED droop. However, this process is only important for a small range of InGaN compositions, and fails to explain the droop observed in LEDs spanning a far wider range of wavelengths.

Recently, the UCSB group has calculated the Auger coefficients for indirect recombination mediated by a scattering mechanism that provides additional momentum and enables Auger transitions to a broader range of final states.

 



According to UCSB calculations, the strongest Auger coefficient for nitride LEDs is the phononassisted hole-hole-electron processes, which is denoted as ‘Cp, phonon’ in the figure

The theorists have found that electron-phonon interactions in the nitrides are strong, due to nitrogen 2p orbitals. “In phosphides, arsenides and antimonides, there is always another p-type orbital lower in energy than the bonding p one, so electrons that participate in bonding see a screened nuclear charge,” explains Van de Walle. “In contrast, nitrogen bonds with the 2 p orbitals see the full unscreened potential of the core.” This makes the energy of the bonds very sensitive to the exact position of the nitrogen nucleus.

 Van de Walle and his colleagues have also calculated the strength of indirect Auger  recombination mediated by alloy scattering. To do this, they employed a 32-atom cell comprising 12 gallium atoms, 4 indium, and 12 nitrogen, distributed in such a way as to reproduce the short-range structure of the fully random alloy. “It is the best possible representation of a ‘random’ alloy that can be achieved with a 32-atom cell,” claims Van de Walle.

Plots of the contribution from the electronphonon and alloy scattering mediated Auger mechanisms, which are based on first principles calculations using density functional theory (local-density approximation and the plane-wave pseudopotential method) are shown in the Figure.

This graph shows that the indirect Auger coefficient triples as the InGaN bandgap  decreases from violet to green. According to Van de Walle, this partly accounts for the ‘green gap’, the very low values of LED efficiency between 530 nm and 580 nm.

However, he says that this gap is also a partly due to a thinning of the wells used in nitride LEDs operating at longer wavelengths.

Reducing the well’s thickness compensates for increased strain and the formation of dislocations. “[However], for a given carrier density, the operating carrier density goes up, increasing the significance of Auger compared to radiative recombination,” says Van de Walle.

In addition, he believes that increases in the polarization fields as nitride LEDs are pushed to longer wavelengths contribute to droop, because they pull apart electrons and holes, reducing radiative efficiency. And he points out that poor hole injection in multi-quantum wells leads to localization of carriers in the active region towards the p-side of the device. This increases the operating carrier density, driving up the ratio of Auger recombination compared to radiative recombination.

Theorists Michele Goano from the Politecnico di Torino, Italy, Enrico Bellotti from Boston University and Francesco Bertazzi, who is affiliated to both institutions, have quested the theoretical approach of the UCSB team. Their criticism concerns the band interpolation to find the indium composition – there is a resonance between the bandgap, and the gap between the first and second conduction bands.

“In this work, we are not invoking this resonance, since electron-phonon coupling and alloy disorder scatter carriers throughout the Brilloin zone,” explains Van de Walle.

He believes that the key to solving droop is a reduction in the operating carrier density. “This can be achieved by making the quantum wells thicker and spreading them over a larger volume, or by using non-polar or semi-polar growth directions that enhance overall recombination and reduce the operating carrier density.”

E. Kiopakis et al. Appl. Phys Lett. 98 161107 (2011)