At the heart of the debate over the origin of droop is the question: Auger or not Auger? Circumstantial evidence for Auger has been mounting, and now this is joined by a ‘smoking gun’, the observation of hot Auger electrons in electro-emission. Detailing their novel experiment and its interpretation are a UCSB-Ecole Polytechnique partnership involving Claude Weisbuch, James Speck, Justin Iveland, Marco Piccardo, Lucio Martinelli and Jacques Peretti.

A biased LED emits blue photons and electrons in the UHV chamber (photo credit: Ph. Lavialle, Ecole Polytechnique).

Droop is the greatest impediment to affordable, highly efficient solid-state lighting. This mysterious malady, which drives down the efficiency of GaN LEDs as the current through them is cranked up, is behind the high total chip costs within the bulb and an efficiency that is only a little better than that of a compact fluorescent.

If, for a moment, you could take you to a world where droop did not exist, you could have LEDs in bulbs delivering efficacies of more than 200 lumens-per-Watt; and they could do this at very high current densities, trimming total chip costs. What’s more, heatsinks could shrink, for gains in efficiency spawn a reduction in device heating.

To try and realise this dream, many researchers throughout the world have been trying to understand and combat droop. This phenomenon was first reported by engineers at Nichia, and detailed analysis followed at Lumileds, where a claim that Auger recombination is responsible for droop emerged in 2007. This non-radiative process, which limits the efficiency in telecommunication lasers and ultra-high efficiency solar cells involves the interaction of three carriers – two electrons and a hole, or two holes and an electron – with one promoted to a higher energy state.

Since Lumileds’ made its claim that Auger recombination causes droop, several alternative theories have been put forward to account for this energy-sapping mechanism. They include electron leakage out of the active region and non-radiative defect recombination, which is activated by increased carrier concentrations.
To try and bring this debate to an end, our team from the University of California, Santa Barbara, and Ecole Polytechnique, France, have performed a novel, insightful experiment that provides irrefutable evidence that Auger is the cause of droop.

Our experiment, which reveals the presence of Auger-generated carriers within the LED, is very challenging to perform. It requires measurements of the kinetic energy of the electrons using an experiment reminiscent of the photoelectric effect, discovered by Hertz in 1887 and explained by Einstein in 1905. In addition, the experiment demands excellent levels of surface cleaning, ultrahigh vacuum conditions, and a high degree of energy resolution for measuring the electrons emitted from an LED into a vacuum. Many universities do not have the facilities to carry out such an experiment, but we can at Ecole Polytechnique, one of the world’s leading centres for electron emission spectroscopy, using LEDs made by Taiwanese chipmaker Walsin Lihwa and prepared for the experiment at UCSB.

How are mechanisms usually identified?

Our approach is remarkably different from that of most analysis of the droop phenomena. The mainstream approach is to curve fit the well-known ABC model, which was first used by Lumileds to describe the effect of Auger process on the external quantum efficiency. Variations in the carrier recombination rate as a function of carrier density (n) are expressed as An + Bn2 + Cn3. (In this expression, A is the Shockley-Read-Hall non-radiative recombination coefficient, B is the bimolecular radiative recombination coefficient and the Cn3 describes Auger recombination.)

Two approaches can be taken with this ABC model. One is to calculate the external quantum efficiency as a function of current density, and compare it with experimental values. In order to do this, you have to know the values of the ABC coefficients and make the assumption that light extraction efficiency and carrier injection efficiency in the quantum wells do not vary with injected current.

The other option, more common, is to analyse experimental plots of external quantum efficiency versus current density, and then fit ABC values. The value for the B coefficient can be obtained by either measuring the recombination lifetime, or calculating it from first-principles, which is an approach taken for instance by Joerg Hader from The University of Arizona and his co-workers.

If you use theABC model, you have to accept two fundamental limitations of this approach. One of them, first pointed out by researchers at Lumileds, is that the ABC coefficients are not constant, but vary with current density. This occurs because at high carrier concentrations, polarization fields in the quantum wells are screened. Compositional fluctuations are one reason behind this, and there is also an inhomogeneous distribution of carriers caused by current crowding. The upshot is that it is not feasible to accurately describe the recombination mechanisms present in the LED with ABC values that do not depend on the current density, and consequently it is impossible to unambiguously identify any mechanism responsible for droop with this approach.

The second major drawback associated with analysis based on the ABC model is that this approach only provides a fit of experimental efficiency data. Consequently, it only gives an indication of the cause of droop: it is not a direct physical observation of any recombination process occurring within the LED.

To make the ABC model compatible with other mechanisms for droop, some researchers have replaced Cn3 with a more complex term, Cf(n), that allows a different functional dependence. Meanwhile, others have added terms to represent carrier localization effects occurring above a carrier density threshold, or added terms to account for the leakage current. By adding new terms and fitting plots of external quantum efficiency as a function of carrier density for different LED designs or operating temperatures, these researchers, through their empirical approaches, will inevitably invoke other mechanisms than Auger for explaining droop.

Support for Auger

At the LED chipmakers Lumileds and Osram, researchers have provided further support for Auger as the cause of droop. Their efforts go beyond fitting of the ABC model, and involve photoluminescence and electroluminescence measurements.

One of the merits of photoluminescence is that it allows droop to be observed under direct excitation within the quantum wells – this measurement may be made with no applied bias, or by applying a bias to induce flatband conditions. By configuring the bandstructure within the LED in this manner, carrier escape and leakage cannot take place, but droop is still observed. What’s more, there is a perfect similarity between the behaviour measured by photoluminescence and electroluminescence, including carrier lifetimes. This led the researchers to conclude that Auger is the culprit for droop under LED electrical operation, because it is then related to a mechanism that is internal to the quantum wells.

More recently, researchers at Osram have fabricated a structure with a range of wells emitting at different wavelengths. Photoluminescence from this structure reveals hot carrier generation that is attributed to the Auger effect (see the feature on p. xxx for a full account of this work).

In addition to all these experimental efforts, the theoretical group at UCSB, which is led by Chris Van de Walle, has provided further support for Auger as the cause of droop. Calculations by this team show a high rate for the indirect Auger effect.

However, despite this mounting support for Auger as the cause of droop, the origin of this mysterious malady is still hotly debated. There are other experimental explanations of droop, also based on circumstantial evidence, that have some merit, while determining the precise experimental value for the C coefficient is hampering progress. Obtaining a precise value for C is tricky, due to uncertainty in injected electron and hole densities, the number of wells that are involved in radiative recombination, carrier localization effects, and practical issues such as current crowding near n-type and p-type contacts.

Figure 1: (a) An LED under current injection. Electrons and holes recombine radiatively in the active quantum wells by emitting photons (b); Shown in (a) is also electron emission in vacuum which only occurs when the LEDs have a specially treated p-type GaN surface (by Cesium deposition); (c) The principle of the non-radiative Auger effect in semiconductors:  an electron-hole pair recombines by exciting another electron to a high kinetic energy. (d) Schematics of the phonon-assisted Auger effect where a phonon (lattice excitation) supplies momentum to the Auger electron, increasing the transition rate.

The smoking gun

The debate on droop should soon be over, however, because our experiment provides overwhelming evidence that Auger is the cause of droop. Our approach is not that dissimilar to that of the US physicist Robert Millikan, who in 1914 measured the kinetic energy of electrons escaping from a metal as a function of exciting energy of incident photons. Since then, one of the leading approaches to determining the energy of electrons within materials is to photo-emit them, and measure their energies.

Our approach differs slightly from this, as rather than firing photons at the LED to liberate electrons, we forward-bias our commercial LED and measure consequent electron emission(see Figures 2 and 3). The active region contains eight wells, and a high proportion of the electrons and holes that are injected into them will undergo radiative recombination. However, at a high injection current density, a fraction of the carriers injected into the wells with the highest carrier density will recombine by an Auger process, and will generate electrons with a high kinetic energy. According to the work of Van de Walle’s group, the most likely Auger process that will take place is an indirect one, with momentum conservation provided by phonon emission or absorption (see Figure 1 d)

Figure 2. In the novel experiment by researchers from UCSB and Ecole Polytechnique,  electrons are ejected into vacuum from a forward-biased LED. The kinetic energy of the electrons is analyzed in a cylindrical electrostatic deflector.


Figure 3. Emission of electrons from an LED in a vacuum:  electrons originate from the active region, the quantum well (marked QW), with some high-energy (‘hot’) electrons generated by the Auger effect.  They give rise to high-energy peaks in the energy distribution of electrons emitted in vacuum.

In our experiment, electrons with various energies, including energetic Auger electrons, reach the surface and are emitted into vacuum (see Figure 3).  Since the energy distribution of electrons in vacuum is the same as that of electrons impinging at the LED-vacuum interface, measurements of the energy of these electrons provide evidence of Auger electrons, so long as some of the Auger electrons reaching the surface sustain a significant fraction of their high initial energy.

To make sure that all thermalized electrons can escape the LED, we treat its p-type surface with cesium, enabling activation to negative affinity. One of the downsides of this treatment is that it rules out annealing of the contacts, so the p-contact is non-Ohmic.

Armed with this modified device, when we crank up the current, we are able to observe higher energy peaks in the vacuum-emitted electrons (see Figure 4). Since no other mechanism can generate hot electrons in the structure, these high-energy peaks represent a clear and direct signature for Auger recombination.

Figure 4: Energy distribution curves, with respect to the bottom of the bulk conduction band minimum (ECBM), of electro-emitted electrons for different injection currents (the base line of each spectrum was shifted). When increasing injected current, high-energy peaks appear around 0.2 eV and 1.2 eV, signalling generation of hot carriers in the structure.

In their transit towards the surface, the Auger electrons will lose some kinetic energy. Fortunately, a number of them lose their energy cascading down in a so-called ‘side’ conduction band (satellite valley), which has a long energy memory time (the ‘L’ band in Figure 3). A peak is observed at this energy, reminiscent of the high energy of the original Auger electrons.

Additional, highly compelling evidence that Auger is the cause of droop is the emergence of these high-energy peaks at exactly the same time that droop kicks in with current (see Figure 5). We can even show that the magnitude of the droop current − the supplementary current needed to reach a given light output in the absence of droop – has a linear relationship with the integrated, high-energy, vacuum-current intensity (see Figure 6).

Figure 5: Plots of the current integrated over the high electron energy peak and of the optical output power as a function of the injected current.  The straight line is the expected optical output power in the absence of efficiency droop, obtained by a linear extrapolation from the maximum internal quantum efficiency (IQE) value. The droop current is the difference between the actual injected current and the current that would give the same optical output if the maximum IQE had been conserved. This supplementary current is the droop current.
 
Figure 6:  Plot of the integrated current over the high electron energy peaks as a function of the droop current resulting from the generation of Auger electrons. The simultaneous onset of droop current and Auger electron generation, and their linear dependence, indicate a common origin. Other droop mechanisms are highly unlikely to account for this observation, because they do not scale with carrier density as Auger electrons do (as the cube of the carrier density)Based on these finding, it is highly unlikely that a mechanism other than Auger can account for droop. All alternative mechanisms proposed so far do not have the same cubic dependence on carrier density as the Auger-related current, and any new theories for droop are unlikely to satisfy these conditions precisely.

So, in short, we believe that our experiment provides the most compelling evidence to date that Auger recombination is the dominant origin for droop in state-of-the-art, nitride-based LEDs.  In the future, through judicious device design, we plan to use this tool to compare active region designs, including those with various quantum well and quantum barrier thicknesses and differing electron barriers and doping crystal plane orientations. All these efforts are focused on reducing droop.

A detailed account of the experiment described in this feature can be found in the paper:

J. Iveland et al. Phys. Rev. Lett. 110 177406 (2013)

Other measurements of Auger recombination are detailed in the following papers:

Y. C. Shen et al. Appl.  Phys. Lett. 91 141101 (2007)
A David and M. J. Grundmann Appl.  Phys. Lett. 97 033501 (2010)
M. Binder et al., Appl.  Phys. Lett. 103071108 (2013)
A. Laubsch et al. Phys. Status Solidi C 6 S913 – S916 (2009)

Reviews of alternative mechanisms of droop are offered here:

G. Verzellesi et al. J. Appl. Phys. 114 071101 (2013)
V. Avrutin et al., 050809 J. Vac. Sci. Technol. A 31 050809 2013
J. Cho et al. Laser Photonics Rev. 7 408 (2013)
J. Hader et al., Proc. of SPIE 8625 86251M-2 2013


Measurements of the energies of electrons emitted by the LED in vacuum were carried out in the CNRS-Ecole Polytechnique Laboratory of Condensed Matter Physics (photo credit: Ph. Lavialle, Ecole Polytechnique)
.

Justin Iveland and James Speck are the part of the team based at UCSB. Iveland prepared the samples, and went to CNRS-Ecole Polytechnique to help with the measurement of these LEDs. Credit: UCSB

How do the various materials and structures compare?

Amongst the leading manufacturers of state-of-the-art c-plane GaN-based LEDs that discuss the origin of droop publicly – the likes of Osram, Lumileds and Soraa – the consensus is that Auger is the dominant mechanism for diminishing efficiency with increasing drive current. Alternative mechanisms, meanwhile, emanate from academic labs. So might these differing views simply stem from differences in the quality of the LEDs under investigation?

One way to answer this question would be to carry out a round-robin analysis of droop on high-performance LEDs. Unfortunately, however, there are yet to be any reports of such an investigation.

What is clear is that after years of optimisation of growth quality, fabrication technology, metals contacting and so on, high-quality commercial grade materials used to make LEDs have probably reached optimal efficiencies for the particular crystal orientation and active region design. Refinements have resulted from optimization of quantum well materials, barriers, layer architectures and so on, through recipes that often are unpublished and kept in secrecy.

Two examples highlighting the extent of this optimisation, and how state-of-the-art LEDs have evolved and improved beyond recognition, are the advances associated with: determining the optimal number of wells within the structure, and the continual improvement in the device’s material quality.

The high number of wells in today’s state-of-the-art LEDs will raise some eyebrows, given the challenge of injecting holes uniformly throughout this structure. Although companies do not publish the details of their active regions, it is known that they use between five and twelve wells in their LEDs. Since un-injected wells lead to inefficient carrier injection, substantial emission must be coming from the entire active region.

Turning to material quality, it has been argued that when defect densities, such as dislocations and various point defects, are high, it is possible to account for droop with a conjecture based on carrier localisation. The argument put forward is that at a low carrier density, compositional or interface fluctuations localise the carriers, leading to efficient emission; but as the current is cranked up, a higher proportion of carriers diffuse to non-radiative centres, and external quantum efficiency falls.

The magnitude of non-radiative emission is associated with the A coefficient in the ABC model. Its value is diminishing all the time, as witnessed by the spectacular improvements in the external quantum efficiency of blue LEDs. At the turn of the millennium, these efficiencies were below 20 percent, but now the figure is nearer 80 percent [Mukai 1999, Krames 2000, and Narukawa 2010]. Since extraction efficiency has doubled during this time frame to 90 percent, the peak internal quantum efficiency must have shot up from 45 percent to 90 percent, and the A coefficient will have plummeted by a factor of about 100. 

What are the arguments of those not convinced?

In our opinion, these experimental results are the long-awaited ‘smoking gun’ evidence that Auger recombination is the dominant cause of LED droop. However, not everyone is convinced, and a handful of researchers have voiced concerns over these results and their interpretation [1-5].

Researchers who are skeptical that an Auger mechanism causes droop claim that the measured Auger coefficient might be too large compared to theoretical values, and that the behaviour with temperature is not perfectly represented. However, it is worth noting that theorists are still to reach a consensus on what the value of theC coefficient should be, and that there are large fundamental imprecisions in its experimental determination which arises from carrier density inhomogeneities − both in plane and in the perpendicular direction − and their variation with injected current.

One theoretical group is arguing that is should not be possible to see Auger-generated hot electrons escaping in vacuum, due to their calculated ultrafast electron energy relaxation [1-4]. These researchers claim that the hot electrons observed outside of the device are the result of electron acceleration in the surface electric field. But this acceleration cannot raise the total energy of electrons above the bulk conduction band minimum. Why?  For the same reason that a stone rolling downhill can gain kinetic energy, but never raise its total energy above its initial energy.

Another critic, Fred Schubert from Rensselear Polytechnic Institute, argues that droop is due to carrier leakage [1-3]. This finding is based on the strong injection regime reached in his LEDs, according to his measurements and analysis. But in our devices, due to the very high doping (greater than 1020 cm-3) of the p-type region (see Figure 3), the electric field is of the order of 100 V/cm. This field, which is typical of that found in commercial LEDs, is very far from inducing strong injection and its resulting carrier leakage.

Concerns have also been voiced that the hot electrons that we observe might be photo-created by LED light. However, if these hot electrons were formed by direct excitation at 450 nm, they would have to result from two-photon absorption from the valence band. Very few hot electrons would be formed in this way, because it tends to require intensities of many megawatts/cm2, many orders of magnitude higher than the light intensities at the surface of our LEDs. 

It is also unlikely that hot electrons are formed by two-step photo-creation, which is the absorption of an LED photon by an electrically injected electron. The absorption probability is in the region of 10-4 in the quantum wells, the surface band-bending region and the p-doped layer, when determined using known and calculated free electron absorption coefficients in the 10-20 cm-1 range for LED carrier densities of around 1018 cm-2.

Recently researchers at the University of Southern California claim to have identified a new mechanism for free carrier absorption that is much larger than any previously predicted or observed [5]. This team have argued that this effect can both account for droop and our observation of hot electrons.

We feel that one weakness of this work is that the mechanism is based on the analysis of differential, picosecond, pump-probe transmission measurements, hitherto analysed in terms of modified interband transitions, not conduction intraband transitions. If such phenomenon could account for sizeable losses in LEDs, where electrons only travel a few tens of nanometres across quantum wells, would not the associated losses for laser modes propagating several hundred microns along such high loss materials (where the carrier density is even higher) prevent laser action?

To directly address these criticisms − and to assess the possibility of LED-light-induced hot electron emission − we performed measurements under LED biasing and also under external laser light excitation. The latter condition mimics LED internal emission. We were able to single-out the electron emission from the laser by chopping, and detecting in-phase, the electron emission. We found that we could only detect thermalized photoemission, so the maximum contribution provided by photocreated hot electrons is 0.4 percent, based on our current counting statistic limitations of the total hot electron current.

[1] Physics Today, July 2013, p. 12
[2] IEEE spectrum, http://spectrum.ieee.org/semiconductors/optoelectronics/a-definitive-explanation-for-led-droop
[3] Compound Semiconductors http://www.compoundsemiconductor.net/csc/news-details.php?id=19736706
[4] F. Bertazzi, M. Goano , E. Bellotti et al., http://arxiv.org/pdf/1305.2512.pdf
[5] D. Dapkus et al., Appl.  Phys. Lett. 103 041123 (2013)