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TECHNOLOGY LEDs


Figure 3. Illustration of Auger leakage: The excess energy of an Auger recombination event (1) is transferred to the third carrier (2). This carrier is expelled from the well (3) and contributes to leakage (4)


data tells a different story, with droop still present. We have thought about this effect and concluded that it is important to consider the overlap integral when calculating Auger recombination. After all, since the Auger effect is a three-carrier process involving the interaction of charged particles, why should the quantum-confined Stark effect be irrelevant here?


Including this effect is far from trivial. That’s because it requires a great deal of care to understand the consequences of these internal fields. As the current is cranked up, the polarization field is screened, so electron and hole wavefunctions move towards each other and the overlap integral increases. This implies that neither the radiative nor the Auger coefficient is constant. For c-plane LEDs, they will increase with current density (see Figure 2), which means that the Auger recombination will not simply increase as the cube of the carrier density, but at an even faster rate.


them in detail, and considering how they may be linked.


We know that nitride materials differ from their arsenide and phosphor counterparts in several ways, including the presence of strong polarization fields in the former semiconductor. This means that quantum wells grown on the predominantly utilised c-plane of this wide bandgap material have band edges that are tilted (see inset to Figure 2). This pulls apart the electrons and holes in the wells – phrased in the language of quantum mechanics, polarization effects result in a de-localisation of the carrier wave functions and a reduced overlap integral. This virtually unquestioned phenomenon, widely referred to as the quantum-confined Stark effect, reduces the probability of radiative carrier transitions from the conduction band to the valence band.


Figure 4. Simulated and measured IQE as a function of the current density of a green, single-quantum-well LED. A parameter calibration has been carried out with Auger leakage turned on (red curve). The blue curve depicts the IQE without Auger leakage, but with all other parameters kept constant. Including Auger leakage, the Auger coefficient can be reduced by a factor of two in comparison to a standard model


Based on this understanding of the nitride LED, one way to improve its performance is to switch the growth direction to either a-plane or m-plane, because these crystal orientations eliminate the interface polarization and thus the quantum-confined Stark effect. With this out of the way, there should be no reduction in radiative recombination and consequently a higher efficiency. But experimental


This is good news for those in the Auger camp: After inclusion of the overlap integral, the Auger mechanism gets stronger with rising current, which results in a steeper droop, as observed in the experiments.


What about Auger expulsion? A fundamental, very important question that is easy to ignore when discussing droop is this: What exactly is the Auger mechanism?


Consult a textbook on semiconductor physics and you’ll find that the excess energy associated with an Auger recombination event is transferred to another, third particle. Conventional models evaluate the Auger recombination rate and add it as a sink term to the electron and hole continuity equation. But why model just two carriers in this three-particle process, and ignore the third one?


One answer is that everything else is hard to examine, and it is possible to preserve the third carrier in terms of a simple current conservation rule. Probe a bit deeper, however, and you’ll find that it is debateable whether direct or indirect Auger recombination is the dominating process, indicating that it is too complex to predict the final state of the third carrier.


Against this backdrop of uncertainty, we believe that there is one fact that we can know for sure: In a quantum well of a large bandgap material, the third carrier is lifted to an energy level far above the barrier band edge. This means that it is no longer confined, but expelled from the well.


We have developed a model based on this Auger expulsion process [3]. In our view, experimental indications that this can take place have been provided by the recent work from the University of California, Santa Barbara and Ecole Polytechnique,


48 www.compoundsemiconductor.net July 2013


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