# Investigating The LED's Dark Side

*Figure 1: One serious, puzzling weakness associated with LEDs manifests itself as (a) intensity saturation or (b) efficiency droop. Auger scattering (c) is a strong candidate for the cause of this problem, which is known as LED droop. Each Auger scattering event involves non-radiative recombination of an electron-hole pair and promotion of a carrier (shown here as an electron) to conserve energy.*

**The contenders**

**Conventional approaches**

*Figure 2: (Left) An outline of the widely adopted Approach A for determining LED efficiency versus pump rate. It is used to evaluate possible efficiency droop mechanisms, and to extract Shockley-Read-Hall, radiative and Auger coefficients from experimental data. (Right) Sketch of the ABC model, which is a simple implementation of Approach A.*

*ABC*model, (see right side, Figure 2). Here, phenomenological constants

*A, B*and

*C*are introduced to account for defect (Shockley-Read-Hall), radiative-recombination, and Auger-scattering carrier losses, respectively. With this approach, the input parameter is total carrier density, and the defect, radiative and Auger rates are assumed to depend on this in a linear, quadratic and cubic manner, respectively.

*ABC*model, the IQE, as indicated in the figure, declines at higher current densities. This approach can also include a term to account for carrier injection efficiency, which is the fraction of injected carriers ending up in the emitting region.

*A, B*and

*C*are treated as fitting parameters, the

*ABC*model is very successful at reproducing practically all experimental curves involving a plot of IQE versus pump rate. However, concerns arise when

*A, B*and

*C*are associated with the physical processes of defect, radiative and Auger losses. Taking this approach oversimplifies carrier-density dependences and leads to disagreement with coefficient values from microscopic calculations that are far more rigorous âˆ' they directly account for the quantum mechanics of electrons and holes, the effects of band structure, and so on. This departure from the results of microscopic calculations is particularly alarming in the Auger case: Here, the values for the

*C*coefficient for fitting experimental data can be several orders of magnitude higher than those provided by microscopic calculations.

*ABC*model. Greater rigour results from using rates for carrier losses that are determined from microscopic theory. This is possible with the radiative contribution, thanks to semiconductor quantum luminescence equations that provide a truly predictive treatment, and include many-body Coulomb effects. And for the defect contribution, it is possible to turn to microscopic models that predict deviations from the linear carrier-density dependence of the widely used Shockley-Read-Hall expression.

**An alternative approach**

*Figure 3: Approach B, which is introduced by Weng Chow from Sandia National Laboratories, follows more closely the sequence of events leading to light emission in an experiment. Starting with the pump, carrier distributions are created, which in turn produce light and losses.*

*Figure 4: a) Carrier transport mechanisms are carrier-carrier and carrier-phonon collisions. b) Change in carrier density leads to changes in band structure, such as envelope wavefunctions for electrons and holes (red and blue curves for quantum wells and barriers, respectively), energy levels (vertical placements of envelope functions) and quantum-confinement potentials (black lines). c) Radiative transitions from quantum well and barrier.*

*Cn*term (where

^{3}*n*is the carrier density), and are based on a combination of the Auger process sketched in Figure 1c and carrier-phonon collisions depicted in Figure 4a. The latter is assumed to be infinitely fast, so that plasma temperature remains at the lattice temperature.

**Modelling real devices**

_{0.37}Ga

_{0.63}N quantum well or a 3 nm In

_{0.20}Ga

_{0.80}N quantum well, respectively. Results of the modelling show interesting similarities with the experimental data (see Figure 5). Changes in the shape of the IQE-versus-current-density curves due to differences in temperature are also seen in the model. At high lattice temperatures, both types of LED exhibit the familiar IQE-versus-current-density behaviour that can be described by the

*ABC*model. However, at low temperatures, the device with the In

_{0.37}Ga

_{0.63}N quantum well has a second bump in its IQE profile that becomes more pronounced with decreasing temperature. An

*ABC*model cannot describe the appearance of this feature, but it exists in the model that I have developed âˆ' and it might also be present in microscopic models based on Approach A that account for emission from barrier regions (this is shortly discussed).

*Figure 5: IQE versus current density for LED with (a) 2nm In*

_{0.37}Ga_{0.63}N and (b) 3nm In_{0.20}Ga_{0.80}N quantum-well active media. Approach B is used to obtain the computed curves. The insets show the experimental results.

_{0.20}Ga

_{0.80}N quantum well, replicating the experimental result. The difference between the devices with In

_{0.37}Ga

_{0.63}N and In

_{0.20}Ga

_{0.80}N wells is fundamental to the quantum-well structures, and depends entirely on the band-structure differences that result from a smaller piezoelectric field in the active region with a lower indium concentration.

*Figure 6: (From top to bottom) The Shockley-Read-Hall coefficient, Auger coefficient and carrier-phonon scattering rate used in producing the curves in Figure 5. An important result is Auger coefficient magnitude range and increasing value with increasing temperature, consistent with first-principles physics.*

*ABC*model, which are thought to be unrealistically high.

_{0.37}Ga

_{0.63}N device at a lattice temperature of 200K. The curves show that the first bump is primarily due to barrier emission, while the dominant cause of the higher excitation bump is quantum-well emission. An interplay of the quantum-confined Stark and Franz-Keldysh effects governs these relative contributions, and explains the blue shift of the emission peak with increasing excitation.

*Figure 7: a) Spontaneous emission contributions from quantum wells and barriers (solid and dashed curves, respectively) versus current density. b) Contributions to IQE from recombination and scattering processes. The solid red curve is the sum of quantum-well and barrier emission,*

*the dotted curve shows the defect loss, and the dashed curve shows the leakage contribution.*

*c) IQE and d) plasma temperature versus current density. Differences between solid and dashed curves indicate the Auger contributions. All results are for an In*

_{0.37}Ga_{0.63}N device at 200K lattice temperature.

*A projected slide shows the equations of motion for a LED model following Approach B. Similar equations have been used to explore dynamical response and instabilities in quantum-dot and quantum-well lasers, under conditions such as the presence of optical feedback or injected signal. Also in the picture are (left to right) Alan Wright, Weng Chow and Jeff Nelson, who contributed to the early GaN research at Sandia National Laboratories. During the early 1990s, they welcomed the emergence of wide-band-gap lasers and solid-state-lighting as providing opportunities to continue exploring many-body physics, and how to handle defects and the d-shell electrons in density-functional-theory calculations.*

^{-31}cm

^{6}s

^{-1}, which was used to produce the 200K lattice temperature curve in Figure 5a; and a value of 10

^{-34}cm

^{6}s

^{-1}, which is what one would expect by extending an Auger coefficient calculation for near-infrared semiconductors to one with roughly a 2.7 eV band-gap energy.

^{-34}cm

^{6}s

^{-1}is used for the current densities considered. These plots also indicate the efficiency loss from Auger scattering when the value for

*C*is 2.3 x 10

^{-31}cm

^{6}s

^{-1}"“ this is the difference between the solid and dashed curves. Plots of the plasma temperature versus current density are shown in Figure 7d. Here, the dashed curve shows the rise in temperature that primarily results from the capture of carriers from barrier to quantum-well states. Indicated by the solid curve is a significant additional rise in plasma temperature because of Auger scattering.

**Further reading**

*Further information on Modeling Approach B:*

**19**21818 (2011)

**22**1413 (2014)

*Information on experiments used to illustrate Approach B:*

**99**181127 (2011)

**6**S913 (2009)

**6**S814 (2009)

AngelTech Live III: Join us on 12 April 2021!

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