Simulations suggest that increasing the number of wells is a great way to combat the mysterious malady known as droop. The optimum number of wells depends on the current density, and it could be a dozen or more, says Simon Li and Changsheng Xia from Crosslight software.

LEDs based on GaN are now starting to penetrate their third ‘killer’ application. At the turn of the millennium they were generating billions of dollars by backlighting the keypads and screens of handsets; more recently they have started to dominate the backlighting of laptops and TVs; and now they are just starting to emerge as the premier lighting source for homes and offices.

When LEDs are used in light bulbs, the total amount of light that they produce needs to be far more than when they backlight screens. To keep chip costs acceptable, this means that the current passing through the device must be cranked up to boost the lumen output. But this has an unwanted downside – droop, the reduction in the external quantum efficiency for reasons that are yet to be fully understood, despite the efforts of many researchers to comprehend this controversial, mysterious malady.

While these researchers continue to debate the cause of droop, LED manufacturers – and laser diode makers too, for that matter – will continue to produce devices based on a conventional active region. This design, which has been used since the 1990s, enhances device performance (and efficiency in particular) by splitting the active region into many thin layers called multiple quantum wells (MQW). The resulting structure, an interlacing of wells and barriers, confines electrons and holes quantum mechanically.

It is widely known that it is possible to enhance the efficiency of this device by inserting an electron-blocking layer (EBL) near the p-side of the MQW in the LED. Adding this thin layer made of a material with a wider bandgap than those employed in the active region produces a potential barrier that impedes electron flow out of the active region and into the p-side of the device.

Overflow of electrons out of the active region is one of two popular conjectures for the cause of efficiency droop in blue, MQW LEDs; the other is a non-radiative process known as Auger recombination. Both of these theories have many followers, but they will not receive universal support until they address two major stumbling blocks: Providing a watertight explanation for droop, and accounting for benefits to LED efficiency resulting from MWQs and EBLs.

Auger versus carrier overflow

Following the argument that Auger recombination is the cause of droop is relatively easy. When an LED is turned on, its active region is populated by electrons (and holes) with a density that we can call N. Since the generation of light requires the interaction of an electron and a hole, the radiative recombination process goes as the square of N.  In contrast, Auger recombination, which is a photon-losing process involving three different carriers (two electrons and one hole, or two holes and one electron), goes as the third power of N. This means that when the current in an LED is cranked up and carrier density rises, the increases in Auger recombination outpace those in radiative recombination. Consequently, LED efficiency diminishes at higher current densities, which is the characteristic known as droop.

Compared to accounting for droop, it is more complex to explain the benefits of MQWs and EBLs with an Auger-based theory of LED behaviour. The argument put forward by the Auger camp is that the MQW and EBL both help spread carriers more uniformly within the MQW.  Thus, for the same N-squared photon generation, the third-power Auger loss would be smaller thanks to a more uniform carrier density.

Meanwhile, those that support the overflow theory argue that a quantum well is analogous to a water bucket, with its capability to capture and hold injected carriers diminishing at higher injection.  When injected carriers are not captured or held, they overflow the active region and are wasted, contributing to droop.

It is easy to explain the benefit of MQWs and EBLs with the overflow theory: Adding another wells leads to recapturing and recycling of overflown carriers that were not captured by the previous quantum well; while inserting an EBL forces overflown electrons to turn back, where they will be recaptured by the MQW. Explaining droop is more tricky, with supporters of the overflow theory relying on a quantum mechanical principle that a quantized state can only hold two electrons of opposite spin. This means that a quantum well starts to saturate as more carriers are injected into it.

Since both schools of thought appear to explain the main features of blue LED behaviour at various current densities, numerical simulation is needed to verify these theories quantitatively. This exercise is not only of academic significance – it is also of great practical importance, because numerical simulation can optimise fabrication and manufacturing processes.

How many wells?

It is common industrial practice to use several quantum wells in a nitride based LED, rather than just one. Given this, it is surprising that until very recently, there were no experimental reports of how the addition of another well into the active region impacts performance. In 2011 researchers at the University of California at Santa Barbara (UCSB) broke this drought, claiming that an increase in the number of wells from six to nine decreased  droop in InGaN/GaN MQW LEDs [1]. 

These experimental results offer a great chance to put the competing theories for droop to the test. And if simulations can replicate the real data, this suggests that they could provide a great tool for industrial design and optimization of LEDs.

At Crosslight Software Inc. – which is based in Vancouver, Canada and Shanghai, China – we have recently simulated the behaviour of the UCSB LEDs with our commercially available APSYS software. Specifically, we employed our simulation program with a non-local QW transport model to understand the optical and electrical properties of blue InGaN/GaN MQW LEDs with differing numbers of wells. The key mechanisms in this modelling effort, carrier capture and carrier overflow, are illustrated in Figure 1.  Note that this model includes Auger recombination and carrier overflow, the two leading candidates for the cause of LED droop.

 

Figure 1. Various physical mechanisms, including carrier overflow and Auger recombination, can cause droop in a multiple quantum well LEDs.

We have performed our simulations using both theories, that is, assuming that Auger recombination is dominant in one case and negligible in the other (all other parameters were adjustable within a reasonable range).  We found that we could produce a good fit to the UCSB experiment using the carrier overflow theory – in that case, we have included negligible Auger recombination (see Figure 2). Details of our successful simulation have been published in the journal Applied Physics Letters [2].



Figure 2. Modelling with Crosslight’s APSYS simulation software can replicate the experimental behaviour of blue LEDs with six and nine quantum wells that were made by researchers at UCSB.

Simulations employing Auger recombination as the dominant non-radiative process at high current densities have been far less capable of replicating the experimental data produced by UCSB. It seems that a model based on Auger recombination causes the carriers to recombine too fast at each quantum well before they can reach the next one. One consequence of this is that the optimal number of quantum wells predicted by the Auger theory was far less than that found by experiment. We have no intention of publishing the failed attempts of the Auger theory, and we note that these findings tentatively favour the supporters of overflow theory.

Our next step in this study has been to study the impact of increasing the number of quantum well indefinitely. To do this, we make the unrealistic assumption that growth conditions and crystal qualities are identical throughout the active region, regardless of the number of quantum wells in this structure.  We found that our model based on overflow theory shows that adding more wells always leads to an increase in internal efficiency. However, adding wells also pays a penalty of increasing the operating voltage, leading to a reduction in wall-plug efficiency. At the injection condition used in this study, the sweet spot for the number of wells is 12, but as the current through the device is cranked up, this number gets higher (see Figure 3). In short, the message we have to makers of high-power LEDs is that their devices could probably benefit from more wells.

 

Figure 3:  At higher drive currents, the optimum number of wells for high output increases.

We know that in the real world, perfection is impossible when growing many wells. As they are added into the structure, strain is added and crystalline quality can suffer. To build this behaviour into our model, we are talking to crystal growers and planning to create simulation software that is more realistic than ever before. Once that is done, we should be able to provide a more accurate figure for the optimum number of wells in an LED.

References

[1] S. Tanaka et al et al. Electron. Lett. 47 335 (2011)
[2] Chang Sheng Xia et a. Appl. Phys. Lett. 100 263504 (2012)