One option for trimming the cost of solid-state lighting is to drive LEDs at higher current densities, because this slashes the semiconductor content in the lighting unit. But this approach does not deliver as great a benefit as might first appear due to a mysterious malady known as efficiency droop, which causes a decline in the efficiency of the LED at higher bias. In some applications, this energy-sapping mechanism is so severe that it has motivated a move to droop-free, laser-based lighting, even though the complexity of these systems is higher.

Efforts to understand the decline in LED output when the device is driven at higher current densities have focused on the efficiency droop. But there is also a reduction in optical power at higher temperatures, a phenomenon known as thermal droop. It is being investigated by our team at the University of Padova. Understand its cause, and an improvement in the overall efficiency of GaN-based lighting systems could follow.

The aims of our work are not actually limited to highlighting the strong effect of thermal droop in real applications. In addition, we are keen to: underline the importance of standardized measurement conditions, which will aid comparisons between different devices; provide technical solutions; and increase the performance of end-user products.

**Surveying the LED**

We have surveyed the temperature-dependent behaviour of high-performance green LEDs produced by every major manufacturer. This has revealed that under nominal operating conditions thermal droop always exceeds 10 percent (see Figure 1). Its magnitude is only slightly less than that of the efficiency droop, and it also plagues laser-based lighting systems, because temperature influences a laser diode’s threshold current and its slope efficiency.

*Figure 1: Efficiency droop and thermal droop vary significantly between high-power green LEDs produced by different manufacturers (data extracted from datasheets). Note that this figure does not allow for absolute chip quality comparison between manufacturers, since (i) it refers to only one LED model and (ii) the measurement conditions in every datasheet are different.*

Note that the data in Figure 1 is not intended to provide a comparison of the overall quality of LEDs grown by different chipmakers. For this reason, the manufacturers are not disclosed, but blindly represented, using letters “A” to “G”. As optical power losses have been extrapolated from datasheets of specific LED models, they lack statistical relevance. Moreover, even though all models under analysis are high-power green LEDs, the nominal operating current and maximum rated junction temperature vary, as does the bias for measurements of thermal droop. Experiments by our team have uncovered a correlation between the extent of thermal droop in the LED and its defect density, evaluated by capacitance deep-level transient spectroscopy. It is well known that defect-related, Shockley-Read-Hall non-radiative recombination is enhanced by temperature. But could this explain our experimentally-detected variations in the optical power of the LEDs? To determine whether it is a possible explanation, we ran computer-aided numerical simulations to estimate the possible impact of this process. Our conclusion: Shockley-ReadHall recombination fails to account for the entire experimental reduction in optical power (see Figure 2).

*Figure 2: The experimental reduction of the optical power with increasing temperature cannot be fitted with a model based on just Shockley-Read-Hall recombination, so this mechanism alone is unable to account for thermal droop.*

Figure 3: Sketches of different temperature-dependent escape processes: (a) pure thermionic escape, (b) phonon-assisted tunnelling (PAT), (c) thermionic trap-assisted tunnelling (TTAT) and (d) the suggested extended thermionic trapassisted tunnelling (ETTAT). The confining potential barrier is denoted V

_{B}.To confirm that Shockley-Read-Hall recombination cannot, in itself, account for thermal droop in these devices, we carried out some additional tests. It is possible to increase Shockley-Read-Hall recombination using an aging test methodology that creates new defects inside the active region. For this reason, we measured the variation in the thermal droop with stress time, observing a decrease in photoluminescence intensity from the quantum well, which is a clear indication of a higher concentration of defects caused by stress. We were even able to directly measure an increase in the Shockley-Read-Hall recombination with differential lifetime measurements.

Surprisingly, we found that increases in non-radiative recombination had no impact on thermal droop, which remained constant over the whole test. So, clearly, a different mechanism accounts for thermal droop. One of the key findings from other groups that have studied the role temperature plays in LED efficiency is that when electron-blocking layers are thicker, or improved, they cut thermal droop. This observation suggests that carrier escape from the quantum well may be the origin of thermal droop. However, before this contender is to be taken seriously, there is a need to clarify the actual physical process, and to understand why defect density has a strong impact.

**A choice of models**

Within the scientific literature there are several possible models for this mechanism, including: pure thermionic escape, phonon-assisted tunnelling, and thermionic trap-assisted tunnelling. A pictorial representation of all three, plus our own model, is provided in Figure 3.

The pure thermionic escape model is based on the idea that the average energy of the electrons inside the quantum well increases with temperature, with some escaping by overcoming the confining potential barrier. With this model, higher temperatures lead to a lower electron concentration in the quantum well, and therefore a lower optical power. But this model has some weaknesses. Significantly, it offers no correlation with the defect density, which is needed to explain our whole available dataset. What’s more, the modelling of the electron fails to consider its wave-like nature, which can allow it to tunnel outside the quantum well.

An improvement is the phonon-assisted tunnelling model, which provides a better description of the quantum behaviour of the electron. Again, higher temperatures increase the average electron energy, but this time electrons are allowed to tunnel out of the quantum well and through the potential barrier to reach the conduction band. Higher temperatures and stronger electric fields enhance this process. However, this model still fails to account for the impact of defect density on thermal droop.

With the thermionic trap-assisted tunnelling model, defects provide a limiting element for the escape rate. In this case, every electron exits the quantum well via a two-step process. First, it is promoted from the quantum well to a defect located at an energetic position between the quantum well and the conduction band. The likelihood that an electron is promoted increases with temperature and the strength of the electric field. The second step involves the tunnelling of the electron from the intermediate deep level to the border of the conduction band. This is a purely field-assisted tunnelling process, according to the Wentzel-Kramers-Brillouin (WKB) approximation, and is independent of temperature.

A very important feature of this model is the intermediate deep level, which acts as an electron reservoir to the second part of the process. This intermediate level limits the escape rate and allows defects to influence device behaviour. However, since the second step of the process is not thermally-assisted, even this model is not capable of reproducing the experimental behaviour.

To include the effects of temperature and defect density on LED behaviour, we have developed a new model, called extended thermionic trap-assisted tunnelling. It includes the influence of the intermediate deep level, which appears in the thermionic trapassisted tunnelling model. However, we use a completely new analytical formulation of the two steps of the process: the equations for thermionic trapassisted tunnelling are discarded, and replaced with those based on phonon-assisted tunnelling. These new equations include the role of thermal emission at zero bias – that is, pure thermal emission that is not field-assisted − whose importance is stated but not computed in the original formulation.

The basic idea behind our model is that electrons inside the quantum well increase their energy with temperature, via interaction with phonons, and then tunnel towards an intermediate deep level under the influence of a local electric field (shown as P1 in Figure 3 (d)). Once inside the deep level, the same process can move electrons to the conduction band (see P2 in Figure 3 (d)). The upshot is the loss of one electron from the quantum well, and therefore one photon from the output optical power.

*Figure 4: The extended thermionic trap-assisted tunnelling model developed by the team from the University of Padova can provide a good fit to the experimental data.*

With our model, the loss of optical power is proportional to the density of the intermediate deep level. This occurs because the greater the density of defects, the greater the number of destination states for each electron, and the greater the number of electrons that are removed from the quantum well. The second part of the process is needed to remove the electrons from the deep level. Without this step, electrons would fill up the deep level until no more could be removed from the well, leading to the absence of a reduction in optical power.

A simple electrical model allows us to understand the impact of this process on the optical power. Let’s imagine it as a current leakage path shunting the quantum wells. The maximum current that can flow through this path is fixed, since it corresponds to the maximum number of electrons that can travel through the intermediate deep level. It is also known that the maximum current is proportional to the defect density. With this model, part of the bias current is drained by the shunt path, leading to a reduction in optical power that is proportional to defect density and temperature.

One virtue of this model is that it predicts an additional feature of the thermal droop mechanism: it should be stronger at a lower bias current, because the proportion of the bias current leaked by the escape process is higher. Experimental data follow this trend: comparing the optical power data in Figure 2 and Figure 4 reveals that the detected thermal droop has a higher impact under low bias.

We have used this last mechanism to model our experimental data. Carrying out these calculations correctly requires a great deal of knowledge about the active region, including the activation energy of the deep level, the position of the lowest allowed electron energy level inside the quantum well, the phonon energy, the Huang-Rhys factor and the electron effective mass. We have obtained some of these values with experimental measurements: capacitance deep-level transient spectroscopy has revealed the deep-level activation energy; and values for phonon energy, and for the Huang-Rhys factor, have been determined from electroluminescence spectra at 83 K. Meanwhile, the energetic structure inside the quantum well has been computed by numerical simulations, and the electron effective mass has been estimated from a critical analysis of the literature. With our model, the main fitting parameter is the strength of the electric field inside the quantum well, because its estimate or computation is not straightforward.

The results of our efforts show that our model is able to fully reproduce the experimental behaviour of the LED (see Figure 4). The implication is that device efficiency is significantly influenced by carrier escape. We believe that our work offers a new insight into the role of carrier escape on device efficiency. Our findings may prove invaluable in designing new devices and luminaires for droop-free lighting applications, even when they involve the use of lasers.