Technical Insight
A watertight explanation for LED droop?
Experimental measurements of LED droop are replicated with a model that includes carrier leakage
A partnership between Fred Schubert’s team at Rensselaer Polytechnic Institute, New York, and Samsung LED, Korea, claims that it has a new, comprehensive explanation for LED droop. The team’s model for droop, the decline in an LED’s efficiency as its current is cranked up, is based on the leakage of electrons out of the active region of the device.
“[Our] model is able to conclusively describe all aspects of efficiency droop,” says Schubert. This includes temperature dependence, the dependence on third-order and fourth-order terms of carrier density and the scale of this efficiency-limiting phenomena in different material systems, such as those based on GaN and AlGaInP.
Strong asymmetry in electron and hole transport characteristics form the basis for the model, which also includes polarization effects. “The polarization fields lower the effective barrier height of the electron blocking layer, thereby facilitating electron leakage,” explains Schubert.
The origin of LED droop is highly controversial, and several groups have argued that it is predominantly caused by Auger recombination, a process involving three carriers. An Auger-effect contribution that is proportional to the third order of the carrier density is included in the model built by Schubert’s team. Fitting this model to experimental data reveals an Auger coefficient of the order of 10-31 cm6 s-1, two orders of magnitude smaller than a drift leakage term, which also depends on the cube of the carrier density.
“Although the Auger effect is real, it is, in the present context, certainly a secondary effect. It’s probably negligible, maybe even irrelevant,” claims Schubert.
His team’s model, which was built from scratch, accounts for high-injection conditions, where electron drift in the p-type layer leads to a reduction in the injection efficiency. According to the team, droop kicks in when LEDs are operating in the high-level injection regime, which is ‘more easily reached’ when the p-n junction is made from materials that have a strong asymmetry in electron and hole mobility and concentration, such as GaN.
When diodes enter the high-level injection regime, some of the applied voltage starts to drop across the low-conductivity p-type layer, and drift current rises with the total current. At high drive currents, it is significant and leads to a reduction in the injection efficiency into the active region. This causes droop in the LED.
Schubert and his co-workers claim that there are three reasons why this leakage current is higher than one might expect: The electron temperature is significantly higher than the lattice temperature (see Figure 1); experimental measurements of tunnelling currents through barriers generally exceed theoretical estimates; and polarization fields can reduce carrier capture and enhance carrier leakage, due to the positive sheet charge at the interface between the electron-blocking-layer and spacer in InGaN LEDs.
Figure 1. Pulsed emission spectra of an InGaN LED reveals the significant difference between lattice and carrier temperatures. Carrier temperatures were extracted from the high energy slope using the an equation: Intensity is proportional to exp(-hv/kT carrier)
An equation that includes third-order and fourth-order terms for drift-induced loss through leakage, plus a third order term for Auger recombination, has been used to fit efficiency-versus-current plots for three high-quality blue LEDs (see Figure 2). The team claims that the theoretical fits to the emission of all three LEDs, which have peak emission between 448 nm and 451 nm, are excellent. They are clearly superior to the widely used ‘ABC’ model, which does not include a fourth-order term.
Figure 2. At high current densities, the well known ABC model fails to fit experimental results. In comparison, the model of Schubert and co-workers, which include a carrier leakage loss term that depends on the third and fourth order of the carrier density, fits the experimental data very well.
“Having the understanding and knowledge available for the cause of droop, we will be able to develop the tools that allow us to reduce the droop for blue as well as green emitters,” says Schubert.
G.-B Lin et. al. Appl. Phys. Lett. 100 161106 (2012)
“[Our] model is able to conclusively describe all aspects of efficiency droop,” says Schubert. This includes temperature dependence, the dependence on third-order and fourth-order terms of carrier density and the scale of this efficiency-limiting phenomena in different material systems, such as those based on GaN and AlGaInP.
Strong asymmetry in electron and hole transport characteristics form the basis for the model, which also includes polarization effects. “The polarization fields lower the effective barrier height of the electron blocking layer, thereby facilitating electron leakage,” explains Schubert.
The origin of LED droop is highly controversial, and several groups have argued that it is predominantly caused by Auger recombination, a process involving three carriers. An Auger-effect contribution that is proportional to the third order of the carrier density is included in the model built by Schubert’s team. Fitting this model to experimental data reveals an Auger coefficient of the order of 10-31 cm6 s-1, two orders of magnitude smaller than a drift leakage term, which also depends on the cube of the carrier density.
“Although the Auger effect is real, it is, in the present context, certainly a secondary effect. It’s probably negligible, maybe even irrelevant,” claims Schubert.
His team’s model, which was built from scratch, accounts for high-injection conditions, where electron drift in the p-type layer leads to a reduction in the injection efficiency. According to the team, droop kicks in when LEDs are operating in the high-level injection regime, which is ‘more easily reached’ when the p-n junction is made from materials that have a strong asymmetry in electron and hole mobility and concentration, such as GaN.
When diodes enter the high-level injection regime, some of the applied voltage starts to drop across the low-conductivity p-type layer, and drift current rises with the total current. At high drive currents, it is significant and leads to a reduction in the injection efficiency into the active region. This causes droop in the LED.
Schubert and his co-workers claim that there are three reasons why this leakage current is higher than one might expect: The electron temperature is significantly higher than the lattice temperature (see Figure 1); experimental measurements of tunnelling currents through barriers generally exceed theoretical estimates; and polarization fields can reduce carrier capture and enhance carrier leakage, due to the positive sheet charge at the interface between the electron-blocking-layer and spacer in InGaN LEDs.
Figure 1. Pulsed emission spectra of an InGaN LED reveals the significant difference between lattice and carrier temperatures. Carrier temperatures were extracted from the high energy slope using the an equation: Intensity is proportional to exp(-hv/kT carrier)
An equation that includes third-order and fourth-order terms for drift-induced loss through leakage, plus a third order term for Auger recombination, has been used to fit efficiency-versus-current plots for three high-quality blue LEDs (see Figure 2). The team claims that the theoretical fits to the emission of all three LEDs, which have peak emission between 448 nm and 451 nm, are excellent. They are clearly superior to the widely used ‘ABC’ model, which does not include a fourth-order term.
Figure 2. At high current densities, the well known ABC model fails to fit experimental results. In comparison, the model of Schubert and co-workers, which include a carrier leakage loss term that depends on the third and fourth order of the carrier density, fits the experimental data very well.
“Having the understanding and knowledge available for the cause of droop, we will be able to develop the tools that allow us to reduce the droop for blue as well as green emitters,” says Schubert.
G.-B Lin et. al. Appl. Phys. Lett. 100 161106 (2012)
