Carrier dynamics in blue, cyan, and green InGaN/GaN LEDs measured by small-signal electroluminescence

Blue and green InGaN/GaN light-emitting diodes (LEDs) are crucial for solid-state lighting and display applications.^1,2 Violet–blue LEDs have achieved a high external quantum efficiency (EQE) of ∼80%.^3,4 However, InGaN/GaN LEDs still suffer from strong efficiency loss in the green region,⁵ which is usually referred to as the “green gap.” The green gap issue has been related to Auger–Meitner recombination (the renaming proposal can be found in Ref. 6),^7–10 the quantum-confined Stark effect (QCSE),^11–14 carrier leakage,^15,16 and defects and carrier localization,^5,17–22 among other causes. To achieve longer emission wavelengths, the indium composition must be increased, leading to several problems. First, high indium content increases lattice mismatch²³ and can potentially introduce additional point defects²⁴ during metalorganic chemical vapor deposition (MOCVD). High indium content also leads to strong polarization-related electric fields in the quantum wells (QWs), lowering the wavefunction overlap and decreasing the radiative and non-radiative recombination rates (i.e., from the QCSE). Studying the carrier dynamics to understand the relative roles of intrinsic effects [e.g., wavefunction overlap, carrier–current density relationship, phase-space filling (PSF)] vs extrinsic effects (e.g., material degradation due to increased defect density and compositional inhomogeneities) is critical to combating efficiency reduction in long-wavelength LEDs.

In this work, we use small-signal electroluminescence (SSEL) to study the carrier dynamics in c-plane LEDs with various emission wavelengths ranging from blue (∼470 nm) to cyan (∼500 nm) to green (∼530 nm). The LED series consists of three wafers grown by Lumileds using state-of-the-art growth conditions with identical active region designs (3×, 3-nm-thick QWs) but indium compositions ranging from 16% to 19%, as measured by energy-dispersive x-ray spectroscopy (EDX). The barriers are GaN and are 18 nm thick. LEDs with mesa diameters of 100 μm and ground-signal-ground electrodes were fabricated. SSEL^25,26 was then used to study the carrier dynamics of the LEDs. Values for each element in an equivalent circuit model were acquired via simultaneous fitting of the impedance and modulation responses, leading to the injection efficiency and total carrier recombination lifetime. Combining the total carrier lifetime with the internal quantum efficiency (IQE) enables the separation of the radiative and non-radiative recombination lifetimes and rates as a function of current density (J) and carrier density (n). A common approach to describe the carrier recombination mechanisms uses the $A n, B n, and C n$ parameters, which are associated with Shockley–Read–Hall (SRH), radiative, and Auger–Meitner recombination, respectively. The experiments reveal that efficiency loss at longer wavelength in the present structures is related to reduction in injection efficiency and confirm that a reduction in radiative recombination and an increase in Auger–Meitner recombination also reduce efficiency, as previously observed in Ref. 27 using optical differential lifetime (ODL) measurements. The interplay between the QCSE and carrier–current density relationship is shown to determine the relative importance of the radiative (⁠ $B n n 2$⁠) and non-radiative recombination rates (⁠ $A nn$ and $C n n 3$⁠) as the indium content is increased.

The LEDs were biased at various DC currents and modulated with a network analyzer (E5061B, Keysight), from 500 kHz to 2 GHz. The amplitude for the small AC signal was ∼20 mV, as a low modulation amplitude is especially important for low current density operation. The LEDs were probed using an RF probe (ACP40-GSG-150, Cascade), and the modulated light was collected into a photodetector (DET025AFC, Thorlabs). A low-noise RF amplifier (PE15A1007, Pasternack) was used to amplify the signal, which was then coupled back to the network analyzer.²⁶ We measured the LEDs to a current density (J) lower limit of 3 A/cm², due to the low light output power at low J.

In SSEL, the differential rate equations are formulated and differential parameters (e.g., differential injection efficiency and differential recombination lifetime) are acquired. Integration is used to convert from differential injection efficiency to injection efficiency. We define the injection efficiency as the current that recombines in the QWs divided by the total current injected into the LED, and the detail can be found in Ref. 28. The injection efficiency decreases at longer wavelengths, as shown in Fig. 1(a), but approaches unity injection at high J. The internal quantum efficiency (IQE) shown in Fig. 1(b) was obtained from Lumileds using external quantum efficiency (EQE) measurements on LEDs with known extraction efficiency. There is significant reduction in IQE at longer wavelengths, a trend that is characteristic of the green gap. The IQE varies from 43.6% (blue) to 34.4% (cyan) to 25.7% (green) at 40 A/cm². The radiative efficiency (⁠ $η r$⁠) is obtained from the IQE (⁠ $η IQE$⁠) and the injection efficiency (⁠ $η inj$⁠) using $η IQE= η inj* η r$ and is shown in Fig. 1(c).

The radiative and non-radiative recombination rates can be calculated from the carrier density in the active region and their respective lifetimes, $R r= n w τ r$ and $R n r= n w τ n r$⁠. In Fig. 3(b), the radiative recombination rate (⁠ $R r$⁠) is lower for longer wavelengths at a given current density, while the non-radiative recombination rate (⁠ $R n r$⁠) is higher for longer wavelengths. Since Auger–Meitner recombination is proportional to n³, and biomolecular recombination is proportional to n², Auger–Meitner recombination will increase faster than radiative recombination at high n. In addition to increased Auger–Meitner recombination, reduction of the radiative rate is evidently an important cause of the green gap. In Fig. 3(c), the radiative and non-radiative recombination rates are lower for longer wavelengths at a given carrier density. This is reasonable because the internal polarization field in the QW is stronger for long wavelength LEDs due to the high indium content; thus, the wavefunction overlap is lower, and the $A n, B n,$ and $C n$ parameters are smaller. The reason for the different behaviors between $R r$ and $R n r$ vs J and n lies in the interplay between the carrier–current density relationship and QCSE. At longer wavelengths, the $A n,B n,$ and $C n$ parameters are lower, but the carrier density is higher at a given J, as shown in Fig. 3(a).

To compute the $A n$⁠, $B n$⁠, and $C n$ coefficients, we use the standard approach of plotting $G n r n$⁠, $G r n 2$⁠, and $C n = ( G n r−A nn)/ n 3.$³¹ As $G n r n$ does not converge even at low $n$⁠, the $C n$ parameter (Auger–Meitner recombination coefficient) is estimated based on the value of the $A n$ parameter. Two bounds are considered for $A n$⁠: The lower bound is zero and the upper bound is $A n= G n r n$ at 3 A/cm². Details are available in the supplementary material. To further the understanding of the origin of the green gap, we calculate the ratios of $B n$⁠, $C n$⁠, and $n$ for the green and cyan LEDs with respect to the blue LED with $A n=0 s − 1$⁠, as shown in Fig. 3(d). The ratio of $C n$ is not significantly affected by the value of $A n$⁠, as the nonradiative recombination is dominated by Auger recombination at high J. Open circles, solid dots, and open squares denote the ratio of radiative recombination rates, non-radiative recombination rates, and carrier densities at a given J, respectively. The colors cyan and green represent the ratios between cyan/blue and green/blue, respectively. Normalized ratios for the various relevant parameters at 40 A/cm² are listed in Table I. Here, we ignore the effect of SRH recombination and assume $C n≈ G n r n 3$⁠, as Auger–Meitner recombination dominates at high J. It is clear that there is a similar relative decrease in $C n$ compared with $B n$ when the wavelength increases. For the cyan LED, $C n$ and $B n$ decrease to 55% and 48% compared to blue, respectively. For the green LED, $C n$ and $B n$ decrease to 15% and 14% compared to blue, respectively. Thus, the radiative and Auger–Meitner coefficients are affected by similar factors when the LED emission wavelength increases.

According to DFT calculations of the intrinsic bulk recombination coefficients,^37,38 $C hhe , bulk B bulk$ is ∼36% larger for green than for blue and ∼15% larger for cyan than for blue. For material degradation or extrinsic trap-assisted Auger–Meitner recombination to be responsible for the decline in the high-current radiative efficiency of InGaN LEDs with increasing wavelength, the ratio $C ( n ) / B ( n )$ would have to substantially increase beyond ∼36% from blue to green and ∼15% from blue to cyan. In contrast, the experimental results of Fig. 4(b) show that the $C ( n ) / B ( n )$ ratios for LEDs of all three wavelengths are within a deviation of 25% from each other, a result that is consistent with the small variation in the ratio of intrinsic recombination coefficients calculated with DFT. This indicates that the behavior of $C ( n ) / B ( n )$ for all three LEDs is consistent with theoretical expectations of the intrinsic recombination mechanics, and neither material degradation nor extrinsic trap-assisted Auger–Meitner recombination needs to be invoked.

Since n is more than 2× higher for the green LED compared to the blue LED at 40 A/cm², the radiative efficiency is mostly affected by larger n, resulting from lower $B(n)$ and $C(n)$ coefficients, rather than changes in $C ( n ) / B ( n )$ at longer wavelengths. This is confirmed by plotting the radiative efficiency vs n in Fig. 4(c), which shows similar radiative efficiencies for all three wavelengths at a given n. However, LEDs operating at longer wavelengths should have less light output at a given n, as the J is lower for longer wavelengths at a given n. Thus, maintaining a low carrier density at a given J is critical to maintaining high efficiency at longer wavelengths. In InGaN/GaN LEDs, there are several possible paths to reduce the carrier density in the QWs by enhancing the wavefunction overlap and/or improving the inter-well carrier transport. Higher wavefunction overlap has been achieved with step potential profiles,³⁹ nonpolar or semipolar orientations,⁴⁰ or very thin QWs.⁴¹ In addition, improving inter-well and lateral carrier transport using V-pit engineering is a very promising approach to achieve higher IQE in long-wavelength LEDs based on numerical modeling^42,43 and experiment.^44–46 

In summary, we studied the carrier dynamics of a series of LEDs with various emission wavelengths near the green gap using a small-signal electroluminescence method. Universal linear scaling between $C n & B(n)$ was observed, and $C ( n ) / B ( n )$ approaches a similar value for all three wavelengths over a range of carrier densities, suggesting a small effect from extrinsic material degradation. However, the carrier density more than doubled in the green LED compared to the blue LED at 40 A/cm² due to the stronger QCSE in the green LED. The increase in carrier density at a given J for longer wavelengths had a much stronger effect than material degradation on reducing the radiative efficiency. Thus, approaches to increase the EQE of green LEDs should prioritize designs that decrease the carrier density in each QW, rather than focus on material quality improvement, particularly in LEDs that already have state-of-the-art epitaxy.