Atomistic Analysis of the Green Gap in InGaN/GaN LEDs: The Role of Random Alloy Fluctuations

1. Introduction & The Green Gap Problem

III-nitride InGaN/GaN-based light-emitting diodes (LEDs) represent the pinnacle of efficiency for solid-state lighting (SSL), with blue LEDs exceeding 80% power conversion efficiency. The prevailing method for generating white light involves using a phosphor to down-convert blue LED emission, a process incurring Stokes losses (~25%). To achieve the ultimate efficiency ceiling, a phosphor-free, direct color-mixing approach using red, green, and blue (RGB) LEDs is essential. However, this strategy is critically hampered by the "green gap" – a severe and systematic drop in the external quantum efficiency (EQE) of LEDs emitting in the green-to-yellow spectrum (approximately 530-590 nm) compared to their blue and red counterparts.

This work posits that a significant contributor to this efficiency drop in c-plane InGaN/GaN quantum well (QW) LEDs is the intrinsic random fluctuation of Indium (In) atoms within the InGaN alloy. As the In content increases to shift emission from blue to green wavelengths, these fluctuations become more pronounced, leading to increased carrier localization and a consequent reduction in the radiative recombination coefficient.

2. Methodology: Atomistic Simulation Approach

To isolate the effect of alloy disorder from other known factors like the quantum-confined Stark effect (QCSE) or material defects, the authors employed an atomistic simulation framework.

2.1 Simulation Framework

The electronic structure of the InGaN/GaN QW system was calculated using a tight-binding or empirical pseudopotential method at the atomistic level. This approach explicitly accounts for the random placement of In and Ga atoms on the cation sublattice, moving beyond the conventional virtual crystal approximation (VCA) which assumes a perfectly uniform alloy.

2.2 Modeling Random Alloy Fluctuations

Multiple random atomic configurations were generated for a given average Indium composition (e.g., 15%, 25%, 35%). For each configuration, the local potential landscape, electron and hole wavefunctions, and their overlap were computed. Statistical analysis across many configurations provided the average behavior and the distribution of key parameters like the radiative recombination rate.

3. Results & Analysis

3.1 Radiative Recombination Coefficient vs. Indium Content

The core finding is that the radiative recombination coefficient (B) decreases significantly with increasing average Indium content in the QW. The simulations show this is a direct consequence of alloy fluctuations. Higher In content leads to stronger potential fluctuations, causing increased spatial separation between localized electron and hole wavefunctions.

3.2 Wavefunction Overlap and Localization

Atomistic simulations visualize the carrier localization. Electrons and holes tend to be trapped in local potential minima created by regions of slightly higher In concentration (for holes) and corresponding strain/potential variations (for electrons). The overlap integral $\Theta = \int |\psi_e(r)|^2 |\psi_h(r)|^2 dr$ , which is proportional to the radiative rate, is found to diminish as these localized states become more spatially separated with larger In fluctuations.

3.3 Comparison with Other Factors (QCSE, Defects)

The paper acknowledges that QCSE (caused by strong polarization fields in c-plane nitrides) and increased defect density at higher In content also degrade efficiency. However, the atomistic simulations suggest that even in the absence of these additional factors, the intrinsic alloy disorder alone can account for a substantial portion of the observed "green gap" by reducing the fundamental radiative rate.

4. Technical Details & Mathematical Formulation

The radiative recombination rate for a transition is given by Fermi's Golden Rule: $$R_{spon} = \frac{4\alpha n E}{3\hbar^2 c^2} |M|^2 \rho_{red}(E) f_e(E) f_h(E)$$ where $|M|^2$ is the momentum matrix element squared, $\rho_{red}$ is the reduced density of states, and $f_e$, $f_h$ are Fermi functions. The key impact of alloy fluctuations is on the matrix element $|M|^2 \propto \Theta$, the wavefunction overlap. The atomistic calculation replaces the average $\Theta$ from VCA with an ensemble average over random configurations: $\langle \Theta \rangle_{config} = \frac{1}{N} \sum_{i=1}^{N} \Theta_i$, which is shown to decrease with In content.

5. Experimental Context & Chart Description

The paper references a typical experimental chart (implied as Fig. 1) plotting External Quantum Efficiency (EQE) vs. emission wavelength for state-of-the-art LEDs. This chart would show:

• A high peak (~80%) in the blue region (450-470 nm) for InGaN LEDs.
• A steep decline in EQE through the green (520-550 nm) and yellow (570-590 nm) region, dropping potentially below 30%.
• A recovery in efficiency in the red region (>620 nm) for AlInGaP-based LEDs.
• The "green gap" is visually the deep trough between the blue InGaN peak and the red AlInGaP peak.

The simulation results for the radiative coefficient $B$ would correlate with this trend, providing a fundamental physical explanation for the left side (nitride-based) of this efficiency valley.

6. Analysis Framework: A Case Study

Case: Evaluating a New Green LED Epitaxy Recipe
A foundry develops a new MOCVD growth recipe claiming to reduce the "green gap." Using the framework from this paper, an analyst would:

1. Isolate the Variable: Characterize the new structure's average In content and well width. Use high-resolution X-ray diffraction (HRXRD) and photoluminescence (PL).
2. Assess Alloy Uniformity: Employ atom probe tomography (APT) or scanning transmission electron microscopy (STEM) with EDS mapping to quantify the scale and magnitude of In composition fluctuations. Compare with standard samples.
3. Model the Impact: Input the measured fluctuation statistics into an atomistic tight-binding solver (like NEMO or equivalent) to compute the expected wavefunction overlap $\langle \Theta \rangle$ and radiative coefficient $B$.
4. Decouple from QCSE/Defects: Measure low-temperature PL efficiency and time-resolved PL to estimate the relative contributions of radiative vs. non-radiative rates. Use piezoelectric measurements to estimate the internal field.
5. Verdict: If the new recipe shows reduced fluctuations and the modeled $B$ increases, the improvement is likely fundamental. If not, any efficiency gain may be due to reduced defects or modified fields, which have different scalability limits.

7. Core Insight & Analyst Perspective

Core Insight: The "green gap" isn't just an engineering nuisance; it's a fundamental materials physics problem baked into the random alloy nature of InGaN. This paper compellingly argues that even with perfect crystals and zero polarization fields, the statistical clustering of Indium atoms inherently damps the radiative rate as we push for longer wavelengths. This shifts the narrative from purely chasing lower defect densities to actively managing alloy disorder at the atomic scale.

Logical Flow: The argument is elegant and sequential: 1) Color mixing requires efficient green emitters. 2) Green emission requires high-In InGaN. 3) High-In means stronger compositional fluctuations. 4) Fluctuations localize carriers and reduce wavefunction overlap. 5) Reduced overlap slashes the radiative coefficient, creating the gap. It cleanly separates this intrinsic limit from extrinsic factors like QCSE.

Strengths & Flaws: The strength is in the methodology—using atomistic simulation to peer below the VCA curtain is powerful and convincing, aligning with trends in other disordered systems like perovskite LEDs. The flaw, acknowledged by the authors, is the isolation of this single factor. In real devices, alloy disorder, QCSE, and defects form a vicious synergy. The paper's model likely underestimates the full gap severity because it doesn't fully couple these effects; for instance, localized states may also be more susceptible to non-radiative recombination at defects, a point explored in later works like those from the group of Speck or Weisbuch.

Actionable Insights: For LED manufacturers, this research is a clarion call to move beyond just measuring average composition and thickness. Metrology for fluctuation statistics must become standard. Growth strategies should aim not just for high In incorporation but for its uniform distribution. Techniques like digital alloying (short-period superlattices), growth under modified conditions (e.g., higher temperature with surfactants), or the use of non-polar/semi-polar substrates to remove QCSE and better expose the alloy-limited ceiling, become critical development paths. The roadmap to ultra-efficient SSL now explicitly includes "alloy engineering" as a key milestone.

8. Future Applications & Research Directions

• Metrology-Driven Growth: Integration of in-situ composition monitoring and real-time feedback control during MOCVD/MBE growth to suppress In clustering.
• Digital Alloys & Ordered Structures: Exploring short-period InN/GaN superlattices as an alternative to random alloys to provide a more deterministic electronic structure.
• Alternative Substrate Orientations: Accelerated development of LEDs on non-polar (m-plane, a-plane) or semi-polar planes (e.g., (20-21)) to eliminate QCSE. This would allow a clearer assessment and targeting of the pure alloy-fluctuation limit.
• Advanced Simulation: Coupling the atomistic electronic structure with drift-diffusion or kinetic Monte Carlo device models to predict full LED efficiency under realistic operating conditions, including the interplay of disorder, polarization, and defects.
• Beyond Lighting: Understanding and controlling alloy fluctuations is also critical for the performance of green InGaN-based laser diodes (LDs) for projectors, visible-light communication (Li-Fi), and quantum technologies.

9. References

1. S. Nakamura, T. Mukai, M. Senoh, "Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes," Appl. Phys. Lett., vol. 64, no. 13, pp. 1687–1689, 1994. (The 1993 breakthrough reference).
2. M. R. Krames et al., "Status and Future of High-Power Light-Emitting Diodes for Solid-State Lighting," J. Disp. Technol., vol. 3, no. 2, pp. 160–175, 2007.
3. B. D. Piercy, "The Case for a Phosphor-Free LED Future," Compound Semiconductor Magazine, vol. 24, no. 5, 2018. (Example of industry perspective on color mixing).
4. E. F. Schubert, Light-Emitting Diodes, 3rd ed. Cambridge University Press, 2018. (Authoritative textbook on LED physics).
5. J. Piprek, "Efficiency Drop in Green InGaN/GaN Light-Emitting Diodes: The Role of Random Alloy Fluctuations," Proc. SPIE 9768, 97681M, 2016. (A related, subsequent review).
6. U.S. Department of Energy, "Solid-State Lighting R&D Plan," 2022. (Official roadmap highlighting the green gap challenge).
7. A. David et al., "The Physics of Recombination in InGaN Quantum Wells," in Nitride Semiconductor Light-Emitting Diodes (LEDs), Woodhead Publishing, 2018. (Detailed discussion on radiative and non-radiative mechanisms).