Optical properties of InGaN quantum wells: accurately modeling the effects of disorder

A model including random alloy disorder is used to account for the outstanding optical properties of InGaN quantum wells (QW). The model provides excellent agreement to experimental observations on various structures. This study clarifies the prevalent role played by disorder in optical features such as the luminescence lineshape, the Stokes shift, and the radiative rate. Finally, the relationship between disorder and the peculiar properties of long-wavelength InGaN emitters is investigated.

💡 Research Summary

This paper presents a comprehensive theoretical framework for modeling the optical properties of InGaN quantum wells (QWs) that explicitly incorporates random alloy (RA) disorder. The authors begin by highlighting two distinctive features of III‑nitride QWs: the strong internal polarization fields (on the order of MV/cm) that give rise to the quantum‑confined Stark effect, and the compositional disorder inherent to the InGaN alloy. While the impact of polarization fields has been extensively quantified using one‑dimensional Schrödinger‑Poisson solvers, the role of alloy disorder has remained largely qualitative. Recent atom‑probe tomography studies have shown that In and Ga atoms follow a random distribution rather than forming large clusters, yet the resulting nanoscale fluctuations still produce localized potential minima that can trap carriers.

To address this gap, the authors develop a two‑band effective‑mass Hamiltonian that includes a spatially varying alloy potential generated by randomly assigning In and Ga atoms on a 2 nm grid and smoothing the composition with a Gaussian filter of standard deviation σ. The parameter σ controls the strength of localization; through systematic comparison with experimental data they identify σ = 0.4 nm as optimal. The Hamiltonian neglects many‑body Coulomb interactions, justified by prior work showing that exciton binding is strongly suppressed by the internal fields in thick QWs and that Coulomb‑enhanced radiative rates are modest under the carrier densities considered.

The computational domain spans 20 nm × 20 nm in the in‑plane directions and includes the QW and surrounding barriers in the growth direction. For each random alloy configuration, the authors solve the discretized Schrödinger equation using a finite‑difference scheme, obtaining several hundred electron and hole eigenstates up to a few hundred meV above the ground state. To capture the statistical nature of disorder, they average over 1 000–5 000 independent configurations, which is sufficient to resolve the Urbach tail down to four decades below the mobility edge. The density of states (DOS) for electrons (ρ_e) and holes (ρ_h) is built as a histogram of all eigenvalues without any artificial broadening, ensuring that the spectral width originates solely from disorder.

Carrier populations are assumed to follow thermalized Fermi‑Dirac distributions. The authors argue that carrier‑carrier scattering between localized and delocalized states rapidly equilibrates the system, an assumption later validated by the excellent agreement with experiment. The joint density of states (JDOS) is computed by weighting each electron‑hole transition with the squared overlap of their wavefunctions. Two JDOS versions are defined: the “bare” JDOS (no carriers) and the “loaded” JDOS (including Pauli blocking at a given carrier density n). From the loaded JDOS the authors derive the absorption coefficient α_n, which can become negative at high carrier densities, indicating transparency.

The luminescence spectrum L(E) is obtained from α_n using a standard spontaneous‑emission formula that includes the photon density of states and a Bose‑Einstein factor with the quasi‑Fermi level splitting ΔE_F. A mild Gaussian smoothing (10 meV) removes numerical noise, and empirical longitudinal‑optical phonon tails are added to reproduce the low‑energy side of the spectra. The radiative recombination coefficient B is then calculated by integrating L(E) over energy and normalizing by the square of the carrier density.

The model is applied to three experimental systems: (i) a blue single‑quantum‑well (SQW) with 15 % In and 3.9 nm thickness, (ii) a series of multi‑quantum‑well (MQW) LEDs spanning the blue‑green region, and (iii) a red‑emitting LED with ~30 % In. For the blue SQW, the calculated electron DOS shows a weak Urbach tail (E_u ≈ 6 meV) reflecting loosely localized electron states, while the hole DOS exhibits a pronounced tail (E_u ≈ 17 meV) due to strongly localized hole states with radii ≈ 1 nm. The simulated JDOS reproduces the experimentally observed Stokes shift and linewidth without invoking any phenomenological broadening. The model also predicts a “mobility edge” in the hole DOS around –0.5 eV, which aligns with the knee in the JDOS and the peak luminescence energy, providing a physical interpretation of the apparent band edge in disordered systems.

In the MQW LED series, the model captures the wavelength‑dependent reduction in radiative efficiency (the “green gap”) as a consequence of increased hole localization and reduced wavefunction overlap, rather than solely attributing it to Auger recombination. By adjusting the carrier density to match the measured current‑voltage characteristics, the simulated absorption bleaching and gain spectra agree quantitatively with electroluminescence measurements.

For the red LED, the higher indium content amplifies compositional fluctuations, leading to even stronger hole localization, a larger Stokes shift, and a pronounced drop in the radiative coefficient B. The calculations reproduce the experimentally observed redshift of the emission peak with increasing injection current and the accompanying spectral broadening.

Overall, the paper demonstrates that a disorder‑aware, statistically robust effective‑mass model can quantitatively predict the full suite of optical observables—DOS, Urbach tails, Stokes shifts, absorption spectra, and radiative rates—across a wide range of InGaN QW structures. The work underscores the pivotal role of alloy disorder in shaping the performance of InGaN‑based LEDs and provides a practical computational tool for optimizing device designs by tuning the disorder parameter σ and the carrier injection conditions. Future extensions could incorporate many‑body Coulomb effects and temperature‑dependent disorder to further refine predictions for ultra‑high‑efficiency, long‑wavelength emitters.