Time-resolved photoluminescence by Neogi, Lee, Everitt, Kuroda, Tackeuchi, and Yablonovitch [Phys. Rev. B 66, 153305 (2002)] demonstrated that spontaneous recombination in an In0.18Ga0.82N/GaN quantum well (QW) is accelerated by up to a factor of 92 when the emission is resonantly coupled to a silver surface plasmon, and a Fermi-golden-rule calculation extrapolated the enhancement to 422 for thick silver and to more than 10410^{4} for a QW only 4 nm below the metal. The same paper identified what its calculation could not do: the bare QW recombination rate was fitted with a phenomenological Lorentzian rather than predicted, the mutual back-action (radiation-reaction) coupling between the QW dipoles and the surface-plasmon field was omitted, inhomogeneous broadening (~100 meV) was expected to limit the usable resonance, and the extreme few-nanometer-separation regime was never fabricated. No self-consistent, parameter-free account of the enhancement spectrum for this system has been published, and the few-nanometer regime remains unrealized, while the general lossy-medium electrodynamics and experimental distance-scaling studies have substantially narrowed the practical content of the 10410^{4} extrapolation. The problem remains open.

Background

A quantum well (QW) is a thin semiconductor layer that confines electrons and holes so that they recombine with a sharp emission spectrum; InGaN/GaN QWs are the active medium of blue-green light-emitting diodes. The spontaneous emission (SE) rate of a dipole emitter can be increased by reshaping the electromagnetic density of states around it — the Purcell effect, conventionally quantified by a Purcell factor, the ratio of the modified to the free-space decay rate. A surface plasmon (SP) is a bound electromagnetic mode propagating along a metal–dielectric interface with its field confined to a fringing depth of order tens of nanometers on the dielectric side; for a thin silver film on GaN, the tangential SP branch approaches a resonance energy of about 2.85 eV, close to the emission energy of blue InGaN QWs. An electron–hole pair in a QW placed within the fringing depth can then recombine by emitting into the SP mode instead of into free space, which accelerates the recombination rate. In 1999 Gontijo et al. [Phys. Rev. B 60, 11564 (1999)] inferred such coupling from a ~55-fold photoluminescence dip in continuous-wave measurements, and in 2002 Neogi, Lee, Everitt, Kuroda, Tackeuchi, and Yablonovitch [Phys. Rev. B 66, 153305 (2002)] confirmed it directly by time-resolved photoluminescence (TRPL), a technique in which the intensity decay after pulsed excitation is fitted to extract recombination decay constants. They measured a 3-nm In0.18Ga0.82N QW located 12 nm beneath an ~8 nm silver film, defined the enhancement factor Fsp=1+τ0/τ1F_{sp}=1+\tau_{0}/\tau_{1} from the unsilvered decay constant τ0\tau_{0} and the fast silvered-side decay constant τ1\tau_{1}, and obtained peak values of 36 and 92. Their theory combined Fermi's golden rule (transition rate proportional to the field amplitude squared times the density of final states) with a quantization-normalized SP field profile and the SP dispersion relation of the Ag/GaN/air trilayer, and it fitted the QW dipole matrix element to the data. The calculation predicted the peak FspF_{sp} to grow with silver thickness (asymptoting to 422 for films thicker than ~26 nm) and to exceed 10410^{4} for a QW only 4 nm below the surface. The paper itself flagged four limits of this account: the frequency-dependent bare recombination rate τ0(ω)\tau_{0}(\omega) of the unsilvered InGaN QW — which reflects alloy-composition fluctuations, carrier localization, and trap-related channels — was only modeled by a phenomenological Lorentzian; the calculation omitted the synergistic 'back action' between the QW dipoles and the SP field (radiation-reaction and self-consistent screening effects that grow as the QW approaches the metal); inhomogeneous broadening of about 100 meV was expected to keep the effective linewidth wide, capping the useful resonance at Δωc/Δω≲30\Delta\omega_{c}/\Delta\omega\lesssim30; and no sample in the few-nanometer-separation regime had been fabricated. A complementary body of theory predates and postdates this work: the electrodynamics of molecular emitters near metal surfaces including radiation reaction and nonradiative energy transfer into the metal was formulated classically (Ford and Weber, Phys. Rep. 113, 195 (1984)) and later embedded in macroscopic quantum electrodynamics for lossy, dispersive media (Scheel and Buhmann, 2008), and loss-aware figures of merit for surface-plasmon-polariton luminescence enhancement were analyzed by Khurgin, Sun, and Soref (J. Opt. Soc. Am. B 24, 1968 (2007)). What is at stake physically is whether the enormous predicted enhancement of the total recombination rate at very small emitter–metal separation survives once the self-consistent back-action and the Ohmic (nonradiative) loss channels of the metal are treated on the same footing, and how the ~100 meV inhomogeneous width of a real alloy QW limits the observable enhancement.

Problem Statement

Construct and experimentally validate a quantitative, parameter-free account of the resonant surface-plasmon enhancement of the recombination rate of an InGaN/GaN quantum well coupled to a silver film — the completion left open by Neogi et al. [Phys. Rev. B 66, 153305 (2002)] — comprising four jointly linked requirements. (1) Predict, rather than fit, the frequency dependence and absolute magnitude of the bare (unsilvered) QW recombination rate τ0(ω)\tau_{0}(\omega) for this InGaN/GaN quantum well, replacing the phenomenological Lorentzian model, so that the enhancement spectrum Fsp(ω)=1+τ0/τ1F_{sp}(\omega)=1+\tau_{0}/\tau_{1} can be computed without fitted parameters. (2) Determine how the self-consistent back-action (radiation-reaction and mutual screening) between the QW dipole emitters and the surface-plasmon field, which grows as the Ag-QW separation aa decreases, and the Ohmic loss channels of the metal, together modify Fsp(ω)F_{sp}(\omega). (3) Quantify, theoretically and experimentally, how the ~100 meV inhomogeneous broadening of the alloy QW limits the width and peak of the achievable resonant enhancement. (4) Determine whether the predicted extreme enhancements — such as Fsp>104F_{sp}>10^{4} for a≈4a\approx4 nm, or the asymptotic Fsp≈422F_{sp}\approx422 for thick Ag — survive once back-action and metal loss are included, and specify the fabrication and time-resolved measurement protocol — including the control of the Ag-QW separation at the few-nanometer scale while preserving QW optical quality — that would test this prediction; as no sample in that separation regime has yet been fabricated, the enhancement at that separation can only be quantified as a prediction, together with the experimental protocol that would test it, not by new data. Throughout, "experimentally validate" means quantitative agreement between the parameter-free Fsp(ω)F_{sp}(\omega) and the multi-observable measurements already published for this system — time-resolved decay constants, photoluminescence spectra and intensities, and the silver-thickness and Ag-QW distance scans.

References

  1. Arup Neogi, Chang-Won Lee, Henry O. Everitt, Takamasa Kuroda, Atsushi Tackeuchi, Eli Yablonovitch, "Enhancement of spontaneous recombination rate in a quantum well by resonant surface plasmon coupling", Phys. Rev. B 66, 153305 (2002). DOI: 10.1103/PhysRevB.66.153305, https://doi.org/10.1103/PhysRevB.66.153305
  2. A. Neogi, Chang-Won Lee, Henry O. Everitt, Takamasa Kuroda, Atsushi Tackeuchi, Eli Yablonovitch, "Enhancement of spontaneous emission in a quantum well by resonant surface plasmon coupling", arXiv:cond-mat/0204150 (2002), https://arxiv.org/abs/cond-mat/0204150 (the arXiv preprint of Ref. 1; its title differs from the published title)
  3. I. Gontijo, M. Boroditsky, E. Yablonovitch, S. Keller, U. K. Mishra, S. P. DenBaars, "Coupling of InGaN quantum-well photoluminescence to silver surface plasmons", Phys. Rev. B 60, 11564 (1999). DOI: 10.1103/PhysRevB.60.11564, https://doi.org/10.1103/PhysRevB.60.11564
  4. Koichi Okamoto, Isamu Niki, Alexander Shvartser, Yukio Narukawa, Takashi Mukai, Axel Scherer, "Surface-plasmon-enhanced light emitters based on InGaN quantum wells", Nat. Mater. 3, 601-605 (2004). DOI: 10.1038/nmat1198, https://doi.org/10.1038/nmat1198
  5. G. W. Ford, W. H. Weber, "Electromagnetic interactions of molecules with metal surfaces", Phys. Rep. 113, 195-287 (1984). DOI: 10.1016/0370-1573(84)90098-X, https://doi.org/10.1016/0370-1573(84)90098-X
  6. Stefan Scheel, Stefan Buhmann, "Macroscopic quantum electrodynamics - concepts and applications", Acta Phys. Slov. 58(5), 675 (2008). DOI: 10.2478/v10155-010-0092-x, https://doi.org/10.2478/v10155-010-0092-x
  7. Jacob B. Khurgin, Greg Sun, Richard A. Soref, "Enhancement of luminescence efficiency using surface plasmon polaritons: figures of merit", J. Opt. Soc. Am. B 24(8), 1968 (2007). DOI: 10.1364/JOSAB.24.001968, https://doi.org/10.1364/JOSAB.24.001968
  8. Yufeng Li, Shuai Wang, Xilin Su, Weihan Tang, Qiang Li, Maofeng Guo, Ye Zhang, Minyan Zhang, Feng Yun, Xun Hou, "Efficiency droop suppression of distance-engineered surface plasmon-coupled photoluminescence in GaN-based quantum well LEDs", AIP Advances 7, 115118 (2017). DOI: 10.1063/1.4998217, https://doi.org/10.1063/1.4998217
  9. Hsiang-Chen Wang, Xuan-Yu Yu, Yu-Lun Chueh, Tadas Malinauskas, Kestutis Jarasiunas, Shih-Wei Feng, "Suppression of surface recombination in surface plasmon coupling with an InGaN/GaN multiple quantum well sample", Opt. Express 19, 18893 (2011). DOI: 10.1364/OE.19.018893, https://doi.org/10.1364/OE.19.018893
  10. Shaobo Yang, Shung-Hsiang Wu, Yu-Sheng Lin, Chun-Jui Chu, C. C. Yang, "Surface plasmon coupling effects on the behaviors of radiative and non-radiative recombination in an InGaN/GaN quantum well", J. Appl. Phys. 133, 023104 (2023). DOI: 10.1063/5.0132941, https://doi.org/10.1063/5.0132941
  11. Muhammad Farooq Saleem, Yi Peng, Kai Xiao, Huilu Yao, Yukun Wang, Wenhong Sun, "Factors Affecting Surface Plasmon Coupling of Quantum Wells in Nitride-Based LEDs: A Review of the Recent Advances", Nanomaterials 11, 1132 (2021). DOI: 10.3390/nano11051132, https://doi.org/10.3390/nano11051132
  12. Lucja Marona, Dario Schiavon, Michal Baranowski, Robert Kudrawiec, Iza Gorczyca, Anna Kafar, Piotr Perlin, "Kinetics of the radiative and nonradiative recombination in polar and semipolar InGaN quantum wells", Sci. Rep. 10, 1235 (2020). DOI: 10.1038/s41598-020-58295-x, https://doi.org/10.1038/s41598-020-58295-x