Molecular Materials with Short Radiative Lifetime for High-Speed Light-Emitting Devices

Abstract

Optical interconnects transmit signals between different parts of integrated circuits using light and have lower power consumption and latency than the conventional metal interconnects. The modulation frequency of the on-chip light sources in optical interconnects determines the signal transmission speed. In principle, on-chip lasers relying on stimulated emission can have high modulation frequency but also have high fabrication complexity and energy consumption. Thus, it is desirable to use light-emitting devices that operate through spontaneous emission as the on-chip light source. However, the operation speed of these devices is limited by the radiative lifetime of the emitting materials. In this perspective, we envision that elaborately designed fluorescence molecules can give rise to materials that have radiative lifetime shorter by several orders of magnitude than conventional inorganic semiconductors through a phenomenon termed superradiance. Optical communication and interconnects utilize high-speed light sources for information transmission. The modulation frequency of light-emitting devices operating through spontaneous emission is fundamentally limited by the material intrinsic radiative lifetime. In this perspective, we examine the radiative lifetime of different materials and identify the superradiant molecular J aggregates as a promising class of materials for high-speed light-emitting devices. These molecular aggregates are relatively unexplored for electroluminescent devices and can have short radiative lifetime on the order of 10 ps while maintaining high photoluminescence quantum yield. The relation between intermolecular interactions, molecular packing geometry, and radiative lifetimes is presented theoretically in the context of Frenkel excitons and is corroborated with experimental examples. We further demonstrate the potential of designing superradiant materials through molecular engineering. We believe that these superradiant molecular materials will open up new opportunities in the fabrication of efficient and high-speed light-emitting devices. Optical communication and interconnects utilize high-speed light sources for information transmission. The modulation frequency of light-emitting devices operating through spontaneous emission is fundamentally limited by the material intrinsic radiative lifetime. In this perspective, we examine the radiative lifetime of different materials and identify the superradiant molecular J aggregates as a promising class of materials for high-speed light-emitting devices. These molecular aggregates are relatively unexplored for electroluminescent devices and can have short radiative lifetime on the order of 10 ps while maintaining high photoluminescence quantum yield. The relation between intermolecular interactions, molecular packing geometry, and radiative lifetimes is presented theoretically in the context of Frenkel excitons and is corroborated with experimental examples. We further demonstrate the potential of designing superradiant materials through molecular engineering. We believe that these superradiant molecular materials will open up new opportunities in the fabrication of efficient and high-speed light-emitting devices. Optical communications and interconnects rely on high-frequency modulation light sources for high-speed information transmission. The commonly used light sources include lasers and light-emitting diodes. Lasers can be modulated at high speed but require complex fabrication steps and are energy intensive. Light-emitting devices operating thorough spontaneous emission can have reduced fabrication complexity and energy consumption, and devices with modulation frequency above 1 GHz have been reported.1Koester R. Sager D. 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Molecular materials can have radiative lifetimes down to tens of picoseconds, which can be further reduced by molecular and crystal engineering. With favorable packing geometry, superradiance can be achieved in molecular aggregates where the radiative lifetime scales inversely with grain size. Thus, designing superradiant molecular crystals can lead to fundamental advancement in high-speed light-emitting devices. In light-emitting devices, the generation of light takes place when electrons and holes recombine radiatively at a rate that depends on the radiative lifetime. For some inorganic semiconductors, the high dielectric constant largely screens the Coulomb attraction between the electrons and holes, which can thus move independently in the conduction and valence band at room temperature. The radiative lifetime of these free carriers depends on the radiative recombination coefficient and the carrier concentration, which are related to the material band structure and doping level. 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The bound electrons and holes have lower energy than the free carriers (Figure 1B) in the conduction and valence band corresponding to their binding energy, which is on the order of 10 meV and can be increased by quantum confinement.13Elward J.M. Chakraborty A. Effect of dot size on exciton binding energy and electron-hole recombination probability in CdSe quantum dots.J. Chem. Theor. Comput. 2013; 9: 4351-4359Crossref PubMed Scopus (61) Google Scholar,14Meulenberg R.W. Lee J.R.I. Wolcott A. Zhang J.Z. Terminello L.J. van Buuren T. Determination of the exciton binding energy in CdSe quantum dots.ACS Nano. 2009; 3: 325-330Crossref PubMed Scopus (140) Google Scholar II–VI quantum dots are a class of materials that host Wannier-Mott excitons, and their radiative lifetime is on the order of 10 ns. Although their radiative lifetime can be reduced by decreasing the particle size,13Elward J.M. Chakraborty A. 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Rev. 1931; 37: 17-44Crossref Scopus (491) Google Scholar An isolated molecule can be conceptually simplified as a two-level system with the two energy levels being the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO, Figure 1D). A molecule at its ground state typically has a pair of electrons with opposite spin occupying the HOMO, which is a singlet state denoted S0. With optical excitation, one electron in the HOMO can be excited into the LUMO without changing its spin. The resulting singlet excited state (S1) is conceptually equivalent to having one electron in LUMO and one hole in HOMO. In molecular solids, these excitations correspond to Frenkel excitons where the electron and hole reside in the same molecule. The radiative lifetime of a molecule is determined by the transition rate between the two states, which is proportional to the transition dipole moment μ (Equation 1). Here ϕg and ϕe denote the molecular ground and excited state wavefunction, q is the elemental charge, r→ is the position operator, and kr is the rate of radiative recombination and the inverse of radiative lifetime. For molecules in singlet excited states, the recombination between the electron and hole gives fluorescence, which has radiative lifetime on the order of 1–100 ns. Besides radiative decay, the singlet excited state can also relax to the triplet state through intersystem crossing, whereby the electron excited into the LUMO would change its spin so that its spin is the same as the electron remaining in the HOMO. Due to the spin-pairing energy, the triplet state would have a lower energy compared with the singlet state. The triplet state can decay to ground state via phosphorescence, which is spin forbidden and has radiative lifetime beyond hundreds of nanoseconds.μ→=⟨ϕg|qr→|ϕe⟩kr=1τrad∝43ν3ℏc3|μ→|2.(Equation 1) The optoelectronic properties of molecular aggregates and crystals are different from isolated molecules due to the many-body Coulomb interactions between the electrons and nuclei of different molecules. When the intermolecular distance is significantly greater than the separation of charges within a molecule, Coulomb interaction can be approximated by the electrostatic interaction of electric dipoles. These materials host Frenkel excitons, which are molecular excitations delocalized in the material with each molecule having a certain possibility to be in the excited state. When the molecules are placed closer to each other, their molecular orbitals start to overlap. In these materials, the intermolecular interactions depend on the shape, phase, and orientation of the molecular orbitals of adjacent molecules and require quantum chemical treatment. The orbital overlap between nearby molecules facilitates charge transfer and delocalization. As a result, an electron from the HOMO of one molecule can be excited into the LUMO of other molecules in the material. This type of excitation gives charge-transfer excitons, which have the electron and hole bound to two different molecules. In actual molecular aggregates, although the intermolecular distance is comparable with the molecular size, the far field dipole approximation of Coulomb interaction is largely valid in materials without significant charge-transfer characteristics. For aromatic molecules with π conjugation, π-π stacking could lead to substantial orbital overlap between adjacent molecules; thus, charge-transfer excitons need to be considered when modeling their optical properties. As the molecules have singlet and triplet excited states, Frenkel excitons in solids have singlet and triplet bands. Phosphorescence from the triplet band, similar to the phosphorescence from molecules, has long lifetime beyond 100 ns. Efficient phosphorescence typically involves heavy atoms that promote spin-orbit coupling.21Sommer J.R. Shelton A.H. Parthasarathy A. Ghiviriga I. Reynolds J.R. Schanze K.S. Photophysical properties of near-infrared phosphorescent π-extended platinum porphyrins.Chem. Mater. 2011; 23: 5296-5304Crossref Scopus (114) Google Scholar,22Sarma M. Tsai W.-L. Lee W.-K. Chi Y. Wu C.-C. Liu S.-H. Chou P.-T. Wong K.-T. 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El-Bayoumi M.A. The exciton model in molecular spectroscopy.Pure Appl. Chem. 1965; 11: 371-392Crossref Scopus (3455) Google Scholar,26Spano F.C. Mukamel S. Superradiance in molecular aggregates.J. Chem. Phys. 1989; 91: 683-700Crossref Scopus (250) Google Scholar In this phenomenon, fluorescence from a certain exciton state can lead to radiative lifetime inversely proportional to the size of the aggregate. Molecular aggregates can be categorized as J and H aggregate depending on the sign of intermolecular Coulomb interactions. As a simple example, we describe the photophysics of molecular aggregates and the origin of superradiance with a linear chain of N molecules where the molecular transition dipole moments are parallel. With a far field dipole approximation, the effect of intermolecular interaction can be treated analytically and can lead to a simple relationship between molecular orientations and material radiative lifetimes. The ground state of the molecular chain is not affected by the intermolecular interactions and can be expressed as the multiplication of the molecular ground state wavefunctions. The excited states of the chain are linear combinations of the degenerate single-molecule excited states (Equation 2) in which the electrons and holes are bound within the same molecule.18Hestand N.J. Spano F.C. Expanded theory of H- and J-molecular aggregates: the effects of vibronic coupling and intermolecular charge transfer.Chem. Rev. 2018; 118: 7069-7163Crossref PubMed Scopus (590) Google Scholar Here, |n> denotes the single-molecule excited states wavefunction where the nth molecule is in the excited state while all other molecules are in the ground state, and |k> denotes the wavefunctions of the Frenkel excitons that form an exciton band. The radiative lifetime of the exciton can be related to the transition dipole moment after substituting the molecular electronic states with the exciton states. If we only consider the interaction between adjacent molecules, the energy of exciton states depends on the relative orientation between the molecular transition dipole and displacement vector connecting the molecular mass centers (Equations 2 and 3; Figure 2).18Hestand N.J. Spano F.C. Expanded theory of H- and J-molecular aggregates: the effects of vibronic coupling and intermolecular charge transfer.Chem. Rev. 2018; 118: 7069-7163Crossref PubMed Scopus (590) Google Scholar With negative Coulomb interaction energy, the all-symmetrical (k = 0) state has lowest energy in the exciton band, which is the state from which the radiative decay will occur. The transition dipole moment of this state is √N times that of the molecular state, which gives the molecular aggregate N times shorter radiative lifetime as well as brighter fluorescence. In the classical picture in which the fluorescent molecules are treated as oscillating dipoles (the transition dipole), these dipoles in the molecular chain are aligned in the same direction into a giant oscillating dipole that has N times the oscillator strength of an isolated molecule. In actual molecular aggregates, due to the presence of disorder and the effect of finite temperature, the number of molecules that “coherently” interact with each other is often smaller than the size of the aggregates. In the absence of disorder, the coherence length is proportional to the square root of the Coulomb energy J divided by thermal energy kT (where k is Boltzmann’s constant and T is temperature).27Yamagata H. Spano F.C. Strong photophysical similarities between conjugated polymers and J-aggregates.J. Phys. Chem. 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The electron excited into this state would decay through internal conversion to the lowest energy state in the exciton band, which has zero transition dipole moment and thus a long radiative lifetime. In this case the aggregate is named H aggregate, as the absorption spectra have hypsochromic shift compared with the molecular monomer. With the existence of faster non-radiative decays, the H aggregate typically has weak fluorescence. Thus, the photophysics of molecular materials depends highly on the geometry of molecular assembly, which dictates the molecular interactions that determine material properties important to high-speed light-emitting devices. The lifetimes of a various fluorescent materials are summarized in Figure 3. The UV-emitting GaN has one of the shortest radiative lifetimes in materials hosting free carriers approaching 1 ns,6Im J.S. Moritz A. Steuber F. Härle V. Scholz F. Hangleiter A. 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