Optoelectric Devices Research Articles

Visualization of Hot Carrier Dynamics in a Single CsPbBr3 Perovskite Microplate Using Femtosecond Kerr-Gated Wide-Field Fluorescence Spectroscopy.

Lead halide perovskites (LHPs) have excellent semiconductor properties. They have been used in many applications such as solar cells. Recently, the hot carrier dynamics in this type of material have received much attention as they are useful for enhancing the performance of optoelectrical devices fabricated from it. Here, we study the ultrafast hot carrier dynamics of a single CsPbBr3 microplate using femtosecond Kerr-gated wide-field fluorescence spectroscopy. The transient photoluminescence spectra have been measured under a variety of excitation fluences. The temporal evolution of bandgap renormalization and the competition between hot carrier cooling and the recovery of the renormalized bandgap are clearly revealed.

Fostering the Dense Packing of Halide Perovskite Quantum Dots through Binary-Disperse Mixing.

Due to their versatile applications, perovskite quantum dot (PQD)-based optoelectrical devices have garnered significant research attention. However, the fundamental packing behavior of PQDs in thin films and its impact on the device performance remain relatively unexplored. Drawing inspiration from theoretical models concerning packing density with size mixtures, this study presents an effective strategy, namely, binary-disperse mixing, aimed at enhancing the packing density of PQD films. Comprehensive grazing-incidence small-angle X-ray characterization suggested that the PQD film consists of three phases: two monosize phases and one binary mixing phase. The volume fraction and population of the binary-size phase can be tuned by mixing an appropriate amount of large and small PQDs. Furthermore, we performed multi-length-scale all-atom and coarse-grained molecular dynamics simulations to elucidate the distribution and conformation of organic surface ligands, highlighting their influence on PQD packing. Notably, the mixing of two PQDs of different sizes promotes closer face-to-face contact. The densely packed binary-disperse film exhibited largely suppressed trap-assisted recombination, much longer carrier lifetime, and thereby improved power conversion efficiency. Hence, this study provides fundamental understanding of the packing mechanism of perovskite quantum dots and highlights the significance of packing density for PQD-based solar cells.

Low-Complexity Conditional Generative Adversarial Network (c-GAN) Based Nonlinear Equalizer for Coherent Data-Center Interconnections

Nonlinear impairments emerging from both fiber optical links and optoelectrical devices are the major bottleneck for enhancing the throughput of photonic data-center interconnection (DCI). Here, we propose a data-driven nonlinear equalizer based on a conditional generative adversarial network (c-GAN) for high-speed and large-capacity photonic DCI. Its performance is experimentally evaluated by transmitting C-band 40-channel 60-GBaud dual polarization-16 quadrature amplitude modulation (DP-16QAM) dense wavelength division multiplexing (DWDM) signals over 20-km standard single-mode fiber (SSMF). Our experimental results verify that, the proposed c-GAN equalizer outperforms both traditional nonlinear equalizers and other data-driven counterparts, in terms of both the bit-error ratio (BER) and computational complexity. Only the proposed c-GAN equalizer can guarantee the BER performance of all 40 channels to reach the threshold of 20% soft decision forward error correction (SD-FEC) at BER=0.027, leading to a net transmission capacity of 16 Tb/s. Meanwhile, the computational complexity of the proposed c-GAN equalizer can be significantly reduced by 31.8%, 80.7%, and 98.8%, respectively, in comparison with Volterra filter equalizer (VFE), multilayer perceptron (MLP), and long short-term memory neural network (LSTM-NN) schemes.

Stability, electronic, thermodynamic, and optical aspects of CsPbI3-xBrx(x=0, 1, 2, 3) compounds: An ab-initio study

All organic metal halide perovskite, due to tunable band gap and stability, has great potential for use in optoelectrical devices. So, we investigate the structural, mechanical, dynamic stability, and electronic, thermodynamic, and optical properties of CsPbI3−xBrx(x=0.1.2.3) compounds. All studied compounds are mechanically stable in the equilibrium temperature and pressure. The phonon dispersion curve of these compounds confirms their dynamical stability. Replacing the halide position with the Br atom is associated with a structural change from cubic to tetragonal, which in turn leads to an increase in stability, hardness, and the value of the direct band gap of CsPbI3−xBrx compounds. Moreover, this structural deformation gives rise to a significant increase of carrier mobility in the asymmetric direction z of the tetragonal structure compared to other symmetric x and y directions.Optical properties calculations show high absorption in the blue-purple frequency region of visible light. The optical conductivity of the deformed structures along the asymmetric z direction is higher than along the symmetric x or y direction, which is in agreement with the charge carrier mobility results. The optical absorption calculations show that the increase of Br concentration in the CsPbI3−xBrx compounds cause the main peak of the absorption to move to a larger amount of energy. The static refractive index of these compounds is comparable to the light-absorbing semiconductor materials in solar cells, and their first peak of refractive index is within the visible energy spectrum of the electromagnetic beam.The direct bandwidth behavior with structural, electronic, and optically adjustable properties makes these compounds attractive for use in optoelectronic devices.

Broadband and ultrafast photodetector based on PtSe2 synthesized on hBN using molecular beam epitaxy

Two-dimensional (2D) van der Waals materials are potential candidates for high-performance optoelectrical devices owing to the bandgap modulation, high on/off ratio, and ultra-stability. However, the challenge of synthesizing large-area, uniform, and high-quality 2D van der Waals materials should be addressed to manufacture large-scale and uniform optoelectrical devices using these materials. Although several previous studies investigated synthesis methods using chemical vapor deposition and molecular beam epitaxy (MBE), there are certain limitations such as the non-uniformity, lots of grain boundaries, and low carrier mobility. Here, by studying a method for synthesizing PtSe2 on hBN buffer layer using MBE, we fabricated a PtSe2-based broadband photodetector. The high-quality PtSe2 synthesized on hBN was evaluated using Raman spectroscopy and scanning transmission electron spectroscopy. These revealed that the synthesized PtSe2 had a high quality and small grain boundary compared with PtSe2 synthesized on SiO2. Owing to the reduction in the carrier scattering and carrier recombination because of the high-quality and small grain boundaries, the photodetector using PtSe2 synthesized on hBN displayed optoelectrical properties that were significantly better than those of PtSe2 synthesized on SiO2. Therefore, using hBN as a buffer layer for PtSe2 growth, a remarkable performance of complex optoelectrical devices could be achieved.

Enhanced Goos-Hänchen shift in a defective Pell quasiperiodic photonic crystal with monolayer MoS2.

Monolayer M o S 2 has attracted wide attention because of its finite bandgap, and it has become a potential candidate for the investigation of the Goos-Hänchen (GH) shift. However, the magnitude of the GH shift in free-standing monolayer M o S 2 is small, which greatly hinders its possible applications in the photoelectric sensors and detectors. We have theoretically designed a defective quasiperiodic photonic crystal and investigated its GH shift, where monolayer M o S 2 is sandwiched between two quasiperiodic photonic crystals arranged by the Pell sequence. By optimizing the thicknesses of all the components and the period number of the Pell quasiperiodic photonic crystal, we find that the GH shift of the designed structure is significantly enhanced at the specific working wavelength. In addition, we discuss the influence of the thicknesses of the dielectric components on the GH shift. Our work confirms that the quasiperiodic photonic crystal structure has the ability to enhance the GH shift of monolayer transition metal dichalcogenides, which provides a new platform for the GH investigations and greatly promotes the applications of this defective structure in optoelectric devices.

Unraveling the unique response behaviors of ultrathin transition metal dichalcogenides to external excitations

Designing novel transition metal dichalcogenides (TMDCs) are highly important for achieving superior performances in advanced optoelectrical devices of broad applications. Although many TMDCs materials have been synthesized and studied, the response behaviors of TMDCs under external excitations still lack in-depth investigations. To address this challenge, we have established a library of TMDCs including 56 types of materials and revealed their response behaviors to the external electric fields and strains as well as the possibility to drive phase transitions under the external excitations. We have explored the thermodynamic stability, band structures, electronic structures, and optical properties of these TMDCs. Under the external electric field, the gradual change of energy results in the conversion from semiconductors to metals, which enables the construction of heterojunctions while the Landau phase transitions are absent. In comparison, the external strain not only lowers the overall symmetry but also induces strong p-π hybridizations to realize unique electronic properties. In particular, Dirac cones are noticed in the 1H-TcTe2 within 45–100 GPa, supporting a novel quasi heavy-fermion topological Kondo insulator induced by the phase transition under the external strains for the first time in TMDCs. This work offers fundamental knowledge to discover novel TMDCs candidates with superior optoelectrical properties.

Tunable Interband Transitions in Twisted h-BN/Graphene Heterostructures.

In twisted h-BN/graphene heterostructures, the complex electronic properties of the fast-traveling electron gas in graphene are usually considered to be fully revealed. However, the randomly twisted heterostructures may also have unexpected transition behaviors, which may influence the device performance. Here, we study the twist-angle-dependent coupling effects of h-BN/graphene heterostructures using monochromatic electron energy loss spectroscopy. We find that the moiré potentials alter the band structure of graphene, resulting in a redshift of the intralayer transition at the M point, which becomes more pronounced up to 0.22eV with increasing twist angle. Furthermore, the twisting of the Brillouin zone of h-BN relative to the graphene M point leads to tunable vertical transition energies in the range of 5.1-5.6eV. Our findings indicate that twist-coupling effects of van der Waals heterostructures should be carefully considered in device fabrications, and the continuously tunable interband transitions through the twist angle can serve as a new degree of freedom to design optoelectrical devices.

Cyano and Isocyano-substituted Tetraphenylethylene with AIE Behavior and Mechanoresponsive Behavior

Dual-functional materials with AIE behavior and mechanoresponsive behavior have attracted considerable attention due to their promising applications in mechano-sensors, optical storage, solid-state optoelectric devices and bioimage systems. AIEgens bearing tetraphenylethylene (TPE) core become elementary building blocks in many fluorescent functional materials. In this article, cyano-and isocyano-electronic withdrawing groups are incorporated with TPE skeleton to form tetracyanophenylethylene (TPE-CN) and tetraisocyanophenylethylene (TPE-NC). Their structures are confirmed by NMR, Mass Spectra and single crystal X-ray measurement. These two isomers reflect aggregation-induced emission (AIE) property in solution state and mechanochromic behavior in solid state. Interestingly, their luminescent intensities, quantum yields and fluorescent lifetime in solid state have an obvious increase upon grinding. The theoretical calculation of these two compounds clarify their difference in optical properties. The mechanochromic mechanism is also intensively explained by powder X-ray measurements.

Visualizing the multi-level assembly structures of conjugated molecular systems with chain-length dependent behavior

It remains challenging to understand the structural evolution of conjugated polymers from single chains to solvated aggregates and film microstructures, although it underpins the performance of optoelectrical devices fabricated via the mainstream solution processing method. With several ensemble visual measurements, here we unravel the morphological evolution process of a model system of isoindigo-based conjugated molecules, including the hidden molecular assembly pathways, the mesoscale network formation, and their unorthodox chain dependence. Short chains show rigid chain conformations forming discrete aggregates in solution, which further grow to form a highly ordered film that exhibits poor electrical performance. In contrast, long chains exhibit flexible chain conformations, creating interlinked aggregates networks in solution, which are directly imprinted into films, forming interconnective solid-state microstructure with excellent electrical performance. Visualizing multi-level assembly structures of conjugated molecules provides a deep understanding of the inheritance of assemblies from solution to solid-state, accelerating the optimization of device fabrication.

Enhanced Photoluminescence and Random Lasing Emission in TiO2-Decorated FAPbBr3 Thin Films.

Herein, titanium-dioxide-decorated organic formamidinium lead bromide perovskite thin films grown by the one-step spin-coating method are studied. TiO2 nanoparticles are widespread in FAPbBr3 thin films, which changes the optical properties of the perovskite thin films effectively. Obvious reductions in the absorption and enhancements in the intensity of the photoluminescence spectra are observed. Over 6 nm, a blueshift of the photoluminescence emission peaks is observed due to 5.0 mg/mL TiO2 nanoparticle decoration in the thin films, which originates from the variation in the grain sizes of the perovskite thin films. Light intensity redistributions in perovskite thin films are measured by using a home-built confocal microscope, and the multiple scattering and weak localization of light are analyzed based on the scattering center of TiO2 nanoparticle clusters. Furthermore, random lasing emission with sharp emission peaks is achieved in the scattering perovskite thin films with a full width at the half maximum of 2.1 nm. The multiple scattering of light, the random reflection and reabsorption of light, and the coherent interaction of light within the TiO2 nanoparticle clusters play important roles in random lasing. This work could be used to improve the efficiency of photoluminescence and random lasing emissions, and it is promising in high-performance optoelectrical devices.

Sapphire crystal growth and solid–liquid interface structure: An investigation by molecular dynamic simulation and Czochralski growth

Sapphire has increasing demand toward optoelectrical devices like LED; its big challenge is to find reasonable growth mechanisms for high quality large size single crystals. In this paper, we proposed both theoretical and experimental studies to clarify multiscale behaviors within the Al2O3 growth system. Molecular dynamics simulation for sapphire crystal growth along c-, a-, and m-axes, and solid–liquid interface structure, and grown 2″ sapphire via the Czochralski method along the c-axis, were reported herein. Our studies show that α-Al2O3 growth behaviors along different crystal directions are different, which is different from the amorphous Al2O3 phase transition at the various α-Al2O3 planes. α-Al2O3 crystal growth in the c-axis system may be a complex process involving solid–liquid and solid–solid transformations, rather than a single solid–liquid transformation that happened in the systems growing along the a- and m-axes. Within the time scale of simulation, the crystals cannot be grown by the lattice period of the seed crystal along the c-axis and transform into γ-Al2O3 rather than α-Al2O3, while it is opposite along the a- and m-axes. This may be the microscopic reason why it is difficult to grow sapphire along the c-axis in the experiment. An abrupt change in the interfacial structure is the key reason to inhibit the transformation of liquid Al2O3 into α-Al2O3 along the c-axis.

Recent Progress on Transparent Microelectrode-Based Soft Bioelectronic Devices for Neuroscience and Cardiac Research.

Transparent microelectrodes have emerged as promising tools to combine electrical and optical sensing and modulation modalities in many areas of biological and biomedical research. Compared to conventional opaque microelectrodes, they offer a number of specific advantages that can enable advances in functionality and performance. In addition to optical transparency, the mechanical softness feature is desired to minimize foreign body responses, increase biocompatibility, and avoid loss of functionality. In this review, we present recent research from the past several years on transparent microelectrode-based soft bioelectronic devices with an emphasis on their material properties and advanced device designs, as well as multimodal application scenarios for neuroscience and cardiology. First, we introduce material candidates with proper electrical, optical, and mechanical properties for soft transparent microelectrodes. We then discuss examples of soft transparent microelectrode arrays tailored to combine electrical recording and/or stimulation with optical imaging and/or optogenetic modulation of the brain and the heart. Next, we summarize the most recent progress on soft opto-electric devices integrating transparent microelectrodes with microscale light-emitting diodes and/or photodetectors into single and hybrid microsystems as powerful tools to explore the brain and heart functions. A brief overview of possible future directions of soft transparent microelectrode-based biointerfaces is provided to conclude the review.

Trans-Reflective Structural Color Filters Assisting Multifunctional-Integrated Semitransparent Photovoltaic Window.

Multifunction-integrated semitransparent organic photovoltaic cells (STOPVs), with high power generation, colorful transmittance/reflectance, excellent UV protection, and thermal insulation, are fully in line with the concept of architectural aesthetics and photoprotection characteristics for building-integrated photovoltaic-window. For the indelible rainbow color photovoltaic window, one crucial issue is to realize the integration of these photons- and photoelectric-related multifunction. Herein, dynamic transmissive and reflective structural color controllable filters, with asymmetrical metal-insulator-metal configurations (20nm-Ag-HATCN-30nm-Ag) through machine learning, were deliberately designed for colorful STOPV devices. This endows the resultant integrated devices with ∼5% enhanced power conversion efficiency than the bare-STOPVs, gifted UV (300-400nm) blocking rates as high as 93.5, 94.1, 90.2, and 94.5%, as well as a superior IR (700-1400nm) rejection approaching 100% for transparent purple-, blue-, green- and red-STOPV cells, respectively. Most importantly, benefiting from the photonic recycling effect beyond microcavity resonance wavelength, a reported quantum utilization efficiency as high as 80%, was first presented for the transparent-green-STOPVs with an ultra-narrow bandgap of 1.2eV. These asymmetrical Febry-Pérot transmissive and reflective structural color filters can also be extended to silicon- and perovskite-based optoelectric devices and make it possible to integrate additional target optical functions for multi-purpose optoelectric devices. This article is protected by copyright. All rights reserved.

Shift Current in Molecular Crystals Possessing Charge-Transfer Characteristics

Further research on organic molecule crystals with spontaneous polarization as a possible candidate for the bulk photovoltaic effect is urgently needed to meet the requirements for optoelectric devices. We demonstrate the shift current in a type of molecular crystal that acts at high temperatures and contains organic molecules with electron donor-acceptor groups, such as paranitroaniline derivatives. We find an extremely strong multicomponent shift-current response along the parallel and perpendicular to polar molecules of the crystals using density-functional simulations, which is more than 10 times larger than the previously reported value for shift current over a broad spectral range from visible to ultraviolet spectrum. Even more intriguing, the remarkable dependency of the conduction- and valence-band dispersions on the lattice constant along polarization allows the shift current in these organic molecule structures to be tuned under stress and doping. Our findings not only suggest a class of organic compounds for realizing the highly controllable shift-current response, but also open up a channel for the search for solar materials.

Understanding the impact of heavy ions and tailoring the optical properties of large-area monolayer WS2 using focused ion beam

Focused ion beam (FIB) is an effective tool for precise nanoscale fabrication. It has recently been employed to tailor defect engineering in functional nanomaterials such as two-dimensional transition metal dichalcogenides (TMDCs), providing desirable properties in TMDC-based optoelectronic devices. However, the damage caused by the FIB irradiation and milling process to these delicate, atomically thin materials, especially in extended areas beyond the FIB target, has not yet been fully characterised. Understanding the correlation between lateral ion beam effects and optical properties of 2D TMDCs is crucial in designing and fabricating high-performance optoelectronic devices. In this work, we investigate lateral damage in large-area monolayer WS2 caused by the gallium focused ion beam milling process. Three distinct zones away from the milling location are identified and characterised via steady-state photoluminescence (PL) and Raman spectroscopy. The emission in these three zones have different wavelengths and decay lifetimes. An unexpected bright ring-shaped emission around the milled location has also been revealed by time-resolved PL spectroscopy with high spatial resolution. Our findings open up new avenues for tailoring the optical properties of TMDCs by charge and defect engineering via focused ion beam lithography. Furthermore, our study provides evidence that while some localised damage is inevitable, distant destruction can be eliminated by reducing the ion beam current. It paves the way for the use of FIB to create nanostructures in 2D TMDCs, as well as the design and realisation of optoelectrical devices on a wafer scale.

Interfacial Self-Assembly of Organized Ultrathin Films of Tripodal Metal-Terpyridyl Coordination Polymers as Luminophores and Heterogeneous Catalysts for Photocatalytic CO2 Reduction.

Metal-directed interfacial self-assembly of well-defined coordination polymer (CP) ultrathin films can control the metal complex arrangement and distribution at the molecular level, providing a convenient route for the design and fabrication of novel opto-electrical devices and heterogeneous catalysts. Here, we report the assembly of two series of CP multilayers with the transition-metal ions of Fe2+, Co2+, Zn2+ and Tb3+ as connectors and tripodal terpyridyl ligands of 4,4',4″-(1,3,5-triazine-2,4,6-triyl)tris(1-(4-([2,2':6',2″-terpyridin]-4'-yl)benzyl)pyridin-1-ium) (TerPyTa) and 4,4',4″-(benzene-1,3,5-triyl)tris(1-(4-([2,2':6',2″-terpyridin]-4'-yl)benzyl)pyridin-1-ium) (TerPyBen) as linkers at the air-water interface. The as-prepared Langmuir-Blodgett (LB) films display strong luminescence, with the emission wavelength and relative intensity dependent on both the metal ions and linkers; among them, the Zn-TerPyTa and Zn-TerPyBen CPs give off the strongest luminescent emission centered at about 370 nm with an emission lifetime of approximately 0.2-0.3 ns. The Tb-TerPyTa CPs can give off emission at approximately 490, 546, 586, and 622 nm, attributed to the 5D4 to 7F3-6 electron transitions of typical Tb3+ ions. Finally, these CP LB films can act as efficient heterogeneous photocatalysts for the CO2 reduction to selectively produce CO. The catalytic efficiency can be optimized by adjusting the experimental conditions (light sensitizer, electron donor, and water content) and CP composition (metal ion and ligand) with an excellent yield of up to 248.1 mmol g-1. In particular, it is revealed that, under the same conditions, the catalytic efficiency of the Fe-TerPyTa CP LB film is nearly 2 to 3 orders of magnitude higher than that of the other metalated complexes investigated in the homogeneous system. UV-vis spectroscopy and cyclic voltammetry studies demonstrated that the dual active sites of Fe-terpyridine and TerPyTa units contribute to the enhanced catalytic activity. This work provides an effective method to introduce the earth-abundant metal complexes into CP films to construct efficient noble-metal-free photocatalysts for the CO2 reduction.

Optoelectronic Memristive Synapse Behavior for the Architecture of Cu2ZnSnS4@BiOBr Embedded in Poly(methyl methacrylate).

The great potential of artificial optoelectronic devices that are capable of mimicking biosynapse functions in brain-like neuromorphic computing applications has aroused extensive interest, and the architecture design is decisive yet challenging. Herein, a new architecture of p-type Cu2ZnSnS4@BiOBr nanosheets embedded in poly(methyl methacrylate) (PMMA) films (CZTS@BOB-PMMA) is presented acting as a switching layer, which not only shows the bipolar resistive switching features (SET/RESET voltages, ∼ -0.93/+1.35 V; retention, >104 s) and electrical- and near-infrared light-induced synapse plasticity but also demonstrates electrical-driven excitatory postsynaptic current, spiking-time-dependent plasticity, paired pulse facilitation, long-term plasticity, long- and short-term memory, and "learning-forgetting-learning" behaviors. The approach is a rewarding attempt to broaden the research of optoelectric controllable memristive devices for building neuromorphic architectures mimicking human brain functionalities.

Synthesis of centimeter-size two-dimensional hybrid perovskite single crystals with tunable, pure, and stable luminescence.

The environment-friendly synthesis and property modulation of two-dimensional organic-inorganic halide perovskite (2D OHP) single crystals with large sizes and high quality are important for the fabrication of optoelectric devices. In this work, plate-like and centimeter-size (BA)2Pb(BrxI1-x)4 (BA = n-butylammonium, x: 0-1) single crystals with high crystallinity were synthesized via the cooling crystallization method in a mixed HX (X: I, Br) acid aqueous solution. The synthesized samples were single-phase with homogenously distributed Br and I ions. The lattice structure and bandgap of (BA)2Pb(BrxI1-x)4 were both finely tuned through halide alloying. Pure photoluminescence with unitary wavelength was obtained in the mixed-halide samples compared to those of monohalides (BA)2PbI4 and (BA)2PbBr4. This is attributed to the structural homogeneity of the alloyed crystals. Moreover, the prepared (BA)2Pb(BrxI1-x)4 samples showed higher photo and thermal stability for a long duration even with ion migration. This study will be an important reference for the fabrication and property modulation of 2D OHP-based light-emitting and other optoelectric devices.

Study of the mechanisms of the phonon bottleneck effect in CdSe/CdS core/shell quantum dots and nanoplatelets and their application in hot carrier multi-junction solar cells.

The hot carrier multi-junction solar cell (HCMJSC) is one of the promising advanced conceptual solar cells with theoretical efficiency greater than 65%, consisting of a thin top junction with a wide bandgap and a thicker junction at the bottom with a medium bandgap for absorption of high and low energy photons. The wide bandgap CdSe/CdS low-dimensional systems (e.g. quantum dots, QDs and nanoplatelets, NPLs) widely used in optoelectrical devices are expected to be an appropriate candidate for the top junction. However, the mechanisms underlying the carrier relaxation rate reduction (or phonon bottleneck effect, PBE) for HCMJSC in these material systems are not well understood so far. In this work, the carrier relaxation mechanisms in CdSe/CdS core/shell QDs and NPLs are quantitatively analyzed by calculating the thermalization coefficient (Qth) through steady state photoluminescence (SSPL) and picosecond-time resolved photoluminescence (ps-TRPL). A significantly extended carrier relaxation time of more than 20 ns was observed in the TRPL of QDs. This could be attributed to both the Auger reheating (AR) at the initial fast decay stage and acoustic phonon folding at the slow decay stage. For SSPL, the Qth value of QDs is much lower due to a 1 order of magnitude higher AR rate. A strong coupling may exist between AR and Qth with a high probability of PBE, where a lower Qth gives a higher AR rate. The AR may dominate carrier thermalization if the PBE level is high. Meanwhile, other mechanisms like acoustic phonon folding will also affect the carrier relaxation if the PBE is at a much lower level.