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At least 289 records · Page 16

Application of unsupervised deep learning to image segmentation and in-situ contact angle measurements in a CO 2 -water-rock system

Rock surface wettability is a critical property that regulates multiphase flows in porous media, which can be quantified using the surface contact angle (CA). X-ray micro-computed tomography (μCT) provides an effective approach to in-situ measurements of surface CAs. However, the CA measurement accuracy depends significantly on the quality of CT image segmentation, which is the clustering of CT pixels into separate phases. Inspired by this, we developed a deep learning (DL)-based CA measurement workflow. Motivated by the recent tremendous progress in unsupervised learning techniques and aiming to avoid expensive manual data annotations, an unsupervised DL pipeline for CT image segmentation was proposed and implemented, which includes unsupervised model training and post-processing. The unsupervised model training was driven by a novel loss function constrained with feature similarity and spatial continuity and implemented by iterative forward and backward paths; the former clustered the pixel-wise feature vectors extracted by convolution neural networks, whereas the latter updated the parameters using gradient descent. An over-segmentation strategy was adopted for model training. The post-processing steps based on agglomerative hierarchical clustering (AHC) were implemented to further merge the over-segmented model output to the desired cluster number, which is intended to improve the efficiency of image segmentation. The developed unsupervised DL pipeline was compared with other commonly-used image segmentation methods using pixel-wise and physics-based evaluation metrics on a synthetic raw-image dataset, which had a known ground truth. The unsupervised DL pipeline showed the best performance. Next, the segmented images were input to an automatic CA measurement tool, and the results were validated by comparisons with manual measurements. The CA values from the manual and automatic measurements showed similar distributions and statistical properties. The automatic measurement demonstrated a wider spectrum because of the much larger number of measurement data points. The primary novelty of the unsupervised DL pipeline developed in this study lies in the novel loss function and the over-segmentation strategy associated with AHC post-processing. Finally, the workflow has been proven an efficient tool for pore-scale wettability characterization, which has a wide range of applications in fundamental studies of multiphase flows in natural porous media, which have critical implications to geological carbon sequestration, hydrocarbon energy recovery, and contaminant transport in groundwater.

42 ENGINEERING↗

Engineering a photoenzyme to use red light

Photoenzymatic reactions involving flavin-dependent “ene”-reductases (EREDs) rely on protein-templated charge transfer (CT) complexes between the cofactor and substrate for radical initiation. These complexes typically absorb in the blue region of the electromagnetic spectrum. Here, we engineered an ERED to form CT complexes that absorb red light. Mechanistic studies indicate that red-light activity is due to the growth of a red-absorbing shoulder off the previously identified cyan absorption feature. Molecular dynamics simulations, docking, and excited-state calculations suggest that the cyan feature involves a π→π* transition on flavin, whereas the red-light absorption is a π→π* transition between flavin and the substrate. Furthermore, differences in the electronic transition are due to changes in the substrate-binding conformation and allosteric tuning of the electronic structure of the cofactor-substrate complex. Microenvironment tuning of the CT complex for red-light activity is observed with other engineered photoenzymatic reactions, highlighting this effect’s generality.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Long-term effects of thinning and woody control on longleaf pine plantation development, understory abundance, and tree damage from an ice storm

Longleaf pine (Pinus palustris) plantations have been established across the southeastern United States as the first step in restoring the declining savanna ecosystem, yet their long-term stability and development to open canopied woodlands may depend on early density and vegetation management treatments. Commercial thinning (CT) was applied in 2012 (year 18) to a long-term study of longleaf pine community restoration at the Savannah River Site near Aiken, SC to increase abundance of herb species. Although precommercial thinning (PCT) and woody vegetation control increased herb species cover during the first five years of the study, measurements from years 17 to 22 indicated a continuing decline in their cover since year 9 despite application of CT in year 18. Herb species richness, however, increased from 21 to 43 species per 100 m2 area during the last six years of the study, likely a result of disturbances associated with CT and an ice storm in year 20. Application of PCT in 1994, when the plantations were 8–11 years old, reduced their susceptibility to stem bending and breakage from the ice storm, which occurred 20 years later in 2014. Measured 5 months before the storm, pine height: dbh ratio (HD) averaged 78 and 90 for trees growing with and without PCT, respectively, and stem breakage (% of trees) from the ice storm increased linearly (r2 = 0.53) with HD. Pine mortality from the combined effects of glaze ice and wind differed with (28%) versus without (45%) PCT, indicating that long-term stability of longleaf pine plantations depends on early density management.

54 ENVIRONMENTAL SCIENCES↗

Multi-scale imaging of high-pressure hydrogen induced damage in EPDM rubber using X-ray microcomputed tomography, helium-ion microscopy and transmission electron microscopy

Ethylene propylene diene (EPDM) rubber has gained increasing interest for use in hydrogen infrastructure due to its excellent sealing performance and low temperature properties. However, severe structural damage has been observed in EPDM O-rings after exposure to high-pressure hydrogen. The origination and propagation mechanisms of this damage are poorly understood. Here, to address this knowledge gap, multi-scale imaging leveraging X-ray micro-computed tomography (micro-CT), helium ion microscopy (HeIM), and transmission electron microscopy (TEM) were used in this work to study a series of sulfur-cured ethylene propylene diene (EPDM) rubber materials with varying additives that were exposed to different hydrogen environments. Micro-CT captured the substantial structural damage due to hydrogen exposure; it revealed an association between zinc oxide (ZnO) particles and damage initiation. Further studies by TEM and scanning TEM with energy dispersive X-ray spectroscopy (EDS) were focused on these particles at the micro-to nano-scale range. TEM indicated that hydrogen causes void formation at the interface between ZnO and the rubber matrix. HeIM enabled imaging of surface morphology of the material at high resolution pre- and post-hydrogen exposure while providing information on chemical composition and that cannot be captured by either micro-CT or TEM.

08 HYDROGEN↗

Comparison of three measurement modalities for 3D characterization of manufactured features and process-induced porosity in titanium alloy additively manufactured parts

Nondestructive characterization of internal features and defects within complex components is vital for many industrial applications, particularly with the advent of additive manufacturing (AM) technologies. However, community understanding of the limitations of nondestructive methods such as X-ray Computed Tomography (CT) can be limited in certain industrial sectors as these may be emergent applications. In this paper, we investigate the limits of X-ray CT measurements and compare extracted data with mechanical polishing serial sectioning (MPSS) and confocal laser scanning microscopy (CLSM). The test object is an additively manufactured titanium alloy disk that contains both process-induced porosity and machined features, including focused ion beam milled features designed to probe the resolution limits of X-ray CT. Results show that each of these characterization techniques has advantages and disadvantages. We compare data acquisition times, spatial resolution, geometric measurement accuracy and defect visualization fidelity across these modalities to establish a practical framework.

Additive manufacturing↗

Diabatization with Electrostatic Embedding for Studying Photophysics in Organic Molecular Crystals

Highly emissive organic molecular crystals find applications in several areas, such as organic electronics, solar cells, and sensors. Understanding the excited-state mechanisms underlying these applications is essential for optimizing and controlling them effectively. Exciton models coupled with nonadiabatic dynamics, particularly quantum dynamics, provide crucial insights into photochemical and photophysical processes in molecular crystals. Nevertheless, there remains a lack of general tools and automated workflows to facilitate such simulations. In this paper, we present a computational strategy to investigate the photoactivated dynamics of organic molecular crystals, bridging methodologies traditionally used for molecular systems and materials science, with a particular focus on the interplay between local excitations and charge transfer (CT) processes. We have implemented an interface between the fromage and Overdia programs, enabling the construction of vibronic Hamiltonians for molecular crystals within an excited-state ONIOM(QM:QM′) framework, incorporating long-range electrostatics through a RESP-based Ewald summation. Fragment-based diabatization provides a route to quantum dynamics simulations in weak-to-intermediate coupling regimes. The method was applied to the photophysics of dibenzo[g,p]chrysene (DBC) crystals using time-dependent DFT. The fromage/ Overdia interface was employed to compute the couplings of local excitations and CT states for 18 unique DBC dimers in the crystal and to quantify the influence of electrostatic embedding, which was found to be modest (10−20%). Simulations on π-stacked dimers reproduced the small red shift observed experimentally from solution to crystal, attributed to electronic interactions among fixed monomers rather than crystal electrostatics. Quantum dynamics simulations revealed ultrafast population transfer from bright local excitations to CT states. This approach establishes a robust framework linking molecular and solid-state excited-state dynamics, with potential applications for studying excitations, defects, and impurities in molecular crystals.

Crystals↗

Photoinduced Charge Transfer and Vibronic Coherence in CdSe Quantum Dots with Methyl Viologen Acceptors

We show herein that photoinduced charge transfer from CdSe quantum dots (QDs) to surface-bound methyl viologen (MV 2+ ) acceptors is mediated by a vibronically coherent, nonadiabatic mechanism. Broadband multidimensional electronic spectra and an analysis of coherences show that a mixed QD–MV charge-transfer (CT) state is populated on the <50 fs time scale after optical preparation of the X3 (1P 3/2 –1P e ) state, well prior to the appearance of the one-electron photoreduced ground state (MV +• ). A partial redistribution of charge from the core of the QD to the acceptor is revealed by excited-state coherences of an out-of-plane vibrational mode local to MV 2+ and of a low-frequency mode mixing a MV 2+ mode with the longitudinal optical (LO) phonon of the QD core. The ultrafast damping of these coherences indicates that excited-state wavepackets travel from the optically prepared, Franck–Condon structure through a conical intersection to reach the CT state. These results suggest that vibronically coherent processes generating CT intermediates can be exploited to improve the efficiency of QD-based solar cells and photocatalysts.

Cadmium selenide↗

Boosting Photoelectric Conductivity in Porphyrin-Based MOFs Incorporating C 60

Electronic structure calculations show that guest C60 in the porphyrin-containing metal organic frameworks Zn 2 (TCPB)(DA-ZnP) (DA-MOF; H 4 TCPB = 1,2,4,5-tetrakis(4-carboxyphenyl)benzene, DA-ZnP = [5,15-bis[(4-pyridyl)ethynyl]-10,20-diphenylporphinato]zinc(II)) and Zn 2 (TCPB)(F-ZnP) (F-MOF; F-ZnP = [5,15-di(4-pyridyl)-10,20-bis(pentafluorophenyl)porphinato]zinc(II)) engenders high photoelectrical conductivity due to efficient donor–acceptor charge-transfer (CT) interactions. Structural modifications at the meso position of the porphyrin influence the preferred positions of C 60 within the frameworks, giving rise to host–guest interactions with different anisotropic structural, electronic, and optoelectronic properties. A preferred slipped-parallel π-stacked interaction of C 60 that is predicted for NH 2 -substituted DA-MOF and F-MOF fosters strong CT transitions and lowers band gaps by ~1.0 eV compared to the pristine DA-MOF and F-MOF. Hopping rates computed using Marcus theory are found to be anisotropic and accelerated by multiple orders of magnitude across π-stacked interfaces created by C 60 incorporation, a consequence of strong electronic coupling between initial and final diabatic states. Calculations indicate that photoinduced electron transfer, as well as direct CT from porphyrin to C 60 upon irradiation, triggers a charge separation process that leads to the formation of what should be long-lived electron-trapped states at the heterojunctions. Lastly, design principles revealed here for the control of photophysical and electron-transfer processes will be useful for constructing new MOF-derived visible- and infrared-based optoelectronics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ultrafast Interlayer Charge Transfer between Bilayer PtSe 2 and Monolayer WS 2

Interlayer charge transfer (CT) between PtSe 2 and WS 2 is studied experimentally. Layer-selective pump–probe and photoluminescence quenching measurements reveal ultrafast interlayer CT in the heterostructure formed by bilayer PtSe 2 and monolayer WS 2 , confirming its type-II band alignment. The CT facilitates the formation of the interlayer excitons with a lifetime of several hundred ps to 1 ns, a diffusion coefficient of 0.9 cm 2 s –1 , and a diffusion length reaching 200 nm. Furthermore, these results demonstrate the integration of PtSe 2 with other materials in van der Waals heterostructures with novel charge-transfer properties and help develop fundamental understanding on the performance of various optoelectronic devices based on heterostructures involving PtSe 2 .

36 MATERIALS SCIENCE↗

Long Excited-State Lifetimes in Three-Coordinate Copper(I) Complexes via Triplet–Triplet Energy Transfer to Pyrene-Decorated Isocyanides

There has been much effort to improve excited-state lifetimes in photosensitizers based on earth-abundant first-row transition metals. Copper(I) complexes have gained significant attention in this field, and in most cases, sterically driven approaches are used to optimize their lifetimes. This study presents a series of three-coordinate copper(I) complexes (Cu1–Cu3) where the excited-state lifetime is extended by triplet–triplet energy transfer. The heteroleptic compounds feature a cyclohexyl-substituted β-diketiminate (CyNacNac Me ) paired with aryl isocyanide ligands, giving the general formula Cu(CyNacNac Me )(CN-Ar) (CN-dmp = 2,6-dimethylphenyl isocyanide for Cu1; CN-pyr = 1-pyrenyl isocyanide for Cu2; CN-dmp-pyr = 2,6-dimethyl-4-(1-pyrenyl)phenyl isocyanide for Cu3). The nature, energies, and dynamics of the low-energy triplet excited states are assessed with a combination of photoluminescence measurements at room temperature and 77 K, ultrafast transient absorption (UFTA) spectroscopy, and DFT calculations. The complexes with the pyrene-decorated isocyanides (Cu2 and Cu3) exhibit extended excited-state lifetimes resulting from triplet–triplet energy transfer (TTET) between the short-lived charge-transfer excited state ( 3 CT) and the long-lived pyrene-centered triplet state ( 3 pyr). This TTET process is irreversible in Cu3, producing exclusively the 3 pyr state, and in Cu2, the 3 CT and 3 pyr states are nearly isoenergetic, enabling reversible TTET and long-lived 3 CT luminescence. The improved photophysical properties in Cu2 and Cu3 result in improvements in activity for both photocatalytic stilbene E/Z isomerization via triplet energy transfer and photoredox transformations involving hydrodebromination and C–O bond activation. Furthermore, these results illustrate that the extended excited-state lifetimes achieved through TTET result in newly conceived photosynthetically relevant earth-abundant transition metal complexes.

14 SOLAR ENERGY↗

Coupled Transport, Reactivity, and Mechanics in Fractured Shale Caprocks

Abstract Shales are low‐permeability caprocks that confine fluid, such as CO 2 , nuclear waste, and hydrogen, in storage formations. Stress‐induced fractures in shale caprocks provide pathways for fluid to leak and potentially contaminate fresh water aquifers. Fractured shales are also increasingly considered as resources for CO 2 sequestration, enhanced geothermal, and unconventional energy recovery. Injecting reactive fluids into shales introduces chemical disequilibrium, causing an onset of a series of dissolution, precipitation, and fines mobilization mechanisms. The reactions have rapid kinetics and significant impact on porosity and permeability; consequently, flow and storage properties of caprocks. While previous research has explored the separate effects of these reactions, this study aims to uncover their simultaneous occurrence and collective influence. This study unveils these highly coupled transport and reactivity mechanisms by tracking and visualizing the reaction‐induced alterations in the matrix, microcracks, and fractures of shales over time. We conducted brine injection experiments sequentially at pH 4 and 2 in a naturally fractured Wolfcamp shale sample while simultaneously imaging the dynamic processes using X‐ray computed tomography (CT). CT images are validated by finer resolution images obtained using micro‐CT and scanning electron microscopy. We also tracked the sample permeability and fluid chemistry using brine permeability and inductively coupled plasma mass spectrometry, respectively. Findings show that fluid primarily flowed through fractures, dissolving reactive minerals and mobilizing fines on fracture surfaces. Dissolution of fracture asperities under confining stress resulted in the closing of fractures. Clogging in narrow fracture pathways, caused by fines accumulation, diverted fluid flow into matrix pores.

58 GEOSCIENCES↗

Time‐And‐Space Averaging Applied to Intermittent Multiphase Flow Experiments

Abstract Various researchers have studied fluctuations in pore‐scale phase occupancy during multiphase flow in porous media using synchrotron‐based X‐ray microcomputed tomography (micro‐CT). However, the impact of these fluctuations on the concept of a representative volume is not yet fully understood. In this study, we performed spatial and temporal averaging of multiphase flow experiments visualized with synchrotron‐based micro‐CT, focusing on oil saturation as the key parameter to determine a representative time‐and‐space average. Our findings revealed that a saturation value representative of both time and space was achieved during fractional flow experiments in drainage mode with fractional flows of 0.8, 0.5, and 0.3. Furthermore, we computed a range of relative permeabilities on the basis of whether momentaneous saturation or time‐and‐space averaged saturation was utilized for direct simulation. Our results highlighted the importance of time‐and‐space averaging in determining a representative relative permeability and indicated that the temporal and spatial scales covered in a typical micro‐CT flow experiment were sufficient to obtain a representative saturation value for sandstone rock under intermittent flow conditions.

Environmental Sciences & Ecology↗

Development of an ERT‐Based Framework for Bentonite Buffers Monitoring From Laboratory Tests: 2. Quantitative Moisture Dynamics Estimation Model

Abstract The long‐term containment of high‐level radioactive waste in geological disposal repositories relies on Engineered Barrier Systems (EBS), with bentonite clay emerging as a candidate material due to its unique properties. Understanding moisture dynamics within bentonite buffers is crucial for EBS performance, as it directly influences the material's swelling capacity, thermal and hydraulic conductivity, mechanical properties, and long‐term evolution under complex thermal‐hydrological‐mechanical (THM) processes. This study develops an advanced Electrical Resistivity Tomography (ERT)‐based framework to quantitatively monitor moisture dynamics under THM conditions. Our framework extends the Waxman‐Smits model to incorporate the coupled effects of temperature, water content, fluid chemistry, and mechanical changes on bentonite's electrical properties. Utilizing HotBENT‐Lab data from our companion paper, which includes electrical conductivity, CT density, and thermocouple measurements, this study offers a novel methodological framework bridging different scales of the model. Our results show that the extended model can estimate water content from ERT data, capturing spatial and temporal variations in moisture distribution within bentonite columns. However, the model tends to overestimate water content compared to CT density‐derived measurements. We address this discrepancy by incorporating a simplified swelling effect model, which improves agreement between ERT and CT density‐based water content estimates. We also discuss model limitations, including simplified treatment of swelling and micropore effects, and propose a conceptual framework for transitioning from laboratory to field applications, addressing challenges such as parameter scalability, field validation methods, and integration of diverse data sources. This ERT‐based framework can potentially advance real‐world moisture monitoring of bentonite‐based EBS in nuclear waste repositories. Plain Language Summary Safely containing high‐level radioactive waste depends on barriers made from materials like bentonite clay, which is effective because it swells and seals in the waste. To ensure these barriers work well over time, it's important to understand how moisture moves through the clay. Our study developed a new method using ERT to monitor moisture levels in bentonite under conditions that mimic those in actual storage sites, including changes in temperature, water content, and mechanical stress. This study improved an existing model to better account for how these factors affect the clay, allowing us to create more accurate moisture maps. Initially, the proposed model overestimated the amount of water in the clay, but its accuracy was improved by factoring in how the clay swells when wet. This study also identified some limitations of the model and suggested ways to adapt it for use in real‐world waste storage sites. This new approach could lead to better monitoring and safety checks for nuclear waste storage systems, helping to ensure long‐term containment. Key Points This work develops an ERT‐based framework extending the Waxman‐Smits model to monitor bentonite moisture dynamics during coupled THM processes The extended model accurately estimates water content from Electrical Resistivity Tomography data, incorporating swelling effects to improve precision This work proposes a conceptual framework for transitioning from laboratory to field applications, advancing EBS monitoring in nuclear waste repositories

Chen, Hang↗

Revealing nanomechanical deformation at the interface and degradation in all-thin-film inorganic electrochromic devices

Recently, progress in electrochromic (EC) devices has been made in optimizing electrode and device configurations and performance. However, the ion insertion/de-insertion induced charge transfer (CT) nanomechanical effect has remained unexplored, i.e., repetitive electrode size changes at the nanoscale and stress/strain generated during electrochemical cycling, which is the focus of this work due to its intimate correlation with the elastic and plastic deformation at the interface. Considering the intervalence electrons, excellent electrochemical kinetics, and dramatic color changes, tungsten oxide (WO 3 ) and nickel oxide (NiO) films are configured as the EC cathode and anode materials, respectively, within a full device. Upon extended cycles (>10 000), the void generation and delamination that occurred at the interface account for performance decay. Encouraged by the findings, nanoindentation mechanical tests and electrical kelvin probe force microscopy were employed to investigate the CT induced effects at the interface. There is a dramatic increase of up to 45% in the elastic Young's modulus in colored/charged WO 3 at ~40 mC cm -2 . Here, the correlation between CT and synergistic mechanical effect is interpreted by the Lippman equation. Interestingly, despite the charged state (colored; lithiated) with a relatively flat morphology bringing an ~3.4 times higher electrostatic surface potential, the electrical work function unexpectedly decreases, arising from the dominant effect of the dipole layer potential over the chemical potential. The interatomic cohesive energy and equilibrium distance increase bury the seeds for mechanical deformation in the long run. This work provides fundamental insights into electro-chemo mechanics and interdisciplinary concerted interfacial effects at the nano/atomic level. The dependence of surface potential, stress, work function, and cohesive energy on electrochemical kinetics has been interpreted.

36 MATERIALS SCIENCE↗

CTRAMER: An open-source software package for correlating interfacial charge transfer rate constants with donor/acceptor geometries in organic photovoltaic materials

In this paper, we present CTRAMER (Charge-Transfer RAtes from Molecular dynamics, Electronic structure, and Rate theory)—an opensource software package for calculating interfacial charge-transfer (CT) rate constants in organic photovoltaic (OPV) materials based on ab initio calculations and molecular dynamics simulations. The software is based on identifying representative donor/acceptor geometries within interfacial structures obtained from molecular dynamics simulation of donor/acceptor blends and calculating the corresponding Fermi’s golden rule CT rate constants within the framework of the linearized-semiclassical approximation. While the methods used are well established, the integration of these state-of-the-art tools originating from different disciplines to study photoinduced CT processes with explicit treatment of the environment, in our opinion, makes this package unique and innovative. The software also provides tools for investigating other observables of interest. After outlining the features and implementation details, the usage and performance of the software are demonstrated with results from an example OPV system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Studies on the compositional dependent structural and electrical properties of CaTiO3-modified K0.5Na0.5NbO3 piezoelectric system

Lead-free piezoelectric ceramics of (1 − x)K0.5Na0.5NbO3-xCaTiO3 were fabricated, and their crystal structure, microstructure, and electrical properties were systematically studied. Rietveld refinement of the x-ray diffraction data and Raman spectroscopic analyses revealed a composition-dependent structural phase transition: three phase transitions, namely, from a pure orthorhombic phase for x ≤ 0.02 to a mixed phase of orthorhombic and tetragonal phases (0.03 ≤ x ≤ 0.08) and finally another mixed phase of tetragonal + cubic for x = 0.10 and 0.15 at room temperature (RT). The morphological study reveals a decrease in grain size along with a more uniform distribution of grains as the concentration of CaTiO3 (CT) increases; notably, a homogeneous distribution of grains is observed for x = 0.05. The temperature-dependent dielectric properties show two phase transitions, from orthorhombic to tetragonal (TO-T) and tetragonal to cubic (TC), for unmodified K0.5Na0.5NbO3 (KNN). However, both the phase transition temperatures (TO-T and TC) decrease, and the transition peaks broaden with an increase in CT substitution, and for x > 0.06, the TO-T shifted below RT. The broadening of the transition peak at TO-T may be due to the relaxation behavior. Among the prepared samples, the 5 mol. % CT-modified KNN shows the optimum electrical properties (d33 = 114 pC/N, ɛr = 412, and 2Pr = 15.25 μC/cm2) at RT. The enhanced electrical properties for x = 0.05 are due to the coexistence of orthorhombic and tetragonal phases, facilitating easy polarization rotation and flattening of the free energy profile. A phase diagram has been constructed based on the information gathered from the temperature-dependent dielectric measurements, RT x-ray diffraction, and Raman spectroscopy data and is discussed in detail.

Physics↗

2D microspatial distribution uniformity of photon detection efficiency and crosstalk probability of multi-pixel photon counters

Two-dimensional (2D) microspatial distribution uniformity of photon detection efficiency (PDE) and optical crosstalk probability P{sub ct} of multi-pixel photon counters (MPPCs) is studied. The experimental results show that the 2D spatial distribution of P{sub ct} is obviously uneven, i.e. P{sub ct} is larger at the corners and edges of a single pixel in MPPCs, which suggest a higher electrical field in the depletion region of the pixel at the corners and edges. The nonuniformity of the 2D spatial distribution of PDE also become evident when the size of the pixels of MPPCs is small, which signifies higher nonuniformity of the electric field distribution in MPPCs with small pixel size. A method is proposed for characterization of the 2D electrical field spatial distribution uniformity in a single pixel of MPPCs, which can be used for guiding the optimisation of the fabrication process of MPPCs and their properties. This promising method can naturally be extended to any Geiger avalanche photodiodes (G-APDs) and their arrays. (laser applications and other topics in quantum electronics)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗