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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

High signal-to-noise ratio differential conductance spectroscopy

The scanning tunneling microscope (STM) has enabled manipulation and interrogation of surfaces with atomic-scale resolution. Electronic information about a surface is obtained by combining the imaging capability of the STM with scanning tunneling spectroscopy, i.e., measurement of current-voltage (I/V) characteristics of the surface. We propose a change in the STM feedback loop that enables capturing a higher quality dI/dV image. A high frequency dither voltage is added to the bias voltage of the sample, and the fundamental frequency component of the resulting current is demodulated. The in-phase component of this signal is then plotted along with the X and Y position data, constructing the dI/dV image. Here, we show that by incorporating notch filters in the STM feedback loop, we may utilize a high-amplitude dither voltage to significantly improve the quality of the obtained dI/dV image.

42 ENGINEERING↗
DOE OSTI2022

Selectively patterned Mg-doped GaN by SiN x -driven hydrogen injection

In this work, we demonstrate a method to achieve selectively patterned Mg-doped GaN layers using hydrogen drive-in through plasma-enhanced chemical vapor deposition (PECVD) silicon nitride (SiN x ) films. Activated Mg-doped GaN layers were selectively deactivated by patterned PECVD SiN x films with low-temperature annealing and showed high-resistive behavior. Spatially resolved photoluminescence measurements were used to optically verify the deactivation of Mg acceptors and showed distinct features corresponding to activated and deactivated Mg in GaN. The method suggested here provides a simple and effective method to achieve patterned Mg-doped GaN regions without thermal and plasma damage, which could cause degradation of device performance. The proposed method could provide a way to achieve future high-performance GaN lateral and vertical devices that rely on laterally patterned doping.

42 ENGINEERING↗
DOE OSTI2024

Contactless Production Testing of Silicon Solar Cells

Critical cost reductions in silicon solar cells are made by minimizing silver usage in their metal contacts. The reason why is both clear and unavoidable—silver is not only expensive, but also a potential limiting resource for scale-up (the PV industry alone used 10.3 % of the global silver supply in 2020 [1]). The result is solar cells with vanishing electrical contact area that are extremely difficult to test prior to module manufacture, when they must be sorted for quality to maximize power output and reliability of the subsequent modules. This project developed a new measurement instrument that enables the transition to solar cells with very low silver content, including cell designs with both minimal busbars and no busbars at all to electrically contact. The resulting instrument at project completion demonstrated the ability to sort cells with comparable—or better—results than existing technology. Compared to existing cell-test instruments, the new tool has minimal contacting requirements, which lowers the maintenance costs and use of consumable parts. We demonstrated innovative, yet pragmatic, solutions for reporting a comprehensive set of measurement results useful for both cell sorting (going forward in the line for module manufacture) and process control (looking backward in the line to identify cell manufacturing issues from wafer to cell-test). In addition to the traditional current-voltage characterization at cell test—short circuit current, open-circuit voltage, power, efficiency and fill factor—the new tool maintains all the advanced parameter characterization of our existing product line such as a substrate doping measurement, carrier recombination (lifetime) analysis, and surface recombination analysis.

14 SOLAR ENERGY↗
DOE OSTI2021

Characterization of front contact degradation in monocrystalline and multicrystalline silicon photovoltaic modules following damp heat exposure

Reliability and durability tests play a key role in the photovoltaic (PV) industry by minimizing potential failure risks for both existing and new cell and module technologies. In this work, a detailed study of contact degradation in monocrystalline and multicrystalline PV modules is performed. The modules are subjected to a sequence of damp heat (DH) exposures followed by electrical characterization after each step. Electroluminescence (EL) imaging shows different darkening patterns for monocrystalline modules compared to multicrystalline modules; the former shows darkening near the busbars and the latter shows it across virtually the entire cell surface. The primary loss mechanism is confirmed to be resistive after comparing the current-voltage (I–V) characteristics at each DH exposure step. Representative samples have been cored out from both the degraded modules and controls for materials characterization to gain further insights into the degradation mechanism. Top-down and cross-sectional scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), and top-down high-resolution X-ray photoelectron spectroscopy (XPS) analysis performed on the cored samples confirm the degradation is due to metallization corrosion. Our study suggests that the difference in the darkening pattern can most likely be attributed to the different silver paste composition used for contacting each cell technology, particularly the composition of the glass frit.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Advanced Functional Materials ZnO@ZIF-8 Heterostructures for Neuromorphic Synaptic Devices

Metal-Organic Frameworks have shown great promise for memristive synaptic devices because of their adaptable electrical properties and inherent porosity, which help in efficient ion transport and storage of functional molecules. However, the limited conductivity and sensitivity to moisture associated with most MOF materials hinder their use in electronic applications. In this study, MOFs derived from metabolites have been synthesized, using ZnO as a self-sacrificial metallic source to grow Zeolitic Imidazolate Framework-8 (ZIF-8), forming ZnO@ZIF-8 heteronanostructures for neuromorphic applications. These hybrids ZnO@ZIF-8 act as promising candidates for advanced electronic applications. Through systematic investigations, including a comparison of ZnO@ZIF-8 bilayer devices with ZnO single-layer counterparts, a significant discovery emerged. The bilayer synaptic devices outperformed their single layer counterparts in electrical characteristics, as evidenced by Current-Voltage curve analysis and Long-Term Potentiation/Long Term Depression (LTP/LTD) measurements. Additionally, the ZnO layer thickness (10, 30, 50 nm) has been emphasized and the effects of annealing at 300°C in a vacuum were carefully studied for Neuromorphic Synaptic Devices. Remarkably, the 10 nm ZnO layer exhibited the lowest set voltage and a consistent On/Off ratio. This work marks a significant advancement in understanding bilayer synaptic devices, highlighting the crucial role of ZIF-8 in shaping the future of neuromorphic systems

Kolleboyina, Jayaramulu↗
DOE OSTI2022

An all optical approach for comprehensive in-operando analysis of radiative and nonradiative recombination processes in GaAs double heterostructures

We demonstrate an all optical approach that can surprisingly offer the possibility of yielding much more information than one would expect, pertinent to the carrier recombination dynamics via both radiative and nonradiative processes when only one dominant deep defect level is present in a semiconductor material. By applying a band-defect state coupling model that explicitly treats the inter-band radiative recombination and Shockley–Read–Hall (SRH) recombination via the deep defect states on an equal footing for any defect center occupation fraction, and analyzing photoluminescence (PL) as a function of excitation density over a wide range of the excitation density (e.g., 5–6 orders in magnitude), in conjunction with Raman measurements of the LO-phonon plasmon (LOPP) coupled mode, nearly all of the key parameters relevant to the recombination processes can be obtained. They include internal quantum efficiency (IQE), minority and majority carrier density, inter-band radiative recombination rate (W r ), minority carrier nonradiative recombination rate (W nr ), defect center occupation fraction (f), defect center density (N t ), and minority and majority carrier capture cross-sections (σ t and σ tM ). While some of this information is thought to be obtainable optically, such as IQE and the W r /W nr ratio, most of the other parameters are generally considered to be attainable only through electrical techniques, such as current-voltage (I-V) characteristics and deep level transient spectroscopy (DLTS). Following a procedure developed herein, this approach has been successfully applied to three GaAs double-heterostructures that exhibit two distinctly different nonradiative recombination characteristics. The method greatly enhances the usefulness of the simple PL technique to an unprecedented level, facilitating comprehensive material and device characterization without the need for any device processing.

14 SOLAR ENERGY↗
DOE OSTI2024

Nonreciprocal Coulomb drag between quantum wires in the quasi-one-dimensional regime

Coulomb drag experiments have been an essential tool to study strongly interacting low-dimensional systems. Historically, this effect has been explained in terms of momentum transfer between electrons in the active and the passive layer. We report Coulomb drag measurements between laterally coupled GaAs/AlGaAs quantum wires in the multiple one-dimensional (1D) sub-band regime that break Onsager's reciprocity upon both layer and current direction reversal, in contrast to prior 1D Coulomb drag results. The drag signal shows nonlinear current-voltage (I-V) characteristics, which are well characterized by a third-order polynomial fit. These findings are qualitatively consistent with a rectified drag signal induced by charge fluctuations. However, the nonmonotonic temperature dependence of this drag signal suggests that strong electron-electron interactions, expected within the Tomonaga-Luttinger liquid framework, remain important and standard interaction models are insufficient to capture the qualitative nature of rectified 1D Coulomb drag.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Modeling Framework to Analyze Performance and Structural Reliability of Solid Oxide Electrolysis Cells

Solid oxide electrolysis cells (SOEC) have been receiving significant attention recently because of their high energy efficiency and fast hydrogen production. In this study a multi-physics model to simulate the SOEC performance and structural reliability of a state-of-the-art planar SOEC design was developed. The electrochemical reactions, fluid dynamics, species transport, electron transfer, and heat transfer were modeled in the commercial computational fluid dynamics (CFD) software STAR-CCM+. The thermomechanical analysis and the associated structural reliability evaluations were conducted using the commercial finite element analysis software ANSYS. The electrochemistry model was validated by using the experimentally obtained current-voltage (I-V) characteristics of the electrode-supported SOECs. The reliability analysis using a risk-of-rupture approach showed low failure probabilities under standard operating conditions considered in this study. For cells operated at voltages well above a thermoneutral voltage, the reliability evaluations indicated a potential risk of cell failure, but the damage was concentrated locally in specific areas of the cell which typically do not lead to total loss of cell function. The presented approach provides insights for evaluating representative cell and stack performances and structural reliability without intensive testing and for developing optimally performing and structurally reliable SOECs for efficient hydrogen generation.

25 ENERGY STORAGE↗
DOE OSTI2020

In-Situ Measurement of Power Loss for Crystalline Silicon Modules Undergoing Thermal Cycling and Mechanical Loading Stress Testing

An in-situ method is proposed for monitoring and estimating the power degradation of mc-Si photovoltaic (PV) modules undergoing thermo-mechanical degradation tests that primarily manifest through cell cracking, such as mechanical load tests, thermal cycling and humidity freeze tests. The method is based on in-situ measurement of the module’s dark current-voltage (I-V) characteristic curve during the stress test, as well as initial and final module flash testing on a Sun simulator. The method uses superposition of the dark I-V curve with final flash test module short-circuit current to account for shunt and junction recombination losses, as well as series resistance estimation from the in-situ measured dark I-Vs and final flash test measurements. The method is developed based on mc-Si standard modules undergoing several stages of thermo-mechanical stress testing and degradation, for which we investigate the impact of the degradation on the modules light I-V curve parameters, and equivalent solar cell model parameters. Experimental validation of the method on the modules tested shows good agreement between the in-situ estimated power degradation and the flash test measured power loss of the modules, of up to 4.31 % error (RMSE), as the modules experience primarily junction defect recombination and increased series resistance losses. However, the application of the method will be limited for modules experiencing extensive photo-current degradation or delamination, which are not well reflected in the dark I-V characteristic of the PV module.

14 SOLAR ENERGY↗
DOE OSTI2020

Enhance coherence time in intensely driven quantum systems

Not long ago, it was shown that a discrete time crystal can be realized if a quantum system is periodically driven to a non-equilibrium state. Proof-of-concept experiments are reported by two groups using trapped ions and nitrogen-vacancy centers in diamond, respectively. The concept of discrete time crystals vividly demonstrates that the coherence time of a quantum system may be enhanced by driving the system out of equilibrium. In this project, we want to test this novel concept in another canonical quantum system, the quantum Hall system in a two-dimensional electron gas (2DEG). Compared to other systems, quantum Hall magnetism (QHM) in high quality, industry-compatible GaAs/AlGaAs heterostructures allows for detailed and quantitative studies in a particularly simple and clean environment. This detailed knowledge should help achieve longer coherence times in a driven QHM system. This report will detail the results from a recent study on the stability of the quantum Hall skyrmions (QHS) state at a Landau level filling close to ν = 1 by measuring its current-voltage (I-V) breakdown characteristics under radio-frequency (RF) radiations. We observe that the critical current increases visibly when the RF frequency is right at the Larmor frequency of 75As nuclei, where the hyperfine interaction between electron and nuclear spins perturbs the QHS state most significantly. We believe that this observation is consistent with the novel concept that the coherence time of a quantum system may be enhanced by driving the system out of equilibrium.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Low-temperature grapho-epitaxial La-substituted BiFeO 3 on metallic perovskite

Bismuth ferrite has garnered considerable attention as a promising candidate for magnetoelectric spin-orbit coupled logic-in-memory. As model systems, epitaxial BiFeO 3 thin films have typically been deposited at relatively high temperatures (650–800 °C), higher than allowed for direct integration with silicon-CMOS platforms. Here, we circumvent this problem by growing lanthanum-substituted BiFeO 3 at 450 °C (which is reasonably compatible with silicon-CMOS integration) on epitaxial BaPb 0.75 Bi 0.25 O 3 electrodes. Notwithstanding the large lattice mismatch between the La-BiFeO 3 , BaPb 0.75 Bi 0.25 O 3 , and SrTiO 3 (001) substrates, all the layers in the heterostructures are well ordered with a [001] texture. Polarization mapping using atomic resolution STEM imaging and vector mapping established the short-range polarization ordering in the low temperature grown La-BiFeO 3 . Current-voltage, pulsed-switching, fatigue, and retention measurements follow the characteristic behavior of high-temperature grown La-BiFeO 3 , where SrRuO 3 typically serves as the metallic electrode. These results provide a possible route for realizing epitaxial multiferroics on complex-oxide buffer layers at low temperatures and opens the door for potential silicon-CMOS integration.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Encapsulating High–Temperature Superconducting Twisted van der Waals Heterostructures Blocks Detrimental Effects of Disorder

High-temperature cuprate superconductors based van der Waals (vdW) heterostructures hold high technological promise. One of the obstacles hindering their progress is the detrimental effect of disorder on the properties of the vdW-devices-based Josephson junctions (JJs). Here, a new method of fabricating twisted vdW heterostructures made of Bi 2 Sr 2 CuCa 2 O 8+δ , crucially improving the JJ characteristics and pushing them up to those of the intrinsic JJs in bulk samples, is reported. The method combines cryogenic stacking using a solvent-free stencil mask technique and covering the interface by insulating hexagonal boron nitride crystals. Despite the high-vacuum condition down to 10 –6 mbar in the evaporation chamber, the interface appears to be protected from water molecules during the in situ metal deposition only when fully encapsulated. Comparing the current-voltage curves of encapsulated and unencapsulated interfaces, it is revealed that the encapsulated interfaces' characteristics are crucially improved, so that the corresponding JJs demonstrate high critical currents and sharpness of the superconducting transition comparable to those of the intrinsic JJs. Finally, it is shown that the encapsulated heterostructures are more stable over time.

2D materials↗
DOE OSTI2020

Dark Lock-in Thermography Identifies Solder Bond Failure as the Root Cause of Series Resistance Increase in Fielded Solar Modules

Correlating the electrical performance of photovoltaic modules to the spatially resolved photoluminescence, electroluminescence, and dark lock-in thermography (DLIT) images is an important long-term goal for developing solar cell technology. These images offer highly sophisticated and detailed information about the spatial distribution and (if imaged at successive time intervals) temporal degradation of local series and shunt resistances. There have been extensive studies to correlate these imaging techniques to local characteristics at the cell level. However, it has been difficult to extract and quantify module-level information from the techniques. In this study, we interpret module current-voltage (I-V) measurements along with corresponding DLIT images within a module-scale simulation framework, demonstrating that series resistance degradation of the module I-V characteristics, in this case, can be attributed to solder bond failures. Our simulations highlight how current crowding associated with a failed solder joint (or a section of the solder pad) translates to the characteristic point-like (asymmetric doublet) heating pattern in neighboring solder joints (or the neighboring regions of the solder pad). Overall, the correlation between series resistance and solder joint degradation could inform expedited diagnosis of field degradation of solar modules.

42 ENGINEERING↗
DOE OSTI2025

Diagnosis of PV Cell Antireflective Coating Degradation Resulting From Hot-Humid High-Voltage Potential Aging

Corrosion of the antireflective coating on a photovoltaic cell ("ARc corrosion") has previously been observed in studies using hot-humid test conditions with external high-voltage (HV) bias. This study primarily focuses on known vulnerable legacy aluminum back surface field cells in mini-modules (MiMos) put through comparative stepped stress tests. Each cell type had MiMos at +1500 V, -1500 V, or unbiased ("Voc") potential, which were sequentially subjected to test conditions of 60 degrees C/60% relative humidity (RH) for 96 h, as in International Electrotechnical Commission Technical Specification 62804-1; 70 degrees C/70% RH for 200 h; and 85 degrees C/85% RH for 200 h. Characterizations at each step included visual camera and electroluminescence (EL) imaging, colorimetry, and current-voltage curve tracing. Final characterizations included: Suns-Voc, spatial mapping of external quantum efficiency, high-resolution photoluminescence, EL, and dark lock-in thermography imaging. Forensics were performed on extracted cores, including scanning electron microscopy (SEM) with energy-dispersive X-ray spectroscopy (EDS), X-ray photoelectron spectroscopy, and scanning Auger microscopy (SAM). Forensics were also conducted on MiMos from previous studies that underwent stepped HV aging and separate outdoor aged full-sized modules. ARc corrosion was specifically seen for the glass/encapsulant/cell side of the +1500 V (HV+) stressed MiMos and modules. Appearance, color, and reflectance were the most distinguishing characteristics relative to glass corrosion, gridline corrosion and delamination, and other concurrent degradation modes. SEM/EDS and SAM identified the conversion of silicon nitride to hydrated silica, hydrous silica, or hydrated amorphous silica, which preferentially occurred at the edges and tips of the pyramidal textured cell surface.

14 SOLAR ENERGY↗
DOE OSTI2025

Diagnosis of PV Cell Antireflective Coating Degradation Resulting from Hot-Humid, High Voltage Potential Aging

Corrosion of the antireflective coating on a photovoltaic cell ("ARc corrosion") has previously been observed in studies using hot-humid test conditions with external high-voltage (HV) bias. This study primarily focuses on known vulnerable, legacy aluminum back surface field (Al-BSF) cells in mini-modules (MiMos) put through comparative stepped stress tests. Each cell type had MiMos at +1500 V, -1500 V, or unbiased ("Voc") potential, which were sequentially subjected to test conditions of 60deg C/60% relative humidity (RH) for 96 h, as in International Electrotechnical Commission (IEC) Technical Specification 62804-1; 70 deg C/70% RH for 200 h; and 85 deg C/85% RH for 200 h. Characterizations at each step included visual camera and electroluminescence (EL) imaging, colorimetry, and current-voltage (I-V) curve tracing. Final characterizations included: Suns-Voc; spatial mapping of external quantum efficiency (EQE); high-resolution photoluminescence (PL), EL, and dark lock-in thermography (DLIT) imaging. Forensics were performed on extracted cores, including scanning electron microscopy (SEM) with energy-dispersive X-ray spectroscopy (EDS), X-ray photoelectron spectroscopy (XPS), and scanning Auger microscopy (SAM). Forensics were also conducted on MiMos from previous studies that underwent stepped HV aging and separate outdoor aged full-sized modules. ARc corrosion was specifically seen for the glass/encapsulant/cell side of the +1500V (HV+) stressed MiMos and modules. Appearance, color, and reflectance were the most distinguishing characteristics relative to glass corrosion, gridline-corrosion and -delamination as well as other concurrent degradation modes. SEM/EDS and SAM identified conversion of silicon nitride to hydrated silica, hydrous silica, or hydrated amorphous silica, which preferentially occurred at the edges and tips of the pyramidal textured cell surface.

14 SOLAR ENERGY↗
DOE OSTI2026

Multiscale Characterization of Electrode-Induced Degradation in Perovskite Solar Cells

The stability of metal-halide-perovskite (MHP) solar cells must be understood and improved for the commercial viability of MHP technologies. Here, we apply multiscale characterization methods to study degradation modes, specifically electrode corrosion, for p-i-n MHP partial device stacks and full devices that are stored in the dark under an inert atmosphere. Our multiscale characterization approaches include full-device electro-optical performance using current-voltage (JV) curves and spatial imaging with electroluminescence (EL) and photoluminescence (PL). We further correlate interface properties using cross-sectional Kelvin probe force microscopy, which maps the nanoscale electric field properties, and electron microscopy, which demonstrates structural and chemical features. Devices stored as a full device stack degrade primarily by metal (Ag) electrode diffusion into the absorber, with formation of AgI byproducts and Ag accumulation near the indium tin oxide (ITO) contact. This causes decomposition of the perovskite absorber domains, loss of the potential drop at the electron transport layer (ETL)/perovskite interface near the metal contact, and increased equivalent resistance at the perovskite/hole transport layer (HTL) interface near the ITO contact. The devices stored without metal show a different degradation pathway dominated by corrosion of the ITO, creating voids at the ITO electrode surface with diffusion of In and Sn into the absorber. We conclude that metal electrode-induced degradation is the most severe degradation pathway under dark storage, but that ITO corrosion and absorber instability must also be mitigated. We further demonstrate mitigation of these degradation pathways by changes to the device stack, including a SnO x blocking layer at the ETL side and replacing ITO with FTO at the HTL side. These results provide a useful demonstration of specific dark degradation pathways at each electrode interface, as well as a unique multiscale example that links degradation of chemical, structural, and electrical interface properties to the full-device electro-optical characteristics.

14 SOLAR ENERGY↗
DOE OSTI2022

Investigating the Role of Copper in Arsenic Doped Cd(Se,Te) Photovoltaics

The open circuit voltage (VOC) deficit in Cd(Se,Te)-based photovoltaics remains a critical obstacle for pushing the technology closer to theoretical performance limits. Arsenic doping has become a dominant and promising route to achieve the higher p-type carrier concentrations necessary for higher VOC, but challenges associated with this alternate defect chemistry and higher doping density have hindered progress. Here we show that while arsenic doping enables high carrier concentrations (>1016 cm-3), co-doping with copper can provide a boost to VOC without a significant change to carrier concentration. A large data set is initially used to explore current-voltage and capacitance-voltage trends associated with arsenic doped devices with and without copper. A smaller subset is then used to probe these trends using a wide variety of characterization techniques. Copper is found to facilitate reduced interface recombination and potentially improved bulk absorber characteristics, though the mechanisms for these improvements are not yet clear. Despite the improved performance of co-doped devices, VOC is still far below its potential especially for highly doped devices. Low emitter doping in conjunction with high absorber doping seems to be a plausible cause for this significant deficit, though other device properties may exacerbate this problem.

CdSeTe↗
DOE OSTI2024

Influence of the Dielectric Constant on the Ionic Current Rectification of Bipolar Nanopores

In this paper, we investigate how the dielectric constant, ϵ, of an electrolyte solvent influences the current rectification characteristics of bipolar nanopores. It is well recognized that bipolar nanopores with two oppositely charged regions rectify current when exposed to an alternating electric potential difference. Here, we consider dilute electrolytes with NaCl only and with a mixture of NaCl and charged nanoparticles. These systems are studied using two levels of description, all-atom explicit water molecular dynamics (MD) simulations and coarse-grained implicit solvent MD simulations. The charge density and electric potential profiles and current-voltage relationship predicted by the implicit solvent simulations with ϵ = 11.3 show good agreement with the predictions from the explicit water simulations. Under nonequilibrium conditions, the predictions of the implicit solvent simulations with a dielectric constant closer to the one of bulk water are significantly different from the predictions obtained with the explicit water model. Further, these findings are closely aligned with experimental data on the dielectric constant of water when confined to nanometric spaces, which suggests that ϵ decreases significantly compared to its value in the bulk. Moreover, the largest electric current rectification is observed in systems containing nanoparticles when ϵ = 78.8. Using enhanced sampling, we have shown that this larger rectification arises from the presence of a significantly deeper minimum in the free energy of the system with a larger ϵ, and when a negative voltage bias is applied. Since implicit solvent models and mean-field continuum theories are often used to design Janus membranes based on bipolar nanopores, this work highlights the importance of properly accounting for the effects of confinement on the dielectric constant of the electrolyte solvent. The results presented here indicate that the dielectric constant in implicit solvent simulations may be used as an adjustable parameter to approximately account for the effects of nanometric confinement on aqueous electrolyte solvents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗