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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Spatially Resolved Potential and Li-Ion Distributions Reveal Performance-Limiting Regions in Solid-State Batteries

The performance of solid-state electrochemical systems is intimately tied to the potential and lithium distributions across electrolyte–electrode junctions that give rise to interface impedance. Here, we combine two operando methods, Kelvin probe force microscopy (KPFM) and neutron depth profiling (NDP), to identify the rate-limiting interface in operating Si-LiPON-LiCoO 2 solid-state batteries by mapping the contact potential difference (CPD) and the corresponding Li distributions. The contributions from ions, electrons, and interfaces are deconvolved by correlating the CPD profiles with Li-concentration profiles and by comparisons with first-principles-informed modeling. Furthermore, we find that the largest potential drop and variation in the Li concentration occur at the anode–electrolyte interface, with a smaller drop at the cathode–electrolyte interface and a shallow gradient within the bulk electrolyte. Correlating these results with electrochemical impedance spectroscopy following battery cycling at low and high rates confirms a long-standing conjecture linking large potential drops with a rate-limiting interfacial process.

25 ENERGY STORAGE↗
DOE OSTI2022

Electrical Potential Investigation of Reversible Metastability and Irreversible Degradation of CdTe Solar Cells

In this paper, we report on the stability of CdTe devices with a structure of TCO/MZO/CdSeTe/CdTe/back-contact. The device showed reversible transitions between the light-soak state (LSS) with the best device efficiency and the dark-soak state (DSS) with an inferior efficiency. However, it showed an irreversible degradation state (DgS) driven by long-hour light soaking at an elevated temperature. We have investigated transitions between these three states from the perspective of the electric field by nm-resolution potential imaging across the devices using Kelvin probe force microscopy (KPFM). The results exhibit different anomalous electric field profiles. At the LSS, the electric field exhibits a main peak inside the CdSeTe layer instead of the MZO/CdSeTe heterointerface, illustrating a buried homojunction (BHJ) of the device. At the DSS, a large electric field peak at the MZO/CdSeTe interface was measured, which probably resulted in the inferior fill factor at the DSS. At the DgS, the electric field peak at the MZO/CdSeTe interface increased further and a third electric field was measured at the back contact of the device. Device modeling using COMSOL software, in alignment with both the electric field and device current-voltage curves, elucidates that a low n-doped CdSeTe in the region near the MZO/CdSeTe interface caused the BHJ in the LSS and a loss of MZO doping and/or increase of the conduction band offset spike due to long-term stress caused the increased electric field near the MZO/CdSeTe interface at the DgS.

CdTe solar cell↗
DOE OSTI2023

Nanometer-scale electrical potential imaging on absorber of CdSeTe solar cells

Here, we report on nm-scale electrical potential imaging throughout As-doped and Cu-doped CdSeTe absorbers using Kelvin probe force microscopy (KPFM). The potential imaging was conducted both laterally and vertically on beveled films using ion milling at small glancing angle. KPFM images electrical potential on the beveled surface and assesses defect charging in the subsurface region within a screening length from the beveled surface. We found that the grain boundaries were positively charged and that there were significant potential fluctuations in both grain boundary versus grain interior and intragrain. We further found that these potential fluctuations decreased significantly toward the front interface. Time of flight secondary ion mass spectrometry imaging shows that Se content increased toward the front interface, consistent with Se passivation of defects. The potential fluctuation was induced by defect charging, and the results elucidate different details of the defect configurations and grain structures of the films with different CdCl 2 treatment temperatures in the As-doped CdSeTe. The defect configurations in the region near the front interface can be a main factor contributing to the device performance difference. Our potential imaging provides insights about the defects throughout the absorber films, and shows that the potential fluctuation has a direct correlation to the V oc deficit.

14 SOLAR ENERGY↗
DOE OSTI2025

Spatial Mapping of Chiral-Induced Spin Selectivity in Chiral Perovskite via Spin-Schottky Junction

Chiral halide perovskite (c-HP) semiconductors exhibit on average a large chiral-induced spin selectivity (CISS) effect. Nevertheless, the microscopic details of CISS and its integration in opto-spintronic constructs remain nascent. Reliable reporting of CISS performance characteristics represents a significant challenge in providing the necessary design rules. We show a Kelvin probe force microscopy (KPFM) method that can quantitatively evaluate and spatially map the chirality-dependent surface contact potential difference resulting from the formation of a spin-Schottky junction. We revealed inhomogeneity in the CISS response, where low-CISS regions in the c-HP films reduce the overall macroscopic average, likely serving as a key factor in optimizing macroscopic performance. We also observed that although c-HP films made from higher precursor concentrations lead to thicker films and higher carrier concentrations with subsequent larger barrier heights in the Schottky junction, stronger spin relaxation due to non-ideal film quality reduces spin polarization.

14 SOLAR ENERGY↗
DOE OSTI2025

Direct observation of strain-enhanced hydrogen segregation and failure at high-angle grain boundaries in nickel

Understanding the mechanisms underlying hydrogen embrittlement remains difficult, even in single-element metals. Both microstructure and stress state influence hydrogen distribution in metals and alloys, which impacts deformation and failure. Here, in this work, we use in-situ Kelvin probe force microscopy (KPFM) to monitor the hydrogen distribution in pure nickel over time at 1.1 % and 3.5 % strain. The sample strained to 3.5 % results in preferential hydrogen segregation to high-angle grain boundaries whereas the sample strained to 1.1 % does not exhibit preferential hydrogen segregation. Optical digital image correlation (DIC) shows that hydrogen charging results in both localized and reduced strains during tensile testing of a notched sample. Later stages of deformation and failure (e.g. microcracking) are studied by using in-situ transmission X-ray microscopy (TXM). TXM reveals nanoscale structural changes to a propagating crack in a hydrogen environment. Localized void growth and secondary cracking occur at grain boundaries near the primary crack front. Correlative electron backscattering diffraction (EBSD) is used to relate the cracking at grain boundaries to the hydrogen segregation observed in KPFM. These findings are unified in a proposed hydrogen embrittlement mechanism that describes the interaction of hydrogen with grain boundaries, and the role of grain boundaries in hydrogen embrittlement.

Grain boundary fracture↗
DOE OSTI2022

Metastability and Degradation of CdTe Solar Cells Investigated by nm-Scale Electrical Potential Imaging

We report on investigations of reversible metastability and irreversible degradation of MZO/CdSeTe/CdTe devices from the perspective of electric field across the device using Kelvin probe force microscopy (KPFM). The device showed reversible transitions between the light-soak state (LSS) with the best device efficiency and the dark-soak state (DSS) with an inferior efficiency. However, it showed an irreversible degradation state (DgS) driven by long-hour light soaking at an elevated temperature. The nm-scale KPFM electric field imaging on cross-sections of the devices revealed different anomalous electric field profiles. The electric field at the LSS exhibits a main peak inside the CdSeTe layer but not at the MZO/CdSeTe heterointerface, demonstrating that working junction of the device is a buried homojunction (BHJ). At the DSS, a second electric field peak was observed at the MZO/CdSeTe interface with a similar strength to the main BHJ, which probably caused the decrease in fill factor at the DSS. At the DgS, the electric field peak at the MZO/CdSeTe interface increased significantly and a third electric field was measured at the back contact of the device. Device modeling using COMSOL and in alignment with both the electric field and device current-voltage curves suggest that a slightly low n-doped CdSeTe in the region near the MZO/CdSeTe interface caused the BHJ, and that either a loss of MZO doping or increase of the conduction band offset spike due to long-term stress caused the fill factor-dominated degradation and the increased electric field near the MZO/CdSeTe interface at the DgS. The former, MZO doping decrease, is more plausible by referring the related literature.

BHJ↗
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

Dopant Compensation within the Intrinsic Poly-Si Isolation Region in Poly-Si/SiOx Passivated IBC Si Solar Cells

We report on the effect of dopant compensation within intrinsic poly-Si regions between p- and n-type fingers of poly-Si/SiOx passivated interdigitated back contact (IBC) solar cells using intrinsic poly-Si as the isolation region between the doped poly-Si fingers. First, we show that dopants from the doped fingers contaminate the intrinsic gap, resulting in doping of the entire intrinsic gap and overlap of the dopant tails from each finger. Next, we show that despite this doping across the gap, shunting between the doped fingers does not occur. We show that this is a result of trap-assisted compensation creating a highly resistive intrinsic region, preventing shunt. We simulate shunt resistance across the gap based on local carrier concentration and deep trap density. We show that trap defects within the poly-Si enhance compensation between the dopant tails. We experimentally confirm these predictions by scanning spreading resistance microscopy of the gap showing ~20 um domain with resistivity ~10^7 ..omega.. cm. Additionally, Kelvin probe force microscopy are compared to finite element simulations which result in the same approximate shape for potential profile, indicating diode behavior across the isolation region. These results demonstrate the powerful effect that trap defects have within the poly-Si isolation region and suggest that precision patterning is not as essential as once thought.

dopant compensation↗
DOE OSTI2022

Multimode Characterization Approach for Understanding Cell-Level PV Performance and Degradation

Cell-level degradation processes impact the economic viability and large-scale deployment prospects for both established and emerging photovoltaic (PV) technologies. This project addresses the need to develop experimental and device-modeling approaches for studying cell-level degradation processes in photovoltaic (PV) devices using a variety of characterization techniques that provide access to complementary material and device properties. Our results demonstrate that by coupling characterization results with device modeling it is possible to develop comprehensive understanding of processes leading to performance limitations and degradation. This project developed a suite of novel measurement techniques including pulsed-light-bias operando X-ray and photoelectron spectroscopy (popXPS), light-biased scanning microwave impedance microscopy (sMIM), and near-field transport imaging (TI). In addition, operando characterization methodologies and in situ stressing capabilities have been developed and applied for techniques including electron-beam-induced current (EBIC), cathodoluminescence (CL), and Kelvin probe force microscopy (KPFM). Device-physics models were developed and applied to simulate correlative, multi-mode measurements to extract material and device parameters that control performance degradation. These characterization and modeling techniques were applied in a multi-mode approach to probe cell-level degradation mechanisms in Cd(Se,Te) and hybrid perovskite PV devices. Together these efforts contribute to foundational PV degradation science by establishing a framework for understanding PV performance degradation at the cell level and benefit the U.S. PV industry by providing resources in the form of novel experimental capabilities, knowledge gained, and available expertise that can accelerate research and development of improved PV device materials and architectures. The project provided a comprehensive understanding of degradation in baseline Cd(Se,Te) solar cells provided by our collaborators at Colorado State University (CSU). EBIC and CL-based measurements and revealed unusual collection and recombination profiles in these devices, which underwent significant changes with during stressing. KPFM and operando XPS measurements showed that device stressing permanently alters energy-band alignments at the (Mg,Zn)O/Cd(Se,Te) interface, which in turn account for an observed loss in fill factor. Studies on hybrid perovskite devices were hampered to a significant extent by delays related to the pandemic. Nevertheless, a set of hybrid perovskite devices (supplied through an NREL-industry partnership) were stress tested and characterized with techniques including EBIC, sMIM, popXPS/popUPS and optically excited TI. Available results from these measurements informed the device modeling effort and suggest that defects and related band offsets at the C60/LiF/hybrid perovskite interface are the primary source of degradation in these devices.

14 SOLAR ENERGY↗
DOE OSTI2025

Multimodal characterization of Te inclusions in Cd 1−x Zn x Te and Cd 1−x Zn x Te 1−y Se y for gamma and X-ray detectors

While CdZnTe (CZT) and CdZnTeSe (CZTS) semiconductors have emerged as compounds for room-temperature gamma and X-ray detection materials, they continue to be constrained by the formation of Te-inclusion defects generated during the growth and post-growth phases of the material, which adversely affect the detector performance. We demonstrate the utility of multimodal microscopic imaging and analysis for the characterization of the optical and electronic properties of Te inclusions in CZT and CZTS crystals at both micron and nanometer length scales. Having first identified regions with micron-scale Te inclusions using confocal Raman microscopy techniques, optically coupled infrared scattering near-field optical microscopic mapping was performed to map the distribution of these inclusions with nanometer spatial resolution and correlate the presence of Te inclusions in the matrix with other properties. Kelvin probe force microscopy was then utilized to characterize the variations of the work function associated with the presence of Te inclusions. Here, we observe an increase of ~ 240 mV in the work function associated with Te inclusions compared to the bulk CZT/CZTS crystals. Additionally, we observe that individual bulk grains in CZT can exhibit slight potential variations. Our findings develop a portrait of the charge trapping mechanisms in CZT and CZTS that act to degrade detector performance, while the demonstration of these combined microscopy techniques provides a new analytical tool that can be utilized for further optimization of the detector performance for these semiconducting compounds.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Tailoring Interlayer Coupling in Few-Layer MoS 2 with Stacking Configuration

Here we manipulated the stacking configuration of a few-layer MoS 2 to investigate the impact of interlayer coupling on electrical band engineering. By simultaneously synthesizing two distinct stacking types of MoS2 islands, wedding cake (W) and spiral (S), on the same substrate, we explored layer-dependent electrical properties under identical experimental conditions. We used multiple scanning probe microscopy techniques to map local electronic properties with respect to the number of layers, stacking configurations, and local heterogeneities. First-principles calculations verified the role of distinct interlayer coupling in terms of the interlayer distance. Our findings highlight the critical role of interlayer coupling in applications of transition metal dichalcogenides.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Effect of organic electroactive crystallites in a dielectric matrix on the electrical properties of a polymer dielectric

In this work, the effects of inserting chargeable α-quaterthiophene (α4T) crystallites in polystyrene (PS) multilayers used as a transistor gate and capacitor dielectric were investigated. X-ray diffraction (XRD), scanning electron microscopy with energy dispersive x-ray spectroscopy (SEM/EDS), and confocal microscopy indicated the formation of α4T crystallites in the PS matrix. A modified saturation-regime current voltage relationship was used to estimate organic field-effect transistor (OFET) threshold voltage V TH shifting, and in turn the quantities of stored charge that were observed as a result of dielectric charging. The crystallites increased the maximum charge storage capacity as well as the charge retention capability of the dielectrics. Kelvin probe force microscopy (KPFM) showed that charges were localized near the α4T crystallites upon charging. Trilayer experiments validated the charge retention improvement of α4T crystallite-embedded PS dielectrics. The crystallites also improved breakdown characteristics in PS used as a capacitor dielectric, suggesting their application to storage capacitors in addition to OFET logic.

25 ENERGY STORAGE↗
DOE OSTI2020

Nanometer-Scale Imaging of Inhomogeneous Active Charge Carriers in Arsenic-Doped CdTe Thin Films

We report nanometer-scale imaging of active carrier distribution of As-doped CdTe films by scanning capacitance microscopy (SCM). We developed SCM sample preparation for CdTe by ion-milling followed by thermal processing. The nanometer-resolution carrier delineation for CdTe was validated by imaging on a CdTe cross-section sample made by a molecular beam epitaxy layer stack with As-doping concentrations of 10^15 ~10^18 /cm 3 . We found that the carrier distribution in As-doped films was significantly nonuniform, with inhomogeneity ranging from sub-um to a few um and concentration variation of one order of magnitude (low 10^16 to low 10^17 /cm 3 ). This nonuniformity is distributed randomly, independent of grain structure and grain boundary (GB). We used Kelvin probe force microscopy (KPFM) and cathodoluminescence (CL) to further map the surface potential and radiative illumination on the same area as the SCM image. Higher potential and lower CL intensity were found on GBs but not on SCM contrast, illustrating positive GB charging and GB recombination but not GB-distinguished doping. The overall KPFM potential image is in rough agreement with the SCM carrier distribution, in terms of Fermi-level position relative to the bandgap edge - thus resulting in the band-edge potential fluctuation. Nonuniform carrier concentration, potential fluctuation, and defect recombination can all together cause the Voc deficit of the As-doped CdTe device.

14 SOLAR ENERGY↗
DOE OSTI2024

In Situ Exploration of Dipole Field Effects on Weak Hysteresis in 3D/2D Perovskites

This research delves into the effects of 2D layers on the functionality of 3D perovskite using lock-in amplifier-based in situ surface photovoltage (SPV) and its phase spectroscopy, with an emphasis on elucidating the connection between the tuning of dipole moments and the photocurrent hysteresis. Conventionally, the SPV of a perovskite/hole transport layer is observed to diminish as positive bias escalates. However, this trend is reversed in the case of 3D perovskite samples, where an augmentation in SPV is noted under positive bias. Notably, 3D/2D perovskite structures initially show a decrease, then an increase in SPV as bias intensifies, a phenomenon more pronounced with larger dipole moments in 2D. However, there is no linear relationship between the dipole moment and the hysteresis factor. Furthermore, using in situ light-chopping-frequency-modulated SPV and Kelvin Probe Force Microscopy, it is revealed that the dipole fields of 2D layers can hinder ion migration. This leads to efficient hole transfer and minimal photocurrent hysteresis in 3D/2D perovskites, providing strong evidence for the underlying cause of hysteresis. Additionally, these findings suggest intricate interplays among the external electric field, interface dipole moments, and surface photovoltaics, offering significant insights into perovskite optoelectronics.

3D/2D perovskite↗
DOE OSTI2023

Vacuum-Healing of Grain Boundaries in Sodium-Doped CuInSe 2 Solar Cell Absorbers

Alkali metal doping and grain boundaries (GB) have been at the center of attention within the Cu(In,Ga)(S,Se) 2 photovoltaics community for years. This study provides the first experimental evidence that the GB of sodium-doped CuInSe 2 thin films may undertake reversible oxidation even at room temperature, whereas undoped films may not. The findings are corroborated by cathodoluminescence imaging, secondary ion mass spectrometry, and Kelvin probe force microscopy on air-exposed films subsequently subject to vacuum. A thermochemical assessment identifies the likely solid-gas equilibria involved. These reactions open new research questions with respect to the beneficial role played by alkali metal dopants in chalcopyrite solar cells and may steer the community toward new breakthroughs.

14 SOLAR ENERGY↗
DOE OSTI2021

Charge Transfer Properties of Heterostructures Formed by Bi 2 O 2 Se and Transition Metal Dichalcogenide Monolayers

Atomically thin bismuth oxyselenide (Bi 2 O 2 Se) exhibits attractive properties for electronic and optoelectronic applications, such as high charge-carrier mobility and good air stability. Recently, the development of Bi 2 O 2 Se-based heterostructures have attracted enormous interests with promising prospects for diverse device applications. Although the electrical properties of Bi 2 O 2 Se-based heterostructures have been widely studied, the interlayer charge transfer in these heterostructures remains elusive, despite its importance in harnessing their emergent functionalities. Here, a comprehensive experimental investigation on the interlayer charge transfer properties of two heterostructures formed by Bi 2 O 2 Se and representative transition metal dichalcogenides (namely, WS 2 /Bi 2 O 2 Se and MoS 2 /Bi 2 O 2 Se) is reported. In this work, Kelvin probe force microscopy is used to measure the work functions of the samples, which are further employed to establish type-II band alignment of both heterostructures. Photoluminescence quenching is observed in each heterostructure, suggesting high charge transfer efficiency. Time-resolved and layer-selective pump–probe measurements further prove the ultrafast interlayer charge transfer processes and formation of long-lived interlayer excitons. These results establish the feasibility of integrating 2D Bi 2 O 2 Se with other 2D semiconductors to fabricate heterostructures with novel charge transfer properties and provide insight for understanding the performance of optoelectronic devices based on such 2D heterostructures.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Mixed Tin-Titanium Oxides by Atomic Layer Deposition on Planar Substrates: Physical and Electronic Structure

Ternary atomic layer deposition of Sn-doped TiO x (Sn:TiO x ) and Ti-doped SnO x (Ti:SnO x ) was performed using tetrakisdimethylamidotitanium (IV) and tin(IV) with water at 150 °C on (1 0 0) Si and quartz substrates. The physical structure of the films was investigated using scanning electron, atomic force, and Kelvin probe force microscopies as well as spectroscopic ellipsometry, Raman spectroscopy, and X-ray diffraction. All as-deposited films are amorphous and possessed flat and conformal topographies with low surface roughness (<1 nm). Annealed Sn:TiO x and Ti:SnO x crystallize into the tetragonal anatase TiO 2 and cassiterite SnO 2 structures, respectively, without large variations to the film topography. The chemical composition of the as-deposited and annealed films was investigated through X-ray photoelectron spectroscopy. While dopants are homogenously mixed, the ternary ALD to form Sn:TiO x and Ti:SnO x surprisingly does not follow the rule of mixtures, despite similarities in both the growth rates of binary SnO x and TiO x and the precursors used. This finding is also supported by spectroscopic ellipsometry. Here, we postulate the deviation from the rule of mixtures is due to non-ideal surface chemistry of the binary ALD of SnO x . The optical bandgap of all films was quantified by the Tauc analysis and the valence band position was investigated by valence band X-ray photoelectron spectroscopy. Intra-bandgap states above the valence band maximum were observed for as-deposited Ti:SnO x and Sn:TiO x and ascribed to 5 s states from Sn 2+ ions. The presence of these intra-bandgap states induces enhanced visible absorption and bathochromic shifts to the apparent bandgap for all as-deposited films. Annealing the films removes the intra-bandgap states and increases the optical bandgap. Simplified band diagrams created using the data available demonstrated that the conduction and valence band positions did not vary between the positions of pure TiO 2 or SnO 2 with monotonic increases to the dopant incorporation.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Electronic interactions and stability issues at the copper-graphene interface in air and in alkaline solution under electrochemical control

A micro-electrochemical cell is sealed with a polymer-free single-layer graphene (SLG) membrane to monitor the stability of Cu nanoparticles (NPs) attached to SLG, as well as the interfacial electronic interactions between Cu NPs and SLG both in air and in a mildly alkaline aqueous solution under electrochemical control. A combination of techniques, including in-situ Kelvin probe force microscopy (KPFM) and ex-situ electron microscopy, are applied. When Cu NPs are metallic at cathodic potentials, there is a relatively bias-independent offset in the SLG work function due to charge transfer at the Cu-SLG contact. When Cu NPs are oxidized at anodic potentials, on the other hand, the work function of SLG also depends on the applied bias in a quasi-linear fashion due to electrochemical gating, in addition to charge transfer at the CuOx-SLG contact. Furthermore, Cu NPs were found to oxidize and detach from SLG when kept under anodic potentials for a few hours, whereas they remain adhered to SLG at cathodic potentials. This is attributed to water intercalation at the CuO-SLG interface associated with the enhanced hydrophilicity of positively polarized graphene, as supported by the absence of Cu detachment following oxidation by galvanic corrosion in air.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗