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DOE OSTI2020

First-Principles Quantum Transport Modeling of Spin-Transfer and Spin-Orbit Torques in Magnetic Multilayers

A unified approach for computing (i) spin-transfer torque in magnetic trilayers like spin valve and magnetic tunnel junction, where injected charge current flows perpendicularly to interfaces, and (ii) spin-orbit torque in magnetic bilayers of the type ferromagnet/spin-orbit-coupled material, where injected charge current flows parallel to the interface, was reviewed. The experimentally explored and technologically relevant spin-orbit-coupled materials include 5d heavy metals, topological insulators, Weyl semimetals, and transition metal dichalcogenides. This approach requires to construct the torque operator for a given Hamiltonian of the device and the steady-state nonequilibrium density matrix, where the latter is expressed in terms of the nonequilibrium Green’s functions and split into three contributions. Tracing these contributions with the torque operator automatically yields field-like and damping-like components of spin-transfer torque or spin-orbit torque vector, which is particularly advantageous for spin-orbit torque where the direction of these components depends on the unknown-in-advance orientation of the current-driven nonequilibrium spin density in the presence of spin-orbit coupling. Illustrative examples are provided by computing spin-transfer torque in a one-dimensional toy model of a magnetic tunnel junction and realistic Co/Cu/Co spin valve, both of which are described by first-principles Hamiltonians obtained from noncollinear density functional theory calculations, as well as by computing spin-orbit torque in a ferromagnetic layer described by a tight-binding Hamiltonian which includes spin-orbit proximity effect within ferromagnetic monolayers assumed to be generated by the adjacent monolayer transition metal dichalcogenide. In addition, it is shown here how spin-orbit proximity effect, quantified by computing (via first-principles retarded Green’s function) spectral functions and spin textures on monolayers of realistic ferromagnetic material like Co in contact with heavy metal or monolayer transition metal dichalcogenide, can be tailored to enhance the magnitude of spin-orbit torque. Furthermore, errors made in the calculation of spin-transfer torque are quantified when using Hamiltonian from collinear density functional theory, with rigidly rotated magnetic moments to create noncollinear magnetization configurations, instead of proper (but computationally more expensive) self-consistent Hamiltonian obtained from noncollinear density functional theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Surface Ligand Management Aided by a Secondary Amine Enables Increased Synthesis Yield of CsPbI 3 Perovskite Quantum Dots and High Photovoltaic Performance

Lead-halide perovskite quantum dots (PQDs) or more broadly, nanocrystals possess advantageous features for solution-processed photovoltaic devices. The nanocrystal surface ligands play a crucial role in the transport of photogenerated carriers and ultimately affect the overall performance of PQD solar cells. Here, significantly improved CsPbI 3 PQD synthetic yield and solar-cell performance through surface ligand management are demonstrated. The treatment of a secondary amine, di- n -propylamine (DPA), provides a mild and efficient approach to control the surface ligand density of PQDs, which has an apparently different working mechanism compared to previously reported surface treatments. Using an optimal DPA concentration, the treatment can simultaneously remove both long-chain insulating surface ligands of oleic acid and oleylamine, even for unpurified PQDs with high ligand density. As a result, the electrical coupling between PQDs is enhanced, leading to improved charge transport, reduced carrier recombination, and a high power conversion efficiency approaching 15% for CsPbI 3 -PQD-based solar cells. In addition, the production yield of CsPbI 3 PQDs can be increased by a factor of 8. These results highlight the importance of developing new ligand-management strategies, specifically for emerging PQDs to achieve scalable and high-performance perovskite-based optoelectronic devices.

36 MATERIALS SCIENCE↗

DOE OSTI2020

A Comparative Study of Imidazolium-Based Ionic Liquid-Single-Walled Carbon Nanotube Composites with Enhanced Conductivity Properties for Supercapacitor Applications

Mixtures of ionic liquids (ILs) containing single-walled carbon nanotubes (SWCNTs) were prepared and characterized to obtain electrolytes with optimized transport properties for use in energy storage devices such as supercapacitors. Imidazolium ILs bearing cations with side chains of different functionality coupled with bis(trifluoromethylsulfonyl)amide (NTf 2- ) or bis(fluorosulfonyl)-amide (FSA-) anions, were used in mixtures containing up to 5 wt% SWCNTs. At and above 2 wt% nanotube loading, the mixtures exhibited higher conductivities than the pure ILs, in spite of the extremely high viscosities. Loadings of 5 wt% produced very high conductivities, and studies of the temperature dependence indicated a change in the charge transport mechanism between 2 and 5 wt% loading. At 5 wt% loading, the highest conductivities (up to 540 mS/cm at 25 °C) were obtained for the ILs containing the NTf 2- anion. Overall, these results can significantly contribute to the development of improved energy storage devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Charge carrier nonadiabatic dynamics in non-metal doped graphitic carbon nitride

Graphitic carbon nitride (GCN) has attracted significant attention due to its excellent performance in photocatalytic applications. Non-metal doping of GCN has been widely used to improve the efficiency of the material as a photocatalyst. Using a combination of time-domain density functional theory with nonadiabatic molecular dynamics, we study the charge carrier dynamics in oxygen and boron doped GCN systems. The reported simulations provide a detailed time-domain mechanistic description of the charge separation and recombination processes that are of fundamental importance while evaluating the photovoltaic and photocatalytic performance of the material. The appearance of smaller energy gaps due to the presence of dopant states improves the visible light absorption range of the doped systems. At the same time, the nonradiative lifetimes are shortened in the doped systems as compared to the pristine GCN. In the case of boron doped at a carbon (B–C–GCN), the charge recombination time is very long as compared to the other two doped systems owing to the smaller electron–phonon coupling strength between the valence band maximum and the trap state. The results suggest B–C–GCN as the most suitable candidate among three doped systems studied in this work for applications in photocatalysis. Finally, this work sheds light into the influence of dopants on quantum dynamics processes that govern GCN performance and, thus, guides toward building high-performance devices in photocatalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Charge carrier dynamics in two-dimensional hybrid perovskites: Dion–Jacobson vs. Ruddlesden–Popper phases

Two-dimensional (2D) halide perovskites are promising materials for environmentally stable next-generation optoelectronic device applications. Besides the widely investigated Ruddlesden–Popper (RP) phases, Dion–Jacobson (DJ) phases are attracting considerable attention due to their rapid emergence as efficient solar cell materials. However, there is very little atomistic understanding of the charge carrier dynamics under ambient conditions for these DJ-phases, limiting the possibilities to tune their optoelectronic performances through compositional engineering routes. In this study, by combining nonadiabatic molecular dynamics with time-domain density functional theory methods at room temperature, we compare the dominant non-radiative carrier recombination and dephasing processes in RP and DJ monolayered lead halide perovskites. Our systematic study demonstrates that performance-limiting nonradiative carrier recombination processes greatly depends on the electron–phonon interactions induced by structural fluctuations and instantaneous charge localization in these materials. The stiffer interlayer packing due to the presence of single spacer dications, which separates the lead iodide slabs, reduces the thermal fluctuations in the DJ-phase to a greater extent than that in the RP-phase 2D-perovskites. Specific electronic coupling between the closely spaced lead iodide layers enhances the delocalization of band-edge charge densities in DJ-phase systems. Compared to the RP-phase, reduced inelastic electron–phonon scattering in DJ-phase perovskites significantly limits intrinsic non-radiative recombination processes. The consequent enhancement in the photogenerated charge carrier lifetime makes DJ-phase perovskites potentially suitable for various optoelectronic devices. The computational insights gained from this study allow us to outline a set of robust design principles for DJ-phase perovskites to strategically tune their optoelectronic properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

The STAR event plane detector

The Event Plane Detector (EPD) is an upgrade detector to the STAR experiment at RHIC, designed to measure the pattern of forward-going charged particles emitted in a high-energy collision between heavy nuclei. It consists of two highly-segmented disks of 1.2-cm-thick scintillator embedded with wavelength-shifting fiber, coupled to silicon photomultipliers and custom electronics. Finally, we describe the general design of the device, its construction, and performance on the bench and in the experiment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Restoring Symmetry and Enhancing Exchange via Chiral Molecular-Magnetic Hexagons

Modified behaviors of molecules, designed for device or energy applications, can occur due to lattice-molecule incompatibilities in point-group symmetries (PGS), long-range interactions between neighboring molecules, or latticemolecule charge transfer. Such sensitivities are prerequisite for the use of quantum molecules as devices, but removing certain broken symmetries is desirable from the standpoint of simplifying their behaviors. Here, we demonstrate symmetry restoration to molecular-magnetic lattices and show that it leads to strengthened exchange-coupling due to dipolar electrostatic interactions between neighboring molecules and due to manifestations of an earlier identification of a spin-sensitive slightly mobile electron by Hooshmand et al. Starting with a broken symmetry molecular magnet of current interest, we demonstrate a more robust structure composed of six molecular magnets on a h-BN-like surface. The broken point-group symmetry is healed by constructing interpenetrating equilateral triangular structures that are appropriately ratcheted to preserve three-fold rotational symmetry and inversion symmetry.

Pederson, Mark R.↗

DOE OSTI2020

Transport of colloidal particles in microscopic porous medium analogs with surface charge heterogeneity: experiments and fundamental role of single-bead deposition

Understanding colloid transport in subsurface environments is challenging due to complex interactions between colloids, ground water, and porous media over several length scales. Here, we study the transport of colloidal particles through bead-assembled microfluidic porous media analogs (PMAs) with surface charge heterogeneity. The pore-scale dynamics of colloidal particle deposition were measured, as well as the breakthrough curves (BTC) and retention profiles (RP) of deposited colloidal particles at the scale of the entire PMA. From pore-scale experiments, the maximum surface coverage (?max = 0.51) was measured directly, from which the surface blocking function and deposition coefficient (kpore = 3.56 s-1) were obtained. Using these pore-scale parameters, the transport of colloidal particles was modeled using a one-dimensional advection-dispersion equation under the assumption of irreversible adsorption between oppositely charged beads and colloids, showing good agreement with experimental data. This work presents a new approach to fabricate chemically heterogeneous porous media in a microfluidic device that enables direct measurements of pore-scale colloidal deposition. The approach allows a quantitative prediction of colloidal breakthrough and retention via coupling of direct measurements and an advection-dispersion-deposition model.

Guo, Yang↗

NASA NTRS2001

The Marshall Magnetic Mirror Beam-Plasma Experiment

Plasma propulsion is an advanced propulsion concept with the potential to realize very high specific impulse. Present designs for plasma propulsion devices share a common feature, the incorporation of a magnetic mirror. A magnetic mirror is a plasma confinement scheme whereby charged particles are trapped (or reflected) between two regions of high magnetic field strength. A cylindrical geometry is most often employed to create a magnetic mirror, which is a natural geometry for propulsion devices. To utilize the magnetic mirror configuration in a plasma propulsion device, however, will require efficient coupling of power into the system. With the development of compact and efficient electron sources, such as hollow cathode sources, coupling power into a magnetic mirror using electron beams may be an attractive approach. A system, the Marshall Magnetic Mirror (M3), has been constructed to study the coupling of an electron beam into a magnetic mirror. A description of the M3 device will be provided as well as data from initial beam-plasma coupling experiments.

Schneider, Todd A.↗

NASA NTRS2005

Electronic Transport through Self Assembled Thiol Molecules: Effect of Monolayer Order, Dynamics and Temperature

We present the charge transport and tunneling conductance of self assembled organic thiol molecules and discuss the influence of order and dynamics in the monolayer on the transport behavior and the effect of temperature. Conjugated thiol molecular wires and organometals such as terpyridine metal complexes provide a new platform for molecular electronic devices and we study their self assembly on Au(111) substrates by the scanning tunneling microscope. Determining the organization of the molecule and the ability to control the nature of its interface with the substrate is important for reliable performance of the molecular electronic devices. By concurrent scanning tunneling microscopy and spectroscopy studies on SAMs formed from oligo (phenelyne ethynelyne) monolayers with and without molecular order, we show that packing and order determine the response of a self assembled monolayer (SAM) to competing interactions. Molecular resolution STM imaging in vacuum shows that the OPES adopt an imcommensurate SAM structure on Au(111) with a rectangular unit cell. Tunneling spectroscopic measurements were performed on the SAM as a function of junction resistance. STS results show that the I-Vs are non linear and asymmetric due to the inherent asymmetry in the molecular structure, with larger currents at negative sample biases. The asymmetry increases with increasing junction resistance due to the asymmetry in the coupling to the leads. This is brought out clearly in the differential conductance, which also shows a gap at the Fermi level. We also studied the effect of order and dynamics in the monolayer on the charge transport and found that competing forces between the electric field, intermolecular interactions, tip-molecule physisorption and substrate-molecule chemisorption impact the transport measurements and its reliability and that the presence of molecular order is very important for reproducible transport measurements. Thus while developing new electronic platforms based on molecules, it is important to have a good control of the molecule-substrate interface, for the devices to perform reliably. While such a control would minimize fluctuations and dynamics in the ensemble, the real challenge is to develop device architectures that are tolerant to fluctuations, since they cannot be totally eliminated in these low dimensional soft systems. Results of temperature dependent STS measurements will also be discussed.

Dholakia, Geetha↗

DOE OSTI2023

Spin–orbit effects on the electronic and optical properties of lead iodide

Lead iodide (PbI2) has gained much interest due to its direct electronic gap in the visible range and layered crystal structure. It has thereby been considered as a promising material for applications in atomically thin optoelectronic devices. In this work, we present a detailed investigation of the effect of spin–orbit coupling (SOC) that arises from the presence of heavy atoms on the electronic and optical properties of PbI2 using first-principles calculations based on density-functional theory and many-body perturbation theory. We find that SOC not only alters the bandgap but also induces the mixing of orbital characters, resulting in a significant change in the overall band structure and charge carrier effective masses. Moreover, the band orbital mixing caused by SOC results in the dramatic change in optical transition matrix elements and, correspondingly, the absorption spectrum. Our experimentally measured absorption spectra validate the calculation results and demonstrate the importance of SOC in the optical processes of PbI2. Our findings provide insights that are important for the potential use of PbI2 as a material platform for visible optoelectronic devices.

Physics↗

DOE OSTI2024

Using Molecular Structure to Tune Intrachain and Interchain Charge Transport in Indacenodithiophene-Based Copolymers

Here, in this work, we compare two structurally near-amorphous rigid-rod polymers-poly(indacenodithiophene-co-benzothiadiazole), p(IDT-BT), and poly(indacenodithiophene-co-benzopyrollodione), p(IDT-BPD)-with orders of magnitude different mobilities to understand the effect charge carrier intrachain delocalization has on electronic transport. Quantum chemical calculations show that p(IDT-BPD) has a barrier to torsion that is significantly lower than that of p(IDT-BT) and is thus more likely to have reduced conjugation lengths. We utilize absorption and photoluminescence spectroscopy to characterize energetic disorder and show that p(IDT-BPD) has higher energetic disorder. Charge modulation spectroscopy (CMS) and model calculations are used to show that charge carriers are substantially delocalized in p(IDT-BT) and occupy near-uniform energetic environments. We find that mobility activated hopping barriers are similar in these two materials. Electronic structure calculations show that both intrachain and interchain couplings of monomer units are poor enough in p(IDT-BPD) that charge carriers collapse to single IDT units and transport via a through-space tunneling mechanism. This work highlights the remarkable charge transport properties of p(IDT-BT) by showing that high mobilities are achievable on device-relevant length scales with only 1D carrier delocalization.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Decoupling excitons from high-frequency vibrations in organic molecules

The coupling of excitons in π-conjugated molecules to high-frequency vibrational modes, particularly carbon–carbon stretch modes (1,000–1,600 cm -1 ) has been thought to be unavoidable. These high-frequency modes accelerate non-radiative losses and limit the performance of light-emitting diodes, fluorescent biomarkers and photovoltaic devices. Here, by combining broadband impulsive vibrational spectroscopy, first-principles modelling and synthetic chemistry, we explore exciton–vibration coupling in a range of π-conjugated molecules. We uncover two design rules that decouple excitons from high-frequency vibrations. First, when the exciton wavefunction has a substantial charge-transfer character with spatially disjoint electron and hole densities, we find that high-frequency modes can be localized to either the donor or acceptor moiety, so that they do not significantly perturb the exciton energy or its spatial distribution. Second, it is possible to select materials such that the participating molecular orbitals have a symmetry-imposed non-bonding character and are, thus, decoupled from the high-frequency vibrational modes that modulate the π-bond order. We exemplify both these design rules by creating a series of spin radical systems that have very efficient near-infrared emission (680–800 nm) from charge-transfer excitons. We show that these systems have substantial coupling to vibrational modes only below 250 cm -1 , frequencies that are too low to allow fast non-radiative decay. This enables non-radiative decay rates to be suppressed by nearly two orders of magnitude in comparison to π-conjugated molecules with similar bandgaps. Our results show that losses due to coupling to high-frequency modes need not be a fundamental property of these systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Monolithic AlScN/SiC phononic waveguides for scalable acoustoelectric and quantum devices

Unlike conventional surface acoustic wave devices, phononic waveguide systems enable higher circuit density and stronger strain and piezoelectric fields, making them promising for advanced acoustoelectric and quantum applications. One such material system for generating and guiding phonons at gigahertz frequencies is AlScN on SiC, which can be synthesized by sputter depositing AlScN directly onto SiC wafers. The AlScN on the SiC platform allows for tightly vertically-confined acoustic modes with high electromechanical coupling, high speed of sound, and simple fabrication of strip and rib waveguides. Until now, this system has only been studied as a slab waveguide platform, i.e., without any lateral waveguiding. Here, we demonstrate a two-dimensionally confined phononic architecture in AlScN on SiC that supports guided modes at 2.95 and 4.05 GHz. These modes exhibit strong electromechanical coupling coefficients (k 2 = 4.27%) and propagation losses on the order of 10 dB/mm. Furthermore, this architecture is well-suited for phononic routing and power-efficient active or nonlinear devices such as amplifiers, mixers, and oscillators, and is compatible with the integration of quantum systems, including vacancy centers, charge carriers, photons, and spins, either embedded in SiC or heterogeneously integrated on the surface.

Electrical components↗

DOE OSTI2025

Role of Superlattice Phonons in Charge Localization Across Quantum Dot Arrays

Understanding charge transport in semiconductor quantum dot (QD) assemblies is important for developing the next generation of solar cells and light-harvesting devices based on QD technology. One of the key factors that governs the transport in such systems is related to the hybridization between the QDs. Recent experiments have successfully synthesized QD molecules, arrays, and assemblies by directly fusing the QDs, with enhanced hybridization leading to high carrier mobilities and coherent band-like electronic transport. Here, in this work, we theoretically investigate the electron transfer dynamics across a finite CdSe-CdS core-shell QD array, considering up to seven interconnected QDs in one dimension. We find that, even in the absence of structural and size disorder, electron transfer can become localized by the emergent low-frequency superlattice vibrational modes when the connecting neck between QDs is narrow. On the other hand, we also identify a regime where the same vibrational modes facilitate coherent electron transport when the connecting necks are wide. Overall, we elucidate the crucial effects of electronic and superlattice symmetries and their couplings when designing high-mobility devices based on QD superlattices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Symmetry‐Breaking Strategy Yields Dopant‐Free Small Molecule Hole Transport Materials for Inorganic Perovskite Solar Cells with 20.58% Efficiency and Outstanding Stability

Abstract Inorganic perovskites are known for their excellent photothermal stability; however, the photothermal stability of all‐inorganic n‐i‐p perovskite solar cells (PSCs) is compromised due to ion diffusion and free radical‐induced degradation caused by the use of doped spiro‐OMeTAD hole transport materials (HTMs). In this study, two isomeric donor–acceptor–donor (D–A–D) type small molecules, namely HBT and HiBT, were developed and used as dopant‐free HTMs, using 2,1,3‐benzothiadiazole or benzo[d][1,2,3]thiadiazole as acceptor moieties. The HiBT molecule, with its symmetry‐breaking features, exhibits a large dipole moment, enhanced coordination‐active sites, and a well‐aligned energy level structure, all of which contribute to passivating perovskite surface defects and improving free charge separation. As a result, inorganic CsPbI 3 PSCs with HiBT HTM achieved an impressive power conversion efficiency (PCE) of 20.58%, the highest reported for dopant‐free HTM‐based inorganic PSCs. Moreover, the enhanced hydrophobic properties of HiBT molecules, coupled with their ability to passivate perovskite surface defects, contribute to significantly improved device stability. The unencapsulated devices based on HiBT HTM retained over 83% and 80% of their initial efficiency after being stored at 85 °C for 50 days and undergoing maximum power point (MPP) tracking at 85 °C for 1100 h, respectively. These results highlight that the symmetry‐breaking strategy is an exceptionally effective approach for designing efficient, dopant‐free small molecule HTMs, significantly contributing to both the high efficiency and enhanced stability of all‐inorganic PSCs.

Chemistry↗

DOE OSTI2022

Codesigning Alloy Compositions of CdSe y Te 1− y Absorbers and Mg x Zn 1− x O Contacts to Increase Solar Cell Efficiency

Thin‐film solar cells such as CdTe are a major commercial photovoltaic technology, with more than 25 GW installed worldwide and levelized costs of electricity competitive with fossil fuels. Further progress may result from integrating CdSe y Te 1− y absorbers with Mg x Zn 1− x O contacts, but the device efficiency is difficult to maximize due to coupled dependence on chemical composition of both alloys. Herein, a high‐throughput approach is demonstrated to codesign chemical compositions in alloyed Mg x Zn 1− x O/CdSe y Te 1− y thin‐film solar cells, using combinatorial libraries of PV devices with orthogonal composition gradients in CdSe y Te 1− y absorbers and Mg x Zn 1− x O contacts. It is found that the solar cell performance is a strong and coupled function of both elemental compositions, with efficiency up to 17.7% ( V OC = 836 mV, fill factor = 69%, J SC = 30.6 mA cm −2 ) at atomic compositions of Mg/(Mg + Zn) ≈18% and average Se/(Se + Te) ≈4%. These performance trends among >100 devices are explained by >100 ns lifetime of photoexcited charge carriers at the Mg x Zn 1− x O/CdSe y Te 1− y interface where strong Se accumulation is also observed. This study reports the optimal compositions of the commercially relevant Mg x Zn 1− x O/CdSe y Te 1− y solar cells and demonstrates a general approach to codesigning performance of alloyed thin‐film solar cells and other optoelectronic devices.

14 SOLAR ENERGY↗

NASA NTRS2008

Discrete Element Modeling of Triboelectrically Charged Particles

Tribocharging of particles is common in many processes including fine powder handling and mixing, printer toner transport and dust extraction. In a lunar environment with its high vacuum and lack of water, electrostatic forces are an important factor to consider when designing and operating equipment. Dust mitigation and management is critical to safe and predictable performance of people and equipment. The extreme nature of lunar conditions makes it difficult and costly to carry out experiments on earth which are necessary to better understand how particles gather and transfer charge between each other and with equipment surfaces. DEM (Discrete Element Modeling) provides an excellent virtual laboratory for studying tribocharging of particles as well as for design of devices for dust mitigation and for other purposes related to handling and processing of lunar regolith. Theoretical and experimental work has been performed pursuant to incorporating screened Coulombic electrostatic forces into EDEM, a commercial DEM software package. The DEM software is used to model the trajectories of large numbers of particles for industrial particulate handling and processing applications and can be coupled with other solvers and numerical models to calculate particle interaction with surrounding media and force fields. While simple Coulombic force between two particles is well understood, its operation in an ensemble of particles is more complex. When the tribocharging of particles and surfaces due to frictional contact is also considered, it is necessary to consider longer range of interaction of particles in response to electrostatic charging. The standard DEM algorithm accounts for particle mechanical properties and inertia as a function of particle shape and mass. If fluid drag is neglected, then particle dynamics are governed by contact between particles, between particles and equipment surfaces and gravity forces. Consideration of particle charge and any tribocharging and electric field effects requires calculation of the forces due to these effects.

Hogue, Michael D.↗