Electrostatic Potential Fluctuations Research Articles

Luminescence properties ofCu2ZnSn(S,Se)4solar cell absorbers: State filling versus screening of electrostatic potential fluctuations

The power conversion efficiency of ${\mathrm{Cu}}_{2}\mathrm{ZnSn}{(\mathrm{S},\mathrm{Se})}_{4}$ kesterite thin-film solar cells is mainly limited by a low open-circuit voltage ${V}_{\text{OC}}$. In the literature, this low ${V}_{\text{OC}}$ has been amongst others attributed to electrostatic potential fluctuations leading to fluctuating band edges. This assignment was mainly based on the observation of a shift of the photoluminescence (PL) maximum to higher photon energies as a function of excitation power, which was interpreted in terms of a screening of the electrostatic potential fluctuations. However, in this paper, we show evidence that the observed shift of the PL maximum is dominantly caused by state filling rather than screening. Our assignment is based on the investigation of the full PL line shape (not only of the PL maximum) and the PL yield as a function of excitation power and temperature. Further support of our interpretation is given by the observation of additional band-tail emission showing up as a second high-energy PL band at the highest excitation powers. The spectral position of this additional band coincides with the absorption-tail deduced from photoluminescence excitation spectroscopy (PLE).

Magnetotransport in single-layer graphene in a large parallel magnetic field

Graphene on hexagonal boron-nitride (h-BN) is an atomically flat conducting system that is ideally suited for probing the effect of Zeeman splitting on electron transport. We demonstrate by magneto-transport measurements that a parallel magnetic field up to 30 Tesla does not affect the transport properties of graphene on h-BN even at charge neutrality where such an effect is expected to be maximal. The only magnetoresistance detected at low carrier concentrations is shown to be associated with a small perpendicular component of the field which cannot be fully eliminated in the experiment. Despite the high mobility of charge carries at low temperatures, we argue that the effects of Zeeman splitting are fully masked by electrostatic potential fluctuations at charge neutrality.

InfiniCharges: A tool for generating partial charges via the simultaneous fit of multiframe electrostatic potential (ESP) and total dipole fluctuations (TDF)

The InfiniCharges computer program, for generating reliable partial charges for molecular simulations in periodic systems, is here presented. This tool is an efficient implementation of the recently developed DM-REPEAT method, where the stability of the resulting charges, over a large set of fitting regions, is obtained through the simultaneous fit of multiple electrostatic potential (ESP) configurations together with the total dipole fluctuations (TDF). Besides DM-REPEAT, the program can also perform standard REPEAT fit and its multiframe extension (M-REPEAT), with the possibility to restrain the charges to an arbitrary value. Finally, the code is employed to generate partial charges for ZIF-90, a microporous material of the metal organic frameworks (MOFs) family, and an extensive analysis of the results is carried out. Program summaryProgram title: InfiniChargesCatalogue identifier: AEYJ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEYJ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License Version 3No. of lines in distributed program, including test data, etc.: 385092No. of bytes in distributed program, including test data, etc.: 4749285Distribution format: tar.gzProgramming language: Python, Fortran 90.Computer: PCs.Operating system: Linux.RAM: Megabytes to Gigabytes depending on problem sizeClassification: 16.13.External routines: NumPy [1]Nature of problem: Generation of partial charges for classical simulations of periodic systems.Solution method: Simultaneous fit of electrostatic potential (ESP) and total dipole fluctuations (TDF). In particular the multiple ESP configurations can be fitted at once.Restrictions: Orthorhombic simulation cellsRunning time: It depends on the system size and on the number of ESP configurations used for the fit. Times reported in this paper vary from 20 s up to a couple of hours.

Identification of the energetic-particle driven GAM in the LHD

n = 0 modes with frequency chirping have been observed by a heavy ion beam probe and Mirnov coils in the large helical device plasmas, where n is the toroidal mode number. The spatial structures of the electrostatic potential fluctuation and the density fluctuation correspond to those of the geodesic acoustic mode (GAM). The modes are observed only during the tangential neutral beam injection with the energy of 175 keV. The energy spectra of fast ions measured by a neutral particle analyzer implies that the modes are excited by the fast ions through the inverse Landau damping. The absolute values and the temperature dependence of the frequency of the mode can be interpreted by the dispersion relation taking into account the measured energy spectra of the fast ions. Therefore, the observed n = 0 modes are identified as the energetic-particle driven GAM.

Examination of electronic structure differences between CIGSSe and CZTSSe by photoluminescence study

In this paper, we elaborate on the interpretation and use of photoluminescence (PL) measurements as they relate to the “donor/acceptor” and “electrostatic potential fluctuations” models for compensated semiconductors. Low-temperature (7 K) PL measurements were performed on high-efficiency Cu(In,Ga)(S,Se)2 and two Cu2ZnSn(S,Se)4 solar cells with high- and low-S/(S + Se) ratio, all fabricated by a hydrazine solution-processing method. From excitation-dependent PL, the total defect density (which include radiative and non-radiative defects) within the band gap (Eg) was estimated for each material and the consequent depth of the electrostatic potential fluctuation (γ) was calculated. The quasi-donor-acceptor pair (QDAP) density was estimated from the blue-shift magnitude of the QDAP PL peak position in power-dependent PL spectra. As a further verification, we show that the slope of the lifetime as a function of photon energies (dτ/dE) is consistent with our estimate for the magnitude of γ. Lastly, the energetic depth of the QDAP defects is examined by studying the spectral evolution of the PL as a function of temperature. The shallow defect levels in CIGSSe resulted in a significant blue-shift of the PL peak with temperature, whereas no obvious shift was observed for either CZTSSe sample, indicating an increase in the depth of the defects. Further improvement on Cu2ZnSn(S,Se)4 solar cell should focus on reducing the sub-Eg defect density and avoiding the formation of deep defects.

Correlation properties of Geodesic Acoustic Modes in the T-10 tokamak

Geodesic acoustic mode (GAM) of electrostatic potential and density fluctuations are simultaneously measured by Heavy Ion Beam Probe (HIBP) and Correlation Reflectometry (CR). The regimes with Ohmic and electron cyclotron resonance heating (ECRH) were studied (B = 2.2 T, Ip = 210 - 240 kA, ne = (2.3 - 3.7) × 1019 m-3, PEC ≤ 0.6 MW). GAMs are more pronounced during ECRH, when the typical frequencies were seen in the narrow band from 22 to 27 kHz for the main peak and 25-30 kHz for the higher frequency satellite peak. The local values of electric potential and density fluctuations show the significant coherency and constant phase shift at GAM frequency range. The existence of the long-distance (one quarter of the torus) correlations of core electric potential and density for GAM implying that GAM is a global mode, was shown for the first time in tokamaks.

On push-forward representations in the standard gyrokinetic model

Two representations of fluid moments in terms of a gyro-center distribution function and gyro-center coordinates, which are called push-forward representations, are compared in the standard electrostatic gyrokinetic model. In the representation conventionally used to derive the gyrokinetic Poisson equation, the pull-back transformation of the gyro-center distribution function contains effects of the gyro-center transformation and therefore electrostatic potential fluctuations, which is described by the Poisson brackets between the distribution function and scalar functions generating the gyro-center transformation. Usually, only the lowest order solution of the generating function at first order is considered to explicitly derive the gyrokinetic Poisson equation. This is true in explicitly deriving representations of scalar fluid moments with polarization terms. One also recovers the particle diamagnetic flux at this order because it is associated with the guiding-center transformation. However, higher-order solutions are needed to derive finite Larmor radius terms of particle flux including the polarization drift flux from the conventional representation. On the other hand, the lowest order solution is sufficient for the other representation, in which the gyro-center transformation part is combined with the guiding-center one and the pull-back transformation of the distribution function does not appear.

Combinatorial Exploration of the Effects of Intrinsic and Extrinsic Defects in Cu<inline-formula> <tex-math>$_{\bf 2}$</tex-math></inline-formula>ZnSn(S,Se)<inline-formula><tex-math>$_{\bf 4}$</tex-math> </inline-formula>

We have systematically investigated native point defect chemistry of Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ZnSn(S,Se) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> and the effects of selected extrinsic dopants by spray coating films from DMSO-thiourea inks. Over 6000 unique compositions of Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ZnSn(S,Se) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> have been analyzed, along with the effects of Cd, Fe, and Na doping. Spectrally resolved absolute intensity photoluminescence is then used to map the optoelectronic properties. The data are analyzed using a full-spectrum fitting technique that allows us to extract the optical bandgap, quasi-Fermi level splitting (QFLS), as well as characteristics of the subbandgap absorption and emission. We find that changes in the optoelectronic properties primarily result from changes in the Cu-content. From stoichiometric, as the Cu-content is decreased, the PL peak shifts to higher energy, the bandgap increases, and the optolectronic quality (QFLS/QFLS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> ) increases. However, the full-width at half-maximum (FWHM) and the average subbandgap absorptivity remain nearly constant, indicating that the magnitude of electrostatic potential fluctuations does not change significantly. The most likely Shockley-Read-Hall (SRH)-active defects appear to be defects and defect clusters involving SnZn, CuSn, and SnCu antisite defects, particularly the cluster [2Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Zn</sub> + Sn <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Zn</sub> ]. We further show the benign effect of Cd doping, the detrimental effect of Fe doping, and the ability to make 9.5% efficient devices with ink-based NaCl doping.

Quasi-Fermi level splitting and sub-bandgap absorptivity from semiconductor photoluminescence

A unified model for the direct gap absorption coefficient (band-edge and sub-bandgap) is developed that encompasses the functional forms of the Urbach, Thomas-Fermi, screened Thomas-Fermi, and Franz-Keldysh models of sub-bandgap absorption as specific cases. We combine this model of absorption with an occupation-corrected non-equilibrium Planck law for the spontaneous emission of photons to yield a model of photoluminescence (PL) with broad applicability to band-band photoluminescence from intrinsic, heavily doped, and strongly compensated semiconductors. The utility of the model is that it is amenable to full-spectrum fitting of absolute intensity PL data and yields: (1) the quasi-Fermi level splitting, (2) the local lattice temperature, (3) the direct bandgap, (4) the functional form of the sub-bandgap absorption, and (5) the energy broadening parameter (Urbach energy, magnitude of potential fluctuations, etc.). The accuracy of the model is demonstrated by fitting the room temperature PL spectrum of GaAs. It is then applied to Cu(In,Ga)(S,Se)2 (CIGSSe) and Cu2ZnSn(S,Se)4 (CZTSSe) to reveal the nature of their tail states. For GaAs, the model fit is excellent, and fitted parameters match literature values for the bandgap (1.42 eV), functional form of the sub-bandgap states (purely Urbach in nature), and energy broadening parameter (Urbach energy of 9.4 meV). For CIGSSe and CZTSSe, the model fits yield quasi-Fermi leveling splittings that match well with the open circuit voltages measured on devices made from the same materials and bandgaps that match well with those extracted from EQE measurements on the devices. The power of the exponential decay of the absorption coefficient into the bandgap is found to be in the range of 1.2 to 1.6, suggesting that tunneling in the presence of local electrostatic potential fluctuations is a dominant factor contributing to the sub-bandgap absorption by either purely electrostatic (screened Thomas-Fermi) or a photon-assisted tunneling mechanism (Franz-Keldysh). A Gaussian distribution of bandgaps (local Eg fluctuation) is found to be inconsistent with the data. The sub-bandgap absorption of the CZTSSe absorber is found to be larger than that for CIGSSe for materials that yield roughly equivalent photovoltaic devices (8% efficient). Further, it is shown that fitting only portions of the PL spectrum (e.g., low energy for energy broadening parameter and high energy for quasi-Fermi level splitting) may lead to significant errors for materials with substantial sub-bandgap absorption and emission.

Nonlinear evolution of the temperature gradient instability in the midlatitude ionosphere

AbstractThe midlatitude Super Dual Auroral Radar Network radars frequently observe quiet time decameter‐scale irregularities in the nightside subauroral ionosphere. Since opposed temperature and density gradients are a persistent feature in the vicinity of the ionospheric projection of the plasmapause, the temperature gradient instability (TGI) is proposed to explain the observed irregularities. In this paper, modeling of the TGI is extended into the kinetic regime appropriate for HF radar frequencies and analyzed as the cause of these irregularities. The nonlinear evolution of the TGI is investigated utilizing gyrokinetic particle‐in‐cell simulation techniques with Monte Carlo collisions for the first time. The purpose of this investigation is to identify the mechanism responsible for the nonlinear saturation as well as the associated anomalous transport. It is found that the saturation amplitude level and the associated diffusion are greatly enhanced as a result of electron collisions. The simulation results indicate that the nonlinear E×Bconvection (trapping) of the electrons is the dominant TGI saturation mechanism. The spatial power spectra of the electrostatic potential and density fluctuations associated with the TGI are also computed, and the results show wave cascading of TGI from kilometer scales into the decameter‐scale regime of the radar observations. This implies that the E region may be responsible for shorting out the F region TGI electric fields before and around sunset. This also suggests that the observed midlatitude decameter‐scale ionospheric irregularities may be produced directly by the TGI or by turbulent cascade from primary longer‐wavelength irregularity structures produced from this instability.

Identification of critical stacking faults in thin-film CdTe solar cells

Cadmium telluride (CdTe) is a p-type semiconductor used in thin-film solar cells. To achieve high light-to-electricity conversion, annealing in the presence of CdCl2 is essential, but the underlying mechanism is still under debate. Recent evidence suggests that a reduction in the high density of stacking faults in the CdTe grains is a key process that occurs during the chemical treatment. A range of stacking faults, including intrinsic, extrinsic, and twin boundary, are computationally investigated to identify the extended defects that limit performance. The low-energy faults are found to be electrically benign, while a number of higher energy faults, consistent with atomic-resolution micrographs, are predicted to be hole traps with fluctuations in the local electrostatic potential. It is expected that stacking faults will also be important for other thin-film photovoltaic technologies.

Global gyrokinetic stability of collisionless microtearing modes in large aspect ratio tokamaks

Linear full radius gyrokinetic calculations show the existence of unstable microtearing modes (MTMs) in purely collisionless, high temperature, large aspect ratio tokamak plasmas. The present study takes into account fully gyrokinetic highly passing ions and electrons. The global 2-D structures of the collisionless mode with full radius coupling of the poloidal modes is obtained and compared with another electromagnetic mode, namely, the Alfvén Ion Temperature Gradient (AITG) mode (or Kinetic Ballooning Mode, KBM) for the same equilibrium profile. Several important characteristics of the modes are brought out and compared, such as a clear signature in the symmetry properties of the two modes, the plasma–β dependence, and radial and poloidal length scales of the electrostatic and magnetic vector potential fluctuations. Extensive parameter scans for this collisionless microtearing mode reveal the scaling of the growth rate with β and the electron temperature gradient ηe. Scans at different β values show an inverse relationship between the ηe threshold and β, leading to a stability diagram, and implying that the mode might exist at moderate to strong temperature gradients for finite β plasmas in large aspect ratio tokamaks. In contrast to small aspect ratio tokamaks where the trapped electron magnetic drift resonance is found to be important, in large aspect ratio tokamaks, a strong destabilization due to the magnetic drift resonance of passing electrons is observed and is identified as a possible collisionless drive mechanism for the collisionless MTM.

Generalized current-voltage analysis and efficiency limitations in non-ideal solar cells: Case of Cu2ZnSn(SxSe1−x)4 and Cu2Zn(SnyGe1−y)(SxSe1−x)4

Detailed electrical characterization of nanoparticle based Cu2ZnSn(SxSe1−x)4 (CZTSSe) and Cu2Zn(SnyGe1−y)(SxSe1−x)4 (CZTGeSSe) solar cells has been conducted to understand the origin of device limitations in this material system. Specifically, temperature dependent current-voltage analysis has been considered, with particular application to the characterization of solar cells with non-ideal device behavior. Due to the presence of such non-ideal device behavior, typical analysis techniques—commonly applied to kesterite-type solar cells—are found to be insufficient to understand performance limitations, and an analysis methodology is presented to account for the non-idealities. Here, the origin of non-ideal device behavior is chiefly considered in terms of electrostatic and band gap potential fluctuations, low minority carrier lifetimes, temperature dependent band edges, high surface/bulk recombination rates, and tunneling enhanced recombination. For CZTSSe and CZTGeSSe, the main limitations to improved device performance (voltage limitations) are found to be associated with significant EA deficits (EA–EG) at 300 K, large ideality factors, and voltage-dependent carrier collection, which we associate with the bulk material properties of the absorbers. The material origin of these non-ideal electrical properties is considered. Additionally, for CZTGeSSe, the effect of Ge-incorporation on the electrical properties of the solar cells is discussed, with improvements in the electrical properties characterized for the Ge-alloyed devices.

The nature of electrostatic potential fluctuations in Cu2ZnSnS4 and their role on photovoltaic device performance

Aberration corrected STEM EELS is used to investigate point defects in Cu2ZnSnS4 (CZTS). Nano-scale clusters of ZnCu anti-site donors are observed with the donor concentration being sufficiently high to degenerately dope the semiconductor. Uncompensated donors and acceptors result in electrostatic potential fluctuations within the material. The effect of these potential fluctuations on the photovoltaic device properties is discussed.

Numerical investigation of frequency spectrum in the Hasegawa-Wakatani model

The wavenumber-frequency spectrum of the two-dimensional Hasegawa-Wakatani model is investigated in the hydrodynamic, intermediate, and adiabatic regimes. A nonlinear frequency and a line width related to energy transfer properties provide a measure of the average frequency and spectral broadening, respectively. In the adiabatic regime, narrow spectra, typical of wave turbulence, are observed with a nonlinear frequency shift in the electron drift direction. In the hydrodynamic regime, broad spectra with almost zero nonlinear frequencies are observed. Nonlinear frequency shifts are shown to be related to nonlinear energy transfer by vorticity advection through the high frequency region of the spectrum. In the intermediate regime, the nonlinear frequency shift for density fluctuations is observed to be weaker than that of electrostatic potential fluctuations. The weaker frequency shift of the density fluctuations is due to nonlinear density advection, which favors energy transfer in the low frequency range. Both the nonlinear frequency and the spectral width increase with poloidal wavenumber ky. In addition, in the adiabatic regime where the nonlinear interactions manifest themselves in the nonlinear frequency shift, the cross-phase between the density and potential fluctuations is observed to match a linear relation, but only if the linear response of the linearly stable eigenmode branch is included. Implications of these numerical observations are discussed.

Band tailing and efficiency limitation in kesterite solar cells

We demonstrate that a fundamental performance bottleneck for hydrazine processed kesterite Cu2ZnSn(S,Se)4 (CZTSSe) solar cells with efficiencies reaching above 11% can be the formation of band-edge tail states, which quantum efficiency and photoluminescence data indicate is roughly twice as severe as in higher-performing Cu(In,Ga)(S,Se)2 devices. Low temperature time-resolved photoluminescence data suggest that the enhanced tailing arises primarily from electrostatic potential fluctuations induced by strong compensation and facilitated by a lower CZTSSe dielectric constant. We discuss the implications of the band tails for the voltage deficit in these devices.

Direct Imaging of Charged Impurity Density in Common Graphene Substrates

Kelvin probe microscopy in ultrahigh vacuum is used to image the local electrostatic potential fluctuations above hexagonal boron nitride (h-BN) and SiO2, common substrates for graphene. Results are compared to a model of randomly distributed charges in a two-dimensional (2D) plane. For SiO2, the results are well modeled by 2D charge densities ranging from 0.24 to 2.7 × 10(11) cm(-2), while h-BN displays potential fluctuations 1-2 orders of magnitude lower than SiO2, consistent with the improvement in charge carrier mobility for graphene on h-BN compared to SiO2. Electron beam exposure of SiO2 increases the charge density fluctuations, creating long-lived metastable charge populations of ~2 × 10(11) cm(-2) at room temperature, which can be reversed by heating.

Experimental Verification of Entropy Cascade in Two-Dimensional Electrostatic Turbulence in Magnetized Plasma

The wave number spectrum (one-dimensional spectrum) of electrostatic potential fluctuations at sub-Larmor scales was measured in two-dimensional (2D) electrostatic turbulence in laboratory magnetized plasma. The spectrum at scales k([perpendicular])ρ(i)>1, where k([perpendicular]) and ρ(i) are the fluctuation wave number perpendicular to the magnetic field and ion Larmor radius, respectively, supports the existence of the k(-10/3) inertial range of the entropy cascade induced by nonlinear phase mixing. This indicates agreement with a theoretical prediction [A. A. Schekochihin et al., Plasma Phys. Controlled Fusion 50, 124024 (2008)] and the result of a 2D gyrokinetic simulation [T. Tatsuno et al., Phys. Rev. Lett. 103, 015003 (2009)]. The cutoff wave numbers of the spectrum, above which the entropy cascade is smeared by collisions, observed in this experiment were consistent with those in the theory.

Spectroscopic Imaging of Photopotentials and Photoinduced Potential Fluctuations in a Bulk Heterojunction Solar Cell Film

We present spatially resolved photovoltage spectra of a bulk heterojunction solar cell film composed of phase-separated poly(9,9'-dioctylfluorene-co-benzothiadiazole) (F8BT) and poly(9,9'-dioctylfluorene-co-bis-N,N'-(4-butylphenyl)-bis-N,N'-phenyl-1,4-phenylenediamine) (PFB) polymers prepared on ITO/PEDOT:PSS and aluminum substrates. Over both PFB- and F8BT-rich domains, the photopotential spectra were found to be proportional to a linear combination of the polymers' absorption spectra. Charge trapping in the film was studied using photopotential fluctuation spectroscopy, in which low-frequency photoinduced electrostatic potential fluctuations were measured by observing noise in the oscillation frequency of a nearby charged atomic force microscope cantilever. Over both F8BT- and PFB-rich regions, the magnitude, distance dependence, frequency dependence, and illumination wavelength dependence of the observed cantilever frequency noise are consistent with photopotential fluctuations arising from stochastic light-driven trapping and detrapping of charges in F8BT. Taken together, our findings suggest a microscopic mechanism by which intermixing of phases leads to charge trapping and thereby to suppressed open-circuit voltage and decreased efficiency in this prototypical bulk heterojunction solar cell film.

Lower Hybrid Drift Waves: Space Observations

Lower hybrid drift waves (LHDWs) are commonly observed at plasma boundaries in space and laboratory, often having the strongest measured electric fields within these regions. We use data from two of the Cluster satellites (C3 and C4) located in Earth's magnetotail and separated by a distance of the order of the electron gyroscale. These conditions allow us, for the first time, to make cross-spacecraft correlations of the LHDWs and to determine the phase velocity and wavelength of the LHDWs. Our results are in good agreement with the theoretical prediction. We show that the electrostatic potential of LHDWs is linearly related to fluctuations in the magnetic field magnitude, which allows us to determine the velocity vector through the relation ∫δEdt·v = ϕ(δB)(∥). The electrostatic potential fluctuations correspond to ∼10% of the electron temperature, which suggests that the waves can strongly affect the electron dynamics.