Fermi Potentials Research Articles

Analysis of a hybrid model for the electro-thermal behavior of semiconductor heterostructures

We prove existence of a weak solution for a hybrid model for the electro-thermal behavior of semiconductor heterostructures. This hybrid model combines an electro-thermal model based on drift-diffusion with thermistor type models in different subregions of the semiconductor heterostructure. The proof uses a regularization method and Schauder's fixed point theorem. For boundary data compatible with thermodynamic equilibrium we verify, additionally, uniqueness. Moreover, we derive bounds and higher integrability properties for the electrostatic potential and the quasi Fermi potentials as well as the temperature.

Design and Simulation of Terahertz Perfect Absorber with Tunable Absorption Characteristic Using Fractal-Shaped Graphene Layers

Graphene material, due to its unique conductivity and transparency properties, is utilized extensively in designing tunable terahertz perfect absorbers. This paper proposes a framework to design a tunable terahertz perfect absorber based on fractal triangle-shaped graphene layers embedded into dielectric substrates with the potential for spectral narrowing and widening of the absorption response without the need for geometric manipulation. In this way, the absorption cross-section spectra of the suggested configurations are achieved over the absorption band. First, the defection impact on the single-layer fractal triangle-shaped graphene structure inserted in insulators of the absorber is evaluated. Then, a flexible tunability of the absorbance’s peak is indicated by controlling the Fermi energy. By stacking fractal graphene sheets as a double graphene layer configuration in both the same and cross-states positioning, it is demonstrated that the absorption characteristics can be switched at 6–8 THz with a stronger amplitude, and 16–18 THz with a lower intensity. The impact of changing the Fermi potentials of embedded graphene layers is yielded, resulting in a plasmonic resonance shift and a significant broadening of the absorption bandwidth of up to five folds. Following, the absorption spectra related to the fractal triangle-shaped structures consist of a multi-stage architecture characterized by a spectral response experiencing a multiband absorbance rate and an absorption intensity of over 8 × 106 nm2 in a five-stage perfect absorber. Ultimately, the variations of the absorbance parameter and plasmonic mode under rotating the graphene sheet are explored for single and double fractal triangle-shaped perfect configurations on the absorption band. The presented mechanism demonstrates the tunability of the absorption spectrum in terms of narrowing or broadening and switching the plasmonic resonance by configuring multi-stage structures that can employ a broad range of applications for sensory devices.

Modelling charge transport in perovskite solar cells: Potential-based and limiting ion depletion

From Maxwell-Stefan diffusion and general electrostatics, we derive a drift-diffusion model for charge transport in perovskite solar cells (PSCs) where any ion in the perovskite layer may flexibly be chosen to be mobile or immobile. Unlike other models in the literature, our model is based on quasi Fermi potentials instead of densities. This allows to easily include nonlinear diffusion (based on Fermi-Dirac, Gauss-Fermi or Blakemore statistics for example) as well as limit the ion depletion (via the Fermi-Dirac integral of order −1). The latter will be motivated by a grand-canonical formalism of ideal lattice gas. Furthermore, our model allows to use different statistics for different species. We discuss the thermodynamic equilibrium, electroneutrality as well as generation/recombination. Finally, we present numerical finite volume simulations to underline the importance of limiting ion depletion.

Energy-dependent diffusion in a soft periodic Lorentz gas

The periodic Lorentz gas is a paradigmatic model to examine how macroscopic transport emerges from microscopic chaos. It consists of a triangular lattice of circular hard scatterers with a moving point particle. Recently this system became relevant as a model for electronic transport in low-dimensional nanosystems such as molecular graphene. However, to more realistically mimic such dynamics, the hard Lorentz gas scatterers should be replaced by soft potentials. Here we study diffusion in a soft Lorentz gas with Fermi potentials under variation of the total energy of the moving particle. Our goal is to understand the diffusion coefficient as a function of the energy. In our numerical simulations we identify three different dynamical regimes: (i) the onset of diffusion at small energies; (ii) a transition where for the first time a particle reaches the top of the potential, characterized by the diffusion coefficient abruptly dropping to zero; and (iii) diffusion at high energies, where the diffusion coefficient increases according to a power law in the energy. All these different regimes are understood analytically in terms of simple random walk approximations.

Normal and Anomalous Diffusion in Soft Lorentz Gases.

Motivated by electronic transport in graphenelike structures, we study the diffusion of a classical point particle in Fermi potentials situated on a triangular lattice. We call this system a soft Lorentz gas, as the hard disks in the conventional periodic Lorentz gas are replaced by soft repulsive scatterers. A thorough computational analysis yields both normal and anomalous (super)diffusion with an extreme sensitivity on model parameters. This is due to an intricate interplay between trapped and ballistic periodic orbits, whose existence is characterized by tonguelike structures in parameter space. These results hold even for small softness, showing that diffusion in the paradigmatic hard Lorentz gas is not robust for realistic potentials, where we find an entirely different type of diffusion.

Construction of Fermi Potentials from Electronic Wave Functions.

The Fermi potential, vF(r), is the nonclassical part of the multiplicative effective potential appearing in the one-particle Schrödinger-type equation for the square root of the electron density. The usual way of constructing vF(r) by inverting that equation produces unsatisfactory results when applied to electron densities expanded in Gaussian basis sets. We suggest a different method that is based on an explicit formula for vF(r) in terms of the interacting one- and two-electron reduced density matrices of the system. This method is exact in the basis-set limit and yields accurate approximations to the basis-set-limit vF(r) when applied to reduced density matrices represented in terms of finite basis sets. Illustrative applications involve atomic and molecular wave functions generated at various levels of ab initio theory. It is also shown how to construct the Pauli and exchange-correlation potentials of any system starting with only vF(r).

Green synthesis of biogenic silver nanomaterials using Raphanus sativus extract, effects of stabilizers on the morphology, and their antimicrobial activities.

The present study explores the reducing and capping potentials of aqueous Raphanus sativus root extract for the synthesis of silver nanomaterials for the first time in the absence and presence of two stabilizers, namely, water-soluble starch and cetyltrimethylammonium bromide (CTAB). The surface properties of silver nanoparticles (AgNPs) were determined by dynamic light scattering (DLS), transmission electron microscopy (TEM), energy dispersion X-ray spectroscopy (EDX), scanning electron microscopy (SEM), X-ray diffraction (XRD), and Fourier transform infrared (FT-IR) techniques. The mean size of AgNPs, ranging from 3.2 to 6.0nm, could be facilely controlled by merely varying the initial [extract], [CTAB], [starch], and [Ag(+)] ions. The agglomeration number, average number of silver atoms per nanoparticle, and changes in the fermi potentials were calculated and discussed. The AgNPs were evaluated for their antimicrobial activities against different pathogenic organisms. The inhibition action was due to the structural changes in the protein cell wall.

On Regge pole trajectories for a rational function approximation of Thomas–Fermi potentials

The positions of two Regge poles caused by the rational function approximate Thomas–Fermi potential (a screened attractive Coulomb potential) are studied in detail as a function of the scattering energy. The leading pole is traced from the right-hand (physical) complex angular momentum plane ℜ(ℓ) > −1/2 to the left-hand (unphysical) complex angular momentum plane ℜ(ℓ) < −1/2 as the scattering energy is increased indefinitely. The second Regge pole is located in the unphysical half-plane at all energies. In this study an exact numerical and an approximate semiclassical WKB methods are discussed in some detail, where the boundary conditions of the regular (physical) Schrödinger solution become important. Transitions in behavior of Regge poles are explained in terms of Stokes lines and turning points evolution. The major change in the direction of Regge trajectories is demonstrated as a transition in the topology of Stokes lines. This phenomenon is caused by switching from one pair of turning points to another pair as the third turning point approaches the Stokes line connecting to the original turning points.

First production of ultracold neutrons with a solid deuterium source at the pulsed reactor TRIGA Mainz⋆

The production rates of ultracold neutrons (UCN) with a solid deuterium converter have been measured at the pulsed reactor TRIGA Mainz. Exposed to a thermal neutron fluence of $\ensuremath \sim 1\cdot 10^{13}$ n·cm^-2·pulse^-1, the number of detected very cold and ultracold neutrons ranges up to 200 000 at 7mol of solid deuterium (sD2) in combination with a pre-moderator (mesitylene). About 50% of the measured neutrons can be assigned to UCN with energies E of $\ensuremath V_{\rm F}({\rm sD}_2)\leq E \leq V_{\rm F}{\rm (guide)}$ where V F(sD 2) = 105 neV and V F(guide) = 190 neV are the Fermi potentials of the sD2 converter and our stainless steel neutron guides, respectively. Thermal cycling of solid deuterium, which was frozen out from the gas phase, considerably improved the UCN yield, in particular at higher amounts of sD2.

Semiclassical approach to Regge poles trajectories calculations for nonsingular potentials: Thomas–Fermi type

A simple semiclassical approach, based on the investigation of anti-Stokes line topology, is presented for calculating Regge poles for nonsingular (Thomas–Fermi type) potentials, namely potentials with singularities at the origin weaker than order −2. The anti-Stokes lines for Thomas–Fermi potentials have a more complicated structure than those of singular potentials and require careful application of complex analysis. The explicit solution of the Bohr–Sommerfeld quantization condition is used to obtain approximate Regge poles. We introduce and employ three hypotheses to obtain several terms of the Regge pole approximation.Please note that the pdf of this article was replaced with a corrected version on 29 June 2004. Minor changes have been made to pages 6950–6953.

The non equilibrium band model of silicon in TMAH and in anisotropic electrochemical alkaline etching solutions

This study presents the energy band diagram of silicon in contact with an aqueous solution of tetra-methyl ammonium hydroxide (TMAH) during the anisotropic electrochemical etch process. The band diagram is constructed from the measured open circuit potential (OCP) and the measured total band bending of the silicon at the OCP which is determined by impedance measurements. Current–voltage as well as capacitance–voltage characteristics of silicon in contact with TMAH solutions are presented. The present study emphasizes the non-equilibrium operation of the electrochemical cell even at the open circuit potential (OCP). In previous studies of the band diagram of silicon in alkaline anisotropic etch solutions, the Fermi levels of the silicon and the electrolyte are aligned at OCP. In contrast, in the present study the Fermi levels are not aligned since steady state rather than equilibrium prevails at this operation point. The value of the measured OCP is used to determine the separation between the two quasi Fermi levels. The assumptions leading to the construction of the band diagram are elaborated. The relationships between OCP, flat band voltage, passivation potentials and Fermi potentials are discussed. The predictions of the model and the effect of conductivity type, doping level, temperature and illumination are compared with experiments. The new model and methodology presented in this study is applicable to additional anisotropic alkaline etch solutions such as KOH and EDP. It is very useful for the appropriate design of the process required for electrochemical etch stop for the fabrication of membranes and controlled micromachining of silicon.

Rare-gas-induced broadening and shift of two-photon transitions to intermediate $\mathsf{(n=9{-}14)}$ Rydberg states of atomic thallium *

Results of broadening and shift measurements of Doppler-free two-photon lines for transitions from the ground state to the \(\) Rydberg states with intermediate principle quantum numbers of atomic thallium perturbed by rare gases are reported. The rates show a distinct behaviour in this range of principle quantum numbers and significant dependence on the total angular momentum of the upper nP state. The experimental results are compared with calculations using a Van der Waals potential and a superposition of polarization and Fermi potentials. Additionally, broadening and shift rates of the transition Tl 6P3/2-9P3/2 have been measured for quadrupolar as well as for mainly scalar excitation. The rates for both kinds of excitation coincide within the limits of error reflecting the small perturbation of the 6P3/2 state compared to that of the upper 9P3/2 state.

Fermi and Coulomb holes of molecules in excited states

AbstractCorrelation holes of electrons with the same (Fermi hole) and different (Coulomb hole) spins in the ground (X1Σ+), first (A1Σ+) and second (B1II) excited states of LiH were constructed from full configuration interaction (CI) wave functions. It was found that the shapes of both the Fermi and Coulomb holes in these states are dependent on the location of the reference electron. When the reference electron is chosen to be close to the Li nucleus, the Fermi correlation results in a large negative hole for all three states. However, the A1Σ+ excited state is further characterized by displaying a second hole around the H nucleus, and in the B1II state, the hole is elongated along the molecular axis. Coulomb correlation shows up strongly in the A1Σ+ state and, in addition, there is clearly correlation of electrons at the two nuclei. These features of the correlation holes were compared with those from a two‐Slater‐determinant model wave function. The Hartree, Fermi, and Coulomb screening potentials in these states were also studied in the light of possible modeling of the correlation functionals for the excited states. © 1995 John Wiley &amp; Sons, Inc.

Surface density profiles and the rate of loss of stored ultracold neutrons

The reflection losses for stored ultracold neutrons have been calculated for various profiles of molecular number density at the wall surface. The results show relatively low sensitivity to realistic departures from a simple step function. For a surface density rising as a linear ramp extending over a depth of 100 Å, in the case where the mean Fermi potentials is 100 neV, the losses are only about 4% higher than those for the abrupt step case. The same degree of insensitivity has been found for other shapes of profile. The effect on the losses of a reduced Debye temperature in the first few atomic layers of the surface is also considered.

SIX-QUARK CLUSTERS IN NUCLEAR MATTER AT LOW TEMPERATURES

The two-phase system consisting of nucleons and six-quark clusters is investigated. The interaction between nucleons and six-quarks is represented by a sum of the Fermi and Yukawa potentials. The temperature behavior of nucleon and six-quark concentrations versus density is found. It is shown that with a normal nuclear density, six-quark clusters may amount to about 10%, which is in agreement with experiment.

A comparison of simple and numerical two-dimensional models for the threshold voltage of short channel MOSTs

The threshold voltage for short channel MOSTs has been derived by two-dimensional numerical computation. The results can be expressed in normalised form with the reduced threshold voltage, V T − V FB − 2 φ, given as a fraction of the reduced long-channel threshold voltage, V T∞ − V FB − 2 φ, where V FB and φ are the flat-band and bulk Fermi potentials respectively. An extremely good fit to the theoretical predictions is then given by V T−V FB−2φ V T∞−V FB−2φ =1− aW sr L b where a≃0.94−0.17 W s rj 1 2 b≃0.90−0.66 log 10 W s r j +0.37 X ox W s where the junction depth, r j , and oxide thickness, x ox , are expressed as fractions of the source depletion layer thickness, W s , and where the channel length, L, is given as a fraction of the one-dimensional theoretical spread, W sr , of a depletion region around a cylindrical step-junction. This empirical expression is valid over a wide range of normalised device geometries (0.4 < L/ W sr < 40, 0.1 < r j / W s < 10, 0.01 < x ox / W s < 0.2) and, except for very shallow junctions ( r j / W s ≲ 1), differs only slightly from the simple model proposed by Yau. A comparison of the theory with experimental results shows good agreement for MOSTs fabricated with channel lengths between 2 and 5 μm using conventional photolithography.

Energy loss of low energy protons channeling in silicon crystals

Abstract Experimental energy loss measurements were made for protons of energy 0.5 to 1.6 MeV channeling through 1 μm thick silicon targets along the (110), (11l), and (211) axial directions, and the {l00}, {110}, (1ll}, and (211) planar directions. These data have a precision of ±5% and are presented graphically along with an extensive summary of other data in the literature. The new data cover a wider range of channels than has previously been examined with protons and are in agreement with the helium data of Eisen et 01.' A standard theory of energy loss is summarized and ampli- tied, and straggling is calculated theoretically. Local electron densities for various channels in silicon are extracted from plane and row averaged Thomas Fermi potentials via v ▿2 V = 4 πρ, and are used in the theoretical energy loss and straggling equations. The results agree with the experimental data to within 5%. The need for more precise measure-ments in order to make a decisive test of the theory is discussed.