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In this paper, we investigate the electron Landau level stability and its influence on the electron Fermi energy, $E_{\mathrm{\text{F}}}(e)$, in the circumstance of magnetars, which are powered by magnetic field energy. In a magnetar, the Landau levels of degenerate and relativistic electrons are strongly quantized. A new quantity $g_n$, the electron Landau level stability coefficient is introduced. According to the requirement that $g_n$ decreases with increasing the magnetic field intensity $B$, the magnetic field index $\beta$ in the expression of $E_{\mathrm{\text{F}}}(e)$ must be positive. By introducing the Dirac-$\delta$ function, we deduce a general formulae for the Fermi energy of degenerate and relativistic electrons, and obtain a particular solution to $E_{\mathrm{\text{F}}}(e)$ in a superhigh magnetic field (SMF). This solution has a low magnetic field index of $\beta =1/6$, compared with the previous one, and works when $\rho \ge 10^7{\mathrm{\text{g cm}}}^{-3}$ and $B_{\mathrm{\text{cr}}}\ll B\le 10^{17}$ Gauss. By modifying the phase space of relativistic electrons, a SMF can enhance the electron number density $n_e$, and decrease the maximum of electron Landau level number, which results in a redistribution of electrons. According to Pauli exclusion principle, the degenerate electrons will fill quantum states from the lowest Landau level to the highest Landau level. As $B$ increases, more and more electrons will occupy higher Landau levels, though $g_n$ decreases with the Landau level number $n$. The enhanced $n_e$ in a SMF means an increase in the electron Fermi energy and an increase in the electron degeneracy pressure. The results are expected to facilitate the study of the weak-interaction processes inside neutron stars and the magnetic-thermal evolution mechanism for magnetars.

In this paper, we use the q-derivative emerging in the non-extensive statistical physics to formulate the q-deformed quantum mechanics. We find the algebraic structure related to this deformed theory and investigate some properties of the q-deformed elementary functions. Using this mathematical background, we formulate the q-deformed Heisenberg algebra and q-deformed time-dependent Schrödinger equation. As an example, we deal with the infinite potential well and compute the Fermi energy in the q-deformed theory.

The Fermi energy and the minimum size for silver (Ag) metallic clusters have been investigated by the electronic structure calculations using density functional theory method. The results reveal that the work function of clusters with metallicity has the same value as that of bulk metals. This result is interpreted by the role of localized surface states in a thin layer and furthermore it is deduced that a nonmetal layer exists at the surface of Ag bulk metals and their clusters. This layer-thickness is about the same as the lattice constant and the minimum diameter for metallic clusters is about twice of the layer-thickness.

The electron gas statistics in semiconducting thin films with arbitrary isotropic energy spectra was found in this theoretical work. General expressions for the density of states of the charge carriers and for the chemical potential were deduced according to the two-band Kane model approach. The ratio of the expression obtained for the density of states to that of the expression deduced according to the parabolic approach was shown to be a function of the energy. The Fermi energy of the electron gas was observed to be a function of the thin film thickness, the non-parabolic parameter, the concentration and the temperature. In the strong non-parabolic approach the dependency of the Fermi energy on the thin film thickness was shown to exhibit non-monotonic characteristics.

In the present work we theoretically develop a k⋅π model to calculate the carrier electronic structure for both n- and p-type SnTe. Here π is the momentum operator in the presence of the spin–orbit interaction. The work is an extension of the theory developed for n- and p-PbTe earlier by one of the authors to evaluate the Fermi energy and the density of states (DOS). We consider a six-level energy basis for SnTe, as proposed by Bernick and Kleinman. One set of calculations was done by diagonalizing the k⋅π Hamiltonian matrix for the band-edge states and treating the far bands using perturbation theory. In the second set we have rediagonalized the k⋅π Hamiltonian matrix for the band edge states, treating the first diagonalization as the basis. The far bands are, as usual, included through perturbation. We have compared the results of both the sets. Results obtained for n- and p-type SnTe are also compared with that of n- and p-type PbTe. The similarities and contrasts are discussed. An indirect comparison with the DOS of the metallic tin suggests that the calculations are fairly reasonable. The results are also compared with some recent results for SnTe.

In this work we have investigated the effect of external electric field on the electronic structure and refractive index changes of a GaN/AlN constant total effective length multiple quantum well. A decreasing oscillatory behavior for energy levels was seen when the electric field increased and in some energy values the energy levels intersected. By increasing the number of wells, oscillator strength dropped suddenly and moved to higher electric field in a critical electric field. By using the number of wells and the total length of the structure as two tuning tools, we were able to select our previously determined critical electric field.

An analysis is made of the low-temperature behavior of the chemical potential $\mu$ of a quasi-two-dimensional electron gas near the resonance point (at the bottom of the miniband) and far from it. Low-temperature analytical formulas for $\mu (T)$ are obtained under the conditions of the existence of an arbitrary number of minibands. It is shown that with the increasing temperature near the resonance point, the chemical potential decreases linearly and exponentially slowly in the middle of the resonance points. Analytical formulas are compared to the numerical solutions.

The Fermi energy level, that is, the chemical potential associated with an excitonic gas in a semiconductor within a non-parabolic quantum dot is calculated by determining previously the corresponding Fermi velocity of excitons conceived as confined in a spherical quantum box on the basis of the energy levels of the hydrogen atom. From the Fermi energy calculation, the reduced effective mass of an electron–hole pair is found to be dependent upon the spatial exciton density. In addition, some aspects related to quantization of the Fermi energy in question and temperature dependence are discussed.

In this paper, we introduce a method for analytically calculating the Fermi energy. As an example, we study the hard-sphere (HS) gas, the gas in porous media and the gas in an external potential field or curved background. These examples are valuable for studying the spectral structure of a real gas.

It is shown that the bipolaron theory of Cooper pairs suggests that there is a possibility for a superconducting phase to exist at low and high levels of doping and be absent at the intermediate level of doping. The results obtained possibly to imply the universal character of 1/8 anomaly.

Graphene nanoribbons are considered potentially suitable and have exhibited excellent results in on-chip interconnects. In order to evaluate the different circuit impedance parameters of multi-layer graphene nanoribbons (MLGNRs), an electrical equivalent single conductor (ESC) along with an analytical model is proposed. On the basis of an electrical model, the impact of intercalation doping on the performance of MLGNRs at 32, 22, and 16nm technology nodes is discussed in this paper. Moreover, it is also discussed that the increase in intercalation doping increases the Fermi energy of the layers of the MLGNR, which increases its overall conductivity. The fact that the variation in the Fermi energy will have a considerable impact on the parasitic parameters of the MLGNR interconnect at three different technology nodes (32, 22, and 16nm) for variable global lengths (500–2000$\mu$m) is also analyzed. To estimate and compare the performance in terms of delay and power delay product (PDP) of MLGNRs, the simulation program with integrated circuit emphasis (SPICE) simulation tool is used. The results also show that the increase in the Fermi energy improves the performance of MLGNRs in terms of delay and PDP at three different technology nodes. Furthermore, a comparative analysis of all three technology nodes is performed with the copper interconnect, and it is revealed that the MLGNR interconnect is considered to be a prominent material for the next-generation on-chip very-large-scale integration interconnects.

The dissipation phenomenon has been studied by simulating the reaction ${}^{129}\mathrm{\text{Xe}}{+}^{129}\mathrm{\text{Sn}}$ with Isospin-dependent Quantum Molecular Dynamics (IQMD) model. The evolution of the isotropic ratio with bombarding energy for the free protons moving forward in the center of mass system in the final state of the reactions, drawn from the experimental measurements by INDRA collaboration, is reproduced with the model in the energy region near and slightly higher than the Fermi energy. Comparison of the data with the simulation obtained using the IQMD model in the cases of different combinations of in-medium effects in two-body collisions, i.e., medium modification of nucleon–nucleon cross-section and Pauli-blocking effect, indicates that the Pauli exclusion principle is indispensable in the microscopic model and the Pauli-blocking in binary interactions dominates the in-medium effects in the heavy-ion reactions in the energy range, even below the Fermi energy. Based on such comparisons, an energy-dependent effective factor responsible for the Pauli-blocking in the binary collisions in heavy-ion collisions in the Fermi energy domain has been extracted.

Based on free-electron model, the calculated inelastic mean escape depth of secondary electrons, experimental one, the energy band of metal, the characteristics and processes of secondary electron emission, maximum number of secondary electrons released per primary electron δ(Φ,E_F)_PEm as a function of parameter K_m, work function Φ and Fermi energy E_F was deduced, where K_m is a constant for a given metal in the energy range 100–800 eV. According to the relationship between maximum secondary electron yield from metal δ(Φ,E_F)_m and δ(Φ,E_F)_PEm, the formula for δ(Φ,E_F)_m as a function of atomic number Z, parameter K_m, Φ and E_F was deduced. Using the deduced formula for δ(Φ,E_F)_m, Z, experimental δ(Φ,E_F)_m, Φ and E_F, K_m relative to alkali metals, K_m relative to earth-alkali metals and the mean value of K_m were computed, respectively. And the formulae for maximum secondary electron yield from alkali metals, earth-alkali metals and metals were obtained and proved to be true, respectively. On the basis of the deduced formula for δ(Φ,E_F)_m and the empirical relation that high Φ are connected with high E_F, it can be concluded that high δ(Φ,E_F)_m are connected with high Φ and vice versa.

In this research paper, we examined the effect of placing the elements of Group 0 as alligator clips with Anthracene molecule binding gold electrodes on the nanometer scale using Extended Huckle Theory (EHT) based semi-empirical model. The electron transport parameters i.e., I-V curves, Conductance-Voltage curves and transmission spectrum were investigated through Anthracene molecule by buffering it between two semi-infinite gold electrodes but via different alligator clips-Helium, Neon, Argon, Krypton, Xenon and Radon, all from Noble gas group or group-0 under finite bias voltages within Keldysh's nonequilibrium green function formalism (NEGF). The simulated results revealed that the Xenon and Radon showed maximum conduction whereas Krypton, Neon, Helium and Argon showed least. The maximum conductance of 0.62G₀ and 70.4 μA current was exhibited by Xenon and thus affirmed to be the most optimal alligator clip amongst noble gases at nanometre scale.

This article investigated the effects of a quantizing magnetic field and temperature on Fermi energy oscillations in nanoscale semiconductor materials. It is shown that the Fermi energy of a nanoscale semiconductor material in a quantizing magnetic field is quantized. The distribution of the Fermi–Dirac function is calculated in low-dimensional semiconductors at weak magnetic fields and high temperatures. The proposed theory explains the experimental results in two-dimensional semiconductor structures with a parabolic dispersion law.

One of the most chemically adaptable elements is boron which is found in the periodic table between two groups, i.e., metals and nonmetals and may create more than 16 polymorphs that are bulk and made of connected boron polyhedra. Given that boron and carbon are comparable elements, it has been questioned whether two-dimensional (2D) boron could serve as a conceptual starting point for the construction of other boron nanostructures. Using boron as fundamental building blocks, boron nanosheets were synthesized known as borophenes. Borophene is found to be a crystalline form of atomic monolayer boron which was theoretically first predicted in mid-1990s and experimentally synthesized very recently in 2015. In this work, we studied both armchair and zigzag formation of borophene and presented a comparative analysis of their minimum sub-band energy, effective mean free path $E_n$, number of conduction channels $N_{\mathrm{\text{ch}}}$, scattering resistance per unit length. The $N_{\mathrm{\text{ch}}}$ for armchair BNR is 3,2,1 for 22nm, 13nm, 7nm, respectively, which is comparatively more than zigzag BNR. We later proposed Top-Contact BNR (TC-BNR) and Side-Contact BNR (SC-BNR). Our analysis shows that SC-BNR offers $96\%$ less resistance compared to TC-BNR and it is of the order of SC-GNR. Further, if we compare with copper interconnects, BNR is better in terms of performance and copper can be replaced with BNR due to high bulk mean free paths 300nm and 400nm compared to copper’s 40nm.