Existence Of Localized Electronic States Research Articles

Electron states in metalized ultrathin film crystals and their thermodynamic behavior

The dispersion law of electron in ultrathin crystalline metal-like film structures was found and analyzed using the method of two-time and temperature-dependent Green’s functions. Unlike unbounded (bulk) structures of the same crystallographic composition, the energy spectra of electrons in the film is strictly discrete, have two gaps and the narrower range of electron energies. Also, the conditions for the appearance and existence of localized electronic states as a function of boundary parameters were investigated. The probability of finding electrons in localized states is higher at more perturbed film boundaries. The electronic contribution to specific heat and entropy depends linearly on temperature, as in bulk structures, but with a different slope coefficient, so it follows that the electronic gas in films is a less ordered system and is closer to the equilibrium state than the same in bulk structures. These results could provide an explanation for the experimental facts about the stronger superconducting properties of ultrathin thin films.

Surface functionalization effect on physical properties and quantum capacitance of Ca2C MXenes

Effects of surface terminal groups on the structural, mechanical, and electronic properties, as well as the quantum capacitance of Ca2CT2 (T = F–, O–, Cl–, OH–) MXenes are studied by first-principles electronic structure computations. Ca2C(OH)2 is determined to be the most stable structure compared with Ca2C and Ca2CT2 (T = F–, Cl–) MXenes, while Ca2CO2 is mechanically unstable. The surface terminations have a strong influence on the work function of MXene as they can alter the Fermi level and the associated electron transfer. Analyzing the atom projected density of states shows the existence of localized electron states at and around the Fermi level, generating a high charge density close to the Fermi level and resulting in relatively high quantum capacitance. The quantum capacitance of Ca2CCl2 is the highest (152 μF/cm2) among the studied cases, while Ca2C(OH)2 has the lowest quantum capacitance. The observed variations in quantum capacitance are mainly attributed to the creation and annihilation of new electronic states and the shift of Fermi level in the studied MXenes. Also, presence of surface terminations of Ca2C MXenes considerably changes the electrode quantum capacitance and Ca2CCl2 is the most promising one among the studied cases.

Electron localization in epitaxial graphene on Ru(0001) determined by moiré corrugation

The interpretation of scanning tunneling spectroscopy (STS) and scanning tunneling microscopy measurements of epitaxial graphene on lattice-mismatched substrates is a challenging problem, because of the spatial modulation in the electronic structure imposed by the formation of a moir\'e pattern. Here we describe the electronic structure of graphene adsorbed on Ru(0001) by means of density functional theory calculations that include van der Waals interactions and are performed on a large $11\ifmmode\times\else\texttimes\fi{}11$ unit cell to account for the observed moir\'e patterns. Our results show the existence of localized electronic states in the high and low areas of the moir\'e at energies close to and well above the Fermi level, respectively. Localization is due to the spatial modulation of the graphene-Ru(0001) interaction and is at the origin of the various peaks observed in STS spectra.

Localization of electrons in type‐II Ge/Si quantum dots stacked in a multilayer structure

AbstractSpace‐charge spectroscopy was employed to study electronic structure of a single layer of Ge quantum dots and of a stack of four layers of Ge islands embedded in an n ‐type Si(001) matrix. For a multilayer sample, the evidence for an electron localization in strained Si in the vicinity of Ge dots was found. From the temperature‐ and frequency‐dependent measurements the electron binding energy was determined to be 40–70 meV for different quantum states. The electron accumulation was not observed in a sample with a single layer of Ge dots. Existence of localized electronic states is explained by a modification of the conduction band alignment induced by inhomogeneous tensile strain in Si around the buried Ge dots. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Localization of electrons in multiple layers of self-assembled GeSi∕Si islands

Space-charge spectroscopy was employed to study the electronic structure of single and multiple layers of GeSi islands embedded in a n-type Si(001) matrix. For a multilayer sample, the evidence for an electron localization in strained Si in the vicinity of GeSi dots was found. From the admittance measurements the electron binding energy was determined to be 40–70meV. The electron accumulation was not observed in a sample with a single layer of GeSi islands. Existence of localized electronic states is explained by a modification of the conduction band alignment induced by inhomogeneous tensile strain in Si around the buried GeSi dots.

Electronic states inGe∕Siquantum dots with type-II band alignment initiated by space-charge spectroscopy

Space-charge spectroscopy was employed to study electronic structure of a stack of four layers of Ge quantum dots (QD's) coherently embedded in an $n$-type Si(001) matrix. Evidence for an electron confinement in Si in the vicinity of neutral Ge dots was found. From the temperature- and frequency-dependent measurements the electron binding energy was determined to be $\ensuremath{\sim}50\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. Existence of localized electronic states is explained by a modification of the conduction band alignment induced by inhomogeneous tensile strain in Si around the buried Ge dots. To support experimental results we performed numerical analysis of three-dimensional strain distribution and electronic structure of the sample under investigation. The strain distribution was found in terms of atomic positions using a valence-force-field model with a Keating interatomic potential. The electronic energy levels were calculated by solving a three-dimensional effective mass Schr\"odinger equation. The carrier confinement potential in this equation is modified by the strain distribution. The calculated confined eigenenergies agree with our experimental values deduced from the admittance spectroscopy. The data obtained in this work may serve as a guideline to interpret efficient photo- and electroluminescence as well as enhanced quantum efficiency of photodetectors and solar cells with Ge QD's stacked in a multilayer structure.

Negative differential resistance in scanning-tunneling spectroscopy of diamond films

Heavily boron-doped diamond film surfaces were investigated using ultra high-vacuum scanning tunneling microscopy. Negative differential resistance (NDR) was observed in the I–V curves measured from the diamond facets using scanning tunneling spectroscopy. NDR peaks with a peak-to-valley ratio as high as 90 were observed in about half of the I–V curves measured at room temperature. The NDR phenomenon is attributed to the existence of localized electron states on the diamond film surfaces. The I–V curves obtained at the diamond grain boundaries showed the characteristics of the graphite phase, while those acquired from the grain facets manifested obvious rectification in accordance with the wide band gap of diamond.

Energy dissipation in suspended micromechanical resonators at low temperatures

We have measured mechanical dissipation in micron-sized single-crystal gallium arsenide torsional resonators. The temperature dependence of the quality factor Q and the shift in resonance frequency can be explained by the presence of two-level systems. The dependence of Q on magnetic field is compatible with the existence of localized electronic states around material defects.

The effect of electronic localized states at dislocations on the ‘chemical’ impurity-dislocation interaction

Abstract The electronic contribution to the interaction energy between impurities and edge dislocations, which is related to the existence of localized electronic states at the dislocation, is calculated within the framework of a simple model. It is shown that the interaction energy varies within the limits of 10−2−-10−1 of the bandwidth and depends essentially on the lattice structure, the Burgers vector b, the type of impurity (‘donor’ or ‘acceptor’) and on the conduction-band filling. These effects are expected to be important in intermetallics with the B2 structure, where plastic deformation is governed by dislocations with b = a{100) (NiAl, CoAl, etc.).

Electronic structures of amorphous Ni1-xPx glasses.

Electronic structures of amorphous ${\mathrm{Ni}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{P}}_{\mathrm{x}}$ glasses for x=0.25, 0.20, and 0.15 are calculated with use of the orbital charge self-consistent orthogonalized linear combination of atomic orbitals method. Periodic structural models containing 100 atoms each are constructed first, using the Monte Carlo method. Results are presented for the total and partial density of states (DOS), joint DOS, localization index for each state, effective charges on each atom, and DOS at the Fermi level (${E}_{F}$). The ${E}_{F}$ is located at the steep edge of the Ni d band resulting in a Ni d-band hole in all three glasses. The local DOS of Ni atoms depends very sensitively on the number of P atoms as nearest neighbors while the local DOS of P atoms is rather insensitive to the atomic environment. For Ni atoms with no P atom as a nearest neighbor, its local DOS has a sharp peak above ${E}_{F}$ and its effective charge is much reduced. Mulliken charge analysis indicates that on average, P atom gains about 0.4 to 0.8 electrons from Ni atoms for x ranges from 0.25 to 0.15. The average conduction electron per Ni atom is calculated to be 1.5 electron. The high resistivity of a-${\mathrm{Ni}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{P}}_{\mathrm{x}}$ glasses may be related to the existence of localized electron states near ${E}_{F}$.

Analytic conditions for the existence of localized electron states in a linear chain with an arbitrary number of impurities

The effective Hamiltonian and the negative eigenvalue theorem are used to obtain an analytic formula for the integrated density of electron states in a linear chain with an arbitrary number of impurities within the tight binding approximation. From this formula, the analytic conditions for the existence of localized electron states lying above or below the band of states of host atoms are obtained. The way of obtaining the energies of localized states and the form of eigenvectors are also discussed.

Existence of localized electronic states at interfaces

A simple self-consistent atomic model is used to show that both true localized interface states as well as interface resonances can occur at the junction between a metal and a non-metal. These results resolve a controversy of long standing over whether or not true localized states (Bardeen states) can exist when one of the electrodes is a metal. Two distinct physical situations are considered for the metal-non-metal interface showing that these interface states may or may not exist depending upon the band gap of the non-metal and the coupling strength across the interface. In addition, results are presented for the case when both electrodes are non-metals (heterojunctions).

Electronic Structure of Stacking Faults in Transition Metals: Nickel

We report the results of a calculation which point out the existence of localized electronic states in the vicinity of stacking faults in a face-centered-cubic transition metal (nickel). The results are fairly insensitive to the parameters of the calculation. The reported states appear between the two $d$ sub-bands of the bulk states, are well received, are fairly well localized, and could be observable by electron emission spectroscopy.

Analytic conditions for the existence of localized electron states in linear chains with two impurities

The negative eigenvalue theorem is used to obtain an analytic result for the integrated density of electron states in several types of low-dimensional lattices with two impurities in the tight binding approximation. From this expression, analytic conditions for the existence of localized electronic states are obtained. The result is directly applicable to the problem of surface states and that of chemisorption on a linear chain.

Nuclear Magnetic Resonance and Relaxation in the "Liquid Semiconductors"In2Te3,Ga2Te3, andSb2Te3

Measurements of the Knight shifts of ${\mathrm{In}}^{115}$, ${\mathrm{Ga}}^{69}$, ${\mathrm{Ga}}^{71}$, ${\mathrm{Sb}}^{121}$, ${\mathrm{Sb}}^{123}$, and ${\mathrm{Te}}^{125}$ in solid and liquid ${\mathrm{In}}_{2}$${\mathrm{Te}}_{3}$, ${\mathrm{Ga}}_{2}$${\mathrm{Te}}_{3}$, and ${\mathrm{Sb}}_{2}$${\mathrm{Te}}_{3}$ are reported for temperatures ranging from roughly 150 K below the melting points to 1400-1500 K. Measurements of the nuclear spin-spin relaxation rates of ${\mathrm{In}}^{115}$, ${\mathrm{Ga}}^{69}$, ${\mathrm{Ga}}^{71}$, ${\mathrm{Sb}}^{121}$, and ${\mathrm{Sb}}^{123}$ are reported for the liquids from the melting points to 1400-1500 K. The data are discussed in terms of various theoretical models for the electronic structure of liquid semiconductors. It is shown that nuclear relaxation-rate measurements provide a means for characterization of the microscopic electronic transport mechanism. In the case of ${\mathrm{In}}_{2}$${\mathrm{Te}}_{3}$ and ${\mathrm{Ga}}_{2}$${\mathrm{Te}}_{3}$ an unusual enhancement of the nuclear relaxation rate relative to the predicted Korringa rate is shown to be consistent with the existence of localized electronic states at the Fermi level. ${\mathrm{Sb}}_{2}$${\mathrm{Te}}_{3}$, on the other hand, exhibits no appreciable enhancement and is characterized as a metallic liquid. A general scheme is proposed for classification of the electron dynamics in electronically conducting liquids by the correlation of the nuclear relaxation rate and the dc conductivity.

Impurity states associated with subsidiary energy-band minima

Two results have been established concerning the existence of localized electronic states associated with a point impurity in a substance having a spherical energy band, E(k) = ϵ0 + ϵ1 × cosk + ϵ2cos2k, where k = ¦k¦, with a subsidiary minimum at k = 0. The 1st result is a generalization of Slater and Koster's result, that in 1 dimension an energy band with a subsidiary minimum has no localized states associated with this minimum if the impurity potential is of the δ-function type; i.e., it has only 1 matrix element between Wannier functions, a diagonal one referring to 1 site. We show that this result also holds for a spherical band in 3 dimensions. Our 2nd result is that, for the Coulomb-impurity potential screened by the static dielectric constant, and the above spherical band, there are hydrogen-like localized states built out of states near the subsidiary minimum, even when all powers of k in E(k) are taken into account in the equation for the envelope function. The deviation of the impurity potential from slow variation causes a long lifetime for decay of the localized state into conduction states of the same energy. For a typical shallow impurity state, the lifetime is ≅ 10−8−10−9 sec.

Impurity states associated with subsidiary energy-band minima

Abstract Two results have been established concerning the existence of localized electronic states associated with a point impurity in a substance having a spherical energy band, E(k) = ϵ0 + ϵ1 × cosk + ϵ2cos2k, where k = ¦k¦, with a subsidiary minimum at k = 0. The 1st result is a generalization of Slater and Koster's result, that in 1 dimension an energy band with a subsidiary minimum has no localized states associated with this minimum if the impurity potential is of the δ-function type; i.e., it has only 1 matrix element between Wannier functions, a diagonal one referring to 1 site. We show that this result also holds for a spherical band in 3 dimensions. Our 2nd result is that, for the Coulomb-impurity potential screened by the static dielectric constant, and the above spherical band, there are hydrogen-like localized states built out of states near the subsidiary minimum, even when all powers of k in E(k) are taken into account in the equation for the envelope function. The deviation of the impurity potential from slow variation causes a long lifetime for decay of the localized state into conduction states of the same energy. For a typical shallow impurity state, the lifetime is ≅ 10−8−10−9 sec.

Possible Approach to the Low-Temperature Resistance Maximum in Dilute Alloys of Transition Metals in Noble Metals

If a dilute alloy of a transition metal in a noble metal becomes ferromagnetic, the spin degeneracy of the ground state of the impurity atom is removed by the local field. Scattering of the conduction electrons by the impurity atoms can then take place by inelastic as well as elastic collisions. Assuming the scattering cross section for elastic scattering is larger for the lower lying nondegenerate states, one gets the following results: (1) There is a maximum in the temperature dependent resistivity. (2) The temperature at which the maximum occurs varies rapidly with concentration of the transition metal. (3) The magnetoresistance is negative up to some temperature higher than the temperature at which the maximum in resistivity occurs. The experimental observations of Gerritsen and Linde and of Gerritsen on the resistivity of these alloys are, for the most part, in qualitative agreement with these consequences. This model does not require the existence of localized electronic states with energy near the Fermi energy as does the model presented by Korringa and Gerritsen.