The bulk and surface electronic structure of ${\text{In}}_{2}{\text{O}}_{3}$ has proved controversial, prompting the current combined experimental and theoretical investigation. The band gap of single-crystalline ${\text{In}}_{2}{\text{O}}_{3}$ is determined as $2.93\ifmmode\pm\else\textpm\fi{}0.15$ and $3.02\ifmmode\pm\else\textpm\fi{}0.15\text{ }\text{eV}$ for the cubic bixbyite and rhombohedral polymorphs, respectively. The valence-band density of states is investigated from x-ray photoemission spectroscopy measurements and density-functional theory calculations. These show excellent agreement, supporting the absence of any significant indirect nature of the ${\text{In}}_{2}{\text{O}}_{3}$ band gap. Clear experimental evidence for an $s\text{\ensuremath{-}}d$ coupling between $\text{In}\text{ }4d$ and $\text{O}\text{ }2s$ derived states is also observed. Electron accumulation, recently reported at the (001) surface of bixbyite material, is also shown to be present at the bixbyite (111) surface and the (0001) surface of rhombohedral ${\text{In}}_{2}{\text{O}}_{3}$.

Band gap, electronic structure, and surface electron accumulation of cubic and rhombohedral In 2 O 3

In nodal-line semimetals, the gaps close along loops in k space, which are not at high-symmetry points. Typical mechanisms for the emergence of nodal lines involve mirror symmetry and the π Berry phase. Here we show via ab initio calculations that fcc calcium (Ca), strontium (Sr) and ytterbium (Yb) have topological nodal lines with the π Berry phase near the Fermi level, when spin-orbit interaction is neglected. In particular, Ca becomes a nodal-line semimetal at high pressure. Owing to nodal lines, the Zak phase becomes either π or 0, depending on the wavevector k, and the π Zak phase leads to surface polarization charge. Carriers eventually screen it, leaving behind large surface dipoles. In materials with nodal lines, both the large surface polarization charge and the emergent drumhead surface states enhance Rashba splitting when heavy adatoms are present, as we have shown to occur in Bi/Sr(111) and in Bi/Ag(111).

/pdf/topological-dirac-nodal-lines-and-surface-charges-in-fcc-2jyvdqadvc.pdf

Topological Dirac nodal lines and surface charges in fcc alkaline earth metals

For almost all $n$-type zinc-blende III-V semiconductor free surfaces a depletion layer is observed InAs is an exception, since $n$-type InAs free surfaces exhibit electron accumulation, due to donorlike surface states which pin the Fermi level far above the conduction band minimum High-resolution electron-energy-loss spectroscopy (HREELS) has been used to investigate the free surfaces of slightly degenerate $(n\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{17}\phantom{\rule{03em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3})$ and highly degenerate $(n\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{18}\phantom{\rule{03em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3})$ InAs From HREEL studies of these InAs samples, an electron accumulation and depletion layer were observed, respectively The Fermi-level pinning mechanism at free surfaces is discussed in terms of the position of the bulk Fermi level with respect to the branch-point energy $({E}_{B})$ Depending on the location of the bulk Fermi level, amphoteric defects are incorporated into the surface, which if ionized facilitate the band bending that results in the surface Fermi level becoming pinned close to ${E}_{B}$ Occupied cation-on-anion antisite defects and unoccupied anion-on-cation antisite defects at the surface are considered to be the ionized surface states responsible for the depletion and accumulation layer profiles, respectively

Electron depletion at InAs free surfaces : Doping-induced acceptorlike gap states

A theory of dynamical screening in heterostructures and semiconductor quantum wells is developed which contains electron–electron interaction and electron–phonon interaction. In this theory both the types of long-wave optical phonons, LO phonons and interface phonons, which occur in those layered structures are included. An expression is derived for the longitudinal screened interaction of subband electrons in heterostructures and quantum-wells. The obtained screened interaction potential allows the derivation of the total longitudinal dielectric function and the dispersion relation of the coupled intra- and intersubband plasmon-phonon modes. This screened interaction potential is used to develope a dynamically screened and finite-temperature theory of the electron–phonon interaction in heterostructures and quantum wells. The leading-order electron self-energy is disscussed. An analytic expression of the polarization function of the quasi-two-dimensional electron gas is calculated within the random-phase approximation. Further approximations, the plasmon pole approximation and the long-wave approximation are discussed and the resulting analytic expressions of the polarization function are given.



Es wird eine Theorie der dynamischen Abschirmung in Heterostrukturen und Quanten-Wells entwickelt. Die dynamische Abschirmung beinhaltet sowohl die Elektron–Elektron- als auch die Elektron–Phonon-Wechselwirkung, wobei in letzterer die zwei Typen von langwellig-optischen Phononen (LO Phononen und Grenzflachen-Phononen), die in solchen schichtformigen Strukturen auftreten, explizit berucksichtigt werden. Das longitudinal abgeschirmte Wechselwirkungs-potential der Subband-Elektronen in Heterostrukturen und Quanten-Wells wird berechnet. Ausgehend von diesem Potential wird ein Ausdruck fur die totale longitudinale dielektrische Funktion und fur die Dispersionsrelation der gekoppelten Intra- und Intersubband-Plasmon–Phonon-Moden abgeleitet. Weiterhin wird aus diesem Potential eine Theorie der dynamisch abgeschirmten Elektron–Phonon-Wechselwirkung bei eindlichen Temperaturen in Heterostrukturen und Quanten-Wells abgeleitet. Die aus dieser Wechselwirkung resultierende Selbstenergie der Elektronen wird diskutiert. Es wird ein analytischer Ausdruck fur die Polarisationsfunktion des quasi-zweidimensionalen Elektronengases in der Random-Phase Approximation abgeleitet. Weitere Naherungen, die Plasmon-Pol-Naherung werden diskutiert und analytische Ausdrucke fur die Polarisationsfunktion abgeleitet.

Dynamical Screening, Collective Excitations, and Electron–Phonon Interaction in Heterostructures and Semiconductor Quantum Wells. General Theory

The surface electronic properties of bulk-grown β-Ga2O3 (2¯01) single crystals are investigated. The band gap is found using optical transmission to be 4.68 eV. High-resolution x-ray photoemission coupled with hybrid density functional theory calculation of the valence band density of states provides insights into the surface band bending. Importantly, the standard linear extrapolation method for determining the surface valence band maximum (VBM) binding energy is found to underestimate the separation from the Fermi level by ∼0.5 eV. According to our interpretation, most reports of surface electron depletion and upward band bending based on photoemission spectroscopy actually provide evidence of surface electron accumulation. For uncleaned surfaces, the surface VBM to Fermi level separation is found to be 4.95 ± 0.10 eV, corresponding to downward band bending of ∼0.24 eV and an electron accumulation layer with a sheet density of ∼5 × 1012 cm−2. Uncleaned surfaces possess hydrogen termination which acts as surface donors, creating electron accumulation and downward band bending at the surface. In situ cleaning by thermal annealing removes H from the surface, resulting in a ∼0.5 eV shift of the surface VBM and formation of a surface electron depletion layer with upward band bending of ∼0.26 eV due to native acceptor surface states. These results are discussed in the context of the charge neutrality level, calculated bulk interstitial hydrogen transition levels, and related previous experimental findings.

Transition from electron accumulation to depletion at β-Ga2O3 surfaces: The role of hydrogen and the charge neutrality level

Field effect devices on the basis of InSb are increasingly used in semiconductor technique. Due to the non-parabolicity of the band structure of the conduction band the theoretical description of such devices is more complicated than for other materials. A simple method for the self-consistent quantum mechanical calculation of the electronic structure of inversion layers in materials with a Kane conduction band is presented which is well suited for the application in semiconductor technique. The method is based on an extension of a modified local density approximation for interface problems. The efficiency of this simple method is shown for the example of InSb by compzring with experiments and with results of earlier laborious self-consistent calculations using wave functions. The necessity is proved to take into account the deviation from the parabolic band structure in the self-consistent calculations.



Feldeffektbauelemente auf der Basis von InSb finden zunehmend Anwendung in der Halbleitertechnik. Die theoretische Beschreibung derartiger Bauelemente ist wegen der Nichtparabolizitat der Bsndstruktur des Leitungsbandes komplizierter als fur andere Materialien. Es wird eine einfache Methode fur die selbstkonsistente quantenmechanische Berechnung der elektronischen Struktur von Inversionsschichten in Materialien mit einem Kane-Leitungsband vorgestellt, die vor allem fur die Anwendung in der Halbleitertechnik geeignet ist. Das Verfahren beruht auf einer Erweiterung einer modifizierten Lokaldichtenaherung fur Grenzflachenprobleme. Es wird die Leistungsfahigkeit dieser einfachen Methode gezeigt, indem am Beispiel des InSb die Ergebnisse verglichen werden mit fruheren aufwendigen selbstkonsistenten Berechnungen unter Verwendung von Wellenfunktionen und mit experimentellen Resultaten. Die Notwendigkeit, die Abweichung von der parabolischen Bandstruktur in selbstkonsistenten Rechnungen zu berucksichtigen, wird nachgewiesen.

A novel self‐consistent theory of the electronic structure of inversion layers in InSb MIS structures

Self-consistent calculations on the quantized electron inversion layer adjacent to the grain boundary in p-doped InSb bicrystals are performed for the first time. A simple model of the fixed positive charge in the grain boundary is applied. Within a self-consistent approximation scheme, taking into account the band non-parabolicity, the band bending and the carrier concentrations in vicinity of the grain boundary are calculated. In addition, the calculation of the complete two-dimensional subband structure is performed. The results are discussed for a wide range of the total electron inversion density n□ = 1011 to 5 × 1012 cm−2. In case that n□ > 2 × 1011 cm−2 charge self-consistency is obtained. The theoretical values are compared with experimental ones taken from literature. The quality of the model and of the approximation scheme is demonstrated.



Es werden erstmalig selbstkonsistente Rechnungen zur quantisierten Elektroneninversionsschicht an Korngrenzen in p-dotierten InSb-Bikristallen vorgestellt. Es wird ein einfaches Modell fur die feste positive Ladung in der Korngrenze angewandt. Im Rahmen eines selbstkonsistenten Naherungsverfahrens, das die Nichtparabolizitat des Leitungsbandes berucksichtigt, werden der Bandkantenverlauf und die Ladungstragerkonzentration in der Nahe der Korngrenze berechnet. Weiterhin wird die gesamte zweidimensionale Subbandstruktur bestimmt. Die Ergebnisse werden fur einen breiten, praktisch relevanten Bereich der totalen Elektroneninversionsdichte n□= 1011 bis 5 × 1012 cm−2 diskutiert. Fur n□ > 2 × 1011 cm−2 wird Ladungsselbstkonsistenz erzielt. Es werden die theoretischen Resultate mit experimentell gewonnenen aus der Literatur verglichen. Die Gute vom Modell und vom Naherungsverfahren wird aufgezeigt.

Self-consistent calculation of the electronic structure of n-inversion layers adjacent to the grain boundary in InSb bicrystals

A new method is described for the self-consistent calculation of electron and hole densities, band bending, and subband energies in inversion layers of MIS-structures. This method makes use of new and simple expressions for carrier densities which take into account the influence of the interface semiconductor–insulator within a modified local density approximation. The method allows for an accuracy which is comparable with that one of explicit self-consistent solutions of the Schrodinger equation for inversion layers. But it is of the numerical simplicity of the classical method. This gives the possibility to calculate electronic properties of MIS-structures in much more detail than before. In part I the method is described and its advantages for modelling MIS-structures are shown. In part II the influence is discussed of quantum effects in inversion layers on electronic properties of MIS-structures in comparison with classical calculations for various semiconductors in a wide range of temperature and doping concentration.



Es wird ein neues Verfahren zur selbstkonsistenten Berechnung von Elektronen- und Locherdichte, des Bandkantenverlaufes und von Subbandenergien in Inversionsschichten von MIS-Strukturen beschrieben. Dabei werden neue, einfache Naherungsausdrucke fur die Ladungs-tragerdichten verwendet, die den Einflus der Grenzflache Halbleiter–Isolator im Rahmen einer modifizierten Naherung der lokalen Dichte berucksichtigen. Mit dem Verfahren wird eine Genauigkeit erreicht, die mit derjenigen ublicher selbstkonsistenter Losungen der Schrodingergleichung fur Inversionsschichten vergleichbar ist, wobei aber der numerische Aufwand dem klassischer Rechnungen entspricht. Dies gibt die Moglichkeit, die elektronischen Charakteristika der Inversionsschicht detaillierter als bisher zu berechnen. Im Teil I der Arbeit werden die Methode beschrieben und ihre Vorzuge bei der Modellierung von MIS-Strukturen gezeigt. Im Teil II wird der Einflus der Quanteneffekte in Inversionsschichten auf die elektronischen Eigenschaften von MIS-Strukturen durch Vergleich mit klassischen Rechnungen fur verschiedene Halbleiter und in einem weiten Bereich der Temperatur und der Storstellenkonzentration diskutiert.

Self‐Consistent Theory of the Electronic Structure of Inversion Layers. I. A New Method Using the Modified Local Density Approximation

A modified Thomas-Fermi method for the calculation of the electronic structure of accumulation layers in MIS-systems is presented which in spite of the simplicity of a “classical” method yields results in good agreement with extensive self-consistent quantum mechanical calculations. It is shown that the modified Thomas-Fermi method is suitable to describe the characteristics of bound and mobile carriers in accumulation layers. The method is used to calculate accumulation layers in n- and p-type GaAs and to discuss the influence of the quantum effects at the interface on the dependence of the total charge in the accumulation layer on the surface band bending. Comparison is made with the classical results.



Eine modifizierte Thomas-Fermi-Methode fur die Berechnung der elektronischen Struktur von Akkumulationsschichten in MIS-Systemen wird vorgestellt, die trotz der Einfachheit einer „klassischen” Methode Resultate liefert, die gut mit denen quantenmechanischer selbstkonsistenter Rechnungen ubereinstimmen. Es wird gezeigt, das die modifizierte Thomas-Fermi-Methode sowohl in der Akkumulationsschicht gebundene als auch im gesamten Kristall frei bewegliche Ladungstrager beschreibt. Die Methode wird verwendet zur Berechnung der elektronischen Struktur von Akkumulationsschichten in n- und p-GaAs und zur Untersuchung des Einflusses der Quantisierungseffekte an der Halbleitergrenzflache auf die Abhangigkeit der Gesamtladung im Halbleiter von der Oberflachenbandverbiegung. Die Resultate werden mit denen klassischer Rechnungen verglichen.

Modified Thomas-Fermi Approximation for Accumulation Layers in MIS Structures

Calculation of the subband structure of inversion layers in p-InSb bicrystals

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