We review the physical properties of diluted magnetic semiconductors (DMS) of the type AII1−xMnxBVI (e.g., Cd1−xMnxSe, Hg1−xMnxTe). Crystallographic properties are discussed first, with emphasis on the common structural features which these materials have as a result of tetrahedral bonding. We then describe the band structure of the AII1−xMnxBVI alloys in the absence of an external magnetic field, stressing the close relationship of the sp electron bands in these materials to the band structure of the nonmagnetic AIIBVI ‘‘parent’’ semiconductors. In addition, the characteristics of the narrow (nearly localized) band arising from the half‐filled Mn 3d5 shells are described, along with their profound effect on the optical properties of DMS. We then describe our present understanding of the magnetic properties of the AII1−xMnxBVI alloys. In particular, we discuss the mechanism of the Mn++‐Mn++ exchange, which underlies the magnetism of these materials; we present an analytic formulation for the magnetic susc...

Diluted magnetic semiconductors

The electronic structure of clean InN(0001) surfaces has been investigated by high-resolution electron-energy-loss spectroscopy of the conduction band electron plasmon excitations. An intrinsic surface electron accumulation layer is found to exist and is explained in terms of a particularly low Gamma-point conduction band minimum in wurtzite InN. As a result, surface Fermi level pinning high in the conduction band in the vicinity of the Gamma point, but near the average midgap energy, produces charged donor-type surface states with associated downward band bending. Semiclassical dielectric theory simulations of the energy-loss spectra and charge-profile calculations indicate a surface state density of 2.5 (+/-0.2)x10(13) cm(-2) and a surface Fermi level of 1.64+/-0.10 eV above the valence band maximum.

Intrinsic electron accumulation at clean InN surfaces.

We present a rigorous investigation of carrier transport near the semiconductor-insulator interface of a MOSFET. Deriving a new current equation we include the quantum mechanical correction on the carrier density distribution near the interface. This equation also contain a new mobility model for the surface field reduced channel mobility, that is derived from Boltzmann's equation. We implemented this new equation into the device simulator MINIMOS and discuss its consequences to real devices.

Carrier transport near the Si/SiO2 interface of a MOSFET

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).

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

Electron accumulation states in InN have been measured using high resolution angle-resolved photoemission spectroscopy (ARPES). The electrons in the accumulation layer have been discovered to reside in quantum well states. ARPES was also used to measure the Fermi surface of these quantum well states, as well as their constant binding energy contours below the Fermi level E(F). The energy of the Fermi level and the size of the Fermi surface for these quantum well states could be controlled by varying the method of surface preparation. This is the first unambiguous observation that electrons in the InN accumulation layer are quantized and the first time the Fermi surface associated with such states has been measured.

Quantized electron accumulation states in indium nitride studied by angle-resolved photoemission spectroscopy.

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

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

In part I a new method was described for the self-consistent calculation of electron and hole densities, band bending, and subband energies in inversion layers of MIS structures. This method is of the numerical simplicity of the classical calculation but the results obtained with this method deviate only slightly from those ones obtained from explicit solutions of the Schrodinger equation. Here the new method is used to investigate the influence of quantum effects in the inversion layer on electronic properties of MIS structures. Since the latter usually are calculated classically the method is compared even with the classical one. The classical method yields in special cases good results for the calculation of MIS structures. The deeper reasons for them are shown and where the classical method is no longer applicable.

Self-consistent theory of the electronic structure of inversion layers. II. Quantum effects and the electronic properties of MIS structures†

The energy gap of the Hg1−xCdxTe-system can be controlled by the mole fraction x of Cd. This offers the possibility to use this material as a model system for systematic investigations especially in the narrow-gap region (corresponding to 0.16 ≦ x ≦ 0.25). The electronic structure, subband occupations, subband energies, and cyclotron masses are calculated for the two-dimensional electron gas in MIS structures with this material using an approximate self-consistent method. Both, inversion and accumulation conditions are considered. Comparisons with existing limited theoretical results and with experimental ones a) show the accuracy of the method used and b) allow to interpret the detailed experimental results from Shubnikov-de Haas and cyclotron measurements available now. Predictions are made on the composition dependence of the electronic structure especially for inversion conditions.



Die Energielucke im Mischkristall Hg1−xCdxTe last sich durch die stochiometrische Zusammensetzung einstellen. Dies eroffnet die Moglichkeit systematischer Untersuchungen insbesondere im Bereich geringer Energielucken (entsprechend 0,16 ≦ x ≦ 0,25). Die elektronische Struktur, insbesondere Subbandbesetzungen, Subbandenergien und Zyklotronmassen werden fur das quasi-zweidimensionale Elektronengas in MIS-Systemen mit diesem Halbleiter berechnet. Dazu wird ein genahert selbstkonsistentes Verfahren verwendet. Es werden sowohl Inversions- als auch Akkumulationsschichten untersucht. Vergleiche mit den vorliegenden, wenigen theoretischen und mit experimentellen Resultaten zeigen a) die Genauigkeit der verwendeten Methode und erlauben b) die Interpretation des umfangreichen experimentellen Materials aus Shubnikov-de Haas- und Zyklotronresonanzuntersuchungen, das inzwischen vorliegt. Es werden Voraussagen zur Abhangigkeit der elektronischen Struktur von der stochiometrischen Zusammensetzung insbesondere fur Inversionsbedingungen gemacht.

J.‐P. Zöllner

Papers

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

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

Modified Thomas-Fermi Approximation for Accumulation Layers in MIS Structures

Self-consistent theory of the electronic structure of inversion layers. II. Quantum effects and the electronic properties of MIS structures†

Theory for n‐Surface Charge Layers in Hg1−xCdxTe MIS Structures