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

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

The one-electron potential, carrier concentration profile, quantized subband state energies, and parallel dispersion relations are calculated for an accumulation layer at a semiconductor surface by solving Poisson's equation within a modified Thomas-Fermi approximation and numerically solving the Schrodinger equation for the resulting potential well. A nonparabolic conduction band, described within the Kane k.p approximation, is incorporated in the model. Example calculations are performed for a typical clean InN surface and for a variety of surface state densities and bulk carrier concentrations. Agreement is found between the model calculations and experimental measurements of the subband energies and dispersions at c-plane InN surfaces from electron tunneling spectroscopy and angle resolved photoemission spectroscopy.

Nonparabolic coupled Poisson-Schrodinger solutions for quantized electron accumulation layers : Band bending, charge profile, and subbands at InN surfaces

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

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

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

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.

G. Gobsch

Papers

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

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

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

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

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