I n the local density approximation (LDA) the density of a many-electron system is expressed as a functionof the spatially varying potential. Here a modifiedLDA is derived applicable for a potential with a high step a t some plane which is e.g. a model for the band edges in an inversion layer a t the semiconductor-insulator interface. The local density of states shows oscillations and decreases t o zero a t the interface as a consequence of quantum mechanical reflection. Simple expressions for the density are obtained for the strongly degenerate and for the non-degenerate system. The comparison with exact results for a model system (triangular potential) shows that the modified LDA yields good results for a wide range of parameters corresponding to real inversion layers.Die Naherung der lokalen Dichte (LDN) liefert die Dichte eines Vielelektronensystems als Funktion des Potentialverlaufes. Es wird eine modifizierte LDN abgeleitet, die fur ein Potential gilt, das an einer Ebene einen groden Sprung aufweist. Dieses System modelliert z. B. den Bandkantenverlauf in einer Inversionsschicht an der Halbleiter-Isolator-Grenzflache. Als Folge der quantenmechanischen Reflexion zeigt die lokale Zustandsdichte Oszillationen und fallt zur Grenzfiche hin auf Null ab. Besonders einfache Ausdrucke fur die Dichte ergeben sich fur die Grenzfalle der Entartung bzw. Nichtentartung. Der VeIgleich mit exakten Ergebnissen fur ein Modellsystem (,,Dreieckpotential") zeigt, daB die modifizierte LDN gut ist fur einen weiten Parameterbereich, der den tatsachlichen Inversionsschichten entspricht.

An approach to evaluate the microwave-detected photoconductance decay (MWPCD) is developed, which allows to extract the minority carrier lifetime as a function of the excess carrier density from a single MWPCD measurement. The method is shown to be applicable to thin (w≲200 μm) silicon wafers with low minority carrier recombination at the surfaces and bulk lifetimes in the range of about 1–100 μs. Comparison of the MWPCD results with minority carrier lifetime measurements using the quasi-steady-state photoconductance method reveals very good agreement between both types of measurement. Only when the photoconductance exceeds 30% of the dark conductivity, is a deviation observed, because then the MWPCD signal is no longer directly proportional to the excess carrier density. Minority carrier trapping is found to affect the MWPCD signal only in the tail of the measured photoconductance decay. The evaluation method is used to map the interstitial iron content with high spatial resolution, as well as to determine the minority carrier trap density. An excellent agreement between numerical simulation and measured MWPCD signal is found revealing the assumptions made for the evaluation approach to be valid. This evaluation of the MWPCD measurement is well suited to characterize silicon of low purity and low crystalline quality, which is often employed to solar cells with high spatial resolution.

For bent bands in a semiconductor near the interface to an insulator, a modified local density approximation is described which takes into account the influence of the interface barrier in the potential. Simple expressions are obtained for the electron and hole densities in a multi-valley semiconductor with non-isotropic parabolic bands. Due to the interface barrier the densities decrease to zero towards the interface. The characteristic length for this decrease is determined by the effective mass tensor and by the orientation of the interface. Results of self-consistent density calculations are reported.Fur die in Nahe der Grenzflache zu einem Isolator verbogenen Halbleiterbander wird eine modifizierte Niherung der lokalen Dichte beschrieben, die den Potentialsprung an der Grenzflache beriicksichtigt. Es ergeben sich einfache Ausdriicke fur die Elektronen-und Locherdichten eines Vieltalhalbleiters mit anisotropen parabolischen Bandern. Durch den EinfluB der Potentialbarriere gehen die Dichten zur Grenzfliche hin gegen Null. Die fiir diesen Abfall charakteristische Lange ist durch den Effektivmnssentensor und durch die Orientierung der Grenzflache bestimmt .Es werden Resultate selbstkonsistenter Dichteberechnungen angegeben.

Field effect devices on the basis of InSb are increasingly used in semiconductor technique. Due t o 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.

A modified Thomas-Fermi approximation (TFA) developed originally for inversion layers is used to calculate electron-density profiles, the spatial dependences of the potential, surface potentials, and the energies of bound states of depletion and accumulation layers in n-type CxaAs. Remarkable agreement with recently published results of self-consistent calculations of Ehlers and Mills [Phys. Rev. B 34, 3939 (1986)] is achieved. All deficiencies of the conventional TFA discussed there are removed. Methodological advantages of the modified TFA are discussed.