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The Green’s function method is used to study the problem of an impurity in a semi-infinite crystal. The connections between impurity and surface states are considered both from a general point of view and in specific models.

The theory of the electronic states of crystals containing point defects in small concentration is reviewed and its application to the case of semiconductors is discussed. The basic properties of scattering and resonant and bound states are related to the band structure of the semiconductor. The form of the impurity potentials and the effect of the dielectric screening and deep levels are also discussed. Applications to the cases of donor acceptor and isoelectronic impurities are described, making use of the effective mass approximation and taking into account interband mixing and central cell corrections. Existing calculations are reviewed and compared with some of the experimentally known levels. Optical processes involving transitions between all types of electronic levels are described and experimental evidence for them is reported. Effects of external perturbations like uniaxial pressure, electric and magnetic fields are finally examined.

A realistic model to discuss resonant states in semiconductors as GaAs and InP is developed. Analytic expressions for the energies and the widths of the resonant states are found and compared with recent experimental optical results in InP. Es wird ein realistisches Modell zur Behandlung resorianter Zustande in Halbleitern wie GaAs und InP entwickelt. Analytische Ausdrucke der Energien und Rasonanzbreiten der Zustande werden berechnet und init neueren Ergebnissen ron optisclien Versuchen an InP verglichen.

A general formulation of the theory of electron impurity states in a lattice in the extended zone scheme is presented. The dependence of the impurity states on the band structure is discussed, and it is shown that the existence of secondary extrema in the band structure may produce additional bound and resonant states. A prescription is given for computing such states and for estimating the probabilities of transitions to them from the ground state; some properties of these transition probabilities are discussed. Solutions of onedimensional models are presented explicitly.

A realistic model is set up in order to study the structure of the donor ground states in the semiconducting III-V compounds. The model is also applied to Si and gives results in agreement with those of Baldereschi. The lifting of the degeneracies, which are present in the effective-mass approximation, is shown to be due to the intervalley interaction of the impurity potential between degenerate minima and also between minima at different energy. The impurity states in GaAs are studied in detail as function of the energy separation between thek = 0 minimum and the subsidiary ones located atk = (2π/a)(1, 0, 0) etc. States of the same symmetry originating from those minima strongly interact, according to the noncrossing rule, when the energy separation is small and this produces a strong shift of the impurity states and a mixing of the wave functions.

The cross-section and the scattering amplitude from an impurity in a crystal are expressed, through formulae which are similar to the classical ones, in terms of quantities which present many ianalogies and some differences with respect to the usual phase shifts. The relations between these phase shifts and the poles of the Green’s function of the total Hamiltonian and other properties are also discussed.

A model, unique for all alkali halides, is built up, which gives energies for theF andK transitions in good agreement with the experimental results, both in absorption and in emission. In this model theL-bands must correspond to transitions in the conduction band.

The realistic model introduced in the previous paper is used to discuss resonant states in an imperfect cubic crystal; we consider resonances associated to the secondary extrema of the band structure located at theX-points of the Brillouin zone. It is shown that the inter-valley impurity interaction splits the threes states, associated to the nonequivalentX-minima into states withГ1 andГ3 symmetries; similarly, the ninep states are split into states withГ4 andГ5 symmetry. The lifetime of these states depends on the density of states of the band structure in the first Brillouin zone. The identification of theL-bands in alkali halides with transitions to such resonant states is discussed, in connection with the experimental results of many authors.

An extended crystal momentum representation is proposed and an alternative form of the Schrodinger equation in the crystal momentum representation (CMR) is given, which can be useful for strong impurity potentials. Moreover, properties of the operators and wave functions, which characterize such a representation, are discussed. Eine nichtreduzierte Kristallimpulsdarstellung wird vorgeschlagen und eine alternative Form der Schrodingergleichung in der Kristallimpulsdarstellung (CMR) gegeben, die fur starke Verunreinigungspotentiale nutzlich sein kann. Daruber hinaus werden die Eigenschaften der Operatoren und Wellenfunktionen, die solch eine Darstellung charakterisieren, diskutiert.

The phase-transition phenomenon in an interacting Bose system with a pair Hamiltonian is studied. For fixed density two temperaturesT1