The off-diagonal matrix element of the non-adiabdicity operator, on which usually the theory of non-radiative multiphonon transitions is based, is recast into a form much more convenient for the calculation of the transition probability W in non-Condon approximation. This is demonstrated first for a. two-level system coupled to a single vibrational mode and then extended to the more general case of a complete set of non-degenerate electronic states coupled linearly t o LV normal modes. The strong anharmonicity of the adiabatic potentials due to the mixture of states caused by the electron-phonon interaction operator is stressed, which limits the applicability of the theory to situations where only transitions well below "level crossing" are important, and, consequently, imposes serious restrictions on the parameters of the system and the temperature. Keeping to these restraints and to two electronic levels, the transformed matrix element of the non-adiabaticity operator is identical with that of the perturbation operator used in the static coupling scheme of Haug and Passler, which turns out in this way t o be equivalent to a closed-form of non-Condon approximation based on a well defined set of adiabatic wave functions. Explicit expressions for W are also given, and some aspects of the theory in general are discussed.
A 12 x 12 representation is given of the valence band Hamiltonian a t k = 0 which includes the spin-orbit interaction. Expressions are derived for the energies and the linear combinations of the wave functions for the r,, r,, and re subbands. The whole valence band is completely determined by eight parameters: three energies, two parameters coupling states of equal spin, and three parameters coupling states of opposite spin. In principle, all parameters can be obtained experimentally from the energy separations and oscillator strengths for interband transitions for polarization 1 c and 11 c. Anisotropic spin-orbit interaction and mixing of states originating from the two anions per unit cell are discussed.
The valence band structure of wurtzite type materials is investigated using a k . p approximation. The E(k) dependence for the bands A, B, and C is completely determined by six parameters: two for k I I c, three for k I I c and one additional parameter for a general direction. Relationships between the effective masses a t k = 0 are given for the three bands. Even near k = 0 the sub-bands are strongly non-parabolic. The constant-energy surfaces retain their rotational symmetry. Numerically calculated E( k) curves are pre-
The solution is given for long persisting controversial problems in the theory of non-radiative multiphonon capture of free carriers. Taking the adiabatic wave functions as basic states for the perturbational treatment of the transition probability particular attention is focused on the correct determination of the transition matrix elements. I n this framework it is shown that to first order in the non-diagonal matrix element of the electron-lattice interaction all approaches developed so far (Condon approximation, non-Condon approximation, static approximation, etc.) lead to the same result, in contradiction to statements in the literature. In particular, the reason is found why earlier results for the transition rate within the adiabatic and Condon approximation are much too small. The static approximation is shown to be the lowest approximation to the adiabatic approach.I n der vorliegenden Arbeit werden iiber mehrere Jahrzehnte andauernde Kontroversen in der Theorie strahlungsloser Vielphononen-Prozesse gelost. Bei der storungstheoretischen Behandlung der UbergangswtLhrscheinlichkeit auf der Grundlage adiabatischer Basiszustiinde wird der korrekten Berechnung der t'bergangsmatrixelemente besondere Aufmerksamkeit gervidmet. I m Gegensatz z u Aussagen in der Literatur wird gezeigt, daO alle bisher bekannten Zugange (CondonXiherung, Xicht-Condonsche Niiherung, Statische Niiherung usw.) in niedrigster Ordnung bezuglich der nichtdiagonalen Elektron-Gitter-Kopplung zu dem gleichen Resultat fiihren. Insbesondere wird gekliirt, warum in friiheren Arbeiten im Rahmen der adiabatischen und CondonNIherung vie1 zu kleine Werte fiir die Ubergangswahrscheinlichkeit erhalten wurden. Die statische Xiherung erweist sich als die niedrigste Approximation fur die adiabatische Theorie.
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