A critical comparison is made of the lattice-vibrational properties resulting within the macroscopic continuum model and a closely parallel microscopic force-constant model. The elastic and electric forces are treated in the same manner. However, the atomic structure of matter and the bulk phonon dispersion are neglected in the continuum approach. For that reason it cannot explain the optical frequency spectrum of a superlattice even not in the long-wavelength limit. On the other hand, the principal line shape of the atomic displacement patterns for optical phonons can be satisfactorily described by envelopes, at least, if the arbitrariness inherent any theory neglecting dispersion is utilized in an appropriate way. This holds particularly for modes which are not accompanied by long-range electric fields. For the other modes -the p-polarized symmetrical phonons propagating not parallel to the superlattice axis -the problem of identification appears additionally since the interface character restricted t o four modes in the dispersionless continuum approach is distributed among all symmetrical phonons within the microscopic theory.Es wird ein kritischer Vergleich der Gitterschwingungseigenschaften, wie sie aus dem makroskopischen Kontinuumsmodell bzw. einem parallelen mikroskopischen Kraftkonstantenmodell resultieren, durchgefuhrt. Die elastischen und elektrischen Kriifte werden gleich behandelt, die Dispersion der Volumenphononen aber in der Kontinuumsnlherung vernachliissigt. Deswegen kann diese auch nicht im langwelligen Grenzfall das optische Phononenspektrum eines Supergitters erkliiren. Andererseits kann im Rahmen der Kontinuumsapproximation die Linienform der atomaren Auslenkungen in befriedigender Weise durch Einhiillende beschrieben werden, zumindestens wenn mit der Unbestimmtheit, die jeder dispersionsfreien Theorie inhirent ist, geeignet umgegangen wird. Diese Aussage gilt besonders fur die Moden, die nicht von langreichweitigen elektrischen Feldern begleitet werden. Fur die anderen Moden -die p-polarisierten symmetrischen Phononen, die sich nicht parallel eur Supergitterachse ausbreiten -taucht zusiitzlich das Problem der wechselseitigen Identifizierung auf, da der Grenzfliichencharakter, der in der dispersionsfreien Kontinuumsniiherung auf vier Moden beschriinkt ist, in der mikroskopischen Theorie auf alle symmetrischen Phononen verteilt wird.
Optical phonons in polar semiconductor superlattices near the zone center are studied. The microscopic theory based on a rigid-ion model is simplified by restriction to one elastic force constant per material and spatial average of the long-range electric field. The theory allows much insight into the mode structure, particularly anisotropy and layer thickness dependence of frequencies, atomic displacements, and accompanying electric fields. Explicit results are given for short-period GaAs-A1As superlattices. The relationship of confined and interface modes is discussed.
The authors report a strict comparison of long-wavelength optical lattice vibrations in a superlattice obtained with the macroscopic continuum model and a closely parallel microscopic model. It is shown that the proper envelopes of the atomic displacement patterns can be found if the uncertainties inherent in any dispersionless theory such as the continuum model are appropriately treated. Apart from small discrepancies due to the discrete nature of the matter and effective material layer thicknesses the main failure of the continuum theory is the neglect of bulk phonon dispersion.
A theory of the scattering spectrum as well as of the resonance enhancement of the Raman scattering by coupled optical phonons and electronic subband excitations in p-type modulation-doped multiplequantum-well structures is developed without and with applied external magnetic fields. The scattering cross section for the interfering vibronic and electronic excitations is derived by means of a Green sfunction formalism and specified for backscattering, parallel light polarizations, and resonance with the incoming photons. In this limit, we can show that the relevant polar Frohlich interaction induces a doubly resonant one-phonon Raman process for confined phonons of a particular symmetry, depending on the resonantly excited hole subband. On the other hand, the same interaction is found to be responsible for the resonant decay of these phonons into electron-hole pairs in the heavy-hole subbands and vice versa. Moreover, noncoupling phonons of another symmetry and weaker resonance behavior are observed. Apart from this weak noncoupling phonon line, the spectrum of the coupled elementary excitations is discussed for different parameters, frequencies, and field strengths. We extract conditions for the occurrence of the limiting cases of a pure two-coupled-mode behavior and an antiresonance Fano effect and compare with experimental findings. Ga&Al, As multiple quantum wells which indicate the existence of coupled LO-phononhole intersubband excitations. Interesting features were observed: there are two types of GaAs-like LO phonons. Apart from a possible rigid shift one phonon does not seem to be influenced by the electronic excitations. The other type couples strongly to the h 3~h 1 (Ref. 30) hole intersubband excitation. Although a strong magnetic field, which produces a complete quantization of the holes, is applied parallel to the growth direction, the resulting line shape can be fitted to a Fano-type profile.This fact is somewhat unexpected and can be explained by the (quasi)continuous behavior of the electronic spectrum due to natural linewidth and broadening by interface disorder. 45 1672 1992 The American Physical Society 45 INTERFERENCE OF RESONANCE RAMAN SCATTERING BY. . . 1673 G(0)( ) JJ 5' fin)i I J and a generalized phonon self-energy operator
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