Anharmonic Sideband Effects of the U‐Center Local Mode

Abstract

Recently t h e r e have appeared s e v e r a l t h e o r e t i c a l t r e a tments (1 t o 4 ) of t h e shape o f t h e sidebands i n t h e infra-red absorption due t o U-centers. I n t h e s e treatments s p e c i f i c assumptions concerning t h e coupling o f t h e l o c a l mode w i t h t h e l a t t i c e modes were made. I n no case t h e agreement between theory and experiment seems t o be r e a l l y s a t i s f a c t o r y . I n t h i s paper we show t h a t one e s s e n t i a l reason might be t h e use o f an oversimplified theory.o f t h e l o c a l mode GL(w) i s neglected. A s mentioned i n (5) t h i s frequency dependence causes s h i f t s and slope changes i n the sidebands. r , (a) i s neglected i n t h e resonance denominator, where rL(w) i s t h e imaginary p a r t o f t h e l o c a l mode self-energy TTL(w) (see equations (7a) and (7e) i n (5)). W e have found t h a t t h i s neglect l e a d s t o e r r o r s o f up t o 50% i n t h e i n t e n s i t y o f t h e f i r s t sideband m a x i m u m .t h e anharmonic self-energy of t h e l o c a l mode i s described by (7e) i n ( 5 ) ) . This means t h a t no c o r r e l a t i o n s between t h e l o c a l mode and t h e l a t t i c e phonon i n t h e sideband r e g i o n a r e taken i n t o account. F o r p e r f e c t c r y s t a l s t h e problem of two-phonon c o r r e l a t i o n s has been discussed by Langer e t a l . (6).The f i r s t point i s t h a t u s u a l l y t h e frequency dependence Secondly, i n equation (7) I n t h e Hartree-Fock approximation (7) t h e imaginary p a r t t h e two-phonon propagator ( l o c a l i s e d mode p l u s band phonon) found t o be -new phy sica

Vibrational Infrared and Raman Spectra of Non-Metals

“…FISCHER (1974) has discussed some qualitative consequences of this approach for the line-width and shift of the resonance frequency. He found, in complete analogy to the simple case of a local mode side-band (ZEYHER and BILZ (1967), see the discussion in Sect. 15 f) a smearing out of features in the selfenergy, in particular a 'filling up' of frequency regions with small damping from the neighboring regions with higher damping.…”

“…A very nice experiment of this kind was performed by . BILZ et al (1967) and ZEYHER and BILZ (1968 proceed along the lines opposite to TIMMESFELD. On the assumption that the experimentally observed sidebands are caused only by the local-mode anharmonicity and not by that of the band modes, they calculate the pure absorption as it would appear if only the local-mode anharmonicity to lowest order were responsible.…”

An Extended Breathing Shell Model for Alkali Halides and Its Test at Experimental Results

“…given by (9) of [S]. Therefore all our results must be compared with a modification of the measured curves as shown in [28]. The modification has to be introduccd to compensate the oversimplification within the used absorption formula (see [8,281).…”