Excitation Fano line shape

Free carriers change Raman spectra, either by single particle contribution to the spectrum, or by phonon- plasmon interaction. In addition, interference of electronic transition continua with single phonon excitations may lead to Fano line shapes, as mentioned in the introduction. The Fano effect is encountered in p-doped Si crystals, as shown in Fig. 4.8-19. The shown lines correspond to the respective Raman active mode at 520 cm for crystals with 4 different carrier concentrations, excited with a red laser. The continuous line is calculated according to Eq. 4.8-6. Antiresonance on the low frequency side and line enhancement on the high frequency side are a consequence of the positive value of Q. A reverse type of behavior is possible in the case of a negative Q. 

Another type of such coupling is the configuration interaction (CI) between a true discrete excitation and a continuum excitation. This autoionization phenomenon is clearly within the TDLDA framework, A nice example can be found in copper where 3d -> ef, ep excitations interfere with the 3p -> 4s transition, The resulting 3d partial photoionization cross section is shown in Figure 8, In addition to the prominent Fano line shape, an overall diminultion (relative to the LDA) of the cross section is found due to intrashell 3d polarization. The interesting dip around 80 eV is again a Cl effect, but this time the 3d ef,ep excitations interfere with the continuum channels, 3p es,ed. 

As discussed in connection with IR absorption, Raman lines from a discrete transition may also assume Fano type shapes if the transition is coupled to a continuum of scattering states. This continuum may originate from various sources like, for example, electronic or two phonon excitations. In general, Raman scattering makes it even easier to observe Fano lines, since the free carrier response very often covers up details of the line shape in IR reflection. Similarly, such line shapes have so far only been shown by classical semiconductors and most recently by superconductors, and it is a challenge to search for them in other conducting organic systems. 

It is known that the position of the Raman D-band shows excitation energy dependence [44]. The 790- and 395-nm excited D-bands indeed appeared around 1,300 and 1,390 cm , respectively [27]. According to the D-band position in the HRS spectmm, both fundamental and harmonic resonances to intermediated states were thought to contribute to the enhancement of the HRS intensity. Conversely, the G-band shape, which is decomposed into G" " and G , suggested the contribution of harmonic resonances to the transition. The observed HRS G -band was able to be fitted with Breit-Wigner-Fano (BWF) type line shape, which is characteristic in Raman spectra of metallic SWNTs [45]. 

Fig. 5.4. Typical Raman spectrum of a semiconducting boron-doped diamond electrode, showing the 1332 cm zero center diamond line with a typical Fano-hke shape and the Si phonon lines[514.5-nm excitation line from Ar+ laser (B/C ratio = 2000 ppm)].

The quantity q is called the shape index and is constant for a Fano profile. In chapter 8, situations in which q varies within an excitation channel will be discussed. However, even in such cases, it can be regarded as a constant over one line. 

When atomic transitions are excited, one is normally dealing with a Rydberg series of autoionising lines, rather than just an isolated line. The profile then lies between two extreme situations either the linewidth is much smaller than the separation between the hydrogenic and the half-hydrogenic points (type 1 profile), or it is much larger (type 2 profile). Type 1 profiles occur in the isolated line limit, and tend to the typical Fano shape. Type 2 profiles correspond to the overlapping line limit, and tend to sinusoidal shapes. 

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