JOURNAL OF RAMAN SPECTROSCOPY J. Raman Spectrosc. 30, 453–462 (1999) Spectral Lineshape Analysis of Four-Wave Mixing Spectra and its Application to Quasi-Zero-Dimensional II–VI Semiconductor Crystallites T. Bischof, G. Lermann, A. Materny and W. Kiefer* Institut f¨ ur Physikalische Chemie der Universit¨ at W¨ urzburg, Am Hubland, D-97074 W¨ urzburg, Germany Theoretical and experimental investigations are presented in order to analyze the lineshape of four- wave mixing spectra recorded by means of electronically resonant folded BOXCARS spectroscopy (special technique of CARS, coherent anti-Stokes Raman scattering). The theoretical framework presented is based on the quantum-mechanical expression of the non-linear third-order susceptibility. In order to obtain model equations those contributions of the third-order susceptibility which give rise to strong electronic resonance enhancement were exclusively used. The participation of two-photon resonances and the inhomogeneous broadening of the electronic transitions is taken into account. The theoretical background presented was applied to a semiconductor model system consisting of quasi-zero-dimensional CdS x Se 1-x nanocrystallites. The inhomogeneous broadening of this low-dimensional system is mainly caused by the size distribution of the nanocrystallites. The lineshapes of the experimentally obtained four-wave mixing spectra are well described within the theoretical framework and the homogeneous linewidth of the resonantly excited electronic state can be deduced. Copyright  1999 John Wiley & Sons, Ltd. INTRODUCTION Semiconductor crystallites with spatial dimensions of less than a few tens of nanometers show certain optical prop- erties which are different from those of the bulk semicon- ductor. In such systems so-called quantum confinement occurs, if the crystal size is comparable to or smaller than the exciton Bohr radius. 1,2 This is reflected in the elec- tronic structure of the semiconductor. In the case of strong confinement the kinetic energy of the electrons and holes (localization energy) becomes dominant as the crystal size decreases. At the same time the Coulomb interaction between the hole and the electron loses in significance. As a result, the absorption edge of the nanocrystallites is blue- shifted with respect to the bulk semiconductor. Moreover, the spatial quantization in nanocrystallites transforms the continuous band structure present in the bulk material to a set of discrete energy levels. The properties of the micro particles obviously show a behaviour intermediate between that of a molecule and that of a solid. Theoretical approaches taking into account discrete electronic states are extensively discussed in the literature. 2–7 Much of the previous work on II–VI semiconduc- tor nanocrystallites is concerned with the carrier relax- ation dynamics and the strength of the electron–phonon coupling. 7–10 However, a general picture of the optical * Correspondence to: W. Kiefer, Institut f¨ ur Physikalische Chemie der Universit¨ at W¨ urzburg, Am Hubland, D-97074 W¨ urzburg, Germany. E-mail: wolfgang.kiefer@mail.uni-wuerzburg.de Contract/grant sponsor: Deutsche Forschungsgemeinschaft; Contract/ grant number: Sondersforschungsbereich 410, Teilprojekt C3. Contract/grant sponsor: Fonds der Chemischen Industrie. properties of these systems does not exist. The complex decay dynamics of photo-excited electrons generated in II–VI semiconductor nanocrystallites is discussed very controversially in the literature. 5,7,11 – 13 Different relaxation mechanisms such as radiative recombination, fast trapping by localized surface states or electron–phonon coupling to optical and acoustic phonons are considered to be the dominant decay channels. The relaxation dynamics of photo-excited electrons seems to be extremely sensitive to the crystallite size and to non-intrinsic effects concerning the crystallite surface (matrix effects) and the experimen- tal conditions used (temperature, laser excitation wave- length, laser intensity). A quantity giving information on the lifetime and the dephasing of the resonantly excited state is the homogeneous linewidth. However, the deter- mination of the homogeneous linewidth is complicated by the fact that the size distribution of the nanocrystal- lites causes substantial inhomogeneous broadening of the electronic transitions. The large optical non-linearities observed in low- dimensional semiconductor crystallites have attracted considerable attention owing to their applicability for optoelectronic devices. 14 Optical non-linearities with picosecond response times are required for ultra-fast optical signal processing systems. Band filling under laser irradiation with consequent bleaching of the ground- state absorption is considered to be the reason for the optical non-linearity. 15 Non-linear optical properties of low-dimensional semiconductors have been extensively studied by degenerate four-wave mixing. 13,16 – 18 Here, we present non-linear four-wave mixing spectra recorded by means of low-wavenumber coherent Raman spectroscopy. In this paper we present theoretical and experimental investigations in order to analyze the lineshape of CCC 0377–0486/99/060453–10 $17.50 Received 6 May 1998 Copyright  1999 John Wiley & Sons, Ltd. Accepted 16 February 1999