Resonance Raman Overtone Intensities and Electron–Phonon Coupling Strengths in Semiconductor Nanocrystals

Abstract

For linear electron-phonon coupling, the Huang-Rhys factor, S, gives the intensity ratio of the one-quantum vibronic transition (0→1) to the purely electronic origin transition (0→0) in a vibrationally resolved, zero-temperature absorption or emission spectrum. It is often assumed that the overtone to fundamental integrated intensity ratio in resonance Raman scattering of semiconductor nanocrystals is equal to or proportional to S, or that S may be determined from the overtone intensity in some other straightforward manner. In fact, this is not generally possible because of different excitation profiles for overtones and fundamentals, differential sensitivity of overtones and fundamentals to electronic dephasing, and interference effects from partially overlapping electronic transitions. Here we examine the relationship between the Huang-Rhys factor and the overtone to fundamental intensity ratio through spectroscopic simulations using parameters appropriate to II-VI semiconductor nanocrystals such as CdSe. A simple equation relating the overtone to fundamental Raman intensity ratio to the Huang-Rhys factor is obtained only in the case of a single resonant electronic state, excitation at the maximum of the inhomogeneously broadened absorption band, and a homogeneous linewidth small compared with the phonon frequency.

Tunable Color Temperatures and Efficient White Emission from Cs2Ag1−xNaxIn1−yBiyCl6 Double Perovskite Nanocrystals

“…Here the electron–phonon coupling was quantitatively characterized by Huang–Rhys factor S , which was derived from the temperature‐dependent FWHM change according to the following equation where ω phonon is phonon frequency, T is temperature (K), and k B is Boltzmann constant. Here, the S value is calculated as 15.5, which is less than one‐third of Cs 2 Ag 0.16 Na 0.84 InCl 6 bulk material ( S = 51.0), but one order magnitude higher than that of the traditional NCs, as summarized in Table S9 (Supporting Information) . According to previous studies, it is clear that the strength of electron–phonon coupling is weak in a strong confinement case, and such strength decreases with decreasing particle size .…”

The electron–phonon coupling of fundamental, overtone, and combination modes and its effects on the resonance Raman spectra

“…In many studies, the resonance Raman scattering spectroscopy is often applied to investigate the structural characteristics of the molecule, which is one of the most useful methods to identify the phonon modes coupled to an electronic system [14]. The electron-phonon coupling constant is an important parameter for describing the interaction between delocalizd electron and vibrational mode, which can account for the frequencies, relative intensities, line shape and width, and excitation profile of the Raman bands [15]. Many researchers have studied the electron-phonon coupling of fundamental mode of polyenes and found several methods to calculate the electronphonon coupling constant [16][17][18].…”

Deep UV resonance Raman spectroscopic study on electron‐phonon coupling in hexagonal III‐nitride wide bandgap semiconductors

“…For example, the separation and migration of photo‐generated carriers in semiconductors are largely affected by EPC in photocatalysis and photoelectrocatalysis . In general, EPC can be defined as the extent to which the distortion of nuclei along a phonon coordinate changes the energy separation between two electronic states, which are mainly valence and conduction bands for semiconductor materials . The magnitude of EPC can be expressed by the Huang–Rhys factor S, given by Δ 2 /2, where Δ is the displacement between the potential energy minima of valence and conduction bands along the dimensionless normal coordinate of phonon mode .…”

“…Besides these methods, resonance Raman spectroscopy is also very useful for studying the EPC of semiconductors, although resonance Raman experiments measure the time integrated coupling strengths or the extrinsic coupling strengths . In certain cases, the first overtone to the fundamental intensity ratio is considered to be proportional to the Huang–Rhys factor .…”

“…[4][5][6] The magnitude of EPC can be expressed by the Huang-Rhys factor S, given by Δ 2 /2, where Δ is the displacement between the potential energy minima of valence and conduction bands along the dimensionless normal coordinate of phonon mode. [4][5][6] There are mainly two kinds of EPC for optical phonons in semiconductors, including the deformation interaction and the Fröhlich interaction. The deformation interaction is a shortrange one with microscopic deformation induced in unit cell by alternating bond length and bond angle.…”