Impact of disorder on optical phonons confined in CdS nano-crystallites embedded in a SiO2 matrix

TLDR: In this paper, the authors used the model proposed by Trallero-Giner et al. (1998 Phys. Rev. B 57 4664) and showed a direct correlation between the width of the Raman peak produced by CdS-like optical phonons and the crystalline quality of the semiconductor phase probed by X-ray diffraction and transmission electron microscopy (TEM).

Abstract: Non-resonant Raman spectroscopy studies of a set of CdS films annealed at different temperatures were performed and showed a direct correlation between the width of the Raman peak produced by CdS-like optical phonons and the crystalline quality of the semiconductor phase probed by x-ray diffraction (XRD) and transmission electron microscopy (TEM). In order to decribe the Raman lineshape a model proposed by Trallero-Giner et al (1998 Phys. Rev. B 57 4664) was used, which considers optical phonons confined in small semiconductor spheres with a size distribution. The model is shown to give a good reproduction of the spectra of samples where the semiconductor phase is most crystalline. However, it required too large values of phonon damping to fit the spectra of several other samples, which, according to XRD and TEM data, do contain CdS nano-crystallites. This large broadening of the Raman peak was considered as inhomogeneous, i.e. associated with disorder. Numerical lattice dynamics calculations were performed for 2D binary clusters of arbitrary shape and three kinds of disorder were considered, (i) random variation of the Cd-S bond frequency from one nano-crystallite to another, (ii) cluster shape irregularities and (iii) fluctuations of the nearest-neighbour interaction constant within one cluster. It is shown that `ensemble disorder' (i) can be responsible for a shoulder above the bulk CdS phonon frequency observed for some of our samples. The effect of shape disorder (ii) is similar to that of the size dispersion producing some inhomogeneous broadening of the peak. In addition, it gives rise to an extra low-frequency mode originating from the top of the acoustic band. The force constant's disorder (iii) is shown to result in a stronger asymmetric broadening of the Raman peak.

Figures

Figure 1. HRTEM micrograph of an rf-sputtering-grown CdS-doped silica film annealed at 500 ◦C for 4 hours. This fragment shows a 10 nm size crystallite with nearly spherical shape, although imperfections of the interface are clearly seen.

Figure 6. Raman spectra for the A8-3/Si sample (same key as for figure 5).

Figure 5. Raman spectra for a ‘sol–gel’-grown sample St-35: experimental (broken curve, the whole spectrum is shown in figure 2) and calculated using the spherical model (dashed curve) and numerically (full curve). See tables 1 and 2 for the parameters used in the spherical model and numerical calculations, respectively.

Figure 9. Numerically calculated Raman intensity for a cluster with D = 30 ML and one or five disordered shells. A typical cluster used in these calculations is shown in the inset. The curve with points corresponds to an ensemble of round (D = 20 ML) clusters with a Gaussian distribution of the n-n force constants. It was obtained by averaging over some 30 realizations. DAM stands for disorder-activated acoustic mode.

Table 1. Annealing parameters for the RF-sputtering grown samples and parameters used in the spherical model calculations.

Figure 8. Calculated Raman intensity for round clusters of different diameter. The full curve was calculated for D = 20 ML using free b.c.s, while rigid b.c.s were used for all the others. SM marks the surface mode produced by superficial atoms with dangling bonds.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Impact of disorder on optical phonons confined in cds nano-crystallites embedded in a sio2 matrix" ?

Vasilevskiy et al. this paper studied the effect of shape disorder on the width of the Raman peak of CdS-like optical phonons. 

Q2. What can be the effect of disordered shape on the CdS bond frequency?

compressive strain caused by the matrix and detected in several studies of semiconductor-doped glasses [26] can lead also to a systematic shift of the CdS bond frequency. 

Q3. What is the optical deformation potential in zinc-blende semiconductors?

The optical deformation potential acting on electrons in zinc-blende semiconductors is proportional to the change in the bond length [21]. 

Q4. How can the authors characterize the crystal/matrix interfaces?

By using high resolution transmission electron microscopy (HRTEM) it is possible to characterize the crystal/matrix interfaces and to determine the size and the shape of nano-crystallites. 

Q5. How was the crystalline quality of the semiconductor phase controlled?

The crystalline quality of the semiconductor phase was controlled by recording x-ray diffractograms (XRDs) of the films in a grazing incidence geometry. 

Q6. What is the effect of disorder on the spectral spectra of nano-cry?

Under resonance conditions, one should also be able to detect another sign of disorder, namely, the low-frequency mode originating from BZ edge acoustic vibrations and activated either by shape irregularities or imperfect crystalline order in nano-particles. 

Q7. What is the simplest way to study the vibrational properties of clusters of arbitrary shape?

To study the vibrational properties of clusters of arbitrary shape or with some atomic disorder, one needs to solve numerically the appropriate microscopic equations of motion. 

Q8. What is the scattering matrix element for the Fröhlich mechanism?

(Note that the scattering matrix element is proportional to the difference between the electron and hole contributions for the Fröhlich mechanism, while there is no electron scattering for the optical deformation potential one.) 

Q9. What is the reason why the authors confine ourselves by the ‘hot solid state’ model?

This is why the authors confine ourselves by the ‘hot solid state’ model although believing that the calculated results can be extrapolated to amorphous particles.) 

Q10. What is the average of the contributions of the confined modes?

Since confined optical vibrons produce neither mechanical nor electric field outsidethe QD, the total Raman cross-section of an ensemble of spheres is simply an average of the individual QD contributions:d2σd dωS ∼ [n(ω) + 1]∫ dR0F(R0) { − 

Q11. What is the effect of the force constant on the lineshape of the sample?

The force constant variation assumed for this sample is quite small and the effect which it produces on the lineshape cannot be distinguished from that of the QD size distribution within the spherical model.