We consider the optical properties of semiconductor – insulator and insulator – insulator nanocomposites, including porous materials such as silicon, gallium phosphide, aluminum oxide, and structures based on them. The main focus is on the effect of form birefringence, which is caused by the anisotropy of pores in the materials under study. The applicability of the effective medium model for describing the optical properties of nanocomposites is discussed. The effects of light localization due to the scattering of light in such inhomogeneous media are analyzed.

Optical properties of porous-system-based nanocomposites

We consider generalizations of the classical symmetrical Bruggeman equation based on the concept of shape-distributed particle systems. The use of the Beta distribution for the particle shape is shown to result in some known as well as unknown equations of the effective medium theory. However, these equations yield no percolation threshold. On the other hand, the use of one- and two-dimensional steplike distributions of spheroidal (ellipsoidal) shapes yields a percolation threshold depending on the distribution parameters. The problem of finding the percolation threshold to fit the systems under consideration, as well as the applicability area of the generalized Bruggeman equation and its relation to the Bergman representation, are discussed.

Generalizations of the Bruggeman equation and a concept of shape-distributed particle composites.

Lead sulfide nanocrystals were grown in toluene solutions of poly(2-methoxy-5-(2′-ethyl-hexyloxy)-p-phenylene vinylene, polyethylene, poly(1-butene), poly(1-decene), and polystyrene. The PbS nanocrystal diameter was controlled by the polymer used for synthesis and ranged from 4 to 9 nm. Strong nonlinear absorption was observed in open aperture Z-scan measurements of solutions containing the synthesized nanocomposites. The best fit to the experimental data gave high values for βeff in the range of 100−200 cm/GW. The nonlinear absorption of these polymer grown nanocrystals was not observed in nanocrystals grown in polyvinyl alcohol or with oleic acid capping. These differences in nonlinear optical absorption were due to surface chemistry, as the polymer synthesized nanocrystals were free of strongly bonding groups such as surfactant capping or hydroxyl groups. The βeff values in these materials also showed no dependence on nanocrystal size.

Nonlinear optical properties of PbS nanocrystals grown in polymer solutions

A study of additional waves in the exciton region of CdS crystals is reported. Transmittivity and reflectivity of thin crystals is measured showing a structure due to the Fabry-Perot interference and the interference of additional waves. This structure is a direct reflection of the polariton dispersion law. Using the formulas for a spatially dispersive platelet and Pekar's additional boundary conditions the theoretical reflectivity curves are obtained numerically reproducing the essential experimental results. Values for all physical parameters defining dispersion and damping of the polaritons are found. Some evident deviations between the experimental curves and the present computer results for the reflectivity are pointed in connection with a discussion of the role of the surface exciton potential.



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Additional Waves and Polariton Dispersion in CdS Crystals

Photoreflectance (PR) spectra have been measured to determine the lowest direct-band edge E0α (α=A, B, and C) of wurtzite CdS single crystal in the temperature range T=13–300 K for both E⊥c and E∥c polarizations. The measured PR spectra can be interpreted by the three-dimensional (3D) excitonic plus one-electron line shapes over the entire temperature range. The temperature dependence of the excitonic and critical-point parameters (energy, amplitude, and broadening parameter) have been determined and analyzed using the Varshni [Physica (Amsterdam) 34, 149 (1967)] equation and an analytical four-parameter expression recently developed for the explanation of the band-gap shrinkage effect in semiconductors. The 3D- exciton binding energies have also been determined to be 27 (A), 31 (B), and 30 meV (C), respectively.

Photoreflectance spectroscopy of wurtzite CdS

High third-order nonlinear optical susceptibility (χ(3)(ω; ω, −ω, ω) = −4,2 × 10−16(m2/V2)). In the visible spectral range may be achieved in PVA composites containing narrow bad gap PbS semiconductor nanocrystals with a strong limitation of the area of charge carrier delocalization.

New Optical Nonlinear Material Based Upon PVA with PbS Quantum Dots

The dispersion of the refractive index of a CdS crystal in the region of its main exciton bands is experimentally investigated at temperatures ranging from 4 to 80 °K. From the change of the birefringence pattern in the region of the lowest state, three specific temperature intervals are revealed. The data obtained show good agreement with the predicted temperature change of the normal wave parameters for media with the spatial dispersion; 1) in the low-temperature region (T 55 °K) one wave dominates all along with the dispersion of the classical character.



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The Spatial Dispersion Effects in CdS Crystals and Their Temperature Dependence

Size Effect in the Refractive Index Dispersion of Thin CdS Crystals

We have measured the absorption spectra and the dispersion of refractive index for porous silicon samples with different porosities in the energy range 1.5–3.5 eV at room temperatures. The experimental data are compared with the dependences calculated by using Bruggeman’s theory for the dielectric constant of a multicomponent system composed of crystal silicon, SiO2, amorphous silicon, and voids (pores). The best agreement between the experimental and theoretical dependences is achieved for a significant percentage of SiO2 in the porous silicon samples.

Optical Properties of Porous Silicon

The data are summarized, obtained by interference measurements at 4.2 K, on the dispersion of the refractive index n(λ) of submicron-thin CdS single crystals. The series of the dispersion curves, n(λ), measured for crystals of different thickness, is approximated by theoretical dependences allowing for spatial dispersion. These data present clear evidence that the refractive index depends on the thickness of crystals provided their dimensions are comparable with the wavelength of light or smaller than the latter.



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M. I. Strashnikova

Papers

New Optical Nonlinear Material Based Upon PVA with PbS Quantum Dots

The Spatial Dispersion Effects in CdS Crystals and Their Temperature Dependence

Size Effect in the Refractive Index Dispersion of Thin CdS Crystals

Optical Properties of Porous Silicon

Dispersion properties of submicron-thin CdS crystals