Optical properties of Si nanocrystals embedded in ${\mathrm{SiO}}_2$

The dielectric function of Si nanocrystals embedded in a ${\mathrm{SiO}}_2$ matrix has been determined in the 1.6–6.2 eV spectral range without any assumption on the dispersion law. The Si nanocrystals have been obtained by thermal annealing of ${\mathrm{SiO}}_x$ layers yielding nanocrystals diameters of 4.5 nm and 1 nm for atomic composition values $x$ of 1.1 and 1.9, respectively. The dielectric function of the large Si clusters exhibited three structures located at 3.5 eV, 4.2 eV, and 5.4 eV ascribed to the $E_1,E_2$, and $E_1^{\prime }$ critical points, respectively. For the smaller Si clusters, the structure associated with the $E_1$ CP, near 3.5 eV, disappeared while those at higher energy remained present.

Figure 1

TEM bright field micrograph in the cross-section geometry of the SiO 1.1 layer after annealing at $1000$°C. The nc-Si appear darker in the image. A close up of a nc-Si where the {111} lattice fringes can be imaged is shown in the inset. The size distribution of the nc-Si extracted from the TEM image is shown in the second inset. The mean size was estimated at 4.5 nm from a fit to a lognormal distribution law (dotted line).

Figure 2

Electron diffraction pattern (a) along $⟨112⟩$ on the ${\mathrm{SiO}}_{1.1}$ layer, (b) along $⟨111⟩$ on the ${\mathrm{SiO}}_{1.9}$ layer, after annealing at $1000$°C. Diffraction rings are observed in both the images. Their positions correspond to the lattice spacing of {111} and {220} planes. They are delineated by dotted lines.

Figure 3

Normalized PL peak of the layers after the $1000$°C annealing step. The position of the band gap of Si is indicated by the dotted line.

Figure 4

Real part (a) and imaginary part (b) of the effective dielectric function of the film with $x=1.1$. The functions obtained on the film after evaporation (dotted line), after annealing at $800$°C (diamonds) and after annealing at $1000$°C (full line) are presented. The vertical lines indicate the positions of the CP’s in crystalline Si.

Figure 5

Imaginary part of the dielectric function of the film around $1100{\mathrm{cm}}^{-1}$ (position of the TO mode). The functions obtained on the film after evaporation (dotted line), after annealing at $800$°C (diamonds) and after annealing at $1000$°C (full line) are presented. The position of the TO mode in fused silica is indicated by the dotted line.

Figure 6

Imaginary part of the dielectric function of the films after annealing at $1000$°C around $1100{\mathrm{cm}}^{-1}$ (position of the TO mode). The effective dielectric functions obtained on (a) the film with the 4.5 nm nc-Si and (b) the 1 nm nc-Si (solid lines) are compared to that of a mixture of silica and silicon.

Figure 7

Real (a) and imaginary (b) parts of the dielectric function of the nc-Si, having a diameter of 4.5 nm, extracted wavelength-by-wavelength (squares) together with the dielectric function of $p$-Si (dotted line). The position of the CP in Si are shown by the vertical lines. The result of the model using Gaussians is also plotted (line).

Figure 8

Real (a) and imaginary (b) parts of the dielectric function of the nc-Si, having a diameter of 1 nm, extracted wavelength-by-wavelength (squares) together with the dielectric function of $p$-Si (dotted line). The position of the CP in Si are shown by the vertical lines. The result of the model using Gaussians is also plotted (line).