Optical properties of silicon nanocrystals embedded in a ${\mathrm{SiO}}_2$ matrix

Optical properties of isolated silicon nanocrystals $\left(\mathit{nc}\text{−}\mathrm{Si}\right)$ with a mean size of $\sim 4\mathrm{nm}$ embedded in a ${\mathrm{SiO}}_2$ matrix that was synthesized with an ion beam technique have been determined with spectroscopic ellipsometry in the photon energy range of 1.1–5.0 eV. The optical properties of the $\mathit{nc}\text{−}\mathrm{Si}$ are found to be well described by both the Lorentz oscillator model and the Forouhi-Bloomer (FB) model. The $\mathit{nc}\text{−}\mathrm{Si}$ exhibits a significant reduction in the dielectric functions and optical constants and a large blueshift $(\sim 0.6\mathrm{eV})$ in the absorption spectrum as compared with bulk crystalline silicon. The band gap of the $\mathit{nc}\text{−}\mathrm{Si}$ obtained from the FB model is $\sim 1.7\mathrm{eV}$, showing a large band gap expansion of $\sim 0.6\mathrm{eV}$ relative to the bulk value. The band gap expansion is in very good agreement with the first-principles calculation of the $\mathit{nc}\text{−}\mathrm{Si}$ optical gap based on quantum confinement.

Figure 1

HRTEM image of $\mathit{nc}\text{−}\mathrm{Si}$ embedded in ${\mathrm{SiO}}_2$.

Figure 2

Multilayer model used in the SE analysis. The $\mathit{nc}\text{−}\mathrm{Si}$ volume fraction is calculated from the SIMS measurement.

Figure 3

Best spectral fittings of $\psi$ and $\Delta$ based on the Lorentz oscillator model and the FB model with the approach described in the text.

Figure 4

Real $\left({\epsilon }_1\right)$ and imaginary $\left({\epsilon }_2\right)$ parts of the complex dielectric function of the $\mathit{nc}\text{−}\mathrm{Si}$ obtained from the spectral fittings based on the Lorentz oscillator model and the FB model. The dielectric function of bulk crystalline silicon is also included for comparison.

Figure 5

Refractive index $\left(n\right)$ and extinction coefficient $\left(k\right)$ of the $\mathit{nc}\text{−}\mathrm{Si}$ and bulk crystalline silicon as functions of wavelength.

Figure 6

Comparison of the dielectric function of $\mathit{nc}\text{−}\mathrm{Si}$ embedded in ${\mathrm{SiO}}_2$ matrix based on the FB model to those of bulk crystalline Si, $\mathit{nc}\text{−}\mathrm{Si}$ layer [a hypothetical dense layer of $\mathit{nc}\text{−}\mathrm{Si}$ particles covered by their native oxide without voids (Ref. 14)] and porous Si layer of 70% porosity (Ref. 24).

Figure 7

Plot of ${\left(\alpha E\right)}^{1∕2}$ versus photon energy $\left(E\right)$ for $\mathit{nc}\text{−}\mathrm{Si}$ and bulk crystalline silicon. $\alpha$ denotes the absorption coefficient and is calculated with $\alpha =4\pi k∕\lambda$, where $k$ is the extinction coefficient and $\lambda$ is the wavelength.

Figure 8

Room temperature photoluminescence of $\mathit{nc}\text{−}\mathrm{Si}$ embedded in ${\mathrm{SiO}}_2$ matrix. The wavelength of the excitation source is 355 nm.