Form birefringence of anisotropically nanostructured silicon

We present a detailed study of the anisotropic optical properties of mesoporous silicon layers prepared from substrates having different doping levels under various preparation conditions. We demonstrate that the morphology of the layers strongly depends on the preparation conditions. It correlates with measured optical anisotropy values and defines the directions of the optical axes. The experimental data are explained in the framework of an effective medium model which takes into account the different morphologies of the layers. Modifications of the optical anisotropy of the layers in a controlled manner by filling the pores with dielectric substances and by oxidation of the structure confirm that form birefringence is the origin of the optical anisotropy.

Figure 1

(a) TEM image of the (110) surface of a $p^{++}\text{−}P\mathrm{Si}$ layer. Bottom left to top right corresponds to the $\left[1\overline{1}0\right]$ crystallographic direction. (b) The TEM image of the (110) surface of a $p^{+}\text{−}P\mathrm{Si}$ layer.

Figure 2

(a) SEM image of a $\left(1\overline{1}2\right)$ plane of a $p^{++}\text{−}P\mathrm{Si}$ layer prepared from a (110) oriented Si substrate. (b) SEM image of a $\left(1\overline{1}2\right)$ plane of a $p^{+}\text{−}P\mathrm{Si}$ layer prepared from a (110) oriented Si substrate.

Figure 3

Angular dependence of the refractive index of a $p^{+}$- (a) and $p^{++}$- (b) $P\mathrm{Si}$ layers obtained from reflectivity measurements of linearly polarized light. The polarization direction of a linearly polarized ${\mathrm{Ar}}^{+}$-ion laser beam $(\lambda =514\mathrm{nm})$ has been rotated around an axis perpendicular to the layer surface. The zero degree corresponds to the in-plane $\left[1\overline{1}0\right]$ crystallographic direction. Solid lines are results of a fit.

Figure 4

(a) Transmittance spectrum of a $p^{++}$ (110) $P\mathrm{Si}$ layer for linearly polarized infrared light. (b) Reflectance spectrum of a $p^{++}$ (110) $P\mathrm{Si}$ layer for randomly polarized incident light.

Figure 5

Dependencies of refractive index values for a $p^{++}\text{−}P\mathrm{Si}$ layer on the angle of incidence of infrared radiation $(400–4000{\mathrm{cm}}^{-1})$ polarized along [001] and $\left[1\overline{1}0\right]$, respectively. Error bars result from uncertainties in the layer thickness and the angle of incidence. A solid line shows the result of calculations.

Figure 6

$I_{\perp }∕I_{\Vert }$ obtained for a $p^{++}\text{−}P\mathrm{Si}$ layer $(j=30\mathrm{mA}∕{\mathrm{cm}}^2)$ prepared from a (110) Si substrate. Phase shifts are related to the maxima and minima are indicated.

Figure 7

Spectral dependence of the anisotropy parameter $\Delta n$ of $P\mathrm{Si}$ layers prepared from substrates having different doping levels. All layers have been prepared with equal etching current densities $(j=50\mathrm{mA}∕{\mathrm{cm}}^2)$.

Figure 8

Spectral dependence of the anisotropy parameter $\Delta n$ of $p^{++}$- (a) and $p^{+}$- (b) $P\mathrm{Si}$ layers prepared from a (110) Si substrate with different etching current densities.

Figure 9

A comparison of the spectral dependence of $\Delta n$ for a $p^{+}$- (a) and a $p^{++}$- (b) $P\mathrm{Si}$ layer with the results of calculations according to the Bruggeman EMA (solid lines).

Figure 10

(a) Shift of the minimum $(\Delta \varphi =4\pi )$ in the $I_{\perp }∕I_{\Vert }$ curve after filling of the pores by different dielectric substances. 1—empty pores; 2—liquid nitrogen $(n=1.2)$; 3—liquid argon $(n=1.22)$, 4—acetone $(n=1.36)$; 5—cyclohexane $(n=1.43)$; and 6—benzene $(n=1.5)$. (b) A comparison of the spectral shift shown in (a) with the result of a calculation according to the Bruggeman EMA (solid line).