Highly sensitive strain detection in silicon by reflectance anisotropy spectroscopy

Reflectance anisotropy spectroscopy (RAS) measurements were performed on strained silicon (Si) stripes cut from crystalline silicon wafers. Strains were externally applied using a device developed especially for the study of layers and layered structures. The dependence of the RAS signal intensity on strain was measured for (100), (110), and (111) silicon wafers strained along [001] and [011]. In these configurations, the RAS spectra show a derivativelike structure at 3.4 eV, which increases in amplitude linearly with strain. While RAS line shapes depend on the orientation of the Si wafer and the crystallographic directions along which strains are applied, RAS intensities depend on strain magnitude. Strains as low as ${10}^{-5}$ can be measured, which is two orders of magnitude smaller than those detected with standard techniques such as Raman, piezoelectroreflectance spectroscopy (PERS), or x-ray diffraction (XRD). The experimental RAS spectra are found to be in good agreement with spectra calculated on the basis of the spectral response of the published piezo-optical tensor components. It is concluded that RAS provides a highly sensitive tool for the detection of strain induced bulk anisotropies. Strain calibrated RAS spectra can be used for strain-stress characterization of semiconductor layers and microstructures with a higher efficiency than that achieved by Raman, PERS, and XRD. Combined with growth techniques, RAS spectroscopy can be also used for in situ control of strain during semiconductor growth.

Figure 1

(Color online) Beam path in the RAS spectrometer: the sample is adjusted with its strain axis under 45° to the polarizer and PEM axis.

Figure 2

Schematic drawing of a silicon stripe under strain induced by the movement of a sharp edge in the direction of the z-axis (stripe curvature enlarged by a factor of ${10}^3$).

Figure 3

Spectra of reflectance anisotropy $(r_{010}-r_{001})$ of Si(100) stripes strained along [010] or [001] (for clarity, spectra are shifted in $\Delta r∕\overline{r}$; zero strain lines are indicated).

Figure 4

Spectra of reflectance anisotropy $(r_{011}-r_{0\overline{1}1})$ of Si(100) stripes strained along [011] or $\left[0\overline{1}1\right]$ (for clarity, spectra are shifted in $\Delta r∕\overline{r}$; zero strain lines are indicated).

Figure 5

(Color online) Comparison of (a) the experimentally measured reflectance anisotropy $(r_{011}-r_{0\overline{1}1})$ of the Si(100) surface strained along [011] or $\left[0\overline{1}1\right]$ with the reflectance anisotropy calculated from the piezo-optical tensor components (Ref. 17) according to (b) Eqs. (4, 8b), and (c) Eqs. (6, 8b).

Figure 6

(Color online) Comparison between (a) the experimentally measured reflectance anisotropy $(r_{010}-r_{001})$ of the Si(100) surface strained along [010] or [001] and (b) the reflectance anisotropy calculated from the piezo-optical tensor components (Ref. 17) according to Eqs. (4, 7b).

Figure 7

(Color online) Dependence of the RAS-signal intensity on applied strain in the following configurations: reflectance anisotropy $(r_{010}-r_{001})$ of Si(100) stripes strained along [010] or [001] (∎, solid line), reflectance anisotropy $(r_{\overline{1}10}-r_{001})$ of Si(110) stripes strained along [001] (●, dashed line), reflectance anisotropy $(r_{\overline{1}10}-r_{11\overline{2}})$ of Si(111) stripes strained along $\left[\overline{1}10\right]$ (▴, dashed line).

Figure 8

(Color online) Reflectance anisotropy spectra $(r_{\overline{1}10}-r_{001})$ of the strained and unstrained Si(110) surface, which is optically anisotropic [strains are varied between $e_x=0$ (solid line) and $e_x=8.74\times {10}^{-4}$ (dot-dashed line), see also Fig. 9].

Figure 9

Spectra of reflectance anisotropy $(r_{\overline{1}10}-r_{001})$ of Si(110) stripes strained along $\left[\overline{1}10\right]$ after subtraction of the spectrum of the unstrained stripe (for clarity, spectra are shifted in $\Delta r∕\overline{r}$ of the spectrum at strain $e_x=1.75\times {10}^{-4}$; zero strain lines are indicated).

Figure 10

(Color online) Comparison of RAS spectra $(r_{\overline{1}10}-r_{001})$ of the Si(110) surface strained along $\left[\overline{1}10\right]$ (dotted line) and [001] (solid line).

Figure 11

(Color online) Comparison between (a) the experimentally measured reflectance anisotropy $(r_{\overline{1}10}-r_{001})$ of the Si(110) surface strained along [001] and (b) the reflectance anisotropy calculated from the piezo-optical tensor components (Ref. 17) according to Eqs. (4, 9b) for three different ratios (0.5, 1, and 1.5) of the components $X_y∕X_x$ of a biaxial stress in the $xy$ plane.

Figure 12

Spectra of reflectance anisotropy $(r_{\overline{1}10}-r_{11\overline{2}})$ of Si(111) stripes strained along $\left[\overline{1}10\right]$ (for clarity, spectra are shifted in $\Delta r∕\overline{r}$; zero strain lines are indicated).

Figure 13

(Color online) Comparison between (a) the experimentally measured reflectance anisotropy $(r_{\overline{1}10}-r_{11\overline{2}})$ of the Si(111) surface strained along $\left[\overline{1}10\right]$ and (b) the reflectance anisotropy calculated from the piezo-optical tensor components (Ref. 17) according to Eqs. (4, 11b).

Figure 14

Comparison of the 3.4 eV resonance at $E_0^{\prime }$-gap energy in the reflectance anisotropy spectra of the silicon (100), (110), and (111) surfaces strained along low index crystallographic axes. The $e_z$ strain can be estimated in dependence of the $e_x$ strain, the elastic compliances $S_{ij}$, and the piezo-optical tensor $P_{ij}$.