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Linearized radially polarized light for improved precision in strain measurements using micro-Raman spectroscopy

V. Prabhakara, T. Nuytten, H. Bender, W. Vandervorst, S. Bals, and J. Verbeeck

Open Access Open Access

Abstract

Strain engineering in semiconductor transistor devices has become vital in the semiconductor industry due to the ever-increasing need for performance enhancement at the nanoscale. Raman spectroscopy is a non-invasive measurement technique with high sensitivity to mechanical stress that does not require any special sample preparation procedures in comparison to characterization involving transmission electron microscopy (TEM), making it suitable for inline strain measurement in the semiconductor industry. Indeed, at present, strain measurements using Raman spectroscopy are already routinely carried out in semiconductor devices as it is cost effective, fast and non-destructive. In this paper we explore the usage of linearized radially polarized light as an excitation source, which does provide significantly enhanced accuracy and precision as compared to linearly polarized light for this application. Numerical simulations are done to quantitatively evaluate the electric field intensities that contribute to this enhanced sensitivity. We benchmark the experimental results against TEM diffraction-based techniques like nano-beam diffraction and Bessel diffraction. Differences between both approaches are assigned to strain relaxation due to sample thinning required in TEM setups, demonstrating the benefit of Raman for nondestructive inline testing.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (15)
Fig. 1.
Fig. 1. Experimental Raman spectra on SiGe blanket structure (see text for detailed explanation on the material) consisting of the strained Ge region. The spectra are normalized with respect to the Ge peak. Note the broad Ge peak in the TO mode clearly indicating the presence of both TO and LO peaks. The dotted lines indicate the expected theoretical peak positions of TO and LO in the strained Ge showing the difficulty to resolve them as separate peaks in the experimental setup.

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Fig. 2.
Fig. 2. Normalized electric field distribution of radially polarized light at the focal plane.

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Fig. 3.
Fig. 3. Normalized electric field distribution of linearly polarized light at the focal plane.

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Fig. 4.
Fig. 4. Normalized intensity distribution of electric field components on the focal plane. The spatial resolution is the diametric distance or the diameter of the disc within which 68.5% of the total intensity lies.

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Fig. 5.
Fig. 5. Relative intensity distribution of electric field components as a function of defocus distance [μm] (defocus zero being the exact focal distance) for linearly (in x) and radially polarized light.

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Fig. 6.
Fig. 6. Normalized intensity distribution of the radial electric field Er for a) radially polarized light and b) linearized radially polarized light. The linear polarizer transmission axis is parallel to the x axis.

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Fig. 7.
Fig. 7. Normalized electric field distribution of the linearized radially polarized light at the focal plane.

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Fig. 8.
Fig. 8. Normalized intensity distribution of electric field components of the linearized radially polarized light. The spatial resolution is the diametric distance within which 68.5% of the total intensity lies.

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Fig. 9.
Fig. 9. Relative intensity distribution of electric field components as a function of the defocus distance [μm] (defocus zero being the exact focal distance) for linearized radially polarized light.

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Fig. 10.
Fig. 10. Raman spectrum of the Si-Ge blanket structure in the TO mode a) linearly polarized light, radially polarized light and c) linearized radially polarized light. Notice the strong LO component observed experimentally for the radially polarized light and the strong suppression brought after linearization as observed from the linearized radially polarized light. Note the shift in the peak position with respect to the expected position for unstrained bulk Ge and the higher peak intensity of the sGe TO peak for the linearized radially polarized light.

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Fig. 11.
Fig. 11. Stress measured on the blanket structure on different locations near the center of the blanket structure using a) linearly polarized light setup and the b) linearized radially polarized light setup. Note the clear indication of biaxial nature of stress in these structures.

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Fig. 12.
Fig. 12. Strain maps on the blanket structure from Nano-beam diffraction (NBD) and Bessel diffraction. The strain maps shown are from two perpendicular cross section lamellae in the xz and yz planes. The line profiles drawn are averaged horizontally over a distance of 16 nm.

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Fig. 13.
Fig. 13. Raman spectra obtained on a 16nm finFET using oil immersion lens from a linearly polarized and a linearized radially polarized setup. The plasma lines are associated with the Rayleigh scattering of laser light and are positioned respectively at 180.2 cm-1, 286.2 cm-1 and so on and are fitted using the Gaussian profile [52].

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Fig. 14.
Fig. 14. a) The schematic showing the building block of the finFETs array where the finFETs are 16nm wide and are distanced apart by a constant pitch of 200 nm. The building blocks are spatially repeated next to each other to form an array of 16nm finFET nanodevices. In Raman measurements, two to three building blocks are probed depending on the spatial resolution or the electric field distribution of light. b) Stress measured at different locations on the length of the structure using oil immersion lens and linearly polarized setup and the linearized radially polarized setup. Note the clear indication of uniaxial stress in these structures.

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Fig. 15.
Fig. 15. Strain measurement on a 16nm finFET. The εxx, εyy and εzz maps are drawn from two perpendicular cross section TEM lamellae. The line profiles are drawn vertically over the maps and are averaged horizontally over 16 nm.

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Tables (8)

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Table 1. Raman phonon selectivity for different experimental configurations considering x = [110], y = [-110] and z = [001]

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Table 2. Relative intensity contributions of electric field components for linearly and radially polarized light at the focal plane.

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Table 3. Comparison of obtainable spatial resolution for linearly and radially polarized light. The spatial resolution is calculated as the diametric distance or the diameter of the disc which contains 68.5% of the total intensity

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Table 4. Relative intensity and obtainable spatial resolution for linearized radially polarized light. The spatial resolution is calculated as the diametric distance which contains 68.5% of the total intensity.

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Table 5. Stress values measured used linearly polarized and linearized radially polarized incoming light setup on the Ge layer of the blanket structure. The error values on the stress measurements quoted here are the standard deviations obtained from multiple measurements.

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Table 6. Strain values in the three perpendicular directions in strained Ge region with respect to bulk Ge as reference. The values obtained from the Raman are calculated from the measured stress values using Hooke’s law and stress-strain relations in the elastic regime. The εzz values from the TEM measurements are an average of the individual measurements in the xz and yz planes from the two perpendicular cross section lamellas. The uncertainty values are a measure of standard deviation from the observed strain values in the data.

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Table 7. Stress values measured using linearly polarized and linearized radially polarized incoming light setup on the 16 nm finFET Ge channel. The error values on the stress measurements quoted here are the standard deviations obtained from multiple measurements.

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Table 8. Strain values from the three perpendicular directions in the strained Ge region for the finfet structure. The values obtained from the Raman are calculated from the measured stress values using Hooke’s law and stress-strain relations in the elastic regime. The uncertainty values are a measure of standard deviation from the observed strain values in the data.

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Equations (16)

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I = C ∑ j ⁡ | e out T R j e in | 2
R 1 = [ 0 0 0 0 0 d 0 d 0 ] , R 2 = [ 0 0 d 0 0 0 d 0 0 ] , R 3 = [ 0 d 0 d 0 0 0 0 0 ]
Δ ω LO = 1 2 ω 0 ( p S 12 + q ( S 11 + S 12 ) ) ( σ x + σ y )
ω T O 1 = 1 2 ω 0 [ ( 1 2 ( S 11 + S 12 ) ( p + q ) + q S 12 + r 2 S 44 ) σ x + ( 1 2 ( S 11 + S 12 ) ( p + q ) + q S 12 − r 2 S 44 ) σ y ]
ω T O 2 = 1 2 ω 0 [ ( 1 2 ( S 11 + S 12 ) ( p + q ) + q S 12 − r 2 S 44 ) σ x + ( 1 2 ( S 11 + S 12 ) ( p + q ) + q S 12 + r 2 S 44 ) σ y ]
Ix ( ρ , z ) = − iA π ∫ 0 2 π ⁡ ∫ 0 α ⁡ co s 1 / 2 θ sin ⁡ θ cos ⁡ θ c o s ( φ ) I o ( θ ) e ik ( z cos ⁡ θ + ρ sin ⁡ θ cos ( φ − φ s ) d φ d θ
Iy ( ρ , z ) = − iA π ∫ 0 2 π ⁡ ∫ 0 α ⁡ co s 1 / 2 θ sin ⁡ θ cos ⁡ θ sin ( φ ) I o ( θ ) e ik ( z cos ⁡ θ + ρ sin ⁡ θ cos ( φ − φ s ) d φ d θ
Ir ( ρ , z ) = − iA π ∫ 0 2 π ⁡ ∫ 0 α ⁡ co s 1 / 2 θ sin ⁡ θ cos ⁡ θ cos ( φ − φ s ) I o ( θ ) e ik ( z cos ⁡ θ + ρ sin ⁡ θ cos ( φ − φ s ) d φ d θ
Iz ( ρ , z ) = − iA π ∫ 0 2 π ⁡ ∫ 0 α ⁡ co s 1 / 2 θ si n 2 θ I o ( θ ) e ik ( z cos θ + ρ sin ⁡ θ cos ( φ − φ s ) d φ d θ
I 0 ( θ ) = exp [ − β 2 ( sin θ sin α ) 2 J 1 ( 2 β sin θ sin α ) ]
T ( φ ) = ( T 1 − T 2 ) co s 2 φ + T 2
Ix ( ρ , z ) = − iA π ∫ 0 2 π ⁡ ∫ 0 α ⁡ T ( φ ) co s 1 2 θ sin ⁡ θ cos ⁡ θ cos ( φ ) I o ( θ ) e ik ( z cos ⁡ θ + ρ sin ⁡ θ cos ( φ − φ s ) d φ d θ
Iy ( ρ , z ) = − iA π ∫ 0 2 π ⁡ ∫ 0 α ⁡ T ( φ ) co s 1 / 2 θ sin ⁡ θ cos ⁡ θ s i n ( φ ) I o ( θ ) e ik ( z cos ⁡ θ + ρ sin ⁡ θ cos ( φ − φ s ) d φ d θ
Ir ( ρ , z ) = − iA π ∫ 0 2 π ⁡ ∫ 0 α ⁡ T ( φ ) co s 1 / 2 θ sin ⁡ θ cos ⁡ θ cos ( φ − φ s ) I o ( θ ) e ik ( z cos ⁡ θ + ρ sin ⁡ θ cos ( φ − φ s ) d φ d θ
Iz ( ρ , z ) = − iA π ∫ 0 2 π ⁡ ∫ 0 α ⁡ T ( φ ) co s 1 / 2 θ si n 2 θ I o ( θ ) e ik ( z cos ⁡ θ + ρ sin ⁡ θ cos ( φ − φ s ) d φ d θ
I ( ω ) = 1 2 [ 1 − sign ( ω − ω 0 ) I 0 ] ( ω − ω 0 W 1 ) 2 + 1 + 1 2 [ 1 − sign ( ω − ω 0 ) I 0 ] ( ω 0 − ω W 2 ) 2 + 1
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