Quantitative Analysis of Stress Relaxation in Transmission Electron Microscopy Samples by Raman Spectroscopy with a High-Numerical Aperture Lens

Abstract

We present a 1-loop toroidal membrane winding sum reproducing the conjectured M -theory, four-graviton, eight derivative, R 4 amplitude. The U -duality and toroidal membrane world-volume modular groups appear as a Howe dual pair in a larger, exceptional, group. A detailed analysis is carried out for M -theory compactified on a 3-torus, where the target-space SL(3, Z) × SL(2, Z) U -duality and SL(3, Z) world-volume modular groups are embedded in E 6(6) (Z). Unlike previous semi-classical expansions, U -duality is built in manifestly and realized at the quantum level thanks to Fourier invariance of cubic characters. In addition to winding modes, a pair of new discrete, flux-like, quantum numbers are necessary to ensure invariance under the larger group. The action for these modes is of Born-Infeld type, interpolating between standard Polyakov and Nambu-Goto membrane actions. After integration over the membrane moduli, we recover the known R 4 amplitude, including membrane instantons. Divergences are disposed of by trading the non-compact volume integration for a compact integral over the two variables conjugate to the fluxes -a constant term computation in mathematical parlance. As byproducts, we suggest that, in line with membrane/fivebrane duality, the E 6 theta series also describes five-branes wrapped on T 6 in a manifestly U-duality invariant way. In addition we uncover a new action of E 6 on ten dimensional pure spinors, which may have implications for ten dimensional super Yang-Mills theory. An extensive review of SL(3) automorphic forms is included in an appendix.

Evaluation of Anisotropic Strain Relaxation in Strained Silicon-on-Insulator Nanostructure by Oil-Immersion Raman Spectroscopy

“…As a result, the TO phonon modes in Si can be effectively excited by z-polarization even under the (001) Si backscattering geometry; on the other hand, exciting the TO phonon modes is difficult in conventional Raman measurements, e.g., the aperture angle is 9.8 in the case of using NA ¼ 0:7 objective. [7][8][9] We selectively obtained each optical phonon mode in Si by controlling incident and scattered electrical fields using polarizers and by sample rotation, which was based on the Raman polarization selection rules. 39) Figure 2 shows the various configurations in oil-immersion Raman measurements.…”

“…9) In our previous study, the strain relaxation in transmission electron microscopy (TEM) samples of strained Si-oninsulator (SSOI) substrates was evaluated by oil-immersion Raman spectroscopy. 7) Our purpose was to distinguish the stress in the long direction from that in the short direction in the TEM samples of SSOI. As a result, the stress in the short direction, which means the thinned direction, dominantly relaxed: the stress relaxations of 70 and 30% were confirmed in the thinned direction and long direction, respectively, in the TEM samples with a thickness of 240 nm.…”

Channel Strain Measurement in 32-nm-Node Complementary Metal–Oxide–Semiconductor Field-Effect Transistor by Raman Spectroscopy

“…Moreover, the relaxation is not uniform. 33) Thus, both the value and distribution of the detected strain are not necessarily the same during device operation. Moreover, the specimen preparation and even strain measurement need complicated and skill-requiring processes.…”

Stress evaluation in thin strained-Si film by polarized Raman spectroscopy using localized surface plasmon resonance

“…The present experiment proved that the SERS by LSPR can efficiently excite the TO phonons, which has been hard to obtain in the (100) Si backscattering geometry. As we have previously reported, 11,12 TO phonon excitation in conjunction with LO phonon excitation make two-axis stress analyses possible even for the (100) Si.…”

“…We also measured LO and TO phonon peak shifts selectively only by high-NA objective lens without SERS. 11,12 The calculated stresses were 1.41 GPa and 1.36 GPa. The strain in SGOI measured by x-ray diffractometry was 0.765%, corresponding to 1.42 GPa.…”