Anisotropic strain

The three-dimensional thermoelastic anisotropic strain-stress relations are... 

Gray, M.Fk, J.W.P. Hsu, L. Giovane, M.T. Bulsara. 2001. Effect of anisotropic strain on the crosshatch electrical activity in relaxed GeSi films. Phys. Rev. Lett. 86 3598-3601. 

A primary focus of our work has been to understand the ferroelectric phase transition in thin epitaxial films of PbTiOs. It is expected that epitaxial strain effects are important in such films because of the large, anisotropic strain associated with the phase transition. Figure 8.3 shows the phase diagram for PbTiOs as a function of epitaxial strain and temperature calculated using Landau-Ginzburg-Devonshire (lgd) theory [9], Here epitaxial strain is defined as the in-plane strain imposed by the substrate, experienced by the cubic (paraelectric) phase of PbTiOs. The dashed line shows that a coherent PbTiOs film on a SrTiOs substrate experiences somewhat more than 1 % compressive epitaxial strain. Such compressive strain favors the ferroelectric PbTiOs phase having the c domain orientation, i.e. with the c (polar) axis normal to the film. From Figure 8.3 one can see that the paraelectric-ferroelectric transition temperature Tc for coherently-strained PbTiOs films on SrTiOs is predicted to be elevated by 260°C above that of... 

The local variation A d/d (microstrain) due to anisotropic strain in crystallites, lattice defects, and/or local compositional variations A (20) = -2A d/d tan0 [5]. Figure 3 shows the comparison of the temperature-dependent behavior of two samples of Ndo.sSro.sMnOs with nominally the same composition. This material shows giant-magnetoresistive behavior. The first sample phase separates into three coexisting macroscopic phases at low temperatures a ferromagnetic phase that is orthorhombic and exists at high temperatures (HTO),... 

Darakchieva V, Paskova T, Schubert M, Arwin H, Paskov PP, Monemar B, Hommel D, Heuken M, Off J, Scholz F, Haskell BA, Fini PT, Speck JS, Nakamura S (2007) Anisotropic strain and phonon deformation potentials in GaN. Phys Rev B 75 195217... 

Inner G, Brumme T, Herms M, Wernicke T, Kneissl M, Weyers M (2008) Anisotropic strain on pnonons in a-plane GaN layers studied by Raman scattering. J Mater Sci Mater Electron 19 S51-S57... 

Both the ionic and dissociative reaction products (Fig. 9b and 9c, respectively) are quenchable at room temperature at all pressures studied (between 10 and 55 GPa). The ionic phase (NO NOj ) is stable in a wide pressure region to 55 GPa, the maximum pressure applied. No reverse transition of NO NOj to the molecular phases of N2O4, N2O, or NO2 was observed even below the N2O-I/III transition pressure 4-5 GPa. This is contrarily to the high pressure-temperature phases of CO2 (phases II, III, IV, and V and its ionic dimer phase [95]), all of which transform back to the phase I Pa3) near 11 GPa. Note that the splitting of the V4 mode above 35 GPa probably resulted from the anisotropic strain developed in the lattice. 

Certain factors such as anisotropic strain energy contributioiis can lead to a preference for other shapes, but this is beyond the scope of the present text. 

Xu SH, Wang LW (2009) Porous silicon microtube structures induced by anisotropic strain. J Appl Phys 106 073516... 

This technique allows the real-time volume change to be mapped in situ in the out-of-plane direction. This has shown that the PPy(DBS) film fliickness increased by over 35 % in the reduced state compared to the oxidized state (Fig. 24). This compares with an in-plane strain of 2 % found in prior studies using bilayers, showing that the volume change of PPy(DBS) is anisotropic. The anisotropic strain of PPy(DBS) supports the view that it has a lamella structure with planes orientated parallel to the substrate (Wemet et al. 1985). 

The anisotropic strain in the nonpolar nitride materials films heteroepitax-ially grown in nonpolar directions inevitably leads to more complex behavior of the optical phonons. The theory predicts that some of the phonons in the nitrides split under anisotropic strain. Recent reports on a-plane nonpolar GaN... 

The in-plane polarization anisotropy can be enhanced by anisotropic strain. This can be achieved by choosing a nonpolar orientation with an appropriate substrate. In the extreme case of M-plane GaN on liAl02, the degree of linear polarization can be increased to its maximum value of one for all three transitions between the three uppermost valence bands (VBs) and the conduction band (CB), corresponding to complete linear polarization for all three transitions. This optical anisotropy can be observed in transmission (absorption) and reflection, as well as photoluminescence (PL) and photoreflectance (PR) spectroscopy. It can therefore be used for polarization filtering, polarization-sensitive photodetectors (PSPDs), and polarized light emitters. For anisotropically strained C-plane GaN films on (1120) sapphire, the in-plane polarization properties have been previously reported in Refs. 1-3. 

The calculated oscillator strengths ff, where k denotes x, y, or z, for the three transitions Ti, T2, and T3 are shown in Figure 7.5 as a function of the in-plane strain e and Syy for C-plane GaN. For isotropic strain, the oscillator strengths and are always equal. Therefore, there are no strain values for which all three transitions become completely linearly polarized. However, for anisotropic strain, there are strain values for a particular transition, for which the oscillator strength becomes one for one direction, while it is zero for the other two directions. For the same strain values, the oscillator strength of another transition becomes one for a different direction and zero for the two orthogonal ones. Therefore, for anisotropic strain, all three transitions become completely linearly polarized for certain values of the in-plane strain. 

The transition energies for two M- and two A-plane GaN films, which are all anisotropically strained, have been determined from a line-shape analysis of the polarized PR spectra measured at low and room temperature. In all cases, the anisotropic strain together with the reduced crystal symmetry of the M- and A-planes films results in a strong optical anisotropy. Due to the large strain in at least one of the in-plane directions for the M-plane GaN films, the polarization anisotropy is much more pronounced in the M-plane than in the A-plane films. The polarized PL spectra of M-plane GaN films and M-plane (In,Ga)N/GaN MQWs clearly exhibit a strong polarization anisotropy with degrees of polarization of about 0.90 for the films and 0.96 for the MQW. However, as a result of the large separation of the two uppermost... 

Optical Phonons in a-plane GaN under Anisotropic Strain... 

In this chapter, we review recent studies of optical phonons in relation to the anisotropic strain in GaN heteroepitaxial layers and quantum dots (QDs) with nonpolar orientations. For reasons of comparison, results on anisotropically strained c-plane GaN films grown on a-plane sapphire is also presented where appropriate. The application of GIRSE and Raman scattering to the studies of optical phonon frequencies of anisotropic wurtzite GaN is described to reveal the phonon mode behavior. The assessment of anisotropic strain components in a-plane GaN films and their evolution with thickness... 

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