Phonon Deformation Potentials

The frequencies of the zone-center optical phonons in GaN are shifted or split with respect to the strain-free values. In the linear strain limit, these shifts and splittings are related to the strain tensor via [14,16]  

Using Hooke s law (Equation 5), and defining the mode deformation potentials for a given stress, dj, bj, and Cj, we can obtain an alternative form of Equation 8 that relates the mode frequency shift with the stress tensor [14]. 

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The derivative terms are known as the phonon deformation potentials, and each is a component of a full phonon deformation potential matrix For cubic crystals, symmetry considerations reduce the number of independent phonon deformation potentials to three ... 

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... 

This has been used for two-level tunnelling systems in insulating glasses. The coupling coefficient Fip from the phonon deformation potential should be independent of T and A, because the density of phonon modes in the Debye model is proportional to co up to the maximum frequency cod and this co-dependence counteracts the smaller overlap for larger A. The electron rate Re may therefore dominate the total rate at small values of A, while Rip may be faster for large A up to the Debye energy k T. ... 

W. Richter, Resonant Raman Scattering in Semiconductors Electric Susceptibility. Light Scattering. Experimental Method.s. One-Phonon Deformation Potential Scattering. Infrared Active LO Phonons. Multiphonon Scattering. Conclusions. List of Symbols. References. Subject Index. 

The optical phonon spectrum is one of the most fundamental characteristics of the crystals. It reflects the specific features of the interatomic interactions and gives very comprehensive and detailed information about the thermal and optical properties involving the efficiency of the optoelectronic devices. The vibrational properties in all the nitride systems have heen investigated in detail over the years by Raman scattering (RS) spectroscopy. Recent studies of nonpolar a-plane GaN by RS confirmed the finding in the c-plane GaN [107, 108]. However, in some cases there is a lack of agreement between the values of some phonon deformation potentials and strain-free phonon-mode positions in GaN and AlN, as determined theoretically and by employing RS spectroscopy. The nonpolar materials allow an access to the complete set of phonons by infrared spectroscopic ellipsometry (IRSE). This provides an alternative tool to study the vihrational properties and to establish very important and useful fundamental parameters of the nitrides. 

Phonon frequencies are often employed as a tool for strain assessment in mismatched semiconductor heterostructures [1]. This involves IR and Raman measurements of phonon frequency shifts with respect to unstrained material, and their conversion into strain or stress components via the phonon deformation potentials. The knowledge of precise values of the strain-free frequencies and the phonon deformation potentials is of key importance in such studies. Phonon deformation potentials can be obtained from control experiments, in which the frequencies of the phonons under consideration are calibrated versus well-defined applied strains (or stresses) on otherwise strain-free material. Alternatively, the phonon frequencies can be caKbrated versus strain components in layers exhibiting different intrinsic strains. The latter requires determination of the intrinsic strain components. 

The c phonon deformation potentials for the Ei(TO), Ei(LO), and Ej phonons can then be estimated using the experimental results for the strain components and the phonon frequency splittings [17, 18). The results obtained for anisotropically strained nonpolar a-plane and polar c-plane GaN films are listed in Table 9.5. 

Table 9.5 Anisotropic phonon deformation potentials, C ,(to)i C ,(LO). and Ce, in cm, and the respective standard deviations.

A correlation between phonon mode frequencies and strain components in films with different strains can, in principle, allow determination of the isotropic deformation potentials, a and b (see Equations 9 and 8). a-Plane GaN films offer a unique opportunity to obtain the Ai(TO) phonon deformation potentials by GIRSE. This is particularly important in view of the existing discrepancy in the literature between the values of the Ai(TO) phonon deformation potentials determined by Raman scattering [54] and theory [14]. Further, the aEi(io) and fcii(LO) have not been experimentally determined yet. 

Figure 9.17 Contour plot of A] (TO) frequency versus the strain components, e, and ffzz. according to Equation 23 and using the results about the phonon deformation potentials (o = —664 cm and b = —1182 cm ) and strain-free frequency...

The regression does not account for the errors of the experimental strains, and therefore may limit the accuracy with which the deformation potentials are determined (see Figure 9.17 and Equation 23). The large uncertainties in the stiffness constants and the narrow frequency range could also contribute to large standard deviations of the deformation potentials. We note, however, that experimentally obtained phonon deformation potentials of GaN and AlN typically suffer from uncertainties as large as 20-23% [10,11). 

The inconsistency in the strain components in the a-plane QD samples reported in [57, 58] indicates a significant impact of the assumptions made in their estimation from the phonon frequencies. We note that in aU estimations of the strain components, the anisotropic phonon deformation potentials chj(to) and ce were assumed to be zero [57]. The results of the anisotropically strained GaN films presented in Sections 9.4.2 and 9.4.3 show clear splittings of the El and 2 indicating nonzero anisotropic deformation potentials for these phonon modes (Tables 9.4 and 9.5). We point out, however, that the values of the C j(xo) and c in Ref. 17 may be also affected by the assumptions made in the strain component determination by XRD (for instance the deviation from hexagonal symmetry is assumed to be small). The studies of the vibrational properties of nitride materials with nonpolar surface orientations are scarce and clearly, further experimental and theoretical investigations are needed to clarify these issues. 

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