An improved deviation parameter for the simulation of dynamical X-ray diffraction on epitaxic heterostructures

Zaus, Robert

doi:10.1107/s0021889893005643

Cited by 64 publications

(32 citation statements)

References 9 publications

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“…These findings are caused by the fact that the ͑422͒ glancing-out reflection for a ͓100͔-oriented GaAs crystal is strongly asymmetric, and some approximations of the CDT are not verified. This result was evidenced also by Zaus, 37 who introduced an improved expression of the deviation parameter in the CDT in order to take into account the asymptotic sphericity of the dispersion surface for strong glancing-out asymmetric Bragg reflections. However, this simplified approach to the problem of considering only two roots of the secular equation leads to an improved theory that is not generally valid.…”

Section: Comparison With the Conventional Dynamical X-ray Theorymentioning

confidence: 72%

Generalized Laue dynamical theory for x-ray reflectivity at low and high incidence angles on strained multilayers

Giannini

Tapfer

1997

Phys. Rev. B

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In this work, we present a generalized dynamical theory for strained multilayers within the Laue formalism valid for x-ray Bragg diffraction. In the generalized theory we take into account all the four solutions of the secular equation, the asymptotic sphericity of the dispersion surface, the difference between electric and displacement fields, and the boundary conditions of continuity at the heterointerfaces for the tangential components of the electric and magnetic fields. Only the following approximations are made: to consider a two-beam case, and to neglect quadratic terms of the dielectric susceptibility. Our general equations give the correct x-ray reflectivity in the whole angular range between 0 and /2, i.e., also very far from the Bragg peaks. Great differences between the predictions of the conventional and generalized theories are obtained in several cases, for important features of the rocking curves, like angular position, peak intensity, and full width at half maximum of superlattice satellite or epitaxial layer peaks. We discuss in detail the following cases for which only the generalized theory describes correctly the x-ray scattering: coplanar diffraction ͑i͒ very far from the Bragg condition, ͑ii͒ near to the Bragg condition for strong asymmetric reflections, and ͑iii͒ for highly mismatched heterostructures.

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Section: Comparison With the Conventional Dynamical X-ray Theorymentioning

confidence: 72%

Generalized Laue dynamical theory for x-ray reflectivity at low and high incidence angles on strained multilayers

Giannini

Tapfer

1997

Phys. Rev. B

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“…For this comparison, the expression for q, recently reported by Zaus (1993), was used, which proved more effective than (2) for large deviations from the Bragg condition. Moreover, the above f parameter [(3)], suitable only for e_L values below 1%, was replaced by the exact expression already used in a previous study (Servidori, Cembali, Fabbri & Zani, 1992) for the general case of an asymmetric reflection.…”

Section: Comparison Between Approximate and More Exact Expressionsmentioning

confidence: 99%

X-ray Rocking-Curve Analysis of Crystals with Buried Amorphous Layers. Case of Ion-Implanted Silicon

Milita¹,

Servidori²

1995

J Appl Cryst

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X-ray rocking-curve analysis of implanted silicon is commonly used to investigate damage accumulation with increasing ion dose. The damage build-up is observed by the trends of either the maximum of the lattice strain normal to the surface (e.L) or the depth integral of the eL profile. However, for doses high enough to produce a buried amorphous layer, the determination of the peak value of the e.L depth profile, and hence of its integral, is not possible. This is demonstrated by means of a simple diffraction model which describes the amorphous layer as a material for which the structure factor is reduced to zero by sufficiently high values of the static Debye-Waller factor and for which the expansion u normal to the surface is given by the product of the fractional change of the interplanar spacing of the perfect crystal (exo) and the thickness of the amorphous layer (to). Since this expansion can be written as u = e±,to~ = (n + x)d, where n is an integer (n = 0, 1,2 .... ), 0 _< x < 1 and d is the spacing of the diffraction planes of the perfect crystal, the diffraction model shows that, for given thickness to and fraction x of d, there exists a discrete, in principle infinite, set of u values able to give identical rocking curves. This prevents the rigid outward displacement of the damaged surface crystalline region with respect to the substrate from being determined.

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“…The angular separation between the layer and substrate peak Do L;S is given by [29] Do L;S ¼ k 1 e > þ k 2 e J ; ðB:3Þ k 1 ¼ cos 2 F tan W þ 1 2 sin 2F; ðB:4Þ k 2 ¼ sin 2 F tan W À 1 2 sin 2F; ðB:5Þ…”

Section: Appendix Bmentioning

confidence: 99%

Synthesis of AlGaAs-based strained separately confined heterostructure laser diodes by low temperature liquid-phase epitaxy

Chandvankar

Shah

Bhattacharya

et al. 2004

Journal of Crystal Growth

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An improved deviation parameter for the simulation of dynamical X-ray diffraction on epitaxic heterostructures

Cited by 64 publications

References 9 publications

Generalized Laue dynamical theory for x-ray reflectivity at low and high incidence angles on strained multilayers

Generalized Laue dynamical theory for x-ray reflectivity at low and high incidence angles on strained multilayers

X-ray Rocking-Curve Analysis of Crystals with Buried Amorphous Layers. Case of Ion-Implanted Silicon

Synthesis of AlGaAs-based strained separately confined heterostructure laser diodes by low temperature liquid-phase epitaxy

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