Erratum: Dynamical x-ray diffraction from nonuniform crystalline films: Application to x-ray rocking curve analysis [J. Appl. Phys. <b>5</b>
                  <b>9</b>, 3743 (1986)]

Wie, C. R.; Tombrello, T. A.; Vreeland, T.

doi:10.1063/1.350381

Cited by 29 publications

(42 citation statements)

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“…In particular, the diffraction intensity depends on both the the amplitude of a particular acoustic wavevector (A(q)) as well as the phase (φ m ) of the acoustic mode. Several computational methods have been developed which can calculate the x-ray rocking curve due to a known the crystalline structure profile 31,35,36 , however, a direct inversion from a single x-ray diffraction peak is quite difficult. In cases where the one-dimensional strain is both static and monotonic, it has been shown that the diffraction pattern can be uniquely inverted to reveal the strain profile 37 .…”

Section: B Time-resolved X-ray Diffractionmentioning

confidence: 99%

“…This superposition can be demonstrated by numerically calculating x-ray rocking curve of a strained crystal. To model the diffraction pattern of a longitudinal strained crystal, we use the diffraction algorithm developed by Wie et al 31 . This algorithm numerically solves the Takagi-Taupin equations 32-34 governing dynamical xray diffraction for perfect crystals with a strained surface.…”

Section: A One-dimensional X-ray Diffractionmentioning

confidence: 99%

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Reconstructing longitudinal strain pulses using time-resolved x-ray diffraction

et al. 2013

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Time-resolved x-ray diffraction is a very powerful tool for visualizing transient one-dimensional crystalline strains, ranging from crystal growth to shockwave production. In this work, we use picosecond x-ray diffraction to visualize transient strain formation from nanometer scaled laser excited gold films into crystalline substrates. We show that there is a direct correspondence between the measured time-resolved x-ray diffraction pattern and the transient acoustic wave, providing a straightforward method to make a reconstruction of the transient strain. In addition, we discuss real-world experimental constraints that place limits on the validity of the reconstructed transient acoustic wave.

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Section: B Time-resolved X-ray Diffractionmentioning

confidence: 99%

Section: A One-dimensional X-ray Diffractionmentioning

confidence: 99%

Reconstructing longitudinal strain pulses using time-resolved x-ray diffraction

et al. 2013

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“…The lack of inversion symmetry in InSb is ignored, except in the determination of the structure factor for the 222 reflection. The rocking curves are calculated for a particular strain profile using the method given by Wie et al [23]. The strain is calculated using the model of Thomsen et al [15], who solved the elastic equations for an instantaneous and exponentially decaying stress due to short-pulse laser absorption.…”

Section: (Received 28 November 2000)mentioning

confidence: 99%

Probing Impulsive Strain Propagation with X-Ray Pulses

et al. 2001

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Pump-probe time-resolved x-ray diffraction of allowed and nearly forbidden reflections in InSb is used to follow the propagation of a coherent acoustic pulse generated by ultrafast laser-excitation. The surface and bulk components of the strain could be simultaneously measured due to the large x-ray penetration depth. Comparison of the experimental data with dynamical diffraction simulations suggests that the conventional model for impulsively generated strain underestimates the partitioning of energy into coherent modes. 78.47.+p 61.10.-i 63.20.-e The absorption of ultrafast laser pulses in opaque materials generates coherent stress when the pulse length is short compared with time for sound to propagate across an optical penetration depth [1]. The resulting strain field consists of both a surface component, static on time scales where thermal diffusion can be ignored, and a bulk component that propagates at the speed of sound (coherent acoustic phonons). This strain is typically probed by optical methods that are sensitive primarily to the phonon component within the penetration depth of the light [1,2]. However, such methods give little information about the surface component of the strain, and, moreover, they are unable to give a quantitative measure of the strain amplitude.Due to their short wavelengths, long penetration depths, and significant interaction with core electrons, x-rays are a sensitive probe of strain. We note that coherent lattice motion adds sidebands to ordinary Bragg reflection peaks due to x-ray Brillouin scattering if the momentum transfer is large compared to the Darwin width, equivalent to phonons of GHz frequency for strong reflections from perfect crystals. This effect was demonstrated many years ago with acoustoelectrically amplified phonons using a conventional x-ray tube [3].With the recent availability of high brightness short-pulse hard x-ray sources, including third generation synchrotron sources and optical laser based sources [4-6], coherent strain generation and propagation can now be probed by x-ray methods in both the frequency and time domains. Recently, time-resolved diffraction patterns of cw ultrasonically excited crystals were obtained with a synchrotron source [7]. Other experiments have employed picosecond time-resolved x-ray diffraction to study transient lattice dynamics in metals [8], organic films [9], and impulsive strain generation and melting in semiconductors [10][11][12][13][14]. In particular Rose-Petruck et al.[10] demonstrated transient ultrafast strain propagation in GaAs by laser-pump x-ray-probe diffraction. In that experiment, x-rays were diffracted far outside the Bragg peak; however, no oscillations in the diffraction efficiency were detected, and the data were consistent with a unipolar strain pulse. In a similar experiment, Lindenberg et al. [13] detected oscillations in the sidebands for an asymmetrically cut InSb crystal using a streak camera. These oscillations were due to lattice compression and were probed for discrete phonon frequencies i...

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“…Calculation of the rocking curve for an arbitrary semiconductor heterostructure is based on the solution of the Takagi-Taupin equation [4][5][6][7] for dynamical diffraction,…”

Section: Theorymentioning

confidence: 99%

“…Dynamical [1][2][3][4][5][6] and kinematical [7][8][9][10][11] simulations have been used in conjunction with a curve-fitting procedure to extract the profiles of strain and composition, but are based on perfect, dislocation-free laminar crystals, and this renders the analysis inapplicable to mismatched structures with dislocation densities greater than 10 6 cm À2 . Krivoglaz and Ryaboshapka 12 and Levine and Thomson 13 have analyzed the line profiles of Bragg peaks from crystals containing straight, parallel screw dislocations with precisely known atomic displacements.…”

Section: Introductionmentioning

confidence: 99%

Dynamical X-ray Diffraction from ZnS y Se1−y /GaAs (001) Multilayers and Superlattices with Dislocations

Rago

Suarez

Jain

et al. 2012

Journal of Elec Materi

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High-resolution x-ray diffraction is a valuable nondestructive tool for structural characterization of semiconductor heterostructures, and the diffraction profiles contain information on the depth profiles of strain, composition, and defect densities in device structures. Much of this information goes untapped because the lack of phase information prevents direct inversion of the diffraction profile. The current practice is to use dynamical simulations in conjunction with a curve-fitting procedure to indirectly extract the profiles of strain and composition. These dynamical simulations have been based on perfect, dislocation-free laminar crystals, rendering the analysis inapplicable to structures having dislocation densities greater than about 10 6 cm À2 . In this work we present a dynamical model for Bragg x-ray diffraction in semiconductor device structures with nonuniform composition, strain, and dislocation density, which is based on the Takagi-Taupin equation for distorted crystals and accounts for the angular and strain broadening of dislocations. We show that the x-ray diffraction profiles from ZnS y Se 1Ày multilayers and superlattices are strongly affected by the depth distribution of the dislocation density as well as the composition, suggesting that it should be possible to extract the profiles of composition, strain, and dislocation density by the analysis of measured diffraction profiles.

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Erratum: Dynamical x-ray diffraction from nonuniform crystalline films: Application to x-ray rocking curve analysis [J. Appl. Phys. 5 9, 3743 (1986)]

Cited by 29 publications

References 0 publications

Reconstructing longitudinal strain pulses using time-resolved x-ray diffraction

Reconstructing longitudinal strain pulses using time-resolved x-ray diffraction

Probing Impulsive Strain Propagation with X-Ray Pulses

Dynamical X-ray Diffraction from ZnS y Se1−y /GaAs (001) Multilayers and Superlattices with Dislocations

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