Theoretical discussions on the geometrical phase analysis

Rouvière, Jean-Luc; Sarigiannidou, E.

doi:10.1016/j.ultramic.2005.06.001

Cited by 170 publications

(98 citation statements)

References 9 publications

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“…Strain field maps were obtained by geometrical phase analysis ͑GPA͒ of HRTEM images. 9,10 In our HRTEM measurements, we did not take into account the thin foil relaxation effect. 11 We observe no significant gradients in the relative deformation as a function of the sample thickness in different examined images, far enough from both the sample surface and the buffer layer, which confirms that thin foil effects can be neglected in a first approximation.…”

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confidence: 99%

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Strain distribution in GaN∕AlN quantum-dot superlattices

Sarigiannidou

Monroy

Daudin

et al. 2005

Applied Physics Letters

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The two-dimensional strain distribution in a GaN / AlN quantum-dot ͑QD͒ superlattice is measured from high-resolution transmission electron microscopy images using the geometrical phase analysis. The results are compared to elastic theoretical calculations using a combination of Fourier transform and Green's function techniques. The GaN / AlN system appears to be a model system for a comparison between theory and experiments as interdiffusion between GaN and AlN is negligible. We verify that for the case of a three-dimensional system, such as a QD, the biaxial strain approximation is not valid. Furthermore, we demonstrate that the presence of QDs induces a modulation in the strain state of the AlN barriers which is the driving force for the vertical alignment of the GaN QDs in the AlN matrix. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.2123394͔ During the last decade, semiconductor quantum-dot ͑QD͒ heterostructures have been the subject of extensive research due to their unique electronic and optical properties. 1 In particular, nitride QDs, have potential applications in optoelectronic devices, either in the visible or ultraviolet energy range. 2 Moreover, with their piezoelectric characteristics, nitride QDs have particular behavior. The piezoelectric polarization, which has a magnitude comparable to the spontaneous polarization, induces a significant redshift of the luminescence lines of GaN / AlN QD heterostructures. Therefore, the knowledge of the strain distribution in QDs is essential to understand the emission wavelength and to expect to tune this wavelength to the desired application.Despite the large number of reports on the growth and/or optical/structural characterization of wurtzite GaN / AlN QD, only a few theoretical studies address the strain state of these nanostructures. 3,4 From the experimental viewpoint, Raman spectroscopy measurements 5 provide information on the average strain of the GaN and AlN in the structures, indicating that the QDs are almost completely strained by the matrix, and the AlN is under a slight tensile strain. Anomalous grazing-incident x-ray diffraction experiments resolve two strain states in the AlN matrix 6 but the results were not compared to detailed elastic calculations.In this letter, we investigate the two-dimensional strain distribution in vertically correlated GaN QD structures embedded in an AlN matrix by combining experimental data from high-resolution transmission electron microscopy ͑HRTEM͒ with elastic theoretical calculations.Wurtzite GaN / AlN QD superlattices ͑SLs͒ with metal polarity, were grown on a 6H-SiC substrate by plasmaassisted molecular beam epitaxy in a MECA2000 chamber equipped with standard effusion cells for Al and Ga. Active nitrogen was produced in a radio-frequency plasma cell. Prior to the growth of the SL structure, a 0.5 m thick AlN buffer layer was deposited. The SL consists of 80 periods of GaN QD layers with 10 nm thick AlN barriers. The growth of GaN on AlN was made under N-rich conditions, by depositing an amount of ...

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“…This definition of strain, called here "GPA strain," is also known as GPA Lagrange strain. 10 In this letter, we have chosen the AlN matrix situated between two WLs as the reference region. In general, strain is measured with respect to the bulk lattice parameters of the material.…”

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Strain distribution in GaN∕AlN quantum-dot superlattices

Sarigiannidou

Monroy

Daudin

et al. 2005

Applied Physics Letters

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“…Defect analysis was performed on cross-section specimens by TEM at 200 keV (STEM/TEM JEOL 2200 FS) operated in the two beam diraction contrast, high resolution (HR-TEM) and high angle annular dark eld (HAADF) modes. Strain maps to locate the dislocations at the interface were obtained by geometric phase analysis (GPA) [23,24] processing of HR-TEM images using the STEM--CELL software package [25,26]. The 110 cross-section specimens were prepared by sandwiching a piece of the sample between two slabs of Si, followed by mechanical grinding down to 30 µm.…”

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confidence: 99%

A Structural Characterization of GaAs MBE Grown on Si Pillars

Frigeri¹,

Bietti²,

Scaccabarozzi³

et al. 2014

Acta Phys. Pol. A

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Growth on deeply patterned substrates, i.e. on pillars instead of a continuous substrate, is expected to be very promising to get crack free epilayers on wafers without any bowing. We report here on a structural investigation of GaAs MBE deposited on patterned (001) ocut Si, consisting of pillars 8 µm high and 5 to 9 µm wide, to check mostly the behaviour of the threading dislocations. It is found that only very rarely they propagate up to the GaAs top that will serve as active region in devices. Twins were also detected which sometimes reached the topmost part of GaAs. However, as twins have no associated dangling bonds, they should not be electrically active. Rare antiphase boundaries exist at the interface, hence not harmful for device operation.

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“…The HAADF STEM image analysed in Fig. 2 had a 0.133-nm pixel size with a 2048×2048 scanning pixels (272 nm × 272 nm field of view) and σ = 10, which produces ∼13-nm lateral resolution (Rouvière & Sarigiannidou, 2005). Although the HAADF STEM microscope at 300-keV imaged lattice planes through the 323-nm-thick specimen, some artefacts due to phase wrapping in the GPA process were observed as indicated in Fig.…”

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“…The application of a Gaussian filter in Fourier space, exp(−(g−g i ) 2 /2σ 2 ), where g is the reciprocal coordinate, g i is the centre of the reflection of interest and σ is the usual Gaussian parameter, corresponds to a convolution by the inverse Fourier transform of the Gaussian filter in direct space. Such a convolution acts to smooth strain information within a circular region of direct space with a radius of 3/2πσ (Rouvière & Sarigiannidou, 2005). In general, 5-nm lateral resolution can be achieved from a 200 nm × 200 nm field of view image with a standard deviation of 0.25% strain.…”

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Comparison of convergent beam electron diffraction and geometric phase analysis for strain measurement in a strained silicon device

Diercks¹,

Lian²,

Chung³

et al. 2011

Journal of Microscopy

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Key words. Convergent beam electron diffraction (CBED), geometric phase analysis (GPA), high-angle annular-dark-field scanning transmission electron microscopy (HAADF STEM), local strain measurement. SummaryConvergent beam electron diffraction and geometric phase analysis were used to measure strain in the gate channel of a p-type strained silicon metal-oxide-semiconductor field-effect transistor. These measurements were made on exactly the same transmission electron microscopy specimen allowing for direct comparison of the relative advantages of each technique. The trends in the strain values show good agreement in both the [110] and [001] directions, but the absolute strain values are offset from each other. This difference in the absolute strain measured using the two techniques is attributed to the way the reference strain is defined for each.Because strained silicon is being used on a highly localized scale to enhance the electrical performance of complementary metal-oxide-semiconductor (CMOS) devices (Chidambaram et al., 2004;Thompson et al., 2004), techniques for the quantitative measurement of elastic strain with high spatial resolution are increasingly necessary. Although convergent beam electron diffraction (CBED) and geometric phase analysis (GPA) have been used previously by several groups for these types of measurements (Toda et al., 2001;Hÿtch et al., 2003;Benedetti et al., 2004;Toh et al., 2005;Chung et al., 2008;Hüe et al., 2008), there have been no reports directly comparing the strain measurements from the two techniques for the same device structure. Because there are relative advantages and limitations of these techniques for strain measurement, a direct comparison of these two techniques should provide a better understanding of these. In CBED, a small, convergent probe is used to produce diffraction from both the zero-order and higher-order Laue zones (ZOLZ and HOLZ, respectively). The HOLZ diffraction appears as pairs of lines in the diffraction patterns -rings of excess lines diffracted to a relatively large angle and corresponding deficit lines in the central disk. Because these lines occur due to Bragg diffraction at relatively large angles, their positions are very sensitive to small changes in the crystal lattice. The sensitivity of lattice measurements using this technique can be on the order of 10 −4 . (Twigg et al., 1987;Kramer & Mayer, 1999) However, most silicon-based devices are oriented along 110 directions, and CBED patterns along this direction do not produce HOLZ lines under typically utilized CBED-operating conditions due to the large spacing between planes in the reciprocal lattice along this direction. Therefore, measurements using this technique are performed by tilting away from the 110 axis, typically along the 004 Kikuchi band, resulting in a loss of lateral resolution. This is particularly important as the scale of microelectronic devices continues to decrease. The degree of resolution loss depends on the angle of tilt from the [110] direction, so efforts have been ...

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Theoretical discussions on the geometrical phase analysis

Cited by 170 publications

References 9 publications

Strain distribution in GaN∕AlN quantum-dot superlattices

Strain distribution in GaN∕AlN quantum-dot superlattices

A Structural Characterization of GaAs MBE Grown on Si Pillars

Comparison of convergent beam electron diffraction and geometric phase analysis for strain measurement in a strained silicon device

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