Interpretation of X-ray Powder Diffraction Patterns . By H. Lipson and H. Steeple. Pp. viii + 335 + 3 plates. (Mac-millan: London; St Martins Press: New York, May 1970.) £4.

X-Ray Diffraction

Modeling hardness of polycrystalline materials and bulk metallic glasses

The III-nitrides include the semiconductors AlN, GaN and InN, which have band gaps spanning the entire UV and visible ranges. Thin films of III-nitrides are used to make UV, violet, blue and green light-emitting diodes and lasers, as well as solar cells, high-electron mobility transistors (HEMTs) and other devices. However, the film growth process gives rise to unusually high strain and high defect densities, which can affect the device performance. X-ray diffraction is a popular, non-destructive technique used to characterize films and device structures, allowing improvements in device efficiencies to be made. It provides information on crystalline lattice parameters (from which strain and composition are determined), misorientation (from which defect types and densities may be deduced), crystallite size and microstrain, wafer bowing, residual stress, alloy ordering, phase separation (if present) along with film thicknesses and superlattice (quantum well) thicknesses, compositions and non-uniformities. These topics are reviewed, along with the basic principles of x-ray diffraction of thin films and areas of special current interest, such as analysis of non-polar, semipolar and cubic III-nitrides. A summary of useful values needed in calculations, including elastic constants and lattice parameters, is also given. Such topics are also likely to be relevant to other highly lattice-mismatched wurtzite-structure materials such as heteroepitaxial ZnO and ZnSe.

https://iopscience.iop.org/article/10.1088/0034-4885/72/3/036502/pdf

X-ray diffraction of III-nitrides

We report on the first experimental observation of Tamm plasmon polaritons (TPPs) formed at the interface between a metal and a dielectric Bragg reflector (DBR). In contrast to conventional surface plasmons, TPPs have an in-plane wavevector less than the wavevector of light in vacuum, which allows for their direct optical excitation. The angular resolved reflectivity and transmission spectra of a GaAs∕AlAs DBR covered by Au films of various thicknesses show the resonances associated with the TPP at low temperatures and room temperature. The in-plane dispersion of TTPs is parabolic with an effective mass of 4×10−5 of the free electron mass.

/pdf/tamm-plasmon-polaritons-slow-and-spatially-compact-light-3m38dsy33i.pdf

Tamm plasmon polaritons: Slow and spatially compact light

The refractive index of GaAs has been measured in the wavelength range from 0.97 to 17 μm, which covers nearly the entire transmission range of the material. Linear and quadratic temperature coefficients of the refractive index have been fitted to data measured between room temperature and 95 °C. In the midinfrared, the refractive index and temperature dependence are obtained from analysis of etalon fringes measured by Fourier-transform spectroscopy in undoped GaAs wafers. In the near infrared, the refractive index is deduced from the quasiphasematching (QPM) wavelengths of second-harmonic generation in orientation-patterned GaAs crystals. Two alternative empirical expressions are fitted to the data to give the refractive index as a function of wavelength and temperature. These dispersion relations agree with observed QPM conditions for midinfrared difference-frequency generation and second-harmonic generation. Predictions for various nonlinear optical interactions are presented, including tuning curves f...

/pdf/improved-dispersion-relations-for-gaas-and-applications-to-16kp258zqj.pdf

Improved dispersion relations for GaAs and applications to nonlinear optics

The refractive indices of AlxGa1−xAs epitaxial layers (0.176⩽x⩽1) are accurately determined below the band gap to wavelengths, λ<3 μm. The layers are grown on GaAs substrates by molecular beam epitaxy metal organic and chemical vapor deposition with thicknesses ranging from 4 to 10 μm. They form improper waveguide structures with the GaAs substrate. The measurements are based on the excitation of the improper waveguide modes with grating couplers at 23 °C. The refractive indices of the layers are derived from the modal propagation constants in the range of 730 nm<λ<830 nm with an estimated uncertainty of Δn=5×10−4. The temperature coefficient of the refractive index is investigated in the same spectral range. From the effective indices of the TE and TM modes, we derive the strain-induced birefringence and the elasto-optic coefficients. High-resolution x-ray diffraction is used to determine the strain of the layers. The layer compositions are obtained with inductively coupled plasma atomic emission spectro...

The refractive index of AlxGa1−xAs below the band gap: Accurate determination and empirical modeling

We have studied InAs/GaSb superlattices ~SL’s ! grown with either InSb-like or GaAs-like interfaces ~IF’s ! on top of a GaSb buffer layer on ~100! GaAs substrates. The InAs layer thickness was varied from 4 to 14 monolayers ~ML! while the GaSb layer thickness was kept fixed at 10 ML. The type of IF bonds realized was verified by Raman scattering from mechanical IF modes. High-resolution x-ray diffraction using one- and two-dimensional mapping of symmetric and asymmetric reflections allowed us to determine independently the lattice parameters parallel and perpendicular to the growth direction. The GaSb buffer layer was found to be fully relaxed whereas the SL’s with InSb-like IF’s were coherently strained to the in-plane lattice parameter of the GaSb buffer for InAs layer thicknesses exceeding 6 ML. The strain distribution within the SL’s with GaAs-like IF’s was obtained from simulations of the x-ray reflection profiles. The SL’s were found to be coherently strained close to the GaSb buffer and showed increasing strain relaxation with increasing distance from the buffer layer. In addition, these simulations provide an accurate determination of the SL periods. Well-resolved Raman spectra of backfolded longitudinal acoustic ~LA! phonons were observed showing for SL’s with InSb-like IF’s folded LA phonon lines up to the seventh order. The spectrum of quasiconfined optical SL phonons was examined by Raman spectroscopy and by IR reflection. A detailed analysis of the IR reflection spectra allowed an independent determination of the individual layer widths within the SL stack, including the spatial extent of the GaAs-like IF mode. @S0163-1829~96!06820-8#

Effect of interfacial bonding on the structural and vibrational properties of InAs/GaSb superlattices

Vibrational modes introduced by the incorporation of N into GaAs and GaInAs have been studied by Raman spectroscopy on samples grown by molecular-beam epitaxy using a rf nitrogen plasma source. When proceeding from GaAs1−xNx to Ga1−yInyAs1−xNx with x⩽0.04 and y⩽0.12, the nitrogen-induced vibrational mode near 470 cm−1 observed in GaAsN was found to broaden and to split into up to three components with one component at a frequency higher than that of the Ga–N mode in GaAsN. This observation shows that the incorporation of In into GaAsN strongly affects the local bonding of the N atoms by changing the local strain distributions as well as the formation of a significant fraction of In–N bonds. The resonant enhancement in the scattering cross section of the Ga–N vibrational mode, observed in low N-content GaAs1−xNx (x≈0.01) for incident photon energies matching the mostly N-related E+ transition at around 1.8 eV, was found to broaden significantly upon increasing N content as well as upon the addition of In t...

N-induced vibrational modes in GaAsN and GaInAsN studied by resonant Raman scattering

Optical and structural investigations of intermixing reactions at the interfaces of InAs/AlSb and InAs/GaSb quantum wells grown by molecular-beam epitaxy

Near infrared Brillouin scattering and high resolution x-ray diffraction is used for a precise determination of the elastic constants and the relaxed lattice parameters of ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ epitaxial layers $(0.1l~xl~1.0).$ The composition of the layers is specified by inductively coupled plasma atomic emission spectroscopy, photoluminescence, and Raman spectroscopy. For the elastic constants we get a composition independent value of $118.9\ifmmode\pm\else\textpm\fi{}0.7 \mathrm{GPa}$ for ${\mathrm{C}}_{11},$ a nonlinear increase in ${\mathrm{C}}_{12}$ and a linear decrease in ${\mathrm{C}}_{44}$ with increasing Al composition. The Poisson ratio shows a linear increase for $xl0.8$ and a downward bowing for higher Al concentrations to the AlAs value of $\ensuremath{\nu}=0.325\ifmmode\pm\else\textpm\fi{}0.004.$ The effect of lattice mismatch induced strain on the elastic properties is investigated on free standing epitaxial layers. The trend in ionicity from the GaAs to the AlAs bonds are deduced from phenomenological expressions for the bond-bending and bond-stretching forces which are calculated from the elastic constants. The lattice parameters of the unstrained crystals are obtained from the measured full metric of the tetragonally strained layers and the Poisson ratios. The combined results of Brillouin scattering, x-ray diffraction, and compositional analysis confirm the deviation of the ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ lattice parameter from Vegard's law, and provides the first direct and accurate determination of the quadratic bowing parameter.

N. Herres

Papers

The refractive index of AlxGa1−xAs below the band gap: Accurate determination and empirical modeling

Effect of interfacial bonding on the structural and vibrational properties of InAs/GaSb superlattices

N-induced vibrational modes in GaAsN and GaInAsN studied by resonant Raman scattering

Optical and structural investigations of intermixing reactions at the interfaces of InAs/AlSb and InAs/GaSb quantum wells grown by molecular-beam epitaxy

Compositional dependence of the elastic constants and the lattice parameter of Al x Ga 1-x As