X-ray double-crystal rocking curves in GaAlAs/GaAs heterostructures

Abstract

ricevuto il 9 Marzo 89; manoscritto revisionato ricevuto il 16 Aprile 1990)Summary. --X-ray double-crystal rocking curves of Gal_~AI~As/GaAs heterostructures have been calculated using a dynamical diffraction model for the general case of Bragg reflection geometry. Different experimental configurations have been considered and the possibility of studying both slightly mismatched and relatively thin layers has been investigated. Experimental rocking curves have been measured using the Cu Kal radiation, the 004 symmetric reflection and a perfect crystal as the monochromator. An excellent agreement between calculated and experimental rocking curves has been found and this demonstrates the reliability of both the experimental procedure and the theoretical approach.PACS 61.55 -Specific structures ef elements and alloys. -Introduction.The X-ray double-crystal diffractometry (DCD) provides a rapid and nondestructive means of assessing hetero-epitaxial structures. A great deal of information is contained in the DCD rocking curves. The lattice mismatch Aa/a between epflayers and substrate can be obtained from the angular spacing of the Bragg peaks; since angular differences as low as a few tens of seconds of arc can be revealed, Aa/a values of the order of a few 10 -4 or less can be easily evaluated. The elastic tetragonal distortion of the unit cell of the epilayers is usually determined by a suitable choice of the experimental geometry. The shape of the Bragg peaks is related to the crystal perfection. More specifically, the full width at half-maximum (FWHM) of the Bragg peak is related to the crystal quality of the sample investigated." Finally, DCD rocking curves allow to measure the epilayer thickness.A quantitative analysis of the DCD rocking curves needs a reliable theoretical model and computation programs. In this paper a theoretical approach similar to that reported elsewhere [i, 2] has been used. This approach provides two main advantages: i) it is quite general, since it comes from the dynamical X-ray diffraction theory of distorted crystals; ii) it does not require long computation times, owing to the fact that an analytical solution of the basic differential equations is used. The theoretical model has been applied to Gal_~Al~As/GaAs heterostructures. The 1 -Il Nuovo Cime~o D 1

Growth and optical characterization of indirect-gap AlxGa1−xAs alloys

“…From the K ␣ ͑Cu͒ line ͑400͒ Bragg diffraction rocking curves, the aluminum content was obtained by measuring the angle difference ⌬ between the GaAs and Al x Ga 1Ϫx As peaks, and using the relation ⌬ϭ367Љx. 26 The average DCD rocking curve full width at half maximum ͑FWHM͒ of the Al x Ga 1Ϫx As layers was 30Љ. The angular accuracy in the experiment was 2Љ which guarantees an error below 0.5% in the aluminum content determination.…”

X-Ray double crystal rocking curves of Ga1−x Al x As/GaAs laser structures

“…The theoretical approach used here, based on the Takagi-Taupin equation, is similar to that proposed by Halliwell and coworkers [7] and has been discussed in detail elsewhere [8].…”