A double crystal x-ray diffraction characterization of Al<i>x</i>Ga1−<i>x</i>As grown on an offcut GaAs(100) substrate

Abstract

Important corrections are required for x-ray diffraction characterization of epitaxial AlxGa1−xAs grown on offcut GaAs substrates. These corrections can have technological impacts for thin film fabrication where precise and reproducible process control is required. Double crystal x-ray diffraction measurements of AlxGa1−xAs grown on an offcut GaAs(100) substrate are interpreted in terms of a three step distortion of the film unit cell producing ‘‘defect free’’ heteroepitaxy: the film unit cell is first tetragonally, then triclinicly distorted, and finally tilted with respect to the substrate unit cell. The results indicate that the unit cell distortion and tilt angles oppose each other, forming a crystal geometry where the vector normals of the film and substrate (100) planes are approximately coplanar with the vector normal of the substrate’s surface. The film unit cell is triclinicly distorted in a way such that the film 〈100〉 axis remains approximately parallel to the substrate 〈100〉 axis. Application of conventional x-ray diffraction formalism based on a tetragonal distortion of the film unit cell to this more complicated unit cell geometry, can result in significant errors. Double crystal x-ray diffraction formalism is presented which accounts for a triclinic distortion and external tilt of the AlxGa1−xAs unit cell, leading to correct measurement of the film concentration and film/substrate crystal geometry.