X-ray double crystal characterisation of epitaxial layers

Double crystal x-ray diffractometry is a well established method for the measurement of the lattice parameter difference between expitaxial layers and substrates. The diffracted intensity profile versus angle, rocking curves, are highly sensitive to such variations giving rise to complex peak shapes. Consequently, computer simulation is required to enable complete interpretation of the measured data. A detailed description of a computer simulation technique suitable for calculating rocking curves from arbitary III-V structures, based on the Takagi-Taupin equations for dynamical diffraction from a non uniform crystal, is presented. Radiation from synchnotron and laboratory sources has been used to measure rocking curves from single uniform and single graded layers of (Ga,In)(As,P) on (001) InP substrates and artificial superlattices of both (Ga,AL)As on (001) GaAs and (Ga,In)As on (001) InP. Excellent agreement has been obtained between computed and experimental curves for all types of structure, enabling the layer thicknesses and compositions to be determined to within 0.1um and 10 ppm respectively. For single layers less than 0.5 um thick highly asymmetric reflections are shown to give greatly increased diffracted intensities from the layer, enabling more accurate interpretation. There will always be doubt as to the validity of the lattice parameter profile deduced for a graded layer from a single curve. Rocking curves at various wavelengths, using synchotron radiation, have been used to confirm the profile determined previously using a single measurement from a laboratory source. For superlattices, the dynamical theory approach permits satellite peaks, allowing the individual layer thicknesses and compositions to be determined in addition to repeat period. Further, this dynamical approach is particularly suitable for calculating the complete rocking curve where thick confining layers are present and is also directly applicable to multiple layers with varying layer thicknesses.