Study of residual strains in wafer crystals by means of lattice tilt mapping

A high-resolution X-ray diffractometer equipped with an accurate X-Y translation stage has been used to obtain Bragg angle maps of large-area crystal wafers. It is found that the Bragg angle shifts observed by this method in conventional reflection geometries are mainly due to the local lattice tilts rather than to the lattice parameter changes. The formula to calculate from the lattice tilt maps the displacement of the crystal lattice sites with respect to the ideal unperturbed lattice is obtained. It is shown that such lattice displacement is quantitatively correlated to the wafer dislocation density and to the distribution of the Burgers vectors of the dislocations in the crystal. Semi-insulating Czochraslki-grown GaAs wafers with dislocation densities ranging from 10(4) to 10(5)cm(-2) have been analysed by this technique and by double-crystal X-ray topography. From the lattice tilt maps the dislocation density evaluated appeared similar to those determined by topography and etch pit density in this material. It is concluded that the majority of dislocations in the wafer have the same Burgers-vector component along the (100) growth axis. Finally the method is proposed as a new tool for characterizing large-area wafer crystals.