Kinematical x‐ray diffraction in nonuniform crystalline films: Strain and damage distributions in ion‐implanted garnets

摘要

A kinematical model for general Bragg case x‐ray diffraction in nonuniform films is presented. The model incorporates depth‐dependent strain and spherically symmetric Gaussian distribution of randomly displaced atoms. The model is applicable to ion‐implanted, diffused, and other single crystals. Layer thickness is arbitrary, provided maximum reflecting power is less than ∼6. Strain and random displacement (damage) distributions in He+‐implanted Gd, Tm, Ga:YIG, and Ne+‐implanted Gd3Ga5O12are obtained by fitting the model to experimental rocking curves. In the former crystal the layer thickness was 0.89 mgr;m with strain varying between 0.09 and 0.91. In the latter crystal a wide range of strain and damage was obtained using successively higher doses. In each case layer thickness was 1900 A˚, with 2.49 strain corresponding to 0.40‐A˚ standard deviation of random displacements. The strain distributions were strictly linear with dose. The same, closely linear relationship between damage and implantation‐induced strain was determined for both crystals.