The determination of rigid lattice shifts across delta-doped layers using regressional analysis

We present a simplified approach for determining the rigid lattice shift across an interlayer from a high-resolution lattice image. The approach is illustrated through the analysis of delta-doped layers in Si and GaAs, for which the lattice shifts are measured to accuracies of better than ±7 pm. The results are compared with the predictions of continuum elasticity theory, and some surprising discrepancies are noted. In particular, for Si delta-doping in GaAs the measured lattice contractions do not follow the predicted linear increase with dopant concentration and are much larger than the theory would predict.