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. (C) 1998 Elsevier Science B.V. All rights reserved.