Figure 1: Homogeneous versus heterogeneous doping for lanthanum cuprate.

The crystal structures for two cases are schematically represented in a,b, respectively (the oxygen ions are omitted for clarity). In a, are randomly distributed as point defects, whereas in b they are ordered into a crystallographic plane forming a negatively charged layer. In both cases, in proximity of the defects, structural as well as compositional (that is, formation of compensating charge defects) modifications are expected. The resulting defect concentration profiles are depicted in c,d for the zero-dimensional and the two-dimensional doping case, respectively. The disordered spatial distribution of defects leads, in the first, to a homogeneous increase in hole () and oxygen vacancy concentration, and to a depressed negatively charged oxygen interstitial concentration with respect to the undoped material. In d, as a consequence of two-dimensional doping, the formation of a sharp hole accumulation layer with the space-charge layer is predicted.