Dielectric mismatch and shallow donor impurities in GaN/HfO2 quantum wells

In this work we investigate electron–impurity binding energy in GaN/HfO2 quantum wells. The calculation considers simultaneously all energy contributions caused by the dielectric mismatch: (i) image self-energy (i.e., interaction between electron and its image charge), (ii) the direct Coulomb interaction between the electron–impurity and (iii) the interactions among electron and impurity image charges. The theoretical model account for the solution of the time-dependent Schrödinger equation and the results shows how the magnitude of the electron–impurity binding energy depends on the position of impurity in the well-barrier system. The role of the large dielectric constant in the barrier region is exposed with the comparison of the results for GaN/HfO2 with those of a more typical GaN/AlN system, for two different confinement regimes: narrow and wide quantum wells.