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

TL;DR

This paper investigates how dielectric mismatch affects electron-impurity binding energies in GaN/HfO2 quantum wells, considering all energy contributions and comparing with GaN/AlN systems across different well widths.

Contribution

It presents a comprehensive theoretical model that accounts for dielectric mismatch effects on electron-impurity binding energies in GaN/HfO2 quantum wells, including all relevant energy interactions.

Findings

Binding energy depends on impurity position within the well.

Large dielectric constant in HfO2 significantly influences binding energies.

Comparison shows differences between GaN/HfO2 and GaN/AlN systems.

Abstract

In this work we investigate electron-impurity binding energy in GaN/HfO$_2$ 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 Schr\"odinger 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/HfO$_2$ with those of a more typical GaN/AlN system, for two different confinement regimes: narrow and wide quantum wells.