Critical Evaluation of Various Spontaneous Polarization Models and Induced Electric Fields in III-Nitride Multi-Quantum Wells

Abstract

In this paper, ab initio calculations are used to determine polarization difference in zinc blende (ZB), hexagonal (H) and wurtzite (WZ) AlN-GaN and GaN-InN superlattices. It is shown that a polarization difference exists between WZ nitride compounds, while for H and ZB lattices the results are consistent with zero polarization difference. It is therefore proven that the difference in Berry phase spontaneous polarization for bulk nitrides (AlN, GaN and InN) obtained by Bernardini et al. and Dreyer et al. was not caused by the different reference phase. These models provided absolute values of the polarization that differed by more than one order of magnitude for the same material, but they provided similar polarization differences between binary compounds, which agree also with our ab initio calculations. In multi-quantum wells (MQWs), the electric fields are generated by the well-barrier polarization difference; hence, the calculated electric fields are similar for the three models, both for GaN/AlN and InN/GaN structures. Including piezoelectric effect, which can account for 50% of the total polarization difference, these theoretical data are in satisfactory agreement with photoluminescence measurements in GaN/AlN MQWs. Therefore, the three models considered above are equivalent in the treatment of III-nitride MQWs and can be equally used for the description of the electric properties of active layers in nitride-based optoelectronic devices.

Polarization Doping in a GaN-InN System—Ab Initio Simulation

“…Again, we expect that this contribution may affect the obtained electric field jump at this interface. Therefore, the deviation in polarization difference obtained here and reported in the previous publications may be attributed to these factors [ 13 , 14 , 46 ].…”

“…Ref. [ 14 ] provides similar dependence on the lattice parameters but the values are systematically lower for to for [ 14 , 46 ]. These values are slightly smaller than those obtained in the present simulations.…”

“…The polarization change should give a bulk charge density , which is related to the electrical potential in accordance with Poisson equation: where is the static dielectric constant of the semiconductor and dielectric permittivity. The dielectric constants of InN and GaN are different therefore, the Vegard law is used for graded region , where and [ 46 ]. Using this approximation, the variation of the dielectric constant along z coordinate in the graded region can be represented as , where these parameters are: …”

“…Thus these values can be used to calculate the InN-GaN polarization difference as: (a) and (b) . The critical evaluation of the polarization difference was given in [ 46 ]. The obtained polarization difference was calculated using the piezoelectric constants from [ 13 , 14 ].…”

“…Invoking the mechanical stability rule , the polarization difference may be obtained as a function of a lattice parameter. The data collected in [ 46 ] indicate that the polarization difference obtained in [ 13 ] changes from for to for [ 13 , 46 ]. Ref.…”