Two types of quantum-confinement characters for the bound states in the InGaN/GaN quantum wells

Abstract

The ( Ga 1 − x In x N ) Nw ( GaN ) Nb single and multiple quantum wells (SQWs and MQWs) are investigated theoretically using the sp 3 s ⁎ tight-binding (TB) method with inclusion of spin–orbit interaction. This study explores the effects of barrier thickness L b , well width L w , indium content x and valence-band offset (VBO) on the quantum confinement (QC) characteristics of the bound states in the well and on the electronic transitions. The calculations are based on the validity of two assumptions: the virtual crystal approximation (VCA) for the structure of the alloyed Ga 1 − x In x N wells, and the macroscopic theory of elasticity (MTE) for the structure of the computational supercell as a whole. The results demonstrate the following main trends: (1) the existence of two types of QC characteristics for the bound states in the GaInN alloyed wells. The nitrogen p-level ( E p N = 2.71 eV , which is associated with InN TB parametrization), displays a threshold/edge that divides the bound states into two types: (i) block-like localized states (in the energy range E p N < E < E g GaN , where E g GaN = 3.3 eV is the energy gap of zinc-blende GaN) and (ii) singlet-like localized states (in the energy range E g InN < E < E p N , where E g InN = 0.71 eV is the energy gap of zinc-blende InN). The confinement energy versus well width L w is found to follow an exponential rule in the former energy region and a power-law rule in the latter one. A stronger localization should be expected as the level becomes deeper in the quantum well. (2) The TB results of E g were compared with the available photoluminescence (PL) data of 1-ML and 2-ML thick SQWs. Taking into account the error bars due to the lattice relaxation and interface specific effects, the TB results provide evidence that the high-energy emissions ( E 0 1 W = 3.125 eV and E 0 2 W = 2.845 eV , for 1-ML- and 2-ML-thick wells, respectively) must have originated from wells with fractional filling (i.e., low indium contents). (3) The TB results predict that the indium content would rise as the well width increases. Unfortunately, overcoming this limitation of fractional monolayers is likely to remain beyond the capability of the currently existing growth techniques. The indium content being kept low is a natural authenticity which is the compromise to make in growing ultrathin GaInN/GaN quantum wells free of misfit dislocations.