Pseudopotential theory of dilute III–V nitrides

We review the empirical pseudopotential method and its recent applications to the III–V nitride alloys GaAsN, GaPN, GaInAsN and GaAsPN. We discuss how studies using this method have provided an explanation for many experimentally observed anomalous nitride phenomena, including sharp photoluminescence lines in dilute alloys, high effective masses, Stoke’s shift between emission and absorption in higher concentration alloys for GaAsN and GaPN ternaries. We also discuss predictions of unusual effects that remain to be experimentally discovered in GaInAsN quaternaries and complex GaAsPN solid solutions. 1. The unusual phenomenology of III–V nitrides Although the primary interest in anion-mixed III–V nitrides has been due to the large reduction in bandgap observed on addition of nitrogen, many other properties are now known to be different from conventional, non-nitride II–V alloys (InGaAs, GaAsP, etc). In the ultra-dilute regime (nitrogen concentration x < 0.01%) one observes: (i) Localized, single-impurity levels appear near the bandgap [1–5]. In conventional isovalent alloys such as GaAs:P or GaAs:In the ensuing perturbation potential VAs−VP orVGa−VIn is too weak to create a bound state in the gap. In contrast, absorption and photoluminescence excitation (PLE) of GaP:N and GaAs:N show the ‘Nx centre’ due to anion-substitutional isolated nitrogen. In GaP:N this level appears as in impurity-bound exciton at ECBM − 33 meV below the conduction band minimum (CBM) [1–4], whereas in GaAs:N it appears as a sharp resonance at ECBM + 180 meV [5–8] above the CBM. (ii) Anomalously small pressure dependence of single impurity states is observed. Shallow, effective-mass like impurity levels (GaAs:Zn or GaAs:Si) are constructed from the wavefunction of the single nearest host crystal state. Consequently, when pressure is applied, such impurity levels change their energy at the same rate as the energetically nearest host crystal state [9]. In contrast, the impurity levels in dilute GaP:N and GaAs:N have anomalously small pressure coefficients: in GaP:N the energy of the impurity-bound exciton is almost pressure independent [10, 11], whereas the X1c CBM of the GaP host crystal descends at a rate of −14 meV GPa−1. In GaAs:N, the nitrogen level moves with pressure to higher energies at a much slower rate (∼40 meV GPa−1 [7, 8]) than the 1c CBM of GaAs [12] (+110 meV GPa−1). Such small pressure coefficients are usually indicative of localization, whereby the wavefunction is constructed from many bands of the host crystal, rather than from the nearest host crystal state [13]. In the intermediate concentration regime (up to ∼1% nitrogen), one observes: (iii) Sharp photoluminescence (PL) lines appear due to impurity clusters. Even random substitution of impurities onto the atomic sites of a host crystal creates, by chance, impurity pairs and higher-order clusters. In conventional isovalent III–V alloys, such pairs give rise to broad resonances, within the valence and conduction continua [14–18], but no gap levels. In contrast, in GaPN and GaAsN, the N–N pairs form discrete levels inside the bandgap extending in GaP down toECBM−160 meV [4, 19–21] and in GaAs down to ECBM − 10 [8, 7, 22] or ECBM − 80 meV [23–25]. Such clusters do not appear to create deep levels in ordinary, non-nitride, alloys. (iv) Redshift between absorption/PLE and emission is observed. In high structural quality random, direct-gap III–V alloys, absorption and emission occur at the same energy. In contrast, already at a concentration of 0.05–0.1% nitrogen in GaAs, the emission lines are redshifted with respect to absorption [26]. At higher concentrations the shift increases in energy [27, 23]. 0268-1242/02/080851+09$30.00 © 2002 IOP Publishing Ltd Printed in the UK 851