Electronic structure of thin heterocrystalline superlattices in SiC and AlN M. S. Miao and Walter R. L. Lambrecht Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106-7079, USA ~Received 18 June 2003; published 21 October 2003! The spontaneous polarization, the valence band offset, and the quantum confinement effect for thin SiC and AlN cubic/hexagonal heterocrystalline superlattices are studied by use of a full potential linear muffin-tin orbital method ~FP-LMTO!. We find that the polarization is screened and suppressed while the length of the cubic region grows. The band offsets do not change with layer thickness. For thin superlattices, the quantum confinement effects dominate and result in a band gap which stays larger than the gap of the bulk cubic structure. Furthermore, the energy levels of the bound states in the quantum well resemble the pattern of the energy levels of conventional III-V based quantum wells and superlattices but at a much smaller length scale, which is due to the higher quantum well depth and the larger effective masses in SiC and AlN systems. DOI: 10.1103/PhysRevB.68.155320 PACS number~s!: 73.21.Cd, 71.20.Nr One of the pronounced features of SiC is the systematic variation of the band gap with polytype. This feature led Bechstedt et al. 1 to propose heterocrystalline superlattices ~HCSL!. Surprisingly, they found that these heterocrystalline structures had band gaps smaller than bulk 3C. It was ex- plained as a consequence of their type-II band-offset charac- ter and the appearance of a linear contribution to the electro- static potential caused by the charge localized at the interface 2 between materials with and without spontaneous polarization. Recently, 4H/3C and 6H/3C quantum wells have been grown successfully by molecular beam epitaxy ~MBE!. 3,4 The photoluminescence measurements exhibit fea- tures consistent with a gap smaller than that of bulk 3C. A rough estimation based on a triangular quantum well due the spontaneous polarization appears to explain these observations. 4 However, PL features below the band gap may also be related to defect bound excitons. Similar studies have also been performed for AlN and SiC HCSL using LMTO within the atomic sphere approximation ~ASA!. 2 ASA results support that the superlattice band gap could be smaller than 3C but according to our own experience may overestimate the spontaneous polarization effect. Another motivation for studying the heterocrystalline structures stems from the recent observations of stacking fault ~SF! growth in 4H SiC diodes under forward bias 5,6 and in annealed heavily n-type doped epilayers. 7–9 The growth of the double stacking faults ~DSF’s! can result a six-layers cu- bic inclusion in 4H SiC. The localized electron states near the conduction band minimum can trap electrons and can cause a driving force toward increasing the SF area in n-type SiC. 10 The electronic structures of double and triple SF have been calculated and the gaps obtained are all larger than those in pure 3C. 11–13 As shown in Fig. 1, the gap of the 3C/2H HCSL is deter- mined by ~1! the quantum confinement effect of the electron states caused by the conduction band offset ~CBO!, ~2! the occurrence of a linear contribution to the potential caused by the accumulation of the charges at the interfaces between materials with different spontaneous polarization, and ~3! the type band offsets of the valence bands. If the VBO is of type II, and the spontaneous polarization effect latter is promi- nent, the band gap of the superlattice could become smaller than that of the bulk phase with the smaller band gap. Oth- erwise, if the confinement effect dominates, the gap will be larger than that of 3C. On the other hand, it is interesting to see how the properties of the SL changes with the layer thickness. In this paper, we define the SL size based on the layer type and perform a series of calculations with growing number of cubic inclusion layers. The changes of the quan- tum confinement, the polarization effect, and the VBO versus the layer thickness will be carefully analyzed. This is crucial to resolve the conflicting results on the band gaps. We choose here the simplest case of the 3C/2H SL because it maximizes both the spontaneous polarization and the VBO effects. If no gaps smaller than 3C occur in this case, they can safely be ruled out also in the 3C/4H and 3C/6H cases. In Refs. 1 and 2, the heterocrystalline structures are formed by attaching a few 3C units consisting each of three cubic layers with a 4H, 6H, or 2H region in such a way that the resulting cell is always hexagonal and such that the total size of the system is fixed. Inclusions of six, seven, or eight cubic layers are obtained in this manner depending on whether the hexagonal region is 2H, 4H, or 6H. In the stack- ing fault studies, the inclusion of cubic layers is defined by glide induced SF’s. 10–13 The systems with one, two, or three SF’s contain two, five, or six continuous cubic layers. In this paper, we define the HCSL by the number of continuous cubic and hexagonal layers. We calculated a series of HCSL’s with an inclusion of one to twelve cubic layers in a FIG. 1. The lineups of the VBM’s and CBM’s in the 3C and 2H regions of HCSL. The final band gap and the three major effects are denoted. PHYSICAL REVIEW B 68, 155320 ~2003! 0163-1829/2003/68~15!/155320~5!/$20.00 ©2003 The American Physical Society 68 155320-1