Polytypism of GaAs, InP, InAs, and InSb: An ab initio study

More documents

Recommendations

Info

PANSE, KRIEGNER, AND BECHSTEDT PHYSICAL REVIEW B 84, 075217 (2011) TABLE III. Relative deviations of lattice constants from those of most stable 3C polytype (in percent). The deviations without (w/o) and with (w) inclusion of the finite cell-internal parameters from Table II are given separately. a/a c/c 2c pa / 2c pa w/o w w/o w w/o w GaAs 2H −0.30 −0.35 0.48 0.55 0.77 0.91 4H −0.17 −0.19 0.24 0.28 0.40 0.47 6H −0.13 – 0.14 – 0.26 – InP 2H −0.18 −0.21 0.30 0.36 0.48 0.57 4H −0.10 −0.11 0.14 0.17 0.24 0.28 6H −0.07 – 0.09 – 0.16 – InAs 2H −0.20 −0.23 0.35 0.42 0.55 0.65 4H −0.11 −0.13 0.16 0.20 0.27 0.33 6H −0.08 – 0.11 – 0.18 – InSb 2H −0.20 −0.25 0.38 0.47 0.58 0.73 4H −0.11 −0.13 0.17 0.22 0.28 0.35 6H −0.07 – 0.12 – 0.18 – C. Comparison with experiment Experimental data of the structural properties for hexagonal polytypes of bulk III-V compounds are generally not available. However, very recently lattice constants of the 2H and 4H phases of InAs and InSb 20 have been obtained from XRD in grazing incidence. Asymmetric reciprocal space maps have been recorded in order to obtain the lattice parameters of the 3C, 2H , and 4H polytypes independently. The nanowires were grown using chemical beam epitaxy (InAs) and metal-organic vapor phase epitaxy (InAs and InSb). The cubic reference values used in this study were a 0 = 6.058 Å (InAs) and a 0 = 6.478 Å (InSb) taken from Ref. 62. The experimental studies 20 yielded the relative changes a/a =−0.23%, c/c = 0.42% for 2H -InAs, a/a = −0.23%, c/c = 0.54% for 2H -InSb, a/a =−0.14%, c/c = 0.19% for 4H -InAs, and a/a =−0.14%,c/c= 0.28% for 4H -InSb. The signs and the absolute values are in excellent agreement with the computed deviations in Table III. This holds especially after inclusion of the atomic relaxation, which improves the agreement. Only for c/c of InSb the calculated results seem to slightly underestimate the measured ones. However, taking the inaccuracies of the computational approaches and uncertainties due to the nanowire measurements into account, we can state a excellent prediction of the atomic geometries of the hexagonal III-V polytypes by the DFT studies. Only the absolute distances have to be rescaled by the small deviations (
POLYTYPISM OF GaAs, InP, InAs, AND InSb: AN ... PHYSICAL REVIEW B 84, 075217 (2011) FIG. 4. (Color online) Influence of atomic relaxation on the relative lattice constant deviations from their ideal (i.e., 3C) values for InAs and InSb. Constant effective 2c/(pa) ratios are indicated by blue dotted lines, while black dotted lines represent constant volumes V pair per cation-anion pair for the 3C value and small deviations. Theoretical results (a) without and (b) with internal relaxation are connected by arrows. For comparison also the result (c) for one full optimization, i.e., a, c,andε are optimized independently, is shown for 2H -InAs. Experimental data (c/c, a/a) 20 are given by squares. and J 1 /J 2 as variables. In the interesting parameter region one multiphase degeneracy appears. For J 3 = 0 and J 1 =−2J 2 the phases of low hexagonality 3C, 6H , and 4H degenerate. The III-V compounds are far away from the phase boundary between 3C and 6H . Nevertheless, there are differences. While 3C-InSb is clearly most stable, the 3C polytype of InAs and InP are much closer to the phase boundary. Therefore, these compounds should show the strongest stacking fluctuations in the nanorods under equilibrium conditions. The comparison with the energy differences in Table I makes obvious that the energy differences between wurtzite and zinc-blende phases not only solely determine such a tendency. The phase diagram directly reflects the chemical trend with respect to the charge asymmetry coefficient g given in Table IV. As the ionicity (respectively, the charge asymmetry coefficient g and the covalent radii difference) increases the distance to the 3C-6H phase boundary decreases. In a simple picture one can explain this fact with an increasing intrinsic inhomogenity due to the bigger difference of the covalent radii, which makes easier the incorporation of stacking faults or twist of atomic layers. C. Stacking faults Further information can be extracted from the ANNNI model. Most important is the energetics of the formation of stacking faults in the zinc-blende polytype. 64 Since the normal stacking in the zinc-blende polytype is ABCABC... the intrinsic stacking fault (ISF) represents a removed bilayer from the infinite stacking sequence. It may result in a ABCA/CAB... stacking if a B layer is taken away. A possible formation process could be related to condensation of vacancies. Another process generating an ISF is a plastic glide caused by TABLE IV. Interaction parameters J i (in meV per cation-anion pair) of the ANNNI model (5). For comparison SiC values 64 are also given. To illustrate the chemical trend the charge asymmetry coefficients 57,65 g as a measure of the ionicity are given. g J 1 J 2 J 3 J 3 /J 2 J 1 /J 2 InSb 0.294 10.80 −0.38 −0.45 1.200 −28.8 GaAs 0.316 12.03 −0.58 −0.48 0.828 −20.9 InAs 0.450 9.85 −0.73 −0.30 0.414 −13.6 InP 0.506 5.68 −0.40 −0.38 0.938 −14.2 SiC 0.476 1.18 −2.34 −0.32 0.137 −0.5 FIG. 5. (Color online) Phase diagram for the polytypes within the ANNNI model. The 3C equilibrium structures are indicated by black dot (GaAs), blue square (InP), red triangle (InAs), and green diamond (InSb). For comparison the 4H equilibrium structure of SiC is indicated by an open circle. 075217-7
Page 1 and 2: PHYSICAL REVIEW B 84, 075217 (2011)
Page 3 and 4: POLYTYPISM OF GaAs, InP, InAs, AND
Page 5: POLYTYPISM OF GaAs, InP, InAs, AND
Page 9: POLYTYPISM OF GaAs, InP, InAs, AND

Polytypism of GaAs, InP, InAs, and InSb: An ab initio study

Create successful ePaper yourself

Delete template?

Save as template?