RELAXATIONS AT GAN(1010) AND (110) SURFACES

Alessio Filippetti, Manuela Menchi and Andrea Bosin

INFM and Dipartimento di Scienze Fisiche, Universitd di Cagliari, Italy

Giancarlo Cappellini

INFM and Istituto di Fisica, Facolta di Medicina e Chirurgia, Universitd di Cagliari,Cagliari, Italy

ABSTRACT

We present an ab-initio calculation of GaN wurtzite (1010) and zinc-blende (110) surfacestructures and formation energies. Our method employs ultrasoft pseudopotentials andplane-wave basis. These features enable us to obtain accurate results using small energycut-off and large supercells. The (110) surface shows a Ga-N surface dimer rotation of- 140, i.e. about one half that of the ordinary III-V non-nitride compounds, and a 5%contraction of the surface bond-length (more than the double that occurring in GaAs). Forthe (1010) surface, a layer rotation angle of about 110 and a bond-length contraction of6% has been found. Zinc-blende GaAs (110) and wurtzite ZnO (1010) surfaces have beenstudied as well, for the sake of comparison. GaAs results are in good agreement with theexperimental findings. For ZnO a large bond contraction and a rotation angle of around11% result. Thus, our findings place GaN closer in behaviour to the highly ionic 1I-VIcompounds than to the non-nitride III-V semiconductors.

Introduction

A great effort is devoted today to the study of gallium nitride (GaN) properties, due to itslarge range of applications in the field of high-temperature electronics and near-ultravioletelectro-optics[l]. GaN is a wide band-gap semiconductor crystallizing at room environmentin the wurtzite structure. At room temperature it shows a direct band gap of 3.4 eV.Although the natural structure is wurtzite, GaN thin films having zinc-blende structurehave been epitaxially grown on various substrates[2]. For this reasons, detailed studies ofGaN surfaces in both wurtzite and zinc-blende structures are now whortwhile. In this paperwe report results concerning the structure of non-polar (1010) wurtzite and (110) zinc-blendsurfaces and their formation energies. Their relaxations, as well as that of all II-VI andIII-V compounds, are characterized by the contraction and the rotation (with respect tothe surface plane) of the anion-cation planar bonds. The chemical picture of what happensat surface, at least for the non-nitride compounds, is well understood[3]. The symmetrybreaking due to the surface formation causes a partial broken bond dehybridization. Incase of GaAs (one of the best known III-V semiconductors) the (110) surface atoms presenta dehybridized dangling bond (mainly s-like for As and surface normal p-like for Ga) andrehybridized backbonds (sp9-like for Ga and p-like for As). To this end a dimer rotation(with As moving outwards and Ga inwards with respect to the substrate) is needed. Itgives rise to an angle between the ideal surface plane and the plane formed by the surfacedimer chains (tilt angle). For GaAs the tilt angle is quite large (around 300). Also a(small for GaAs) charge transfer from the cation to the anion and a resulting contraction of

953

Mat. Res. Soc. Symp. Proc. Vol. 449 01997 Materials Research Society

GaN(110) GaAs(l10)This work ref.[4] This work ref.[4] exp.

0 14.30 2.060 30.10 24.30 31.10W 7.30 1.000 16.50 13.40 16.70

BC 4.9 6.5 0.9 1.3 2

Table I: Layer rotation angle (0), bond rotation angle (w) and bond contraction (BC) in percentage of itsideal value for the zinc-blende (110) GaN and GaAs surfaces

bond length occurs. GaAs can be considered as prototype of sp3-coordinated weakly ionicsemiconductor, while ZnO is generally taken as an example of highly ionic structure. Itsstrong ionicity causes the surface dimers to have a smaller rotation and a considerably largercontraction. Thus, the surface relaxations can be understood as a competition betweenionicity (leading to large contraction and small bond rotation) and dehybridization forces(causing strong rotations and weak contractions). It seems clear that surface relaxationsfaithfully reflect the ionicity degree of the structure. Then, our calculations will addressto the question of how GaN can be placed into this ionicity trend. To our knowledge,only one previous theoretical calculation[4] (performed within a quite different method)about GaN (110) surface is present in the literature, whereas two calculations about GaN(1010) surface have been reported[4, 5]. At present, no experimental results exist for GaNsurfaces. For the sake of completeness, we also determined formation energies and relaxedstructures of GaAs (110) and ZnO (1010) surfaces. In particular, for the latter, theoreticaland experimental results are not as reliable as for the former, therefore a further accuratecalculation seemed to be needed for ZnO (1010). Our ab-initio calculations are performedby means of plane-wave basis and ultrasoft (Vanderbilt)[6] pseudopotentials. Ultrasoftpseudopotentials, a key tool of our calculations, allow to employ a very reasonable cut-offenergy (25 Ryd), overcoming the well known difficulties related to the strongly localizednature of nitrogen p electrons. For both Ga and Zn, 3d electrons are taken into accountas valence states. The theoretically determinated bulk structure parameters result in closeagreement with experiments and have been reported elsewhere[7]. Large size cells (8 atomiclayers for wurtzite and 9 for zinc-blende surfaces) have been used. Relaxations have beenperformed by allowing all slab layers to relax within a force threshold of 1 mRyd/a.u., k-point grids have been downfolded by bulk sets to allow an accurate evaluation of formationenergies. The paper is organized as follows. We show in section I results for (110) surfacerelaxations, in section II the relaxations related to the (1010) surfaces, and in section IIIthe surface formation energies of all the investigated compounds.

I) Structure of Zinc-Blende GaN(llO) Surface

The (110) surface relaxations are characterized by a rotation of the planes formed bythe [1T0]-oriented atomic chains with respect to the surface plane (see Fig.i). Also, acontraction of the dimer bond length occurs. We call layer rotation angle (0) the angle

954

formed by the (110) plane and the chain plane, and bond rotation angle (W) that one betweenthe (110) plane and the line connecting surface first neighbours. The bond contraction (BC)corresponds to the first neighbour distance change, in percentage of its ideal value. In TableI we show our calculated values of 0, w and BC for GaN (in comparison with that obtainedby Jaffe et al.[4]) and GaAs (compared with ref.[4] and LEED experiments). Our results,on some extent, confirm the anomalous behavior of GaN with respect to GaAs and to the

N

Z

•X

Figure 1: Side view of zinc-blende GaN (110) relaxed surface.

AX AZAi -0.04 0.05C, 0.17 -0.18A2 -0.05 0.0

rc21-0.03 0.07

Table II: Displacements of first layer (A1 and Cj) and second layer (A2 and C2) atoms from their idealpositions (in A) for the zinc-blende GaN (110) surface. A and C indicate anion and cation, respectively.

other III-V non-nitride compounds (rotation angles of GaN are near half that one of GaAsand the bond contraction is strongly increased), although our values are far away from thatof ref.[4] (obtained by means of an Hartree-Fock method). We believe such a discrepancycan be ascribed to the approximations (small size cells and top-layer only relaxations) usedin the calculations presented in ref.[4]. On the other hand we tested our scheme in thecase of GaAs obtaining very good agreement between our results and experiments. Thus,GaN shows the characteristic of an highly ionic compound, with relaxations similar to thattypical of II-VI semicondutors. This features will be better appreciated in next section,where we compare results for the wurtzite (1010) surface of GaN and ZnO. Anyway, if for

955

GaAs the driving force to relaxation is the surface bond dehybridization, for GaN one hasto consider the role of ionicity also. Our preliminary results about the other III-V nitrides(i.e. AIN and InN) suggest that this is a common feature of all the nitride compounds.

In Table 11 the atomic displacements (in A) with respect to the ideal positions arereported for the first two layer atoms. (see also Fig. 1). As expected, the anion goes up, butthe largest displacement is that of the first layer cation, moving deeply inside the surface.Also, surface anions and cations come one to the other along x.

II)Structure of Wurtzite GaN(1010) Surface

As pointed out before, the wurtzite structure is the natural phase in which GaN crys-tallizes. The (1010) surface relaxations consist on a contraction and rotation of the [0001]-oriented first-neighbour bonds at surface. In Table III we report our results for BC and W(in such a case coincident with 0) of (1010) GaN and ZnO surfaces compared to that ofother theoretical and experimental works.

GaN(101O) ZnO((10-O)This work ref.[5] This work ref.[8] exp.

w 11.50 70 11.50 3.60 11.470 ± 50BC 6.0 6 6.0 8 -0.9

Table III: Bond rotation angle (w) and bond contraction (BC) in percentage of the(1010) GaN and ZnO surfaces.

ideal value for the

Table IV: Displacements of first layer (A 1 and Ci) and second layer (A2 and C2) atoms from their idealpositions (in A) for the wurtzite GaN and ZnO (10-0) surfaces. A and C indicate anion and cation,respectively.

956

GaN ZnOThis work ref. [5] This work

AX Az Ax Az AX AzA, 0.04 0.08 0.01 0.02 0.02 -0.13C, -0.15 -0.28 -0.11 -0.20 -0.14 -0.50A2 0.04 -0.02 0.05 0.05 -0.02 -0.09C2 0.05 0.15 0.05 0.05 0.03 -0.09

formed by the (110) plane and the chain plane, and bond rotation angle (W) that one between

the (110) plane and the line connecting surface first neighbours. The bond contraction (BC)corresponds to the first neighbour distance change, in percentage of its ideal value. In TableI we show our calculated values of 0, w and BC for GaN (in comparison with that obtainedby Jaffe et al.[4]) and GaAs (compared with ref.[4] and LEED experiments). Our results,on some extent, confirm the anomalous behavior of GaN with respect to GaAs and to the

N

Z

•X

Figure 1: Side view of zinc-blende GaN (110) relaxed surface.

AX AZA, -0.04 0.05C1 0.17 -0.18A2 -0.05 0.02ffC271 -0-03 7

Table II: Displacements of first layer (A1 and C1 ) and second layer (A2 and C2) atoms from their idealpositions (in A) for the zinc-blende GaN (110) surface. A and C indicate anion and cation, respectively.

other III-V non-nitride compounds (rotation angles of GaN are near half that one of GaAsand the bond contraction is strongly increased), although our values are far away from thatof ref.[4] (obtained by means of an Hartree-Fock method). We believe such a discrepancycan be ascribed to the approximations (small size cells and top-layer only relaxations) usedin the calculations presented in ref.[4]. On the other hand we tested our scheme in thecase of GaAs obtaining very good agreement between our results and experiments. Thus,GaN shows the characteristic of an highly ionic compound, with relaxations similar to thattypical of I1-VI semicondutors. This features will be better appreciated in next section,where we compare results for the wurtzite (1010) surface of GaN and ZnO. Anyway, if for

955

III) Surface Formation Energies

In table V formation energies of GaN and GaAs (110), and GaN and ZnO (10T0)surfaces are reported. a is the formation energy per atom (i.e. one half the two-atom unitcell formation energy), and refers to the fully relaxed surfaces, whereas Aa, is the relaxationenergy (i.e. the difference between relaxed and ideal surface energy). Our results for a' lookequal (to within one percent of eV) to previous calculations for GaN (1010)[5] and GaAs(110)[11]. Formation energies can be understood in terms of the energy needed to break

(110) (1010)GaN GaAs GaN ZnO

a 0.97 0.60 0.99 0.85Aa 0.22 0.34 0.39 0.37

E,0h/4 1.09 0.81 1.09 0.94

Table V: Surface formation energies (u), relaxation energies (Au) and bond cutting energy (i.e. 1/4 thecohesive energy). All results are in eV/atom.

a bond (and, in turn, in terms of cohesive energy). In Tab.V we also show, for all theconsidered compounds, the bond cutting energies. (i.e. 1/4 the cohesive energies). Thisare in fair agreement with a (within 0.1-,0.2 eV, a discrepancy noticeably smaller than thesurface relaxation energies), and delineates the same trend: the surface energy increaseswith the ionic character that clearly enhances the bond strength. Also, notice that, althoughthe GaN (110) and (1010) values of a are nearly the same, a quite larger relaxation energyis found for the latter.

Summary

We calculated structures and formation energies of GaN (1010) wurtzite and (110) zinc-blende surfaces. The resulting features pose GaN nearer to I1-VI compounds than to thenon-nitride Ill-V semiconductors. The relaxation mechanism comes out to be an interplaybetween hybridization and ionic forces.

Acknowledgement

We wish to thank Riccardo Valente for providing us with the parallel code. IBM-SP2computer time was provided by the Center for Advanced Studies, Research and Develop-ment in Sardinia (CRS4, Cagliari, Italy).

958

REFERENCES

1. S. Nakamura, T. Mukai, M. Senoh, Appl. Phys. Lett. 64, 1687 (1994)

2. Diamond, Silicon Carbide and Related Wide Bandgap Semiconductors, edited by J. T. Glass,R. Messier, and N. Fujimori, MRS Symposia Proceedings No. 162 ( Materials Research Society,Pittsburgh, Pa, 1990); M.J. Paisley, Z. Sitar, J.B. Posthill, and R.F. Davis, J. Vac. Sci.Technol. A. 7, 701 (1989); G. Martin, S. Strite, J. Thornton, and H. Morkoc, Appl. Phys.Lett. 58, 2375 (1991).

3. F. Bechstedt and R. Enderlein, Semiconductor Surfaces and Interfaces (Akademie-Verlag,Berlin, 1988)

4. J.E. Jaffe, R. Pandey, P. Zapol, Phys. Rev. B 53,4209 (1996)

5. J.E. Northrup, J. Neugebauer, Phys. Rev. B 53, 10477 (1996)

6. K. Laasonen, A. Pasquarello, R. Car, Changyol Lee, D. Vanderbilt, Phys. Rev. B 47, 10142(1993)

7. A. Satta, V. Fiorentini, A. Bosin, F. Meloni and D. Vanderbilt, Gallium Nitride and re-lated compounds MRS Proceedings Vol.395, R.D. Dupuis, J.A. Edmond, F. Ponce, and S.Nakamura, eds. (Material Research Society, Pittsburgh, PA, 1996), p.503

8. P. Schrder, P. Kriiger, J. Pollman, Phys. Rev. B 49, 17092 (1994)

9. J.E. Jaffe, N.M. Harrison, A.C. Hess, Phys. Rev.49, 11153 (1994)

10. C. B. Duke, R. J. Meyer, A. Paton and P. Mark, Phys. Rev. B 18, 4225 (1978)

11. G. X. Qian, R. M. Martin and D. J. Chadi, Phys. Rev. B 37, 1303 (1988); 38 7649 (1988).

959