Ab initio study of mg doped inn(0001) surface

Ab initio study of Mg doped InN(0001) surface Ab initio study of Mg doped InN(0001) surface A Belabbes, J Furthmüller, and F Bechstedt Citation AIP Advances 3, 012102 (2013); doi 10 1063/1 4774295 Vie[.]

Ab-initio study of Mg-doped InN(0001) surface A Belabbes, J Furthmüller, and F Bechstedt Citation: AIP Advances 3, 012102 (2013); doi: 10.1063/1.4774295 View online: http://dx.doi.org/10.1063/1.4774295 View Table of Contents: http://aip.scitation.org/toc/adv/3/1 Published by the American Institute of Physics AIP ADVANCES 3, 012102 (2013) Ab-initio study of Mg-doped InN(0001) surface A Belabbes,a J Furthmuller, and F Bechstedt ă Institut făur Festkăorpertheorie und -optik and European Theoretical Spectroscopy Facility (ETSF), Friedrich-Schiller-Universităat, Max-Wien-Platz 1, 07743 Jena, Germany (Received 26 September 2012; accepted 20 December 2012; published online January 2013) We study the incorporation of Mg atoms into the InN(0001) surface Energies and atomic geometries are described within density functional theory, while the electronic structure is investigated by an approximate quasiparticle method that yields a gap value of 0.7 eV for bulk InN The formation of substitutional Mg is energetically favored in the surface layer The surface electronic structure is less influenced by Mg-derived states The Fermi level is pinned by In-derived surface states With increasing depth of Mg beneath the surface the Fermi-level position moves toward the valence band top, suggesting formation of holes and, hence, p-doping of Mg in bulk-like layers Copyright 2013 Author(s) This article is distributed under a Creative Commons Attribution 3.0 Unported License [http://dx.doi.org/10.1063/1.4774295] Wurtzite InN has attracted much interest because of its potential application in optoelectronic, photovoltaic and electronic devices Its energy gap of only 0.7 eV1, is much smaller than that of other nitrides, AlN and GaN One precondition for the application of InN in devices is its p-doping Progress has been reported in achieving p-type InN using Mg as dopant.3, However, experimental techniques, capacitance voltage measurements, Hall measurements, thermopower measurements, photoluminescence, electron loss spectroscopy, and x-ray photoemission spectroscopy (XPS), have demonstrated different types of conductivity, n or p.3–8 It is obvious that the major obstacle to detect p-conductivity is the presence of n-type conductive layers due to surface accumulation of electrons.5, 7, Theoretical studies can contribute to a better understanding of the Mg acceptor in InN as has been recently demonstrated for bulk InN.9 Because of the possible n-accumulation7, surface studies of InN by means of first-principles methods are especially important.10, 11 However, electronic structure studies based on density functional theory (DFT) and a local or semilocal approximation to exchange and correlation (XC), e.g using the local density approximation (LDA), suffer from a substantial underestimation of the fundamental gaps because the quasiparticle (QP) excitation aspect is not included in the calculations.12 In the InN case the situation is more worse The DFT descriptions give rise to zero or negative gaps13 instead of the experimental value of 0.7 eV.1, Consequently, for the Mg-doped InN the Mg and N valence states can be erroneously mixed with conduction bands This induces a large energetic uncertainty, mainly due to the wrong position of the Fermi level with respect to conduction and valence band edges Even the shallow or deep nature of the Mg acceptor cannot be established Therefore, more sophisticated methods are needed to elucidate the electronic structure of Mg-doped InN surfaces Until now only empirical corrections of the applied pseudopotentials have been used to simulate a finite fundamental gap.14 Unfortunately, converged (QP) calculations12 are computationally too demanding for surfaces whose ab-initio investigations ask for modeling within the slab method where many atoms belong to the atomic basis of one supercell We have recently demonstrated that this problem can be circumvented by a somewhat simplified QP approach, the LDA-1/2 method.15 The LDA-1/2 method significantly improves the band gap of InN The resulting value of 0.71 eV is in good agreement a E-mail: abderrezak.belabbes@uni-jena.de 2158-3226/2013/3(1)/012102/6 3, 012102-1  C Author(s) 2013 012102-2 Belabbes, Furthmuller, and Bechstedt ă AIP Advances 3, 012102 (2013) with recent experiments.12 This gives an important energy window for possible dopant-induced gap states The success of this method has been recently shown for clean InN surfaces.16 In this letter we study the substitutional incorporation of Mg impurities on In sites in wurtzite (wz) InN surfaces by ground-state and excited-state calculations The In-terminated InN(0001) one is considered as a model surface Experiments,5, 7, indicate the formation of an n-accumulation layer and, hence, a Fermi-level pinning at the surface in agreement with ab-initio studies.16, 17 By contrast for non-polar surfaces, e.g the a-plane, no Fermi-level pinning has been observed, neither experimentally18 nor theoretically.16, 17 Moreover, the [0001] direction is the common growth direction Buried p-type conductivity has been recently confirmed on Mg-doped In-polar samples.3, 19–22 The parameter-free total-energy and force calculations are performed in the framework of the DFT within the LDA as implemented in the VIENNA AB-INITIO SIMULATION PACKAGE (VASP).23 The all-electron wave functions and the pseudopotentials for the electron-ion interaction are described within the projector-augmented wave (PAW)24 method, where for the XC potential the parametrization by Perdew and Zunger25 is used The semicore In4d electrons are treated as valence electrons The Kohn-Sham wave functions are expanded in plane waves up to an energy cutoff of 550 eV, which ensures the energy convergence within 1mRy per atom With these settings the lattice parameters of wz-InN have been computed to c = 5.685 Å, a = 3.517 Å, and u = 0.377, in good agreement with previous calculations and measurements (see, e.g Ref 26) In order to simulate the (0001) surface with two-dimensional translational symmetry we use the repeated slab method.27 We use slabs of six InN bilayers with a lateral (2 × 2) surface unit cell and a vacuum thickness corresponding to six bilayers (15 Å) Tests performed with more than 10 bilayers showed that the six-bilayer slabs give converged results The N-terminated bottom side of each slab is passivated by partially charged pseudohydrogen atoms with Z = 0.7528 to avoid spurious charge transfer from the back to the top surface of the slab The atoms in the top three bilayers are allowed to fully relax until the forces are smaller than meV/Å, while the remaining layers of the slab were kept fixed An ( × × 1) -centered Monkhorst-Pack mesh is applied for the Brillouin zone (BZ) integrations Eventually occurring electrostatic fields are compensated by a dipole correction.29 The Bader charges of atoms are calculated using the method of Henkelman et al.30 In order to investigate the effect of doping with Mg, we replace In atoms in different surface layers by Mg atoms at different sites to simulate locally the Mg-doped InN Experiments of Blan et al.31 suggested that Mg atoms occupy substitutional sites We study the replacement of In by Mg atoms The (2 × 2) lateral unit cell allows for additional degrees of freedom The successive replacement of the four In atoms in one layer by Mg simulates surfaces coverages of 0.25 to monolayer Since our test calculations showed only quantitative changes of bonding behavior and the electronic structure in agreement with other theoretical studies,10 we only present results for the replacement of one In atom by a Mg dopant For corresponding growth experiments that means that growth is achieved under Mg-poor conditions The partial pressure of Mg should be much lower than that of In Otherwise, under Mg-rich conditions the formation of Mg3 N2 precipitates may occur In fact, the growth of high-quality In-terminated (0001) surfaces in the presence of dilute Mg concentrations has been evidenced.3, 20 Consequently, we consider three different configurations with substitutional Mg impurities in the first, second, and third bilayer, respectively Such configurations are displayed in the insets of Fig Of course, many other configurations are conceivable This especially holds for the incorporation in the first bilayer where besides the substitution also exchange processes or Mg adsorption may happen.14, 16, 32 The total energies resulting for the three atomic arrangements with a single Mg impurity are plotted in Fig The energetics of the Mg incorporation in the InN(0001) surface indicates that the uppermost bilayer contains the most energetically favorable substitutional site The accompanying low formation energy is due to the formation of strong Mg–N bonds in the first bilayer The doped surface with (2 × 2) translational symmetry possesses a total of two paired electrons in the four surface dangling bonds which makes the doped system stable compared to the clean surface with three electrons in the In dangling bonds The total energy for Mg in the second bilayer is by about 0.4 eV higher in energy, while the energy further increases by 0.5 eV for Mg substitution in the third bilayer Formation energies of Mg in the first, second, and third layer are calculated to be 0.75, 1.15, and 1.68 eV, respectively They are computed including the difference of the chemical potentials of Belabbes, Furthmuller, and Bechstedt ă Relative total energy (eV) 012102-3 AIP Advances 3, 012102 (2013) 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 1st 2nd Incorporation layer 3rd FIG The total energy of the slab where an In atom is substituted by a Mg atom in one of the first three bilayers The energy of the Mg incorporation in the surface is used as energy zero The three atomic arrangements are also displayed Yellow (blue, red) dots indicate In (N, Mg) atoms Mg and In (μIn − μMg = 1.17 eV) The formation energies agree qualitatively well with previous theoretical results.11, 33 The stabilization of Mg incorporation in layers close to the surface can be also explained by arguments based on the electronegativity, the size of atoms as well as the electron-counting rule: (i) The substitutional Mg reduces the number of excess electrons in the clean In-terminated surface Mg only donates two electrons to the total amount of valence electrons, versus three electrons per In atom When Mg substitutes an In atom in the surface, according to the Bader analysis, the In ion charge amounts to +1.29 in average, i.e., is bigger than the value +1.08 of In in an undoped InN(0001) surface (ii) There is a strong correlation between In-N interlayer distances and the Mg position Because of the small size of Mg compared with the In atom, strong local geometrical relaxations occur The main effect is on the Mg-N bond lengths For Mg in the first bilayer we find a contraction of the first double layer spacing dIn-N In atoms show an inward relaxation, even stronger than that at the clean surface, and become almost coplanar with the nitrogens The calculated average value of the Mg-N bond length in the first bilayer is 2.23 Å, about 3% larger than the bulk In-N bond length, which is 2.16 Å On the contrary, the substitution of Mg in the third bilayer does not lead to a relevant variation of the Mg-N distance, which becomes as small as 2.16 Å, i.e., the In-N bond length Structurally, almost InN bulk-like behavior is observed for Mg incorporation into the third bilayer The preference of Mg incorporation in the first bilayer is due to the reduced number of valence electrons of Mg dopants Near to the surface, a Mg acceptor is negatively charged by about 1/4 of an electron in order to form the three bonds with the N neighbors The compensating fraction of electrons originates from the surface In atoms Away from the surface layer (at least in the third bilayer) the compensation mechanism is reduced It may cause the energy increase of Mg incorporation from the first bilayers to the deeper (bulk-like) layers Our results support the viewpoint of Song et al.11 that unoccupied (p-type) states of nitrogen around Mg are compensated by extra electrons (n-type) of an In surface as Mg approaches the surface This behavior is supported by Bader charge analysis of the N atoms surrounding the Mg atom in different layers The surface N atoms have an ion charge 1.62 compared with the value 1.50 for Mg in the third layer The different strengths of compensation seem to lead to two different types of carriers, p-type carriers dominate in central bulk-like layers while n-type carriers dominate in the surface region To get further insight in the site dependence, we examine the electronic band structure of Mg-doped InN surfaces Figure shows the LDA-1/2 band structures for the clean In-terminated 012102-4 Belabbes, Furthmuller, and Bechstedt ă AIP Advances 3, 012102 (2013) FIG Slab band structure of the Mg-doped InN(0001)(2 × 2) surface (b, c, d) together with that of the clean In-terminated one (a) The shaded regions indicate the projected bulk band structure, whose occupied top is used as energy zero The band structures are aligned using the plane-averaged electrostatic potentials The surface bands are indicated by red solid lines The theoretical Fermi level Ef is indicated by the blue horizontal line The right panels display the position of the substitutional Mg atom and the wave-function square of the lowest hole states 012102-5 Belabbes, Furthmuller, and Bechstedt ¨ AIP Advances 3, 012102 (2013) (0001) surface (a) and of those (b), (c), and (d) with a Mg incorporation in the first, second or third bilayer The shaded area represents the projected band structure of bulk InN, whereas the solid lines in the gap of the projected band structure represent bands of surface states Band energies for bulk and surface states are aligned with respect to the average electrostatic potentials of the bulk and of the slab calculations Most salient, the surface band structure in Fig 2(a) clearly shows Inderived dangling-bond bands in the projected fundamental gap These bands are partially occupied, giving rise to a metallic clean surface Because of the strong dispersion of surface bands and the bulk conduction band near the BZ center , the intrinsic Fermi level is pinned 0.82 eV above the conduction-band minimum (CBM) and, hence, 1.52 eV above the valence-band maximum (VBM) The pinning behavior is more clearly visible in the density of states (see also Refs 16 and 17) Qualitatively, the pinning position above the CBM remains valid also for thicker slabs as used here, although, it tends to move down somewhat in energy The pinning position is in near agreement with the branch-point energy calculated to be in the lowest bulk conduction band for wurzite InN.34 Our findings are consistent with the existence of an electron accumulation layer at the polar Interminated InN surfaces,7, 35 similar to that at the surface of other undoped In compounds, for example InAs and In2 O3 The value of the Fermi-level position at the In-terminated InN(0001) surface in Fig 2(a) also compares well with the experimental results of Mahboob et al.7, 35 using high-resolution electron-energy loss spectroscopy and valence-band x-ray photoemission spectroscopy The authors measured a Fermi level of 1.64 ± 0.10 eV above the VBM and 0.89 ± 0.10 eV above the CBM The Fermi-level pinning due to surface states with respect to VBM and CBM is modified as a function of the Mg dopant position in Figs 2(b)–2(d) However, contrary to our original intention, we find that substituting Mg for In in the surface or a subsurface layer [see the two QP band structures in Figs 2(b) and 2(c)] does not much affect the position of the Fermi level The reason is the almost identical dispersion of the In-derived surface bands along high-symmetry lines of the surface BZ, which is still similar to that in undoped InN The Mg perturbation mostly influences the band crossing regions A small fundamental gap is opened between In-dangling-bond-derived surface bands at the BZ boundary Still bulk-like conductions band states remain occupied with electrons The lowest occupied surface (bulk) band near ¯ is only slightly shifted downward (upward) from Fig 2(b) to 2(c) These results are in agreement with the compensation effect resulting in n-type surface carriers Conversely, the QP band structure in Fig 2(d) for Mg in the third, i.e., bulk-like (in a slab) bilayer shows a significant shift of the Fermi level with Mg incorporation toward the uppermost bulk valence bands It is accompanied by a similar displacement of the surface bands Thereby, the lowest part of the In-dangling bond-derived surface bands is occupied with two electrons and Ef is pinned at the VBM In the slab this level is formed by p-like orbitals located at the N atoms surrounding the Mg dopant but not by Mg orbitals The critical changes with the bilayer of the In substitution by Mg is also illustrated in the right panels in Fig 2, which display hole wave functions For Mg in the second bilayer the hole wave function is mainly localized at N atoms in the first bilayer (Fig 2(c)), while for the third bilayer Mg position the wave function is mainly related to p-orbitals localized at the three nearest-neighbor N atoms in the same bilayer (Fig 2(d)) The strong influence of the Mg substitutional site on the surface-state and Fermi-level positions is mainly of electrostatic nature The shift of the In-derived states together with the Fermi level by about 1.5 eV with respect to their position in the bare InN surface is due to a noticeable change in the density of states at the Fermi level, however without influencing the projected band gap itself Only the surface dipole is remarkably modified The substitution of a surface In atom by a Mg one only requires the transfer of a quarter of an electron to the Mg dopant In the case of the incorporation of Mg in the third bilayer a complete electron is attracted by Mg, in order to form bonds to the four N neighbors This electron should come from the surface In dangling bonds This tendency indicates that p-doping of InN in the bulk-like region is possible, it even seems that the n-accumulation layer can be modified or even avoided Indeed, after removal of the In adlayer the clean InN(0001) surface has been observed together with the absence of downward surface band bending due to Mg doping.36 This result is in agreement with observations of Kudrawiec et al.37 using photoreflectance to study the energy gap related to undoped and Mg-doped InN (0001) layers The observed Franz-Keldysh oscillations are not expected for n-type InN layers Also recent XPS studies38 confirm a reduction of the surface electron accumulation with increasing concentration of Mg atoms The reduction of the 012102-6 Belabbes, Furthmuller, and Bechstedt ă AIP Advances 3, 012102 (2013) electron concentration in the electron accumulation layer of the surface was also observed by Hall measurements.21, 22 Altogether, there are indications for carrier compensation in the surface region due to p-type doping beneath the surface In summary, we have shown by first-principles methods that the incorporation of Mg impurities at In sites in the InN(0001) surface is energetically favorable compared to bulk-like layers The effect on the surface states and the position of the surface Fermi level relative to these states is weak However, for incorporation of Mg atoms in bulk-like In-N bilayers the Fermi level and surface bands are shifted down toward the VBM Holes in acceptor states become possible We predict a compensation mechanism for the surface region that stabilizes the occurrence of p-type carriers in subsurface regions We acknowledge financial support by the EU ITN RAINBOW (grant No 2008-2133278) and the SFB 25 IR-ON of FFW (Austria) V Davydov, A Klochikhin, R Seisyan, V Emtsev, S Ivanov, F Bechstedt, J Furthmăuller, H Harima, A Mudryi, J Aderhold, O Semchinova, and J Graul, Phys Stat Sol B 229, R1 (2002) J Wu, W Walukiewicz, K M Yu, J W A III, E E Haller, H Lu, W J Schaff, Y Saito, and Y Nanishi, Appl Phys Lett 80, 3967 (2002) R E Jones, K M Yu, S X Li, W Walukiewicz, J W Ager, E E Haller, H Lu, and W J Schaff, Phys Rev Lett 96, 125505 (2006) K Wang, N Miller, R Iwamoto, T Yamaguchi, M A Mayer, T Araki, Y Nanishi, K M Yu, E E Haller, W Walukiewicz, and J W Ager, III, Appl Phys Lett 98, 042104 (2011) A Yoshikawa, X Wang, Y Ishitani, and A Uedono, Phys Stat Sol A 207, 1011 (2010) N Miller, J W Ager, III, H M Smith, III, M A Mayer, K M Yu, E E Haller, W Walukiewicz, W J Schaff, C Gallinat, G Koblmuller, and J S Speck, J Appl Phys 107, 113712 (2010) I Mahboob, T D Veal, C F McConville, H Lu, and W J Schaff, Phys Rev Lett 92, 036804 (2004) P D C King, T D Veal, C F McConville, F Fuchs, J Furthmuller, F Bechstedt, P Schley, R Goldhahn, J Schormann, D J As, K Lischka, D Muto, H Naoi, Y Nanishi, H Lu, and W J Schaff, Appl Phys Lett 91, 092101 (2007) J L Lyons, A Janotti, and C G Van de Walle, Phys Rev Lett 108, 156403 (2012) 10 A Belabbes, J Kioseoglou, P Komninou, G Evangelakis, M Ferhat, and T Karakostas, Appl Surf Sci 255, 8475 (2009) 11 J.-H Song, T Akiyama, and A J Freeman, Phys Rev Lett 101, 186801 (2008) 12 F Fuchs, J Furthmă uller, F Bechstedt, M Shishkin, and G Kresse, Phys Rev B 76, 115109 (2007) 13 F Bechstedt and J Furthmă uller, J Cryst Growth 246, 315 (2002) 14 T Akiyama, K Nakamura, T Ito, J.-H Song, and A J Freeman, Phys Rev B 80, 075316 (2009) 15 L G Ferreira, M Marques, and L K Teles, Phys Rev B 78, 125116 (2008) 16 A Belabbes, J Furthmă uller, and F Bechstedt, Phys Rev B 84, 205304 (2011) 17 D Segev and C G V de Walle, EPL (Europhysics Letters) 76, 305 (2006) 18 C.-L Wu, H.-M Lee, C.-T Kuo, C.-H Chen, and S Gwo, Phys Rev Lett 101, 106803 (2008) 19 P A Anderson, C H Swartz, D Carder, R J Reeves, S M Durbin, S Chandril, and T H Myers, Appl Phys Lett 89, 184104 (2006) 20 J W L Yim, R E Jones, K M Yu, J W Ager, W Walukiewicz, W J Schaff, and J Wu, Phys Rev B 76, 041303 (2007) 21 V Cimalla, M Niebelschă utz, G Ecke, V Lebedev, O Ambacher, M Himmerlich, S Krischok, J A Schaefer, H Lu, and W J Schaff, Phys Stat Sol (a) 203, 59 (2006) 22 X Wang, S.-B Che, Y Ishitani, and A Yoshikawa, App Phys Lett 91, 242111 (2007) 23 G Kresse and J Furthmă uller, Phys Rev B 54, 11169 (1996) 24 G Kresse and D Joubert, Phys Rev B 59, 1758 (1999) 25 J P Perdew and A Zunger, Phys Rev B 23, 5048 (1981) 26 J Furthmă uller, P H Hahn, F Fuchs, and F Bechstedt, Phys Rev B 72, 205106 (2005) 27 F Bechstedt, Principles of Surface Physics (Springer-Verlag, Berlin, 2003) 28 K Shiraishi, J Phys Soc Jpn 59, 3455 (1990) 29 J Neugebauer and M Scheffler, Phys Rev B 46, 16067 (1992) 30 G Henkelman, A Arnaldsson, and H J´ onsson, Comp Mat Sci 36, 354 (2006) 31 A Blant, T Cheng, N Jeffs, L Flannery, I Harrison, J Mosselmans, A Smith, and C Foxon, Mat Sci Eng (B) 59, 218 (1999) 32 J Wang, X Wu, X Dai, and D Bai, Phys Lett A 373, 1796 (2009) 33 S Ding, X Qu, and G Fan, Physica B: Cond Matt 404, 1279 (2009) 34 A Schleife, F Fuchs, C Ră odl, J Furthmăuller, and F Bechstedt, Appl Phys Lett 94, 012104 (2009) 35 I Mahboob, T D Veal, L F J Piper, C F McConville, H Lu, W J Schaff, J Furthmă uller, and F Bechstedt, Phys Rev B 69, 201307 (2004) 36 P D C King, T D Veal, P H Jefferson, C F McConville, H Lu, and W J Schaff, Phys Rev B 75, 115312 (2007) 37 R Kudrawiec, T Suski, J Serafinczuk, J Misiewicz, D Muto, and Y Nanishi, Appl Phys Lett 93, 131917 (2008) 38 W M Linhart, T D Veal, and C F McConville, Private communication  ...AIP ADVANCES 3, 012102 (2013) Ab- initio study of Mg- doped InN(0001) surface A Belabbes,a J Furthmuller, and F Bechstedt ă Institut făur Festkăorpertheorie... preference of Mg incorporation in the first bilayer is due to the reduced number of valence electrons of Mg dopants Near to the surface, a Mg acceptor is negatively charged by about 1/4 of an electron... modified The substitution of a surface In atom by a Mg one only requires the transfer of a quarter of an electron to the Mg dopant In the case of the incorporation of Mg in the third bilayer a