Electric field gradient calculations in ZnO samples implanted with 111In(111Cd)

Solid State Communications 152 (2012) 399–402

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Electric field gradient calculations in ZnO samples implanted with 111 In(111 Cd) Y. Abreu a,∗ , C.M. Cruz a , P. Van Espen b , C. Pérez c , I. Piñera a , A. Leyva a , A.E. Cabal a a

Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Calle 30 No. 502 e/5ta y 7ma Ave., Miramar, Playa, La Habana, Cuba

b

Micro and Trace Analysis Center (MiTAC), Department of Chemistry, University of Antwerp, Campus Drie Eiken, Building B., Universiteitsplein 1, BE-2610, Antwerp-Wilrijk, Belgium c

Instituto Superior de Tecnologías y Ciencias Aplicadas (InSTEC), Ave. Salvador Allende y Luaces, Quinta de los Molinos, La Habana, AP 6163, Cuba

article

info

Article history: Received 15 April 2011 Received in revised form 11 November 2011 Accepted 1 December 2011 by E.G. Wang Available online 8 December 2011 Keywords: A. ZnO semiconductor D. Electric field gradient E. Density functional calculation

abstract A first-principles study of the electric field gradient (EFG) calculated for ideal and 111 In(111 Cd) implanted ZnO samples is reported in the present work. The study was made for ZnO ideal hexagonal structures and supercells were introduced in order to consider the possible implantation environments. The calculation was done using the ‘‘WIEN2k’’ code within the density functional theory, the exchange and correlation effects were determined by the GGA approximation. Three possible 111 In(111 Cd) implantation configurations were studied, one substitutional incorporation at cation site and two interstitials. The obtained EFG values for the ideal structure and the substitutional site are in good agreement with the experimental reports measured by perturbed angular correlation (PAC) and high precision nuclear magnetic resonance (NMR). Thus, the ascription of substitutional incorporation of 111 In(111 Cd) probe atom at the ZnO cation site after annealing was confirmed. © 2011 Elsevier Ltd. All rights reserved.

1. Introduction The zinc oxide semiconductor ZnO has an increasing scientific and technological interest for optoelectronic and other applications [1–6]. To build such devices it is necessary to use n- and p-type ZnO materials obtained through doping with selective elements. Indium is known as one of the most efficient donor impurity used to improve optoelectronic properties of ZnO [1–3]. Dogra et al. [1] studied the radiation damage annealing of 111 In probe atoms implanted in ZnO samples. They measured the electric field gradient (EFG), at room temperature, through perturbed angular correlation (PAC) at the 111 In site in as-implanted samples and after subsequent furnace annealing in ambient nitrogen at various temperatures between 200 and 1000 °C. The as-implanted samples showed a broad distribution of EFG at the probe atoms, characterized by two main quadrupole interaction frequencies: νQ 1 = 30.9(5) MHz and νQ 2 = 113(2) MHz [1]. The samples annealing over temperature of 400 °C reduced the EFG distribution width and produced a complete diminution of the νQ 2 component in favour of νQ 1 ; indicating a majority fraction of probe atoms occupying a unique lattice site with equal surroundings. This site was ascribed to substitutional incorporation of probe atoms at cationsites of ZnO [1].

∗ Correspondence to: Departamento de Física, Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Calle 30 No. 502 e/5ta y 7ma Ave., Miramar, Playa, Ciudad de la Habana, Cuba. Tel.: +53 7 2066109; fax: +53 7 2021518. E-mail address: [email protected] (Y. Abreu). 0038-1098/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2011.12.001

Thus, the purpose of the present communication concerns with the numerical simulation of EFG values, calculated at ZnO structure sites involving regular cation and anion ones at the ideal hexagonal ZnO crystal structure; as well as EFG values emerging from 111 In(111 Cd) radioactive probe implanted ZnO matrix. Then, in the 111 In(111 Cd) radioactive probe implanted ZnO matrix three possible as-implanted and annealed 111 Cd nearest neighbourhood configurations are studied in order to establish their connections with the experimental observed values. These calculations were performed using the WIEN2k code [7] based on the full-potential (linearized)-augmented-plane-wave plus local orbitals (L/APW + lo) method [8] within the density functional theory (DFT). Previous DFT studies have been done in ZnO [4–6,9–12], but reports for EFG calculation of In doped or implanted ZnO samples in this approximation were not found. The only available values are reported by Dogra et al. [1] and by Mitchell et al. [13], using the classic point charge model (PCM) and the Hartree–Fock (HF) cluster procedure respectively. 2. Calculation details The EFG is defined as the second derivative of the electrostatic potential Vij = ∂ 2 V /∂ xi ∂ xj evaluated at the nuclear site of the probe atom imbibed in the material. ZnO normally crystallizes in a Wurtzite crystal structure with hexagonal crystal symmetry (P63mc space group), whose experimental lattice parameters reported in [14] were used in the present research, as a first calculation approach. In a second approach, ZnO lattice parameters

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Fig. 1. ZnO 2 × 2 × 2 supercells doped with Cd used in the studied configurations: (a) cation substitutional site (Cd(s)), (b) octahedral interstitial site (Cd(io )) and (c) tetrahedral interstitial site (Cd(it )). The black ball inside the polyhedral coordination figure indicates the possible 111 In(111 Cd) incorporation sites, the grey balls indicate the Zn cations and the white balls indicate the O anions.

Table 1 Optimized lattice parameters a, c /a and the internal structural parameter u, using the GGA approximation. Experimental data were taken from Ref. [14]. Parameter

Opt.

Exp.

a (Å) c /a u

3.269 1.618 0.378

3.249 1.602 0.381

were also optimized by minimizing the total energy as function of volume and c /a ratio. The optimized ZnO lattice parameters obtained using the GGA approximation are shown in Table 1. The ideal ZnO crystal structure EFG values at cation and anion regular sites calculated for both approaches were compared with the corresponding EFG experimental data in order to select the most appropriated lattice parameters set to describe the possible implantation environments. The following implantation damage picture on regard of the as-implanted and annealed ZnO matrix was adopted. In the PAC experiment the 111 In(111 Cd) concentration was very small (≈3 × 1014 cm−3 ) [1]. According to In transport simulation on a ZnO matrix applying the SRIM code [15], for the implanted samples it is expected a vacancy concentration of ≈6.5 × 1018 cm−3 due to atom displacements. This means that the average distance between two implanted ions and between vacancies should be dIn−In > 103 Å and dV −V > 102 Å respectively. Both distances will rise after the high temperature annealing head treatment as a result of 111 In(111 Cd) and vacancies diffusive motions, as well as vacancy annihilation by trapping, which means that in the annealed ZnO samples the defects concentration should be lower than in the asimplanted samples. In the PAC experiment the EFG is measured at the crystalline site occupied by the 111 Cd probe resulting from a 111 In β decay. Therefore, it was assumed that in the annealed ZnO samples the 111 Cd probe did occupied any of the regular and interstitial sites in the ZnO crystal structure according to those predicted by the P63mc space group symmetry properties. Furthermore, it was also considered that in the 111 Cd occupied site neighbourhood other crystal defects do not exists within the supercell borders below defined for the EFG calculations. This assumption is supported by the PAC experimentally observed drastic EFG value distribution width diminution at the 111 Cd probe site after high temperature annealing treatment of the as-implanted ZnO samples. According to the foregoing approach and taking into account the Cd atomic radius and the bound distances in the ZnO crystal structure, three possible Cd implantation sites were considered: cation substitutional site (Cd(s)), octahedral interstitial site (Cd(io )) and tetrahedral interstitial site (Cd(it )), as shown in Fig. 1. In order to reproduce the 111 Cd implantation site neighbourhood in the

ZnO crystalline structure a standard 2 × 2 × 2 supercells (SC) with 32 atoms and ≈ 7.8 Å of average distance between two adjacent dopants were studied. However, for the implantation sites that give EFG values close to the experimental observations, the calculation precision was increased considering a 3 × 3 × 2 SC with 72 atoms and an average distance between two adjacent dopants of ≈ 10.0 Å. For all calculated SC’s structures the internal atomic positions were minimized to a force limit below 1 mRy/Å. Good EFG value convergences were found in the calculations with the following set of parameters. The non-overlapping muffintin spheres radii Rmt were set to 2.14, 1.92 and 1.74 a.u. for Cd, Zn and O respectively. For the interstitial region, the plane wave expansion was carried out with a cut-off value of Rmt Kmax = 7.0. The maximum multipolarity l quantum number for the wave function expansion within the atomic sphere was confined to lmax = 12. The √ electrical charge density was Fourier expanded up to Gmax = 16 Ry. The number of k points in the irreducible part of the Brillouin zone was set to 264 for the ZnO ideal structure, 50 for the 2 × 2 × 2 SC and 27 for the 3 × 3 × 2 SC. To describe the exchange and correlation effects, the generalized gradient approximation (GGA) due to Perdew et al. [16] was used. 3. Results and discussion In all studied positions, the EFG tensor is axially symmetric (η = 0) and its symmetry axis is oriented along the ⟨001⟩ lattice direction. Thus, in the present discussion, only the EFG principal component (Vzz ) will be analysed. The contributions to Vzz from a given type of electronic states of harmonic character l (l = 0; 1; 2 for s, p and d electrons) are also taken into account, which can be estimated using the following equation [17,18]: Vzzll = (4π /5)1/2

Rmt

 0

ll ρ20

r3

r 2 dr .

(1)

The obtained Vzz values for the two ideal crystalline structure parameter sets are shown in Table 2. The individual contributions from s, p and d electrons for the experimental lattice parameters are also summarized in Table 2. In this table the EFG measured by high precision nuclear magnetic resonance (NMR) (Vzz (exp.)) in ideal ZnO samples [19] and the calculated values for this case using HF cluster procedure (Vzz (HF)) [13] are also shown for comparison. The Vzz values calculated for the set of experimental structure parameters (Vzz (Exp.)) show a better agreement with Vzz (exp.) in comparison with the values calculated for the optimized structure (Vzz (Opt.)). On the other hand, the Vzz (Opt.) values are far from the Vzz (exp.) values for both ideal sites. This finding might relay on the fact that experimental structural parameters

Y. Abreu et al. / Solid State Communications 152 (2012) 399–402

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Fig. 2. Local density of states (LDOS) for p electrons present in the Cd dopant studied sites. The solid, broken and dotted lines correspond to LDOS of p, pz and px+y electrons respectively. The Fermi energy is at 0 eV. Table 2 Experimental (exp.) and theoretical electrical field gradient component Vzz (in 1021 V/m2 ) for the two studied ZnO crystalline structures: optimized (Opt.) and experimental (Exp.) ones, where Vzz (Exp.) main electronic contributions are also shown. The EFG value using HF cluster procedure [13] is also included for comparison purposes. Site

Zn

O

Vzz (Opt.) Vzz (Exp.) Vzzsd

0.351 0.511 −0.004

−0.033 −0.27

Vzz

pp

0.521

Vzzdd

−0.006

Vzz (HF) [13] Vzz (exp.) [19]

0.73 0.659(2)

Table 3 Theoretical Vzz values (in 1021 V/m2 ) calculated for Cd probe at the studied implantation sites (substitutional Cd(s), orthorhombic interstitial Cd(io ) and tetragonal interstitial Cd(it )) for the 2 × 2 × 2 SC’s and the expanded 3 × 3 × 2 SC. The Vzz main electronic contributions are also shown for each studied site. Vzz (Cd)exp. denotes the EFG value corresponding to the experimental main quadrupole interaction frequency νQ 1 [1]. The EFG value calculated using PCM reported in [1] is included for comparison purposes. Site

Cd(s)

−0.258

Vzz Vzzsd

−0.009

pp

0.001

Vzz

Vzzdd Vzz (PCM) [1] Vzz (Cd)exp. [1]

1.380 1.52(24)

0.011

–

−0.233(1)

a

measured on a real crystalline sample reflect an average effect including the combined presence of structural undisturbed and disturbed crystalline regions, the last ones containing crystalline defects, as point defects; while the optimized crystal structure considers only a perfect ideal structure ruled out straightly by the crystalline translation invariance, which certainly should not be applied directly to the studied ZnO samples, including the non-irradiated and the irradiated one. Therefore, the experimental lattice parameters were selected to reproduce the implantation environments using the previously described SC’s. From the table is also clear that the dominant contribution to the EFG comes from electrons with strong p character. On the other hand, the Vzz (HF) value becomes closer to Vzz (exp.) than our results; suggesting that further improvements could be done for EFG calculations in the ideal ZnO structure. The Vzz calculated values for the 2 × 2 × 2 SC’s doped with Cd are presented in Table 3; where the Vzz (Cd)exp. value corresponds to the experimental main quadrupole interaction frequency νQ 1 and the previous PCM calculated value is also included for comparison. For the cation substitutional site (Cd(s)) the Vzz calculated value is closer to Vzz (Cd)exp. in comparison to the corresponding values calculated for the interstitial sites (Cd(io ) and Cd(it )). The difference between the Vzz (Cd)exp. and the Vzz calculated for the Cd(s) site is around 8.9%, while it rises for both interstitial sites to over 30%.

Cd(io )

Cd(it )

Cd(s)a

1.630

−1.001 −0.012 −1.691

−12.546

1.723

−0.227

0.667

2.892

−0.123

1.384

−9.479

1.565

0.206

−0.029

3 × 3 × 2 SC.

Then, for the Cd(s) site the electronic structure description was improved by increasing the SC size to 3 × 3 × 2, as described before, assuming that in the 3 × 3 × 2 SC the Cd atoms stay sufficient far from each other to avoid significant impurity–impurity interactions. The Vzz values for Cd(s) site obtained in this case are also included in Table 3 (see last column), becoming even closer to Vzz (Cd)exp. in about 3%. From Table 3 is also clear that the main contribution to the Vzz values of Cd atoms comes from electrons with strong p-character. Furthermore, in previous EFG calculations with Cd atoms has been pp reported that the magnitude of the component Vzz is proportional to the p electrons anisotropy evaluated at the Fermi energy, defined as [20,21]:

1np (EF ) =

1 2

npx+y (EF ) − npz (EF ),

(2)

where npi (i = x + y, z ) are the number of electrons in the pi orbital. This quantities can be obtained from the local DOS for the p electrons as described in [20,21]. The local DOS for the p electrons of Cd incorporated in ZnO are shown in Fig. 2 and the p electrons anisotropy (1np ) as function of energy are shown in Fig. 3 for the studied implantation sites.

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Fig. 3. p electrons anisotropy (1np ) of Cd dopant studied sites. The Fermi energy is at 0 eV.

The 1np value at the Fermi energy is positive in the Cd(s) site and negative in the other two cases. This is perfectly consistent pp with the Vzz sign observed in those cases. This implies that for the pp Cd(s) site the largest contribution to Vzz comes from px+y electrons and for the Cd(io ) and Cd(it ) sites comes from the pz electrons. The 1np steep behaviour observed in the Cd(s) and Cd(io ) cases near the Fermi energy suggest that the EFG at these Cd occupied sites could be sensitive to small Fermi level changes. Regarding the Vzz previously reported with the PCM approximation, the values presented here increase the precision in the electronic structure description; giving a better understanding of the EFG origin in the 111 In(111 Cd) implanted ZnO samples. 4. Conclusions The EFG parameter behaviours in the ideal and 111 In(111 Cd) implanted ZnO samples were studied in details. The calculated EFG parameters are close to the experimental values in the ideal ZnO experimental crystalline structure and far for the optimized one. This suggest that further improvements could be done for EFG calculations in this case. Three possible 111 In(111 Cd) implantation configurations were considered: one substitutional incorporation at cation site and two interstitials. The obtained EFG values give better agreement with the experimental report for the substitutional site. Then, the present electronic structure study confirms the ascription of substitutional incorporation of the 111 Cd probe atoms as well as, presumptively, of the implanted 111 In ions, in the ZnO cation site after annealing over 400 °C in ambient nitrogen. Acknowledgements This study was done thanks to the collaboration agreement between the University of Antwerp, Belgium, the Instituto

Superior de Tecnologías y Ciencias Aplicadas, and the Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear, Cuba. It was also supported by the Agencia de Energía Nuclear y Tecnologías de Avanzada from the Ministerio de Ciencia, Tecnología y Medio Ambiente of Cuba through the project PRN/6-2/3. References [1] R. Dogra, A. Byrne, M. Ridgway, Opt. Mater. 31 (2009) 1443. [2] U. Özgür, Y. Alivov, C. Liu, A. Teke, M. Reshchikov, S. Doˇgan, V. Avrutin, S. Cho, H. Morkoç, J. Appl. Phys. 98 (2005) 041301. [3] C. Klingshirn, Phys. Status Solidi B 244 (9) (2007) 3027. [4] M. Bouderbala, S. Hamzaoui, B. Amrani, A.H. Reshak, M. Adnane, T. Sahraoui, M. Zerdali, Physica B 403 (2008) 3326. [5] Y. Saeed, A. Shaukat, N. Ikram, M. Tanveer, J. Phys. Chem. Solids 69 (2008) 1676. [6] C. Persson, C. Dong, L. Vayssieres, A. Augustsson, T. Schmitt, M. Mattesini, R. Ahuja, J. Nordgren, C. Chang, A.F. da Silva, J. Guo, Microelectron. J. 37 (2006) 686. [7] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties, ISBN 3-9501031-1-2, Karlheinz Schwarz, Techn. Universität Wien, Austria, 2001. [8] G.K.H. Madsen, P. Blaha, K. Schwarz, E. Sjöstedt, L. Nordström, Phys. Rev. B 64 (2001) 195134. [9] G. Zhou, L. Suna, X. Zhong, X. Chen, L. Wei, J. Wanga, Phys. Lett. A 368 (2007) 112. [10] M. Ferhat, A. Zaoui, R. Ahuja, Appl. Phys. Lett. 94 (2009) 142502. [11] Y. Azzaz, S. Kacimi, A. Zaoui, B. Bouhafs, Physica B 403 (2008) 3154. [12] C.L. Dong, C. Persson, L. Vayssieres, A. Augustsson, T. Schmitt, M. Mattesini, R. Ahuja, C.L. Chang, J.-H. Guo, Phys. Rev. B 70 (2004) 195325. [13] D.W. Mitchell, S.B. Sulaiman, N. Sahoo, T.P. Das, Phys. Rev. B 44 (13) (1991) 6728. [14] A. Janotti, C.G.V. de Walle, J. Cryst. Growth 287 (2006) 58. [15] J.F. Ziegler, M. Ziegler, J. Biersack, Nucl. Instr. Meth. B 268 (2010) 1818–1823. [16] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [17] D. Torumba, V. Vanhoof, S. Cottenier, Phys. Rev. B 74 (2006) 014409. [18] S. Mohanta, S. Mishra, S. Srivastava, M. Rots, Solid State Commun. 150 (2010) 1789. [19] G. Denninger, D. Reiser, Phys. Rev. B 55 (8) (1997) 5073. [20] S. Cottenier, V. Bellini, M. Çakmak, F. Manghi, M. Rots, Phys. Rev. B 70 (2004) 155418. [21] S.J. Asadabadi, S. Cottenier, H. Akbarzadeh, R. Saki, M. Rots, Phys. Rev. B 66 (2002) 195103.