APPLIED PHYSICS LETTERS 97, 141914 共2010兲
CdTe surfaces: Characterizing dynamical processes with first-principles metadynamics Fabio Pietrucci,1 Guido Gerra,1 and Wanda Andreoni1,2,a兲 1
Centre Européen de Calcul Atomique et Moleculaire (CECAM), Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland 2 IBM Research–Zurich, 8803 Rüschlikon, Switzerland
共Received 5 August 2010; accepted 20 September 2010; published online 7 October 2010兲 We study dynamical processes at CdTe surfaces using ab initio metadynamics simulations. The c共2 ⫻ 2兲 to 共2 ⫻ 1兲 transition of the Te-terminated 共001兲 surface is found to involve a “c共2 ⫻ 2兲 + 共2 ⫻ 1兲” intermediate, consistent with experiment, and crossing of ⬃0.5 eV free-energy barriers at 400 K. Higher free-energy barriers 共1.6–2.5 eV兲 are estimated for desorption of a Cd ion from Cd-terminated 共001兲 and a CdTe unit from either Te-terminated 共001兲 or 共110兲 surfaces. Cd and Te exhibit a very different behavior. Concomitant to desorption, Te surface diffusion is observed as well as Te dimerization and bulk-surface Cd exchange events. © 2010 American Institute of Physics. 关doi:10.1063/1.3499430兴 Cadmium telluride 共CdTe兲 has long been at the heart of semiconductor technologies, in particular, as substrate for the growth of ternary II-VI semiconductors in optoelectronic devices.1 Recently CdTe thin-film-based technology has emerged as the most viable for an efficient and cost-effective alternative to silicon-based photovoltaic modules2,3 Also, recently proposed nanoscale photovoltaics have CdTe as ubiquitous component.4 Clearly any of the mentioned applications requires specific information on the state of CdTe surfaces and their changes under thermal or chemical treatments. Nevertheless, there is a surprisingly limited understanding of the state of CdTe surfaces under realistic physical conditions. A complex scenario, in which different reconstructions coexist and compete with desorption events, emerges from experimental studies carried out over 20 years with a variety of surface spectroscopy techniques 共for a review see Ref. 5兲. In striking contrast, theoretical approaches were restricted to idealized models, which were however adequate for accurate density-functional-theory 共DFT兲 calculations of static properties,6–8 leading to the determination of structural and electronic properties of surfaces of different orientations and of their relative stability. In particular, it was established that the 共001兲 Te-terminated surface with full coverage 关共001兲-Te兴 exhibits two 共main兲 types of reconstruction, namely 共2 ⫻ 1兲 and c共2 ⫻ 2兲, both involving Te dimerization, whereas the thermodynamically stable phase of the Cdterminated 共001兲 surface 关共001兲-Cd兴 corresponds to halfcoverage and a c共2 ⫻ 2兲 reconstruction. Information on the dynamical behavior comes only from lattice gas models9 or estimates of energy barriers for the migration of adsorbates from DFT static calculations of embedded-cluster models.10 We present an ab initio investigation of the dynamics of the 共001兲-Te and 共001兲-Cd surfaces, which are most relevant for epitaxial growth, and the cleavage 共110兲 surface. Our search is based on DFT-molecular dynamics 共MD兲 共Ref. 11兲 and aided by the metadynamics 共MTD兲 method,12 which allows us to observe the system cross high free-energy barriers a兲
Electronic mail:
[email protected].
0003-6951/2010/97共14兲/141914/3/$30.00
within the 共necessarily short兲 time of the simulation. As such, MTD has proved to be a unique tool for the understanding of protein conformational changes 共see e.g., Ref. 13兲 and structural transitions in bulk solids 共see e.g., Ref. 14兲. Here we explore dynamical paths leading to surface structural changes like reconstruction and desorption, and provide a quantitative characterization of the corresponding barriers at finite temperature. Our simulations reveal a complex behavior in which single processes interact and influence each other, and are fully consistent with experimental observations. Our DFT calculations rely on the Perdew–Burke– Ernzerhof15 exchange-correlation functional, scalarrelativistic angular-momentum dependent pseudopotentials,16 and plane-wave expansion of the valence wave functions up to a 80 Ry cutoff.17 Twelve-layer-slab models were used to represent the truncated solid 关in the zinc-blende 共ZB兲 structure兴, with periodic boundary conditions on the 共x,y兲 plane 共4 ⫻ 4 supercell兲 and a vacuum of 12 or 24 Å. For the polar 共001兲 surfaces, the Mortensen–Parrinello solver18 was applied to obtain image decoupling along the z-direction. First, ultrashort 共⬃2 ps兲 DFT Born–Oppenheimer MD simulations were run for both Te-terminated reconstructed 共001兲 surfaces 关Figs. 1共a兲 and 1共c兲兴 at T ⬃ 420 K. The c共2 ⫻ 2兲 modification was found to be higher in energy by only 6 meV per surface unit cell, a value which is one order of magnitude smaller that the energy difference obtained between the optimized structures 关82 meV 共this work兲; 70 mev 共Ref. 7兲; and 84 meV 共Ref. 8兲兴. Then, MTD was run using as collective variable the number of Te–Te B-bonds that form
FIG. 1. 共Color online兲 Te共001兲: 共a兲 initial c共2 ⫻ 2兲 and 共c兲 final 共2 ⫻ 1兲 state of the structural transition; 共b兲 intermediate state exhibiting both domains. 97, 141914-1
© 2010 American Institute of Physics
141914-2
Pietrucci, Gerra, and Andreoni
upon the transition from the c共2 ⫻ 2兲 关Fig. 1共a兲兴 to the 共2 ⫻ 1兲 关Fig. 1共c兲兴 reconstruction, at the expense of the Te– Te A⬘ bonds. This bond switch goes through highly strained configurations exhibiting a “chain” of three Te atoms 共A⬘ + B bonds兲. Correspondingly, free-energy barriers of 0.5⫾ 0.1 eV were calculated from 共a兲 to 共b兲 and from 共b兲 to 共c兲.19 Configurations as in Fig. 1共b兲 where both local reconstructions are present, are the intermediate 共metastable兲 states of this transformation. This is consistent with the frequent observation of a “c共2 ⫻ 2兲 + 共2 ⫻ 1兲” phase in which both structural domains coexist.20 We note that the two rows of dimers form independently, namely, without the intervention of a concerted mechanism, and the corresponding freeenergy barriers are equal within the accuracy of these calculations. Although our simple model does not allow the nature of the transition of the real system to be characterized, these findings suggest an Arrhenius-type conversion process, activated by the crossing of a local barrier. Desorption processes were simulated by using the signed distance D共X兲 of a selected surface atom X from the plane of the alike atoms in the outmost layer and the coordination number 共CN兲, which is defined to include atoms of both types, as collective variables. The two-dimensional 共2D兲 free-energy surface 共FES兲 was then reconstructed as a function of them. Starting again from the c共2 ⫻ 2兲共001兲-Te surface, we found that important rearrangements of the Te dimers occur also when a Te atom 共Teⴱ兲 is driven to desorb from it. Initially Teⴱ is bound to one Te on the outermost layer and two Cd ions underneath it. Within the duration of our simulations 共10 ps兲, we did not observe its full detachment and thus could only estimate a lower limit 共2.5 eV兲 for the free-energy barrier of this process. We could however establish a few interesting characteristics of the dynamical behavior of this surface. 共i兲 Teⴱ showed a clear tendency to desorb as a CdTe unit. Indeed after 共easily兲 losing its original bonds, Teⴱ diffuses on the surface and underneath generating other bonds with the cations, until it pulls one away from the inner layer; only then did it start to move upward 共along the z-direction兲. 共ii兲 The hindering factor to desorption was then the high tendency to diffuse on the surface, in the form of a CdTe, with Teⴱ experiencing an attractive interaction with the alike atoms of the outmost layer. 共iii兲 Eventually, the development of a Te vacancy leads to the formation of a chain of dimers along the y-direction as in the 共2 ⫻ 1兲 reconstruction 关Fig. 1共c兲兴. This simulation clearly shows the coexistence on the surface of atom diffusion, vacancy formation and reconstruction processes, and their mutual influence. Molecular desorption occurs also from the nonpolar 共110兲 surface. We recall that this surface does not reconstruct and that the structural relaxation induced by bulk truncation raises the outmost Te layer by 0.22 Å above its ideal position and depresses the Cd layer by 0.57 Å; each Te is bonded to two Cd’s just underneath 共at 2.82 Å兲 and to a third Cd on the inner layer 共at 2.85 Å兲. When subject to the MTD biasing potential, Teⴱ follows a complex path and eventually leaves the surface not as an isolated atom but bound to one cation 共Cd⬘兲, as shown in 共Fig. 2兲. The barrier for the desorption of a CdTe unit is estimated to be 1.8⫾ 0.2 eV and corresponds to the loss of the coordination of Teⴱ with the cation on the inner layer. During the simulation 共10 ps兲 Teⴱ is also seen to respond to the first bond-breaking in a different way, namely
Appl. Phys. Lett. 97, 141914 共2010兲
FIG. 2. 共Color online兲 CdTe 共110兲: FES for the desorption of Teⴱ. White regions are not explored.
by penetrating the bulk to include more alike atoms within 3.1 Å 共CN rising up to 5兲 without significantly disturbing the network. The sizable changes induced by the detachment of the CdTe molecule 共d = 2.82 Å兲 are confined to the close environment of the vacancy: 共i兲 both Cd’s initially bound to Teⴱ that relax outward from the vacancy 共by 1.21 Å and 0.87 Å in the first and second surface Cd layers, respectively兲 so as to strengthen the other bonds 共bond length reduced by 5%兲, and 共ii兲 both Te atoms initially coordinated to Cd⬘ that relax toward the vacancy by 0.64 Å and 0.25 Å in the second and first Te layers, respectively. The simulation of the half-coverage c共2 ⫻ 2兲共001兲-Cd surface also yields an unforeseen picture. The outmost layer is modeled as an alternate Cd-vacancy geometry as evidenced experimentally.21 As a consequence of their strong inward relaxation, the cations can be described as occupying bridging positions between the almost-coplanar Te sites 共d = 0.1 Å at ⬃400 K 共this work兲; d = 0.07 Å at ⬃400 K 共Ref. 21兲. Figure 3 shows the 2D-FES corresponding to the detachment of one cadmium atom 共Cdⴱ兲. Cdⴱ is seen to follow a complex path prior to desorption: it penetrates into the bulk to explore the large cavity present in the ZB structure and thus include up to five Te atoms within a shell of 3.1 Å radius, without significantly perturbing the rest, and also exchanges with an alike atom of the bulk. The desorption pathway 共dotted blue line兲 involves the sequential breaking of both Cd–Te bonds on the surface; the desorption barrier is essentially associated with the first event and is estimated to be 1.8⫾ 0.2 eV. This value interestingly coincides with the one we obtained for the breaking of the Cd– Teⴱ bond on the dissimilar environment of the 共110兲 surface. The tendency of
FIG. 3. 共Color online兲 Cd共001兲: FES for the desorption of Cdⴱ. White regions are not explored.
141914-3
Pietrucci, Gerra, and Andreoni
Te to dimerize again manifests itself: whenever Cdⴱ leaves the surface, both during its “embedding” in the bulk and during the desorption process, a dimer forms at the vacancy between the Te atoms that recover a 共mixed兲 threefold coordination. A calculation of the charge localized around the desorbed Cdⴱ shows that it is in the +1 ionization state. A comparison of the free-energy barriers we estimate for desorption with activation energies derived from experiment can be made although there is no one-to-one correspondence. Estimates from experiment for Cd desorption from surfaces of various orientations all are in the range 1.9–2.1 eV.5 The value we find for Cd from the 共001兲 surface is 1.8⫾ 0.2 eV. This agreement may not be fortuitous because, as we have shown, it corresponds to the breaking of a CdTe bond. For the more complicated case of Te, on the other hand, previous interpretations of experiments did not even consider the possibility of a CdTe desorption but indicated barriers of 1.0 to 1.4 eV for the desorption of Te.5 Our simulations unambiguously show that surface Te has a lower tendency to desorb than Cd, having a high propensity to form additional bonds with the alike atoms. Therefore, we believe that those measurements might refer to Te atoms adsorbed on the surface10 or at steps 共not considered in our model兲. For the sake of comparison, we have performed classical MD using interatomic potentials parametrized on bulk ZB CdTe and validated in the liquid.22 These turned out to be inadequate to represent the properties of the surfaces. For example, the Cd-共001兲 model with Cd’s in bridge positions is unstable, and for the Te-共001兲 the energy difference c共2 ⫻ 2兲 versus 共2 ⫻ 1兲 is too high 关0.59 eV 共0 K兲; 0.52 eV 共420 K兲兴. Other detailed results will be published elsewhere. In conclusion, our study provides an unprecedented characterization of CdTe surfaces: 共i兲 for the Te-terminated 共001兲 surface the transformation from the c共2 ⫻ 2兲 to the more stable 共2 ⫻ 1兲 reconstruction is not spontaneous but involves the crossing of barriers as high as 0.5 eV, going through intermediate states in which those domains coexist. This is in agreement with experimental observations of such “composite” phases.5 共ii兲 Contrary to common schemes used for the interpretation of desorption, this is not just a simple process involving an individual atom or molecule but is accompanied by other “unsettling” processes such as change of reconstruction, diffusion, and exchange between bulk and surface atoms. 共iii兲 The behavior of Cd and Te are strikingly different, the latter being less prone to leave the surface, given its high tendency to form bonds also with alike atoms, and pulling out a cation on its way. 共iv兲 The complexity here revealed is hard to be captured with more traditional static calculations. 1
R. Triboulet and P. Siffert, “CdTe and Related Compounds; Physics, Defects, Hetero- and Nano-Structures, Crystal Growth, Surfaces and Appli-
Appl. Phys. Lett. 97, 141914 共2010兲 cations,” European Materials Research Society Monographs 共Elsevier, New York, 2009兲. 2 H. S. Ullal and B. von Roedern, Solid State Technol. 51, 52 共2008兲; M. A. Green, K. Emery, Y. Hishikawa, and W. Warta, Prog. Photovoltaics 18, 144 共2010兲. 3 J. Perrenoud, S. Buecheler, and A. N. Tiwari, Proc. SPIE 7409, 74090L 共2009兲; J. Luschitz, B. Siepchen, J. Schaffner, K. Lakus-Wollny, G. Haindl, A. Klein, and W. Jaegermann, Thin Solid Films 517, 2125 共2009兲; M. Hädrich, C. Kraft, C. Loeffler, H. Metzner, U. Reisloehner, and W. Witthuhn, ibid. 517, 2282 共2009兲; Z. Fan, Nature Mater. 8, 648 共2009兲. 4 T. Nakashima and T. Kawai, Chem. Commun. 共Cambridge兲 2005, 1643; Z. Tang, Z. Zhang, Y. Wang, S. C. Glotzer, and N. A. Kotov, Science 314, 274 共2006兲; L. Manna, D. J. Millron, A. Meisel, E. C. Scher, and A. P. Alivisatos, Nature Mater. 2, 382 共2003兲. 5 J. Cibert and S. Tatarenko, Defect Diffus. Forum 150–151, 1 共1997兲, and references therein. 6 D. Vogel, P. Kruger, and J. Pollmann, Surf. Sci. 402–404, 774 共1998兲. 7 S. Gundel, A. Fleszar, W. Faschinger, and W. Hanke, Phys. Rev. B 59, 15261 共1999兲. 8 B. Rerbal, G. Merada, H. Mariette, H. I. Faraoun, and J. M. Raulot, Superlattices Microstruct. 46, 733 共2009兲. 9 M. Biehl, M. Ahr, W. Kinzel, M. Sokolowski, and T. Volkmann, Europhys. Lett. 53, 169 共2001兲. 10 A. E. Patrakov, R. F. Fink, K. Fink, T. C. Schmidt, and B. Engels, Phys. Status Solidi B 247, 937 共2010兲. 11 R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471 共1985兲. 12 A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 99, 12562 共2002兲. 13 A. Laio and F. L. Gervasio, Rep. Prog. Phys. 71, 126601 共2008兲; F. Marinelli, F. Pietrucci, A. Laio, and S. Piana, PLOS Comput. Biol. 5, e1000452 共2009兲. 14 R. Martoňak, D. Donadio, A. Oganov, and M. Parrinello, Nature Mater. 5, 623 共2006兲; C. Bealing, R. Martonak, and C. Molteni, J. Chem. Phys. 130, 124712 共2009兲. 15 J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 共1996兲; 80, 891 共1998兲; recent applications to CdTe and related compounds prove the validity of the PBE scheme, see e.g., comparison with MP2 calculations for CdTe clusters, J. Wang, L. Ma, J. Zhao, and K. A. Jackson, J. Chem. Phys. 130, 214307 共2009兲; and with experimental observations for CdTe grain boundaries, L. Zhang, J. L. F. Da Silva, J. Li, Y. Yan, T. A. Gessert, and S.-H. Wei, Phys. Rev. Lett. 101, 155501 共2008兲; and CdSe nanocrystals, L. Liu, Z. Zhuang, T. Xie, Y.-J. Wang, J. Li, Q. Peng, and Y. Li, J. Am. Chem. Soc. 131, 16423 共2009兲. 16 S. Goedecker, M. Teter, and J. Hutter, Phys. Rev. B 54, 1703 共1996兲; C. Hartwigsen, S. Goedecker, J. Hutter, ibid. 58, 3641 共1998兲; M. Krack, Theor. Chem. Acc. 114, 145 共2005兲. 17 We used the CPMD code V3.13.3 Copyright IBM Corporation 1990– 2010; MPI für Festkörperforschung, Stuttgart 共DE兲, 1997–2001. A 120 Ry cutoff changed geometric features and energy differences by less than 1%. 18 J. J. Mortensen and M. Parrinello, J. Phys. Chem. B 104, 2901 共2000兲. 19 Local energy minimization of these geometries, extracted from the 400 K trajectories, under geometry constraints, lead to a higher upper limit for the barrier 共⬃0.9 eV兲. An accurate estimate of the potential energy contribution to the free energy barrier would require extensive static calculations that are beyond the scope of this paper. 20 S. Tatarenko, F. Bassani, J. C. Klein, K. Saminadayar, J. Cibert, and V. H. Etgens, J. Vac. Sci. Technol. A 12, 140 共1994兲; S. Tatarenko, B. Daudin, D. Brun, V. H. Etgens, and M. B. Veron, Phys. Rev. B 50, 18479 共1994兲. 21 M. B. Veron, M. Sauvage-Simkin, V. H. Etgens, S. Tatarenko, H. A. Van Der Vegt, and S. Ferrer, Appl. Phys. Lett. 67, 3957 共1995兲. 22 Z. Q. Wang, D. Stroud, and A. J. Markworth, Phys. Rev. B 40, 3129 共1989兲; C. Henager, Jr. and J. R. Morris, ibid. 80, 245309 共2009兲.
