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Ab Initio Study of H2 Associative Desorption on Ad-Dimer Reconstructed Si(001) and Ge(001)-(2×1) Surfaces R. C. Longo,*,† J. H. G. Owen,*,‡ S. McDonnell,† J. B. Ballard,‡ R. M. Wallace,† J. N. Randall,*,‡ Y. J. Chabal,† and K. Cho*,† †

Department of Materials Science & Engineering, The University of Texas at Dallas, Richardson, Texas 75080, United States Zyvex Laboratories, LLC, 1301 North Plano Road, Richardson, Texas 75081, United States

‡

S Supporting Information *

ABSTRACT: We investigate the pathways of hydrogen migration and associative desorption of H2 on the Si(001) and Ge(001)-(2×1) reconstructed surfaces with adsorbed ad-dimers, using density functional theory methods. Although the trends obtained with common semilocal exchange−correlation functionals such as the generalized gradient approximation are correct, we show that the use of exact short-range Fock exchange in the calculations (by means of hybrid functionals) strongly affects the magnitude of the desorption barriers, especially for Ge surfaces, leading to a better estimate of the desorption temperatures. Our results for H2 desorption kinetic barriers are well-supported experimentally and can therefore help to elucidate the mechanisms driving atomic layer epitaxy growth processes.

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respectively).6,16 Experimental studies seem to support the interdimer mechanism, i.e., the recombinative desorption from two Si−H bonds on two adjacent dimers along a dimer row.28 For SiGe alloy surfaces, Ge neighboring atoms (either in the bulk or on neighboring dimers) have a minimal effect on the intradimer H2 desorption.16 For the interdimer desorption mechanism, previous calculations show a wide range of desorption barriers (1.9−3.1 eV), depending on the number of H atoms considered and on the size of the cluster model used to represent the corresponding semiconductor surface (see, e.g., refs 6, 29−31). Hydrogen desorption is critical during film growth as well. For example, our recent work3 on Si2H6 adsorption on both Si(001) and Ge(001)-(2×1) surfaces, using in situ infrared absorption spectroscopy (IRAS) measurements and ab initio density-functional theory (DFT) calculations, showed that reaction barriers are quite small for chemisorption (0.14 eV) and dissociation into a Si2H4 + 2 Hads species on the Si(001)(2×1) surface (0.47 eV). Further decomposition could have involved either formation of ad-dimers across the trench between dimer rows, as proposed in previous studies of disilane decomposition at lower coverages,32,33 or ad-dimers on top of the dimer rows (configuration D through pathway R, configuration R, of ref 3; see Figure 1 of the present paper). A specific IRAS signature for this on-row ad-dimer configuration R was detected at 573 K, indicating that under these experimental conditions, this pathway is operative with a

INTRODUCTION Nanoscale patterning of hydrogen-terminated Si(001) and Ge(001)-(2×1) surfaces using scanning tunneling microscopy (STM) tip-based H-depassivation 1 techniques is being considered as a promising method in atomically precise three-dimensional (3D) nanostructure manufacturing.2 With this approach, H atoms are removed from selected areas of atomically flat H-passivated Si or Ge(001)-(2×1) surfaces by electrons from an STM tip moving over the surface, leaving unsaturated dangling bonds on surface dimers.3 These clean areas are then accessible for deposition of Si or Ge using molecular precursors, thus enabling atomic layer epitaxy (ALE) (after many cycles of H desorption and precursor deposition) and the growth of 3-D nanostructures for nanometer-scale device applications.4 The kinetics of hydrogen on semiconductors surfaces is closely related to the surface reconstruction.5 There have been numerous experimental and theoretical studies on H 2 adsorption, dissociation, and further desorption from the dimerized Si(001)-(2×1) surface.3,6−15 Also, to a lesser extent, the effect of Ge on H2 desorption from Si(001) has motivated a number of experimental and theoretical studies on both Gecovered Si(001)-(2×1) and SiGe alloy surfaces.14,16−27 For H2 desorption from the Si(001)-(2×1) surface, the mechanisms proposed in the literature involve the detachment of two H atoms from the same Si dimer (intradimer or “prepairing” mechanism) or from two different dimers (interdimer mechanism).6,12 From a theoretical point of view, this latter mechanism involves different possibilities, depending on whether both dimers are fully passivated or not, i.e., with 2 or 4 H atoms (H2 or H4 reaction path mechanisms, © 2014 American Chemical Society

Received: January 13, 2014 Revised: April 4, 2014 Published: April 23, 2014 10088

dx.doi.org/10.1021/jp411903z | J. Phys. Chem. C 2014, 118, 10088−10096

The Journal of Physical Chemistry C

Article

these functionals accurately describe highly correlated systems or small band gap semiconductors.36,37 Therefore, it is relevant and important to determine if the HSE hybrid functional34 can yield better desorption barriers. This paper is organized as follows. In Section II we briefly describe the computational methods used in our calculations. Our results are presented and discussed in Section III, and finally, in Section IV, we summarize our main conclusions.

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COMPUTATIONAL METHODS Ab initio calculations were performed using DFT with plane wave basis sets and projector augmented wave (PAW) pseudopotentials, as implemented in the VASP code.38,39 The electronic wave functions were represented by plane wave basis with a cutoff energy of 500 eV. We include the exchange− correlation interactions by using the semilocal Perdew−Burke− Ernzerhof (PBE) functional of the generalized gradient approximation.40 The limitations of DFT to accurately describe small band gap semiconductors (like Ge) are well-known, and semilocal exchange−correlation functionals even predict a metallic behavior for Ge bulk structure.36 To overcome this problem, we also used in our calculations a hybrid HSE functional, which explicitly includes exact Hartree−Fock (HF) exchange for the short-range interactions.34 The HSE functional has proven to be very successful in describing a wide variety of complex systems, like small band gap semiconductors and spin−orbit couplings in heavy atoms.36,37 The unit cell of the ideal Si(001)-(2×1):H and Ge(001)(2×1):H surfaces is made of two Si or Ge atoms per layer, with the surface dimers passivated with hydrogen, forming H:Si/ Ge−Si/Ge:H groups. In our simulations, we modeled both surfaces with a periodic slab containing six Si or Ge atomic layers, with only the bottom Si or Ge layer passivated by two H atoms per atomic site. The thickness of the vacuum region in the direction perpendicular to the slab is 15 Å. The ALE Si2H6 and Ge2H6 molecular precursors were initially adsorbed on the dimer-reconstructed side of the slab following pathway R, as shown in our previous publication.3 To make their interaction sufficiently weak, we employed a (2 × 4) unit cell that involves four dimers along the dimer row and a trench between each one of the two dimer rows. To test the accuracy of our calculations in some specific cases, we extended the simulations to (4 × 4) surface unit cells, thus increasing the lateral periodicity. All the atoms, except the bottom two layers of Si or Ge and the H-passivating layers, were allowed to relax without any constraint. We started our calculations with the experimental lattice constants of 5.431 Å for Si41 and 5.658 Å for Ge.41 Upon relaxation, our obtained values are 5.47 and 5.80 Å for Si and Ge, respectively (using GGA), and 5.46 and 5.71 Å for Si and Ge slabs, respectively, with the HSE exchange−correlation functional. The desorption barriers, transition states, and reaction paths were obtained using the climbing image-nudged elastic band method (CI-NEB).42−44 This method allows us to obtain the minimum energy path (MEP) between a set of two different states. To do that, the reaction path is divided into a set of images “connected with a spring”. During the relaxation, the initial and final states are kept frozen while the images move according to the constraint of the “elastic band”. The MEP is then found when the components of the forces perpendicular to the “elastic band” vanish; the relative positions of the images and the barrier are determined by the parallel components of the forces.43,44

Figure 1. Lateral and top view of the hydrogenated row ad-dimer structure on the Si(001)-(2×1) surface.

maximum kinetic barrier of approximately 1.6 eV, assuming a prefactor of 1013−14 s−1. However, the calculated pathway (which did not include H desorption) from Si2H4 to the R configuration required large activation energies (2.94, 2.24 eV), much too high to be active at the experimentally observed temperature. When H desorption or diffusion from these sites is allowed, the barriers along this pathway become much lower. In the Si/Ge(001) surface, the initial barrier for chemisorption is higher (0.53 eV) and the Si adatoms are experimentally observed to undergo an exchange reaction with the surface Ge dimers at medium temperatures (525 K), which is known to occur only once the H has desorbed from the Si ad-dimer atoms.25,26 Both examples indicate that there may be pathways to H desorption available on this rough growth surface, which are not active on the flat Si(001) or Ge(001) surfaces in this temperature range. This is an important observation because most surfaces are rough, i.e., contain ad-dimers. Our aim in this paper is two-fold. First, we specifically consider the role of adsorbed ad-dimers that add extra degrees of freedom to the possible H2 desorption mechanisms,3 which may account for the experimental observations. Starting from the experimentally observed configuration R of ref 3 (see Figure 1) and using a real surface model (see Computational Methods), our goal is to investigate in detail possible H2 thermal desorption paths after adsorption and further dissociation of ALE Si2H6 and Ge2H6 molecular precursors on both Si(001)-(2×1) and Ge(001)-(2×1) surfaces. Second, we use the Heyd−Scuseria−Ernzerhof (HSE) hybrid functional34 to obtain the aforementioned H2 desorption barriers and compare our results with those obtained using the generalized gradient approximation (GGA) standard functional. Indeed, DFT calculations of H2 desorption intradimer and interdimer mechanisms on Si(001)-(2×1) surface have led to limited agreement with experiments.6,8 While they correctly predict an almost barrierless H4 interdimer adsorption path at high coverages, previous calculations for the intradimer and H2-interdimer mechanisms yielded values for the adsorption barriers too low to explain the experimentally observed small sticking coefficients.11,35 Although the predicted trends are often correct, the desorption barriers obtained with the local density approximation (LDA) or the GGA are always generally lower than the available experimental values.6,11 The reason is the inadequacy of the LDA or GGA to accurately describe the localized Si−H bond. The situation for Ge-based systems is even worse, as LDA or GGA predict a metallic behavior for this small band gap semiconductor.36 Because of that, the use of hybrid functionals with an exact treatment of the short-range part of the exchange interactions has become very popular in the past few years, as 10089



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Table 1. Intradimer and Interdimer H2 Kinetic (from Clean Si(001)-(2×1) and Ge(001)-(2×1) Surfaces without Ad-Dimers) Desorption (Edes) and Adsorption (Eads) Barriers and Reaction Energies (Erxn) as Obtained with the HSE06 Functional (the Values Obtained with GGA are Shown in Parentheses) together with the Available Experimental Results for Monohydride Desorption from Both Surfaces15,23 and Quantum Monte Carlo (QMC) Results6 system

energy (eV)

Si(001)

Edes Erxn Eads Edes Erxn Eads

Ge(001)

intradimer

interdimer

2.33 2.16 0.17 2.17 1.11 1.06

2.34 1.88 0.46 1.62 0.86 0.76

(2.12) (1.86) (0.26) (1.72) (0.85) (0.87)

(2.01) (1.66) (0.35) (1.28) (0.48) (0.80)

exptl

QMC (intradimer)

QMC (interdimer)

2.48 ± 0.1 1.9 ± 0.3 0.58 ± 0.4 1.6

3.03 ± 0.13 2.54 ± 0.13 0.49 ± 0.13

3.11 ± 0.09 2.52 ± 0.09 0.59 ± 0.09

In all cases, we used a (3 × 6 × 1) k-point mesh (this sampling is equivalent to the one obtained with 12 × 12 × 1 grids for the primitive cells of the surfaces) within the Monkhorst−Pack45 scheme to ensure a convergence of 10 meV/unit cell. We performed structural relaxations without including any type of symmetry, to a tolerance of 10−4 eV in the total energy and 0.01 eV/Å in the forces on every atom, for both standard and CI-NEB structural minimizations. In our calculations, Edes represents the desorption barrier of the corresponding reaction, Erxn the reaction energy (energy difference between the final and initial states), and Eads the kinetic adsorption barrier, i.e., (Edes − Erxn).

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RESULTS AND DISCUSSION

Figure 2. Schematic view of the three H2 desorption pathways considered in this work, together with the interdimer and intradimer mechanisms for H2 desorption from clean (without ad-dimers) surfaces. Surface dimer atoms are shown in blue and the ad-dimer atoms are shown in green.

HSE versus GGA Calculations of the Initial H 2 Desorption Steps. As stated previously, although the trends predicted by semilocal GGA-DFT functionals about the H2 desorption from the Si(001)-(2×1) surface or SiGe surface alloys are correct,6,11,16 they can also underestimate the desorption barriers and reaction energies, thus leading to a limited agreement with experiments.11 To overcome these limitations and to have an accurate picture of the desorption barriers and reaction energies of the Si and Ge systems studied in this work, we performed the calculations using the HSE hybrid functional, which includes an exact short-range Fock exchange term.34 Because of the huge amount of computational resources needed to perform the calculations of all the steps of the desorption pathways of the three pairs of hydrogen atoms, in this section we will show only the results corresponding to the desorption of the first pair of H atoms. However, these desorption steps turn out to be the rate-limiting steps and are therefore the most valuable to calculate. Table 1 shows the results obtained for the intradimer and interdimer (Figure 2) H2 desorption mechanisms (from a flat Si(001)-(2×1) or Ge(001)-(2×1) surface, i.e., without addimers), together with the available experimental results for both surfaces.28 If we consider the intradimer and interdimer mechanisms as controls of our methods, it can be noted that the HSE-predicted H2 desorption kinetic barriers are slightly higher than those predicted by GGA: 0.21 and 0.33 eV, respectively, for the Si(001)-(2×1) surface and 0.45 and 0.34 eV, respectively, for the Ge(001)-(2×1) surface. For the Si(001)-(2×1) surface, the desorption barriers of both mechanisms are practically the same (2.33 and 2.34 eV for the intradimer and interdimer, respectively, using the HSE functional) while for the Ge(001)-(2×1) surface the intradimer desorption kinetic barrier is considerably larger (2.17 vs 1.62 eV). In the H2 interdimer adsorption pathway,6,16 the H2 molecule dissociates over two clean Si neighboring dimers, ending with two H atoms at the same side of the dimers. In the

H4 mechanism,6,16 the adsorption occurs on two neighboring Si dimers, which are both already covered on one side with hydrogen atoms, so that adsorption results in a pair of fully saturated dimers. In our case, the interdimer H2 desorption pathway corresponds to the H2 mechanism, as we considered that only two Si or Ge surface atoms are previously saturated with hydrogen atoms. The predicted HSE H2 adsorption kinetic barriers (0.17 and 0.46 eV for the intradimer and interdimer mechanisms, respectively) on the Si(001)-(2×1) surface agree relatively well with previous quantum Monte Carlo (QMC) calculations,6 while the desorption barriers are considerably lower. Both kinetic adsorption and desorption barriers are in good agreement with the published experimental results (0.6 and 2.5 eV, respectively; ref 28). Our calculations for the H4 H2 adsorption mechanism yield 0.12 and 2.41 eV, also in excellent concordance with the available experimental data (this low adsorption barrier is the explanation for the small sticking coefficient at low temperatures: with more hydrogen atoms already adsorbed on the Si(001)-(2×1) surface, there are more barrierless adsorption sites for sticking35). For the Ge(001)-(2×1) surface, our results seem to rule out the H2 intradimer desorption path as the most likely experimental mechanism. The H2 adsorption energies on the Ge are much higher than those on the Si(001)-(2×1) surface, 1.06 and 0.76 eV for the intradimer and interdimer mechanisms, respectively, making it necessary to go to higher temperatures to produce hydrogen-passivated Ge(001)-(2×1) surface samples. H2 Desorption from Ad-Dimers. We identified three different possible desorption pathways from the ad-dimer reconstructed Si(001)-(2×1) and Ge(001)-(2×1) surfaces (Figure 2) depending on the initial position of the desorbed 10090



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the main difference comes from the pathway considered: they are relatively small for the “mixed” pathway 1 (about 0.2−0.3 eV) but a bit larger for both pathway 2 and pathway 3 (where the H2 molecule desorbs only from the ad-dimer or subdimers), 0.5−0.6 eV. Overall, the lowest barriers on the rough surface are lower than those on the flat surface, but not by very much, only 0.1 eV for Si and 0.2 eV for Ge. Also, the use of different functionals affects the electronic structure. Table S1 of Supporting Information shows the electronic band gaps of of the ad-dimer reconstructed Si(001)-(2×1) and Ge(001)-(2×1) surfaces (structures with six hydrogen atoms) and after the first step of the three H2 desorption pathways considered in this work (structures with 4 H atoms), as obtained with the HSE06 and the GGA functionals. Our results confirm the well-known tendency of standard GGA to underestimate the electronic band gaps, establishing a correlation between the band gap (binding energy of the ad-dimer) and the kinetic desorption barrier. After the first desorption step, all the band gaps are narrower, corresponding with the two dangling bonds created in the surface, although little can be said about the influence of the pathway on the corresponding band gap. Perhaps the only exception is pathway 3, where the H2 is desorbed from a subsurface dimer, leading to a smaller band gap for all the systems studied and the two functionals used in the calculations. H2 Desorption from Ad-Dimer Reconstructed Si(001)(2×1) and Ge(001)-(2×1) Surfaces Using GGA Calculations. Starting from the ad-dimer in the R configuration shown in ref 3 (see Figure 1 for the final configuration), we investigated the energetics and kinetics of possible different H2 diffusion and associative desorption pathways, following the three initial processes aforementioned. As an example, Figure 3 shows the most likely desorption paths followed during the H2 desorption process from Si ad-dimers on the Si(001)-(2×1) surface. Tables 3−5 show the desorption barriers (Edes) and

hydrogen atoms: pathway 1, where one hydrogen atom is detached from the ad-dimer and another one from the surface dimer (“sub-dimer”); pathway 2, with both hydrogen atoms desorbed from the ad-dimer; and pathway 3, where both hydrogen atoms are detached from the subdimer. Table 2 lists Table 2. Kinetic Barriers (Edes) and Reaction Energies (Erxn) for the First Step of the Three H2 Desorption Pathways Considered in This Work As Obtained with the HSE06 Functional (the Values Obtained with GGA are Shown in Parentheses) system Si/Si(001) Ge/Si(001) Si/Ge(001) Ge/Ge(001)

energy (eV) Edes Erxn Edes Erxn Edes Erxn Edes Erxn

pathway 1

pathway 2

pathway 3

2.23 2.12 1.77 1.69 1.85 1.73 1.39 1.07

2.67 2.56 2.45 1.72 2.38 2.31 2.26 1.44

2.96 2.93 3.03 3.00 1.59 1.52 1.54 1.46

(1.91) (1.81) (1.50) (1.38) (1.57) (1.44) (1.14) (0.90)

(2.14) (2.10) (1.97) (1.30) (2.07) (1.99) (1.76) (1.11)

(2.51) (2.49) (2.52) (2.49) (1.29) (1.26) (1.26) (1.20)

the desorption barriers and reaction energies of the first step of H2 desorption for the three different pathways and the four systems studied in this work, as obtained with HSE and GGA functionals. Pathways 2 and 3 are expected to show material contrast, as both desorbing atoms are from the ad-dimer (P2) or the subdimer (P3), whereas for pathway 1, one atom desorbs from each. Indeed, for the two systems with a Ge ad-dimer, the pathway 2 barriers are lower than those for the two systems with a Si ad-dimer. However, for pathway 3, the two Si subdimer systems have nearly identical barriers, while the two Ge subdimer systems also have two identical but much lower barriers. Meanwhile pathway 1 shows a general trend of a lower barrier with more Ge, the Si/Si barrier being the highest and Ge/Ge the lowest. Of all the desorption routes, pathway 1 gives the lowest barrier for three out of the four systems studied, the exception being the Si/Ge system, in which the lowest barrier is pathway 3, with two H atoms desorbing from the Ge subdimers. For Ge or Si ad-dimers on Si(001), both pathway 2 and pathway 3 have barriers higher than those for the flat surface mechanisms and are therefore unlikely to be operative. Pathway 1 is about 0.1 eV lower than for the flat surface, which would imply some enhancement of desorption on rough surfaces. On Ge(001) surfaces, the highest barrier for either Si or Ge ad-dimers is pathway 2 and pathway 1 is considerably lower than for the flat surface, by 0.23 eV (cf. Tables 1 and 2). A remarkable aspect of the H2 desorption kinetic barriers and reaction energies for the three different pathways on both addimer reconstructed Si and Ge(001)-(2×1) surfaces is that the readsorption barriers are always very low, as obtained with both HSE and GGA functionals. As can be seen in Table 2, the only exception is the pathway 2 (where both hydrogen atoms are desorbed from the ad-dimer) for Ge ad-dimers (on both Si and Ge(001)-(2×1) surfaces), where the HSE kinetic adsorption barriers are 0.73 and 0.82 eV for Si and Ge(001)-(2×1), respectively. To conclude this section we can note that, although the obtained trends are the same, HSE calculations yield desorption barriers and reaction energies higher than those obtained with GGA. The corrections do not follow a unique tendency and, although they are generally higher for Ge than for Si systems,

Figure 3. Most likely desorption paths followed during the H2 desorption process from Si ad-dimers on the Si(001)-(2×1) surface. The numbers on the arrows show the corresponding Edes kinetic barriers, either for H2 desorption or diffusion. The numbers above the different configurations show the corresponding reaction energies Erxn. The kinetic barriers Edes are always referred to the previous configuration, but to allow a better understanding of the overall process, the reaction energies (Erxn) are always referred to the initial energies (precursor adsorbed on the surface). 10091



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reaction energies (Erxn) of the most stable structures obtained in our calculations, starting from the three different pathways until H2 molecules are completely desorbed, for the four different systems considered in this work (Si and Ge ad-dimers on both Si(001)-(2×1) and Ge(001)-(2×1) surfaces), and Figures 4−6 show the corresponding structures. Finally, in Figures S2−S5 of Supporting Information we show the most likely H2 desorption paths for the four systems studied in this work. The reaction energies of these structures are always referred to the initial configurations, i.e., the structure with the six hydrogen atoms adsorbed on the corresponding ad-dimer− surface system. Although we have shown only the experimental deposition of Si2H6 on both Si(001)-(2×1) and Ge(001)(2×1) surfaces,3 in our calculations we also include the deposition of Ge2H6 on Si(001)-(2×1) and Ge(001)-(2×1) surfaces to study the effect of Ge alloying on H2 desorption. 4H Structures. The initial step of the desorption process constitutes the loss of the first H2 molecule, forming 4H structures. We have identified six 4H isomers, shown in Figure 4. Pathway 1, which is the lowest barrier in 3 out of 4 cases,

Table 3. Kinetic Barriers (Edes) and Reaction Energies (Erxn) of the Most Stable Structures Obtained during the First Step of H2 Desorption from Si and Ge Ad-Dimers on the Si(001)-(2×1) and Ge(001)-(2×1) Surfacesa 4H-A system Si/Si(001) Ge/Si(001) Si/Ge(001) Ge/Ge(001)

4H-B

4H-C

4H-D

4H-E

4H-F

energy (eV)

P1

D

P2

D

D

P3

Edes Erxn Edes Erxn Edes Erxn Edes Erxn

1.91 1.81 1.50 1.38 1.57 1.44 1.14 0.90

0.39 1.54 0.58 1.43 0.33 0.99 0.60 1.00

2.14 2.10 1.97 1.30 2.07 1.99 1.76 1.11

0.99 2.42 1.13 1.81 1.24 1.73 0.91 1.20

0.75 2.48 1.90 2.46 0.57 1.39 1.75 1.32

2.51 2.49 2.52 2.49 1.29 1.26 1.26 1.20

a

Figure 4 shows the corresponding structures. The desorption barriers Edes are always referred to the previous configuration, but to allow a better understanding of the overall process, the reaction energies Erxn are always referred to the initial energies (precursor adsorbed on the surface).

energies for the Si/Si and Si/Ge cases. As a result, 4H-C is the lowest-energy isomer for Ge/Si. 4H-B,E,F, where the two bare atoms are Si, have relative energies for Ge/Si that are almost the same as those for the Si/Si case. For Si/Ge, the same trends are evident. Now isomers 4HB,E,F are similar to the Ge/Ge case with a low energy, while 4H-C is similar to the Si/Si case. 4H-A,B,D are similar to the Ge/Si case, as one bare atom is Si and the other Ge. The lowest-energy isomer is now 4H-B. However, it is unlikely that this structure would be formed from 4H-A, as 4H-A is likely to exchange a Si and a Ge atom as soon as the H atoms are lost. As shown above in Table 2, the lowest barrier of formation of these isomers is pathway 1 for 3 out of 4 cases, leading to 4H-A (and 4H-B via diffusion). The exception is the Si/Ge case, which will form 4H-F. 2H Structures. We can similarly form 6 isomers of 2H structures, shown in Figure 5, by again following the three reaction pathways from each of the 4H structures. The desorption energy barriers will now depend upon which 4H structure is used as a starting point. Pathway 1 forms 2H-A

Figure 4. Most stable structures obtained during the first step of H2 desorption from Si and Ge ad-dimers on the Si(001)-(2×1) and Ge(001)-(2×1) surfaces. Table 3 shows the corresponding Edes desorption barriers and Erxn reaction energies. D stands for diffusion pathways and Px (x = 1−3) for desorption pathways (see text for details). The black lines connecting surface atoms are a guide to the eye to indicate the absence of H atoms.

forms the 4H-A structure, which with a single H diffusion event can form 4H-B (or 4H-D). Pathway 2 forms 4H-C and, with diffusion, 4H-D and 4H-E; pathway 3 forms 4H-F (and with a single diffusion step, 4H-D). The total energies for these isomers in the 4 Si and Ge cases are given in Table 3. In each case, the lowest-energy isomer is shown in bold. Considering the four cases, we can discern trends in the total energies. For the Si/Si case, the lowest-energy isomer is where two Si subdimer atoms are able to dimerize and form a σ-bond (4H-B). Next are those where the two bare Si atoms are in neighboring sites and able to interact to form a weak π-bond (4H-A,C). Finally, where the two bare Si atoms are separated, without a chance of interaction between the two dangling bonds, the total energy is highest (4H-D,E,F). For Ge/Ge, a similar trend is seen, except that the differences are now smaller, suggesting that the Ge−Ge bond energies are weaker than those for Si−Si. The lowest-energy isomer is now 4H-A. For Ge/Si, there is a competing trend: the Ge−H bond is weaker than the Si−H bond; thus, the relative total energy is lower if one or both bare atoms is Ge. Note that isomer 4H-C has low energies for the Ge/Si and Ge/Ge cases and high

Figure 5. Most stable structures obtained during the second step of H2 desorption from Si and Ge ad-dimers on the Si(001)-(2×1) and Ge(001)-(2×1) surfaces. Table 4 shows the corresponding Edes desorption barriers and Erxn reaction energies. Px (x = 1−3) stands for desorption pathways (see text for details). The black lines connecting surface atoms are a guide to the eye to indicate the absence of H atoms. 10092



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from 4H-A, 2H-B from 4H-B, 2H-C from 4H-D, and 2H-E from 4H-F. Pathway 2 forms 2H-C from 4H-B, or 2H-A from 4H-E, and 2H-D from 4H-F. Pathway 3 forms 2H-B from 4HD, 2H-D from 4H-C, 2H-E from 4H-A, and 2H-F from 4H-F. Thus, the same isomers can be formed from different precursors via different routes. The numbers given in Table 4 Table 4. Kinetic Barriers (Edes) and Reaction Energies (Erxn) of the Most Stable Structures Obtained during the Second Step of H2 Desorption from Si and Ge Ad-Dimers on the Si(001)-(2×1) and Ge(001)-(2×1) Surfacesa

system Si/Si(001) Ge/Si(001) Si/Ge(001) Ge/Ge(001)

2H-A

2H-B

2H-C

2H-D

2H-E

2H-F

energy (eV)

P1

P1

P2

P3

P1

P3

Edes Erxn Edes Erxn Edes Erxn Edes Erxn

1.87 3.56 1.65 3.00 1.80 2.56 1.49 2.24

1.86 3.21 1.41 2.69 1.51 2.36 1.10 1.81

2.39 3.39 1.68 2.33 2.05 2.54 1.47 1.53

1.83 3.49 1.42 2.79 1.36 2.57 1.59 1.73

1.38 3.30 1.18 2.82 2.38 2.01 1.10 1.52

1.28 2.85 1.67 2.83 0.98 1.92 1.01 1.97

Figure 6. Starting points for the final step of H2 desorption from Si and Ge ad-dimers on the Si(001)-(2×1) and Ge(001)-(2×1) surfaces. Table 5 shows the corresponding Edes desorption barriers. Dx (x = 1− 5) stands for diffusion pathways and Px (x = 1−3) for desorption pathways (see text for details). The black lines connecting surface atoms are a guide to the eye to indicate the absence of H atoms.

pathway is via pathway 2 (2H-F). For Ge/Si, the lowest barrier is via pathway 1 (2H-E), and for Si/Ge and Ge/Ge, the lowest barrier is pathway 3 (2H-D). To conclude this section, the highest barriers found for all the pathways from 6H to clean ad-dimers is the initial desorption step. As shown in Tables 1 and 2, these barriers are 0.1 to 0.2 eV lower than those for desorption from the flat surface, suggesting that there is some enhancement of H2 desorption on a rough surface. Moreover, the barriers in general decline with decreasing H coverage, e.g., for the Si/Si case, the GGA barriers fall from 1.91 eV to as low as 1.28 eV. The reason for this is possibly that there become more degrees of freedom for the Si and Ge atoms to distort, similar to that found for diffusion off a trench ad-dimer in previous work;33 thus, any unsaturated parts of the surface will act as preferential desorption sites. Furthermore, the diffusion barriers for H2 up and down from ad-dimer to subdimer is much lower than that for diffusion on the flat surface;10 therefore, local rearrangement of H atoms to access the lowest-barrier desorption pathway will be likely. We have constructed reaction pathways following the lowest barriers for each of the Si/Si, Ge/Si, and Ge/Ge cases. Because of the complex network of possible pathways, these cannot be considered definitive. They are presented graphically in Figures S2−S5 of Supporting Information. The relative energy of each structure and kinetic barriers are indicated in the figures. Also, the presence of mixed Si−Ge dimers can also affect the desorption barriers, as they break the symmetry of the homo ad-dimers by means of a piecewise-rotation mechanism,46 thus creating a slightly different geometry array on the surface. This heterodimer configuration can lower the desorption barriers of pathway 2 (both hydrogen atoms desorb from the ad-dimer) for pure Si ad-dimers, as can be inferred from Table 5 comparing both Si and Ge ad-dimers. The results for the other pathways (1 and 3) are more uncertain, as there are two opposite effects: Ge adatoms on the Si(001) surface lower the desorption barrier and Si adatoms on the Ge(001) surface tend to increase it. H2 Desorption and Si/Ge Exchange in Si2H6 on the Ge(001)-(2×1) Surface. We briefly mentioned in the Introduction the fact that after the initial chemisorption of Si2H6 on the Ge(001)-(2×1) surface, the initial barrier for chemisorption and dissociation is noticeably higher (0.53 eV) than that on the Si(001)-(2×1) surface (0.14 eV) and the Si

a

Figure 5 shows the corresponding structures. The desorption barriers Edes are always referred to the previous configuration, but to allow a better understanding of the overall process, the reaction energies Erxn are always referred to the initial energies (precursor adsorbed on the surface).

reflect the lowest-energy possible routes from the 4H structures, as given in the titles. 2H-A is formed from 4H-A via pathway 1, likewise 2H-B from 4H-B and 2H-E from 4H-E. 2H-C is formed by pathway 2 from 4H-B. Pathway 3 converts 4H-C to 2H-D and 4H-F to 2H-F. Note that in this lowercoverage situation, pathway 3 is now the lowest energy for 3 cases, Si/Si, Si/Ge, and Ge/Ge, forming 2H-F from 4H-F. For Ge/Si, the lowest-energy barrier is the formation of 2H-E from 4H-E via pathway 1. The energy trends seen for the Si/Si case are the same as those in the 4H isomers. The lowest-energy isomer is now 2HF, as both subdimers can reform, and the highest-energy isomers are 2H-A and 2H-D, where no subdimers form. For Ge/Ge, however, the lowest isomers are 2H-C and 2H-E. For Ge/Si, the lowest isomer is 2H-C as for Ge/Ge, with the two H atoms bonded to Si subdimer atoms. 2H-F is now the highest energy, as the two H atoms are bonded to the two Ge atoms. For Si/Ge, again the lowest isomer, 2H-F, has the two H atoms bonded to the Si adatoms, and the highest-energy isomers 2HA,C,D, have the H atoms bonded to Ge atoms. In fact, 2H-F is likely to be the only stable Si/Ge isomer because in all other cases at least one Si/Ge exchange will have taken place. Final Desorption of H Atoms. For the final desorption of the 2H atoms (Figure 6), the final energy will be the same for all six isomers, and we are interested in the kinetic barriers to desorption (Table 5). Desorption of H2 can occur directly from 2H-E via pathway 1, 2H-F via pathway 2, or 2H-D via pathway 3. 2H-A requires two diffusion steps (the migration kinetic barriers are also shown in Figure 6 as Dx processes) to reach one of these structures, while 2H-B,C are one step away. The diffusion barriers are all much smaller than the desorption barriers and therefore will occur much faster than the desorption events. In general, there is a lower barrier to jump from Si to Ge than vice versa. For Si/Si, the lowest-barrier 10093



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Table 5. Kinetic Barriers (Edes) for the Last Step of H2 Desorption from Si and Ge Ad-Dimers on the Si(001)-(2×1) and Ge(001)-(2×1) Surfacesa 2H-C

2H-D

2H-E

system

2H-A D1

D2

2H-B D3

D4

D5

P3

P1

2H-F P2

Si/Si(001) Ge/Si(001) Si/Ge(001) Ge/Ge(001)

0.51 0.33 0.73 0.18

1.54 0.73 1.63 0.87

0.86 0.64 0.93 0.81

0.75 1.90 0.57 1.75

0.81 1.49 0.76 0.88

2.58 1.37 1.47 0.77

2.26 1.22 1.68 1.85

1.85 1.28 1.70 1.09

a Figure 6 shows the corresponding starting points for the final H2 desorption. The desorption barriers Edes are always referred to the previous configuration.

and Table 5). The exchange processes always decrease the energy of the system (Erxn = −0.12 eV), indicating that this is a favorable mechanism as soon as the hydrogen atoms diffuse off the Si ad-dimer. The second exchange pathway (after an initial H2 desorption following pathway 1; left-hand side of Figure S4 of Supporting Information) is not as favorable as the previous mechanism because of the high kinetic energy barrier for the second H2 desorption (following pathway 1, Edes = 1.80 eV; see Figure S4 of Supporting Information). After the three H2 molecules have been desorbed, the energy gain of this Si/Ge alloy is Erxn = 2.73 eV, slightly lower than for the Si2H6 adsorbed on the Ge(001) surface, Erxn = 3.07 eV, which also contributes to make the exchange process very likely to happen as soon as the H2 molecule is desorbed from the Si ad-dimers.

adatoms diffuse to subsurface sites at medium range temperatures (≈525 K), resulting in pure Ge surface dimers, as long as the hydrogen atoms are fully desorbed.3 To give an explanation for this experimental evidence, as shown in Figure 7, we have

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CONCLUSIONS We have studied H2 desorption mechanisms from Si and Ge row ad-dimers on both Si(001)-(2×1) and Ge(001)-(2×1) surfaces, which is a necessary step for atomically precise 3D nanostructure manufacturing. Our results show that a “mixed” desorption pathway where one of the hydrogen atoms desorbs from a subdimer and the other one from the corresponding addimer (pathway 1) is the most favorable mechanism for the majority of the systems studied in this work. The only exception is Si on Ge(001)-(2×1), where it is easier to desorb the H2 from a Ge subdimer (pathway 3). However, the reduced desorption barriers from the saturated ad-dimer are still not sufficiently low to account for the experimental observations. We note that the desorption barriers do fall dramatically (by as much as 0.6 eV for the Si/Si case) once the surface H coverage falls below 100%. Any dangling bonds will therefore act as catalysts for H2 desorption locally, and diffusion will allow other H atoms to move to the preferential desorption configurations. In this way, the transition from adsorbed Si2H4 species to addimers or small islands could occur in this temperature range. We have also found a low barrier for Si−Ge exchange, dropping as the surface H coverage falls, which supports the obtained experimental data. Adsorbed hydrogen on the addimer atoms block this subsurface diffusion mechanism. As a consequence, this process is very likely to occur after the initial steps of H2 desorption. While most of the calculations were performed using the GGA, the initial desorption steps, which were found to be ratelimiting in all four systems studied, were also calculated using the more accurate HSE functional. Our HSE calculations show that although GGA predicts the correct trends for the desorption barriers and reaction energies, they are always underestimated: the corrections range from 0.2 eV (pathway 1) to 0.6 eV (pathways 2 and 3). The obtained HSE desorption barriers and reaction energies for the interdimer desorption mechanisms agree quite well with the available experimental

Figure 7. Calculated pathways for Si/Ge exchange in the Si/Ge(001) system. From the 4H- isomer, the exchange barrier is 0.93 eV; for the 2H isomers, the barrier for the exchange process is even lower.

calculated the kinetic barriers and reaction energies for H2 desorption and Si exchange with Ge atoms on the Ge(001)(2×1) surface. For the 4H isomers, only 4H-A, formed via pathway 1, provides a pair of neighboring Si and Ge atoms, which can exchange. However, the most favorable H 2 desorption pathway is pathway 3, which keeps the ad-dimer atoms saturated with H (see Figure S4 of Supporting Information). The barrier for the exchange mechanism is much higher with the H2 molecule adsorbed on the Si addimer, around 2.5−3 eV, depending if the Ge subdimer atom has an adsorbed hydrogen. The first two steps of hydrogen desorption following the lowest-barrier pathway 3 leave the last pair of hydrogen atoms adsorbed on the Si ad-dimer. Then, one of the remaining hydrogen atoms undergoes a surface diffusion process from the Si ad-dimer to a neighboring subdimer Ge atom (with a rather low kinetic energy barrier, 0.78 eV), allowing one of the Si ad-dimer atoms to exchange its position with one of the Ge subdimer atoms. The kinetic barrier for the first exchange step is relatively low, 0.93 eV, and it is even lower for the second exchange process (Edes = 0.60 eV), showing that the Si/Ge exchange is a favorable mechanism. The second hydrogen diffusion step (previous to the second Si/Ge exchange process) can be either between Si ad-dimers or to another Ge subdimer atom (see Figure S4 of Supporting Information). Although the kinetic barrier for diffusion is the same for both processes (Edes = 1.29 eV), the latter is the most favorable mechanism because the final H2 desorption via pathway 3 has a desorption barrier (Edes = 0.77 eV) much lower than that of following pathway 1 (Edes = 1.85 eV; see Figure 6 10094



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(11) Pehlke, E. Highly Reactive Dissociative Adsorption of Hydrogen Molecules on Partially H-Covered Si(001) Surfaces: A DensityFunctional Study. Phys. Rev. B 2000, 62, 12932−12939. (12) Bowler, D. R.; Owen, J. H. G.; Goringe, C. M.; Miki, K.; Briggs, G. A. D. An Experimental-Theoretical Study of the Behaviour of Hydrogen on the Si(001) Surface. J. Phys.: Condens. Matter 2000, 12, 7655−7670. (13) Okamoto, Y. Hybrid Density-Functional Calculations of the Reactions of a H2 Molecule on C, Si, and Ge(001) Surfaces. J. Phys. Chem. B 2002, 106, 570−573. (14) Chen, C. L.; Tsai, D. H.; Jiang, J. C. Study of Pathway of Hydrogen Migration and Desorption on SiGe(100) Surface Using Ab Initio Calculations. Jpn. J. Appl. Phys. 2005, 44, 7625−7633. (15) Dürr, M.; Höfer, U. Dissociative Adsorption of Molecular Hydrogen on Silicon Surfaces. Surf. Sci. Rep. 2006, 61, 465−526. (16) Mui, C.; Bent, S. F.; Musgrave, C. B. A Density Functional Theory Study on the Effect of Ge Alloying on Hydrogen Desorption from SiGe Alloy Surfaces. J. Phys. Chem. B 2004, 108, 6336−6350. (17) Ning, B. M. H.; Crowell, J. E. The Effect of Germanium on the Desorption of Hydrogen from Si(100). Surf. Sci. 1993, 295, 79−98. (18) Wu, Y. M.; Baker, J.; Hamilton, P.; Nix, R. M. MIRIRS Studies of the Growth of Si and Si-Ge Alloys from Molecular Precursors. Surf. Sci. 1993, 295, 133−142. (19) Wu, Y. M.; Nix, R. M. Adsorption of Hydrogen and Disilane on Si(100) and SiGe Surfaces. Surf. Sci. 1994, 306, 59−68. (20) Russell, N. M.; Ekerdt, J. G. Kinetics of Hydrogen Desorption from Germanium-Covered Si(100). Surf. Sci. 1996, 369, 51−68. (21) Angot, T.; Louis, P. Hydrogen Population on Ge-Covered Si(001) Surfaces. Phys. Rev. B 1999, 60, 5938−5945. (22) Ku, J. H.; Nemanich, R. J. Hydrogen Evolution from Strained SixGe1−x(100)2×1:H Surfaces. J. Appl. Phys. 1996, 80, 4715−4721. (23) Kim, H.; Taylor, N.; Adelson, J. R.; Greene, J. E. Effects of H Coverage on Ge Segregation During Si1−xGex Gas-Source Molecular Beam Epitaxy. J. Appl. Phys. 1997, 82, 6062−6066. (24) Kim, H.; Desjardins, P.; Abelson, J. R.; Greene, J. E. Hydrogen Population on Ge-Covered Si(001) Surfaces. Phys. Rev. B 1998, 58, 4803−4808. (25) Rudkevich, E.; Liu, F.; Savage, D. E.; Kuech, T. F.; L, M.; Lagally, M. G. Hydrogen Induced Si Surface Segregation on GeCovered Si(001). Phys. Rev. Lett. 1998, 81, 3467−3470. (26) Angot, T.; Louis, P. Thermodynamically Driven Ge/Si Place Exchange Induced by Hydrogen on Ge-Covered Si(001) Surfaces. Phys. Rev. B 2000, 61, 7293−7296. (27) Qin, X. R.; Liu, F.; Swartzentruber, B. S.; Lagally, M. G. Modification of Si(100) Substrate Bonding by Adsorbed Ge or Si Dimer Islands. Phys. Rev. Lett. 1998, 81, 2288−2291. (28) Höfer, U.; Li, L.; Heinz, T. F. Pathways for Hydrogen Desorption from Si1−xGex(001) During Gas-Source Molecular-Beam Epitaxy and Ultrahigh-Vacuum Chemical Vapor Deposition. Phys. Rev. B 1992, 45, R9485−R9488. (29) Nachtigall, P.; Jordan, K. D.; Smith, A.; Jónsson, H. Investigation of the Reliability of Density Functional Methods: Reaction and Activation Energies for Si−Si Bond Cleavage and H2 Elimination from Silanes. J. Chem. Phys. 1996, 104, 148−158. (30) Radeke, M. R.; Carter, E. A. A Dynamically and Kinetically Consistent Mechanism for H2 Adsorption/Desorption from Si(100)2×1. Phys. Rev. B 1996, 54, 11803−11817. (31) Jing, Z.; Whitten, J. L. Multiconfiguration Self-Consistent-Field Treatment of H2 Desorption from Si(100)-2×1:H. J. Chem. Phys. 1995, 102, 3867−3872. (32) Owen, J. H. G.; Miki, K.; Bowler, D. R.; Goringe, C. M.; Goldfarb, I.; Briggs, G. A. D. Gas-Source Growth of Group IV Semiconductors: I. Si(001) Nucleation Mechanisms. Surf. Sci. 1997, 394, 79−90. (33) Bowler, D. R. Formation of Clean Dimers During Gas-Source Growth of Si(001). Phys. Rev. B 2003, 67, 115341. (34) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Hybrid Functionals Based on a Screened Coulomb Potential. J. Chem. Phys. 2003, 118, 8207−8215.

data for both clean (without ad-dimers) Si and Ge(001)-(2×1) surfaces.

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ASSOCIATED CONTENT

S Supporting Information *

Charts with the most likely desorption paths followed during the H2 desorption process from Si and Ge ad-dimers on the Si and Ge (100) surfaces. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: *E-mail: *E-mail: *E-mail:

[email protected]. [email protected]. [email protected]. [email protected].

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This work is supported by the Defense Advanced Research Project Agency (DARPA) and Space and Naval Warfare Center, San Diego (SPAWARSYSCEN-SD) under Contract N66001-08-C-2040. It is also supported by a grant from the Emerging Technology Fund of the State of Texas to the Atomically Precise Manufacturing Consortium. The authors also acknowledge the Texas Advanced Computing Center (TACC) for providing computational resources that have contributed to the research results reported within this paper.

(1) Lyding, J. W.; Shen, T. C.; Hubacek, J. S.; Tucker, J. R.; Abeln, G. C. Nanoscale Patterning and Oxidation of H-passivated Si(100)-2×1 Surfaces with an Ultrahigh Vacuum Scanning Tunneling Microscope. Appl. Phys. Lett. 1994, 64, 2010−2012. (2) Soref, R. A. Silicon-Based Optoelectronics. Proc. IEEE 1993, 81, 1687−1706. (3) Veyan, J. F.; Choi, H.; Huang, M.; Longo, R. C.; Ballard, J. B.; McDonnell, S.; Nadesalingam, M. P.; Dong, H.; Chopra, I. S.; Owen, J. H. G.; Kirk, W. P.; Randall, J. N.; Wallace, R. M.; Cho, K.; Chabal, Y. J. Si2H6 Dissociative Chemisorption and Dissociation on Si(100)-(2×1) and Ge(100)-(2×1). J. Phys. Chem. C 2011, 115, 24534−24548. (4) Owen, J. H. G.; Ballard, J.; Randall, J. N.; Alexander, J.; Von Ehr, J. R. Patterned Atomic Layer Epitaxy of Si/Si(001):H. J. Vac. Sci. Technol., B: Microelectron. Nanometer Struct.Process., Meas., Phenom. 2011, 29, 06F201. (5) Duke, C. B. Semiconductor Surface Reconstruction: The Structural Chemistry of Two-Dimensional Surface Compounds. Chem. Rev. (Washington, DC, U.S.) 1996, 96, 1237−1259. (6) Filippi, C.; Healy, S. O.; Kratzer, P.; Pehlke, E.; Scheffler, M. Quantum Monte Carlo Calculations of H2 Dissociation on Si(001). Phys. Rev. Lett. 2002, 89, 166102. (7) Dürr, M.; Raschke, M. B.; Höfer, U. Effect of Beam Energy and Surface Temperature on the Dissociative Adsorption of H2 on Si(001). J. Chem. Phys. 1999, 111, 10411−10414. (8) Pehlke, E.; Scheffler, M. Theory of Adsorption and Desorption of H2/Si(001). Phys. Rev. Lett. 1995, 74, 952−955. (9) Kratzer, P.; Hammer, B.; Norskov, J. K. Direct Pathway for Sticking/Desorption of H2 on Si(100). Phys. Rev. B 1995, 51, 13432− 13440. (10) Zimmermann, F. M.; Pan, X. Interaction of H2 with Si(001)(2×1): Solution of the Barrier Puzzle. Phys. Rev. Lett. 2000, 85, 618− 621. 10095



Article

(35) Dürr, M.; Raschke, M. B.; Pehlke, E.; Höfer, U. Structure Sensitive Reaction Channels of Molecular Hydrogen on Silicon Surfaces. Phys. Rev. Lett. 2001, 86, 123−126. (36) Hafner, J. Ab-Initio Simulations of Materials Using VASP: Density-Functional Theory and Beyond. J. Comput. Chem. 2008, 29, 2044−2078. (37) Hummer, K.; Gruneis, A.; Kresse, G. Structural and Electronic Properties of Lead Chalcogenides from First Principles. Phys. Rev. B 2007, 75, 195211. (38) Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals. Phys. Rev. B 1993, 47, 558−561. (39) Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (40) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (41) Madelung, O. Semiconductors: Data Handbook; Springer: Berlin, 1994. (42) Jónsson, H.; Mills, G.; Jacobsen, K. W. In Classical and Quantum Dynamics in Condensed Phase Simulations; Berne, B. J., Ciccotti, G., Coker, D. F., Eds.; World Scientific: Singapore, 1998; pp 385−404. (43) Henkelman, G.; Uberuaga, B. P.; Jónsson, H. A Climbing Image Nudged Elastic Band Method for Finding Saddle Points and Minimum Energy Paths. J. Chem. Phys. 2000, 113, 9901−9904. (44) Henkelman, G.; Arnaldsson, A.; Jónsson, H. Theoretical Calculations of CH4 and H2 Associative Desorption from Ni(111): Could Subsurface Hydrogen Play an Important Role? J. Chem. Phys. 2006, 124, 044706. (45) Monkhorst, H. K.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13, 5188−5192. (46) Lu, Z. Y.; Liu, F.; Wang, C.-Z.; Qin, X. R.; Swartzentruber, B. S.; Lagally, M. G.; Ho, K. M. Unique Dynamic Appearance of a Ge-Si Addimer on Si(001). Phys. Rev. Lett. 2000, 86, 5603−5606.

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