Ge Epitaxial

© Copyright 2002 by the American Chemical Society

VOLUME 106, NUMBER 5, FEBRUARY 7, 2002

LETTERS Dimer-Exchange Mechanism in Surfactant-Mediated Si/Ge Epitaxial Growth Seung Mi Lee*,† Semiconductor Physics Research Center, Jeonbuk National UniVersity, Jeonju 561-756, Korea

Eunja Kim Department of Physics, UniVersity of NeVada, Las Vegas, NeVada 89154

Young Hee Lee Department of Physics, Sungkyunkwan UniVersity, Suwon 440-746, Korea ReceiVed: May 2, 2001; In Final Form: NoVember 28, 2001

The kinetics of the dimer-exchange mechanism in the surfactant-mediated Si/Ge epitaxial growth was investigated by using the density-functional theory calculations. Several dimer-exchange models were evaluated by constructing appropriate pathways. We found that two previously suggested models involved both pushingout and rolling-over processes, giving rise to higher activation barriers than the surface diffusion barrier. We proposed a new pathway that exclusively involved the pushing-out process that gave a relatively lower activation barrier.

Surface segregation and island formation of the Ge atom in the Ge/Si hetero-epitaxial growth were experimentally well observed, because of the lower surface free energy of the Ge than the Si and the lattice mismatch (∼4%) between two materials. To suppress both Ge segregation1,2 and island formation, a surfactant was often introduced.3-13 It has been known that the presence of surfactant atoms reduces an additional Schwoebel barrier at the step edge14 and thus enhances the diffusion process of adatoms on islands, eventually annealing out the islands.7,15 Understanding this phenomenon requires not only energetics but also kinetics of adatoms at the surface. Because a needlelike growth of As dimers on the top surface has been suggested on the basis of the observation from a low * To whom correspondence should be addressed. E-mail: [email protected]. Fax: +49-30-8413-4701. † Current address: Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany.

energy electron microscope,11 several theoretical calculations have been performed to explain the surfactant-mediated dimerexchange mechanism.16,17 Although they predicted some intermediate structures of a Ge dimer which are energetically favorable on surfactant-covered surfaces, The kinetics associated with activation energies between intermediate structures were not evaluated. Recent experimental observations by scattered ion energy distributions18 negate some intermediate structures suggested by the previous works.11,16,17 This reassures us that, unless there is a reasonable activation energy of the dimerexchange process compared to the surface diffusion barrier provided by a reasonable pathway, there is no guarantee that such suggested geometries can be taken in real dimer-exchange process; that is, kinetics plays a crucial role in determining the validity of the reaction pathways. If the activation energy for the dimer exchange is considerably high compared to the surface diffusion barrier, the surface diffusion will be dominant over the dimer-exchange process. Therefore, accurate calculations

10.1021/jp0116555 CCC: $22.00 © 2002 American Chemical Society Published on Web 01/10/2002

892 J. Phys. Chem. B, Vol. 106, No. 5, 2002 of the activation energy for a given pathway are required in order to validate the dimer-exchange mechanism. In this paper, we explicitly show that the Ge segregation to the front growing surface is significantly suppressed, by introducing Sb surfactants prior to deposition of Ge atoms, through the dimer-exchange process with surfactant atoms in the subsurface. We construct appropriate pathways of previously suggested configurations and examine kinetics for the Ge/Sb/ Si(001) system using the density-functional theory (DFT) calculations. We find that the suggested models incorporate necessarily the pushing-out and rolling-over processes that give relatively high activation energies of g2 eV, making these models improbable. We propose a new pathway that involves the pushing-out process only with activation energy of 0.76 eV, which is smaller than the surface diffusion barrier of 1.15 eV. A supercell which contains seven atomic layers of (4 × 2) atoms along the [001] direction is used for our calculations, with bottom layer of the Si surface terminated by hydrogen atoms and the top surface followed by a vacuum region of 7 Å. Both two Si layers and H atoms at the bottom are fixed to prevent any spurious forces from being emitted by H atoms. We have adopted the DFT calculations developed by Car and Parrinello19 in our calculations. The ionic and electronic forces are derived separately from the effective Lagrangian based on the local-density approximation (LDA). (It is well known that the LDA approaches overestimate the binding energies. However, the differences of the energy differences among different geometries between the LDA and the generalized-gradient approximations are negligible.) The interaction between the core electrons and valence electrons is described by nonlocal normconserving pseudopotentials with s and p nonlocality.20 The electronic wave functions are expanded with a kinetic energy cutoff of 12 Ry, and Bloch functions at the Γ point of the supercell surface Brillouin zone are used. The convergency of the cutoff was evaluated with dimers, which provides correct binding energies and bond lengths.21 We searched for the electron energy minimization using a steepest decent approach for a given geometry. Ions were then moved by the fast relaxation scheme. The remaining forces on the surface atoms were less than 2.0 × 10-2 Ry/Å in equilibrium. The energy was converged to 5.0 × 10-6 Ry through the calculations. We calculate the surface free energy for Sb/Ge/Si(001) and Ge/Sb/ Si(001) systems. The total energy of the Sb/Ge/Si(001) system is lower by 3.5 eV/dimer than that of the Ge/Sb/Si(001) system, as expected from the cohesive energy difference between bulk Ge and Sb system. (The top Sb surface in the Sb/Ge/Si(001) system shows (2 × 1) reconstruction with the dimer buckling of 0.2 Å, whereas the top Ge surface in the Ge/Sb/Si(001) system reveals p(2 × 2) with the dimer buckling of 0.3 Å.) This energetics clearly shows that there is a tendency for the Sb to prefer to float to the front growing surface. However, in order for Sb atoms to float to the top surface, they should be able to exchange their sites with the top Ge atoms. It is worth noting that the site-exchange process is possible only when the surface diffusion barrier (Es) for a Ge adatom to migrate on a Sb-covered surface is higher than or comparable to the interdiffusion barrier (Eb). Otherwise the surface diffusion will predominantly overwhelm the site-exchange process. A single Ge-adatom diffusion on the Sb-covered Si surface is examined, before calculating the interdiffusion barrier of a Ge ad-dimer. The z coordinate (normal to the surface) of the adatom and surface atoms on the first two layers are allowed to relax. We find that the Ge adatom can easily migrate along the dimer rows with a relatively low migration barrier of less

Letters

Figure 1. Pathway and the corresponding potential profile for the Ge dimer diffusion on the Sb-covered Si surface. Open circles indicate the points evaluated in intermediate pathways between steps without presenting the corresponding geometries. Step i is taken as a reference energy.

than 0.1 eV. Once it arrives easily to the minimum point in the trough between dimer rows, it has to overcome 0.6 eV to escape to the next dimer row. The migration path of a single Ge adatom on the Sb-covered Si surface is very similar to that on the Ascovered Si surface.16 The low Es will easily induce to a Ge dimer formation in the trough (between dimer rows). It is, therefore, more appropriate to consider a Ge dimer in the exchange process. In experiment, a dimer is easily formed at a relatively high temperature.22 The Ge dimer in the trough between dimer rows (as shown in Figure 1a) gives a lower energy by 0.55 eV than that between two dimers in a same dimer row. The diffusion of a Ge ad-dimer on the surface is investigated, presuming that a Ge ad-dimer can migrate on the surface instead of the site exchange with the subsurface atoms. Among many possible pathways for a surface diffusion, Figure 1 shows the pathway which gives the lowest potential barrier. The ad-dimer atoms are constrained along the x direction (dimer direction), whereas other coordinates including the surface atoms are fully relaxed. No bond breaking of the Ge ad-dimer is observed during the whole process. The barrier of 1.15 eV appears at the step (v) where the bond angles of the Ge ad-dimer are most heavily distorted. Once the Ge dimer reaches at the center of two dimers, the Sb-Sb bond of the surface dimer breaks and strengthens Sb-Ge bonds, gaining the energy of 0.5 eV. This potential barrier of 1.15 eV will be a criteria to judge whether the dimerexchange mechanism is preferable to the surface diffusion or not. We now discuss the Ge dimer-exchange mechanism with the surfactant in the subsurface. Two theoretical models have been suggested on the basis of the needlelike growth mechanism.16,17 Although both models are proposed with some intermediate configurations that are energetically favorable, the kinetics on such models has not been evaluated. Therefore, the validity of the previously proposed models is still questionable. To investigate the kinetics of these models, we first construct an appropriate pathway of each model. Figure 2 shows the pathway and the corresponding potential profile when two Ge dimers (Ge coverage, θ ) 0.5) are located on top of the adjacent dimer rows where the Ge dimer bond length is relatively long as 2.77 Å because of Sb atoms in the subsurface. The configurations

Letters

Figure 2. Pathway and the corresponding potential profile. The configurations in the dotted box are suggested by Ohno.17 Step a is taken as a reference energy. The dotted line in the potential energies is drawn by conjecture because they follow similar steps to those of a-e.

in the dotted box are intermediate configurations suggested by Ohno.17 To evaluate the potential barrier between intermediate configurations, we first construct the appropriate pathway as shown in Figure 2. Ge ad-dimers and other surface atoms are similarly constrained as before. To adopt the suggested intermediate configuration of step f, the Ge ad-dimer on the left is pushed down to the surface which eventually breaks Sb-Si bonds (pushing-out process). This requires the energy cost of 2.67 eV. Then, the Sb dimer rolls over the Ge atoms as shown in step d (rolling-over process) and becomes an ad-dimer to complete the site exchange. The other Ge dimer will follow similar steps (b-e) as shown by the long-dashed line in the potential profile. One more rolling-over process of the Sb dimer is required to accomplish the needlelike growth as shown in steps f-i. This requires an energy cost of 2.3 eV. Although a locally stable configuration (f), as suggested by Ohno, gains energy by about 2 eV compared to step a, kinetics simply negates this model because of the high activation energy compared to the Es of 1.15 eV. One may take a different pathway in steps d through e which may give rise to a different potential profile. However, step b, which requires high energy cost, is still inevitable to reach the step f in any pathway. We next examine another model suggested by Yu and Oshiyama.16 Figure 3a shows another local minimum for a Ge ad-dimer in the trough between dimer rows in the case of θ ) 0.25. The energy is minimized by the strong Ge dimer bond length of 2.59 Å, whereas the adjacent Sb dimer bond lengths of 3.3 Å are weakened by the Ge ad-dimer, which are indicated by the short-dashed lines. The relaxation scheme is similarly taken as before during the exchange process. Pushing down the Ge ad-dimer to the right and exchanging the dimer with the subsurface Sb atoms requires an energy cost of 0.76 eV only, as shown in the potential profile. Its further fully relaxed configuration decreases the energy by 0.5 eV, revealing a locally stable configuration. To reach the suggested intermediate configuration of step g, another rolling-over process of a Sb dimer is necessary. This requires an energy cost of 2 eV, where most energy cost comes from Sb-Sb bond breakings and bond angle distortions as shown in step f. Thus, step g finally gains

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Figure 3. Pathway and the corresponding potential profile. The configurations in the dotted box are suggested by Yu and Oshiyama.16 Step a is taken as a reference energy.

the energy of 1.4 eV compared to the Ge ad-dimer in the trough of step a. Although this model gives a lower activation energy of 2 eV than the previous model by Ohno, it is still too high to compare with the Es of 1.15 eV, again making this model improbable. One may consider a different pathway that the Ge dimer first rolls over and then pushes out the Sb atoms onto the top surface where the order is reversed from the previous pathway. However, it is easy to see that this pathway will give higher activation energy because the Ge rolling-over process costs higher activation energy than the Sb rolling-over process because of the exposed dangling bonds at the Ge dimer. The lesson from these calculations can be summarized as follows: (i) both models require pushing-out and rolling-over processes for the dimer-exchange, (ii) both processes give relatively higher activation energies than that of the surface diffusion, particularly at θ ) 0.5, making these models unrealistic, and (iii) one may begin with a single Ge ad-dimer at low coverage (θ ) 0.25) but should avoid the rolling-over process to have lower interdiffusion barrier. Although these models achieved the experimentally suggested needlelike growth based on energetics, kinetics shows that they are unrealistic because of relatively high activation energies. The intermediate geometries of these models (Figures 2f and 3g) have been further checked by experiments of scattered ion energy distributions.18 However, none of the above pathways could reproduce the energy distributions calculated by Monte Carlo simulation. Although there is an ambiguity on which experimental temperature and coverage can provide the suggested pathways, this implies that it is very unlikely to take such intermediate structures in the dimer-exchange process in experiments. Here we propose a new pathway which gives a lower activation energy than that of the previously suggested models as shown in Figure 4. We still limit the coverage θ e 0.5 in our model. Because a single Ge ad-dimer gives lower Eb for the pushing-out process as described above, we start for a single Ge ad-dimer in the trough between dimer rows and allow first pushing-out process which gives an Eb of 0.76 eV only (step I-a-I-d). Step I-d, the locally stable state, will be maintained for some time. During that time, an additional Ge ad-dimer can easily bind on the adjacent dimer row as shown in the II-a, where the coverage becomes θ ) 0.5, as a result. Note that the energy

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Letters mechanism suggested in the present model will play an important role to achieve the experimentally observed needlelike growth. Islands can also be formed locally during the growth process, but these will soon be annealed out by the presence of the surfactant on island edges which gives rise to the negative Schwoebel barrier.14,15 Thus, the surfactant enhances the dimerexchange process and suppresses the Ge segregation to the front growing surface and furthermore removes the islands effectively so that layer-by-layer growth is promoted. In summary, we have investigated kinetics of several models for the dimer-exchange mechanism in surfactant-mediated epitaxial growth using the DFT calculations. A new pathway, which incorporates the pushing-out process exclusively with a lower activation energy barrier than the surface diffusion barrier, has been proposed. This new pathway is in good agreement with experimental observations in the needlelike growth of Si/ Ge.

Figure 4. Proposed pathway and the corresponding potential profile. The energy of step II-a is taken as reference for step II.

Acknowledgment. This work was supported by the BK212001 program. References and Notes

of step II-a was taken as the reference of step II, which is not directly comparable to that at lower coverage. The floating of Sb atoms to the top surface by another pushing-out process only requires an activation energy of 0.57 eV (step II-a-II-d). The energy loss is less in these pathways because of the sustaining of the bonds with adjacent neighbors. This eventually achieves the experimentally suggested needlelike growth without costing extra energy as shown in step II-c-II-d. Note that no rollingover process is incorporated in this model. With more incoming Ge dimers to the right of the dimer row, the above process can be simply repeated. Thus, our model requires a smaller activation energy of 0.76 eV than the Es of 1.15 eV and furthermore achieves clearly needlelike growth. One may consider another adsorption site of the Ge dimer at θ ) 0.5, where the Ge dimer is located in the trough near the Sb dimer, similar to step I-a. In this case, pushing Sb atoms in the sublayer to the right will lead to the similar pushing-out mechanism, but the activation barrier is expected to be higher than the previously discussed pathway because of the formation of the weaker Sb-Sb dimer compared to the case of the SbGe dimer. Although this pathway still explains a surfactantmediated crystal growth, the experimentally observed needlelike growth cannot be explained. There is a chance that a single adatom plays a dominant role in the exchange process as suggested by Ko et al.23 at low coverage (θ e 0.25) and low-temperature limit. Because the activation energy is very low (about 0.1 eV) in such a case, the single-adatom exchange mechanism will be dominant in this limit. Therefore, at coverage θ g 0.25, the dimer-exchange

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