Observation of Ultrathin Precursor Film Formation during Ge–Si Liquid

Dec 20, 2016 - The results can be understood by the use of thickness-dependent correlated interfacial energies ... material, which can only form under...
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Observation of Ultrathin Precursor Film Formation during Ge−Si Liquid-Phase Epitaxy from an Undersaturated Solution Vedran Vonk,*,†,‡ Diego Pontoni,§ Melissa Cremers,† Anne Kerkenaar,† Arno A. C. Bode,† Wiesiek Szweryn,† Gregor Nowak,‡ Aryan E. F. de Jong,§ Helmut Dosch,‡ and Elias Vlieg† †

Institute for Molecules and Materials, Radboud University Nijmegen, Nijmegen 6525AJ, The Netherlands Deutsches Elektronen-Synchrotron (DESY), Hamburg 22607, Germany § European Synchrotron Radiation Facility, Grenoble 38000, France ‡

S Supporting Information *

ABSTRACT: Our in situ X-ray study shows that a silicon substrate in contact with an undersaturated In(Ge) solution is wetted by an approximately 1 nm thin germanium film, which does not grow any thicker. The results can be understood by the use of thickness-dependent correlated interfacial energies. This near-equilibrium heterogeneous interface structure marks the initial stage of crystal growth before the formation of bulk material, which can only form under conditions of supersaturation. This finding uncovers a fundamental aspect of the thermodynamics at solid−liquid interfaces relevant for understanding the transition from equilibrium to supersaturation and is of importance for nanoscale solution growth methods.

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INTRODUCTION Ever since the groundbreaking work of Gibbs, there is a continuing effort to understand the thermodynamics of surfaces and interfaces in relation to their bulk counterparts. This led to important insights, such as surface melting1 and freezing,2 that is, a selvedge showing different melting or freezing temperatures than the bulk. In multicomponent systems, segregation alters the near-surface composition, which further changes the properties. How these phenomena interplay at heterogeneous interfaces under the influence of a driving force for crystallization is largely unexplored. Such mechanisms are at work during the near-equilibrium solution growth, which is known to produce the highest crystal quality needed in, for example, semiconductor applications and are gaining ever more importance for the fabrication of nanoscale materials. For thin films, the highest quality material is obtained by liquid-phase epitaxy (LPE).3 Because growth takes place at a deeply buried interface, the processes underlying LPE remain for a large part a mystery. The most conventional type of LPE growth experiment consists of bringing a liquid solution in contact with a substrate, onto which a thin film forms during cooling. In a bulk thermodynamic picture, supersaturation is induced by cooling below the liquidus temperature after which the bulk material can crystallize. There are now several basic aspects related to LPE that are not well-understood. First of all, what is the equilibrium solid−liquid interface structure in the absence of supersaturation (before cooling) and what is the influence of a foreign substrate on the thermodynamic energy landscape as encountered in heteroepitaxy? These fundamental © 2016 American Chemical Society

issues play a role in the growth of large bulk crystals, nanowire synthesis via the vapor−liquid−solid method, and are of great importance for solution growth modeling, which is now performed without realistic microscopic descriptions of the solid−liquid interface.4 Experimental access to the buried interface during the growth is challenging. In situ observations are required because the grown structures are often prone to oxidation or because of the so-called shut-off effect,5 which occurs as unwanted surface crystallization during the removal of a crystal from the solution. So far, in situ experiments have focused on microscopy6 or on the growth from saturated solutions.7 By the use of high-energy X-rays in grazing-incidence-transmission geometry,8 it is possible to follow the growth interface during LPE. Here, we show for the first time the experimental results on the initial stages of germanium heteroepitaxy on silicon from an undersaturated indium solution. The results show, as predicted theoretically,9 that new equilibrium structures, forbidden by bulk thermodynamics, can form at the buried interfaces and that these extend over a width of the order of the interaction’s correlation length. Si−Ge LPE. In the case of LPE heteroepitaxy, one is in general faced with a ternary system: solvents, solutes, and substrates.10 Ge and Si can form solid solutions GexSi1−x for all compositions x. The ternary In−Ge−Si phase diagram shows Received: November 3, 2016 Revised: December 19, 2016 Published: December 20, 2016 814

DOI: 10.1021/acs.langmuir.6b03984 Langmuir 2017, 33, 814−819

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energetics significantly. LPE is generally performed at lower growth temperatures than MBE. LPE takes place much closer to the thermodynamic equilibrium, which alters the growth considerably because kinetics plays a completely different role. Growth from undersaturated solutions has been reported before.19−21 The experimental conditions in those studies enabled the growth of thick bulklike films or included multicomponent systems in which substrate dissolution played a role. Both aspects complicate an interpretation based on surface effects because of the presence of a driving force for bulk crystallization. For undersaturated conditions, one can describe the process in terms of wetting, using interfacial energies γ. In literature, there are different terms used for such processes, such as prewetting or adsorption,22 and a comprehensive account of different aspects is given in ref 23. Here, a description is presented using explicit values of γ, which for the Si−Ge system are relatively well-known. The heteroepitaxial growth from undersaturated conditions is expected to stop as soon as the influence of the substrate is completely screened by the film. By definition, the total energy of a crystal is the sum of the surface energy and the bulk contribution. In a heteroepitaxial system, with the growth of additional monolayers, the surface energy changes from the value of the substrate to that of the bulk film; the film becomes so thick that its properties are bulklike. The exact way in which this transition takes place will depend on the atomic interactions as described by the potentials. In general, a distinction is made between short- and long-range interactions,24 such as the Coulomb and van der Waals terms. Describing this process in the continuum limit, the difference in (areal) the Gibbs free energy ΔG as a function of film thickness h for such heteroepitaxial growth can be expressed as25

equilibria between each of the mixed solids and a saturated In solution of specific Ge/Si composition.11 This means that a clean pure Si substrate brought in contact with a solution of In−Ge−Si is not in equilibrium, and it will be overgrown by a solid GexSi1−x film until the equilibrium is reached. The same holds for a clean Si wafer brought in contact with a binary Ge− In liquid because of Si dissolution. The Supporting Information gives a detailed account on the bulk thermodynamics involved in the ternary system. During this process, the compositions of both liquid and solid films can change, for which the latter can be exploited to grow composition-gradient films. How the final equilibrium is reached exactly will mainly depend on the kinetics.12 The driving force for such an LPE process is governed by bulk thermodynamics, and it enables the growth of thick bulklike structures. To prevent or at least slow down Si dissolution, we have used SiO2-capped Si substrates in our experiments. In this way, our experimental conditions are such that the bulk thermodynamics of the system can be described by the In−Ge binary phase diagram, as shown in Figure 1. The undersaturated conditions

ΔG(h) = ( −Δμ + Es)h + γslC1(h) + (γsf + γfl)C2(h)

Figure 1. In-rich part of the In−Ge system. At point A, the liquid is saturated with Ge, after which the liquid is heated (ΔT < 0) at a constant Ge content to point B, which represents an undersaturated liquid; about twice as much Ge can be dissolved at this temperature. The left hand side shows a schematic representation of the bulk Ge growth at supersaturation (ΔT > 0) and the wetting layer formation from undersaturated solutions (ΔT < 0).

(1)

where Δμ is the driving force for bulk crystallization, Es is the elastic strain energy of the film, γi is the energy of interface i, s is the substrate, f is the film, and l is the liquid. Two correlation functions C are used, which describe how the interfacial energy gradually changes as a function of film thickness, much as in the way that surface melting is formalized.26,27 Here, we choose C1(h) = e−h/ξ and C2(h) = 1 − C1(h), where ξ is the correlation length of the exponential, Coulomblike, interaction potential. The choice for an exponential function is made to describe the phenomenology, which suffices to explain our experimental results. Figure 1 can also be used in combination with more sophisticated forms for C, such as the Lennard-Jones potential, to include more details of the interaction. Using the exponential interaction potentials, a minimum is found for a wetting thickness hw = −ξ ln(ξΔΩ/Δγ), where ΔΩ = −Δμ + Es and Δγ = γsl − (γsf + γfl). Under these conditions, a new equilibrium, not predicted by the bulk phase diagram since Δμ < 0, should be formed at which a thin film of finite thickness has formed between the substrate and the liquid.

are established by heating a saturated liquid at a constant Ge content. In this way, there is no driving force for the formation of bulk Ge nor for that of the mixed GexSi1−x compound. Germanium molecular-beam epitaxy (MBE) on SiO2covered Si substrates has been reported quite extensively.13,14 Initially, it was explored as a means to grow very small Ge nanocrystals ( 0) introducing Ge are shown. The different interfacial energies γ as used in eq 1 are indicated as well. The QL indium layer is shown as a wavy line, of which the period and amplitude indicate the amount of densification. After 1 h of contact time, the Ge interface is getting rougher, which is indicated to be the triangular undulations. (c) Ge thickness as a function of contact time. The dashed line represents the average Ge film thickness of the different measurements, and the vertical line represents the average estimated error bar.

optimized. The thickness (1.2 nm) and density (760 e/nm3) of the SiO2 layer were determined from the data taken before introducing Ge, and these values were fixed during the fits of the data taken for t > 0. In this way, each of the fits was obtained approximately with the same number of parameters, corresponding to one solid and one QL slab. It was noted that after introducing Ge into the system, the signal around the critical angle for total reflection, θc(4π sin(θc)/λ = Qc ≈ 0.2 nm−1) was attenuated. Below Qc, the 8 μm beam has to traverse the edge of the Si substrate, which is closest to the liquid. During the contact, it is very difficult to avoid that the rim of the substrate is dipped into the liquid, thereby possibly wetting a few microns of the substrate sides and influencing the transmission of the X-ray beam at these very glancing angles. For higher scattering angles, the beam is passing through a higher part of the substrate, which has not been in contact with the liquid. For these reasons, the very first parts of the XRR curves obtained during the Ge growth have been excluded from the data analysis. The electron density profile obtained for t < 0 is made up of the 1.2 nm SiO2 layer and a 0.7 nm thin QL In layer with a density, that is, about 25% larger than the bulk liquid In. The thickness and density of this layer are slightly lower than when in contact with pure Si(100),32 but this can be attributed to the presence of the oxide.31 This is also in line with the explanation that the properties of the QL layer depend on the electronic properties of the underlying solid. It is believed that the charge transfer from the liquid metal to the conduction band of the solid can be partially responsible for a local densification. Because this phenomenon depends on the band gap of the semiconductor, the presence of the oxide, which has a much larger band gap than silicon, will have a large influence. From 3 h onward, the density profiles do not change too much anymore, and the QL layer has nearly disappeared. As can be seen in Figure 3, the XRR curves are not significantly different, which means that the fits should result in nearly identical electron density profiles. Therefore, we interpret the differences in the electron density profiles as a measure of the error, which in Figure 4c for the Ge film thickness is shown as an estimated standard deviation. It was not possible to obtain the satisfactory fits when completely omitting the QL layer, even if its appearance in the density profile is minimum. This can be partly attributed to the relatively large Ge−QL interface

roughness of approximately 0.4 nm. Such a value seems slightly high for a film in contact and equilibrium with its liquid mother phase, the case in which one would expect very large and flat terraces. We therefore speculate that the Ge islands, through facetting, may have formed. If indeed, such islands start to form after the film has reached a nominal thickness of about 1 nm, this would imply that the critical thickness of the Ge wetting layer is about twice as thick for our LPE growth conditions than it is during widely studied MBE. The possibility of such an increased critical thickness during the LPE growth has been reported before, where the films were studied ex situ without the liquid.33 An explanation for an enhanced surface roughness might be that a flat Ge(001) oriented film does not represent the thermodynamic equilibrium yet because there are other facets with lower surface energy. Such a facetting behavior is closely related to strain, as it appears in MBE through the socalled Stranski−Krastanov growth. In any case, the data obtained here indicate that the Ge film thickness hardly changes and is basically constant within the estimated error throughout the investigated contact times up to 16 h; see Figure 4c. These results can be graphically summarized as shown in Figure 4b and suggest that there is an optimum growth time less than 3 h after which a maximum Ge thickness and possibly smoothness is reached. To test the assumption that when Si is present in the liquid, much thicker bulklike films are grown, we have also conducted an experiment where a Si wafer was placed on the bottom of the crucible holding the liquid. The Ge saturation temperature for this experiment was 523 K, and the growth was performed at 623 K. Because for this growth experiment, the oxide on the substrate was much thicker and rougher, no reliable quantitative XRR data analysis could be performed. Nevertheless, qualitatively, the shape of the XRR curves kept changing, even after 16 h of the contact time. Ex situ postgrowth X-ray analysis of the sample indicates the formation of an approximately 30 nm thick film. From the position of its 111 Bragg reflection, it is concluded that the average composition is close to Ge0.5Si0.5, which corresponds very well with that expected from the ternary phase diagram.11,34 Such a postgrowth ex situ characterization of the 1 nm sample was not possible, owing to the instability under ambient conditions of such a thin Ge film. 817

DOI: 10.1021/acs.langmuir.6b03984 Langmuir 2017, 33, 814−819

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Langmuir The Ge wetting layer thickness can be calculated by Figure 1. In the following, the temperature effects, which are known to lower all surface energies,35 have been neglected. Liquid indium is supposed to wet both Si and Ge.35 For sufficiently small wetting angles, the Young−Dupré equation reduces to γsl = γsv − γlv, where the subscript v represents vapor. The values for liquid In and solid Ge(001) are taken as 56036 and 1710 mJ/ m2,37 respectively. Because the dangling bonds are assumed to be saturated by the liquid, the value for the unreconstructed Ge(100) is taken. The surface energy of the substrate is more difficult to derive, and no accurate data are available in the literature. This is mostly due to the complicated structure of the ultrathin SiO2 layer, which shows residual ordering.38 As discussed in relation to previous MBE results, as a first-order approximation, we assume that the interface energies of the bare and oxide-covered Si are rather similar. We therefore take γSi/SiO2 ≈ γSi = 2390 mJ/m2.37 Finally, the interfacial energy between the solid substrate and the solid Ge has been estimated to be 150 mJ/m2.39 The values for the formation energy term is calculated as follows: Δμ = ΔH(Tsat − T)/T, where ΔH = 5.8 kJ/mol is the formation enthalpy of the bulk Ge at temperature T and Tsat is the saturation temperature (see Figure 1). Using this value for ΔH40 and the experimental temperatures give Δμ = −30 MJ/m3. We also consider the strain energy. Interestingly, also with the oxide, Ge grows epitaxially with the underlying Si.13,14 This epitaxial relationship was also found for our 30 nm Ge0.5Si0.5 film. It is believed that crystalline inclusions in the ultrathin oxide are responsible for passing the epitaxial properties. Because we were not able to determine the strain state of the wetting layer, we consider the two extreme cases of the fully strained and fully relaxed (Es = 0) Ge. The energy for Ge fully strained to the Si lattice can be calculated from41 Es = 2Gϵ2

1+ν 1−ν

Figure 5. Free energy calculation for Ge heteroepitaxy on a SiO2/ Si(100) substrate from an undersaturated In solution. The different energy contributions from Figure 1 versus the Ge film thickness are shown. The effect of strain is shown by calculating eq 1 with (upper solid) and without (lower solid) a contribution from Es, as shown by the two formation energies (ΔΩ = −Δμ + Es) (dash-dotted). The minimum energy gives wetting layer thicknesses, hw, in the strained and relaxed cases.

a thin film may act as a precursor before the conditions of supersaturation are induced in conventional heteroepitaxial LPE. These results uncover a fundamental aspect of the microscopic nature of solid−liquid interfaces relevant for the detailed understanding of the solution growth.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.6b03984. A detailed description of LPE in the ternary system Si− Ge−In (PDF)

(2)

where G is the shear modulus, ϵ is the strain, and ν is the Poisson ratio. When taking the following values G = 70 Gpa,40 ϵ = 0.035, and ν = 0.26 results in Es = 300 MJ/m3. A value of ξ = 0.25 nm is chosen to obtain the experimentally determined wetting layer thickness, and the cases of the strained and relaxed Ge is explored; see Figure 5. These results indicate that it is possible to obtain control over the final thickness of thin films grown from solution, without the need to very precisely control the contact time. The crystal quality should be excellent because the system is allowed to equilibrate. By proper choice of the combination of substrates, solutes and the growth temperature, it is in principle possible to tune the final film thickness in a range of the order of several times the correlation length ξ of the system. This might open up new possibilities for the growth of ultrathin, smooth, and highly perfect structures at low temperatures from solution.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Vedran Vonk: 0000-0001-9854-1101 Elias Vlieg: 0000-0002-1343-4102 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We wish to thank T. Buslaps, B. Wehinger, and H. Reichert for support regarding the UHV equipment. This work is supported by the Netherlands Organization for Scientific Research (NWO) through a VENI grant.

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CONCLUSIONS We have observed the formation of a quasi-equilibrium Ge wetting layer on a Si/SiO2 substrate under conditions of undersaturation, which imply that there is no driving force for the crystallization of bulk material. The thin film formation leads to a change in surface energies of the solid in contact with the liquid, and this acts as a driving force. It is shown that a minimum in free energy occurs at a film thickness on the order of 1 nm, a few times the correlation length of the system. Such

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DOI: 10.1021/acs.langmuir.6b03984 Langmuir 2017, 33, 814−819