Configurable Compliant Substrates for SiGe Nanomembrane

Article pubs.acs.org/crystal

Configurable Compliant Substrates for SiGe Nanomembrane Fabrication Jean-Noel̈ Aqua,*,† Luc Favre,‡ Antoine Ronda,‡ Abdelmalek Benkouider,‡ and Isabelle Berbezier‡ †

Institut des Nanosciences de Paris, Université Pierre et Marie Curie Paris 6, CNRS UMR 7588, 4 place Jussieu, 75252 Paris, France Institut Matériaux Microélectronique Nanoscience de Provence, Aix-Marseille Université, UMR CNRS 6242, Avenue Escadrille Normandie Niemen - Case 142, 13997 Marseille, France

‡

S Supporting Information *

ABSTRACT: The aim of this work is to give quantitative guides for the fabrication of strain-engineered SiGe epitaxial nanomembranes using a compliant substrate. We theoretically determine the effect of the elastic properties (softness and strain level) of a compliant substrate on the morphological evolution of an epilayer. The experimental system under investigation is the SiGe on Si(001) model system, which develops an Asaro−Tiller−Grinfel’d (ATG) growth instability or misfit dislocations for large epitaxial stresses. The compliant substrate is a porous silicon layer whose softness and strain level can be adjusted by varying the density of pores and the annealing conditions. The softness and strain level of the compliant substrate are analyzed independently. We show that the softness of the compliant substrate produces a significant enhancement of the growth instability that normally develops in SiGe/Si systems. We rationalize the counterintuitive and commonly misunderstood instability enhancement by considering the elastic energy in the substrate after deposition of an epilayer. A fundamental result to mention is that in the experimentally relevant system consisting of Si substrate/compliant pseudosubstrate/Si buffer layer/epitaxial layer, a major parameter that controls the instability development is the thickness of the Si buffer layer. For a soft compliant substrate (typically with a Young’s modulus ten times smaller than silicon), a thin buffer layer (20 nm thick) suppresses the compliant effect. This is an important result for experimental studies, which commonly neglect the influence of the buffer layer. We quantify this effect and give an experimental proof, which confirms the theoretical result. We then consider the effect of the strain level of the compliant substrate. We give evidence that, in standard experimental situations, a tensilely strained compliant substrate could kinetically inhibit the development of the instability and could also delay the nucleation of misfit dislocations. The theoretical results are confirmed by exemplary experimental results using a tensilely strained porous silicon substrate obtained by annealing in specific conditions (HT-PSi). Both the inhibition of the ATG growth instability and the delay of the nucleation of misfit dislocations are evidenced for different SiGe alloy concentrations in good agreement with theoretical models. These results strongly highlight the importance of the HT-PSi as a configurable compliant substrate not only for the fabrication of SiGe nanomembranes totally flat and free of dislocation but also for the heterogeneous growth of various systems on silicon. They also give a basic understanding of the elastic mechanisms and the universal rules for producing generic configurable compliant substrates.

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INTRODUCTION Silicon-based strain engineered nanomembranes (NMs) have attracted a great deal of attention due to their surprising structural, mechanical, and electronic properties.1 The goal is to obtain dislocation-free, elastically relaxed, flexible NMs that could be manipulated and integrated into next-generation devices.2,3 These new class of nanostructures on compliant substrates (CSs) that can be stretched, compressed, and deformed are very attractive for flexible micro-opto- and nanoelectronics, photonics, and biological applications.4−8 Various nanofabrication approaches were recently developed for the generic design of nanomechanical architectures based on strained bilayer systems. They allow the fabrication of a variety of nanostructures, such as nanotubes, nanorings, © XXXX American Chemical Society

nanocoils, and nanomembranes using combinations of different materials. New strategies were also developed to fabricate stretchable wavy structures by bonding patterned ribbons or wrinkled stiff layers to prestrained elastic substrate and then releasing the prestrain.9,10 The strain relaxation produces specific configurations with layouts that are determined by the level of prestrain, the mechanical properties of the materials, and their geometrical features.1,11 Methods for transferring and manipulating freestanding Si-based NMs with large 2D sizes and nanometer scale thickness were also developed successfully. Received: April 8, 2015 Revised: May 29, 2015

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DOI: 10.1021/acs.cgd.5b00485 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

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changing the PSi growth and postgrowth treatment, we manage to monitor the prestrain of the CS at constant PSi porosity and softness. Porous Silicon Fabrication. B-doped ⟨100⟩-oriented Si wafers are electrochemically etched in a hydrofluoric acid (HF) solution to fabricate porous silicon layers. A two-step process has been developed to facilitate the epitaxy of the Si buffer layer on the porous substrate: a higher electrocurrent is used to generate a thin, low porous, top layer. The porous silicon layers used in this study have a porosity of 50%. Experimental details of the electrochemical process are given in refs 26−28. Porous Silicon Annealing. Immediately after the electrochemical formation step, either the samples are loaded in the MBE machine after ex situ chemical cleaning (PSi) or the samples are heated ex situ at high temperature between 900 and 1100 °C (HT-PSi) and then loaded in the MBE machine after ex situ chemical cleaning. The aim of the heating treatment is to produce reliable contaminant-free CS using high temperature desorption of the electrochemical solution trapped inside the pores. Substrate Chemical Cleaning. The chemical cleaning consists of four successive steps: a piranha dip [1:3 v/v H2O2 (30 wt %)/H2SO4 (90 wt %)] at 80 °C for 10 min, a rinse in DI water, a dip in HF/H2O2 (1:10) at room temperature for 30 s, and a new DI water rinse. Molecular Beam Epitaxy. To avoid contamination, the substrates are immediately introduced into the UHV chamber at the end of the chemical cleaning. Then, the samples are thermally cleaned in situ at ∼400 °C for 15 min before growth. They are then capped by a thin Si buffer layer, which guarantees a flat and reproducible top surface. The thickness of the Si buffer layer is always 20 nm in all the systems investigated. The root mean square roughness obtained after the buffer layer growth is similar to that of Si(001). This is followed by the epitaxial growth of SiGe layers of thickness h. Such a three-layer system, containing the Si buffer layer, is schematically represented in Figure 1. Further details on the fabrication of the structure are given

It was for instance demonstrated that Si and SiGe NMs could be detached from their substrate and transferred to new supports, providing heterogeneous integration abilities.1 Freestanding 2D semiconductor NMs were also obtained through chemical synthetic approaches using surfactant-directed surface assembly processes and transfer to an arbitrary substrate.12,13 In such systems grown on a CSs, the electronic characteristics (carrier mobility, band offsets, band gap energy, etc.) derive from the specific mechanical properties of the nanofoils that are controlled by engineering the elastic strain at the NM/substrate interface. In the end, the use of these nanofoils for the fabrication of high-speed flexible devices has been demonstrated. However, most of the processes developed involve costly CS and complex nanotechnological steps that are size limited (both the 2D lateral extension and the ultrathin thickness).14−16 Porous silicon (PSi), which is a long-standing studied material with a low fabrication cost and ease of integration in CMOS technology, was suggested as a promising CS for the heterogeneous epitaxy of various systems (III−V, oxides, SiGe, etc.) on silicon. It was suggested that its mechanical softness (which increases with the density of pores), could provide an easy accommodation of the misfit strain.17−20 Moreover, the possibility of tailoring its elastic properties (strain and softness) simply by varying the density of pores produces a configurable compliant material. One of the major problems remaining for the use of PSi in CMOS technology is its chemical instability both in air and during thermal annealing, which prohibits its use in any subsequent technological steps at high temperature (>600 °C). A second problem is its sponge-like morphology and disordered structure, which prevent a reliable production process. A third problem is the wet fabrication process during which electrolytic solution penetrates into the PSi pores with a risk of contamination during the subsequent steps of the microelectronic production chain. To overcome these problems, ex-situ thermal cleaning processes have been developed to reduce the contamination and to provide contaminant-free PSi layers with a reproducible morphology and composition.21 Moreover, engineering of epitaxial strain could be obtained by controlled oxidation steps.22 In this work, we investigate a Si substrate/porous Si/Si buffer layer/SiGe epitaxial layer model system, and we analyze the influence of the elastic properties of the compliant substrate, that is, its softness and strain state, on the morphological evolution of the epilayer independently. The aim is to determine the properties of the CS that could control the development of the Asaro−Tiller−Grinfel’d (ATG) corrugation that usually occurs. 23−25 We thence analyze the morphological evolution of SiGe layers as a function of the CS softness and prestrain state. The analysis demonstrates that CS softness favors the development of the ATG instability while CS tensile strain inhibits this instability and produces flat and thick 2D films. We also determine quantitatively the critical thickness of misfit dislocation on a tensilely strained substrate and show that the CS tensile strain also inhibits the development of dislocations, leading to micrometer thick, flat, and coherent films.

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Figure 1. TEM cross-section image of the complete structure including from bottom to top, the Si(001) substrate, HT-PSi porous Si double layer, the Si buffer layer, and the top SiGe epilayer (dark thin layer). The stacking of the layers is schematically represented. elsewhere.29 The MBE of the Si buffer is performed at 700 °C, while SiGe is deposited at 550 °C. Different types of samples were synthesized with different characteristics: • on Si(001), Si buffer (20 nm)/Si0.85Ge0.15 (h = 45 nm) • on as-grown PSi, Si buffer (20 nm)/Si0.85Ge0.15 (h = 45 nm) • on high temperature annealed PSi (HT-PSi), − Si buffer (20 nm)/Si0.85Ge0.15 (h = 250 nm) − Si buffer (20 nm)/Si0.80Ge0.20 (h = 150 nm) − Si buffer (20 nm)/Si0.65Ge0.35 (h = 27 nm) Membrane Lift-off. The lift-off of the HT-PSi/Si buffer layer/ SiGe layer membrane using the HT-PSi to separate the epitaxial layer from the substrate has already been reported.30 The process makes use of the formation of extended buried voids at the Si/HT-PSi interface, which accompany the morphological transformation of PSi double layer during the annealing at high temperatures (in the range of 900−

EXPERIMENTAL SECTION

We deposited by molecular beam epitaxy (MBE) SiGe layers on top of different compliant substrates made of a PSi (obtained by electrolytic anodization of bulk Si(001)) covered by a thin Si buffer layer. By B



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1100 °C). The voids weaken the interface and allow a subsequent release of the membrane by applying either an external stress or a thermal shock. A similar process was already reported for other porous materials.31 The process developed here consists of a rapid cooling of the structure after the MBE growth. The lift-off is attributed to the different coefficient of thermal expansion between HT-PSi and Si(001) bulk. The weak interfacial layer serves as a breaking point for the lift-off. An example of the membrane after the lift-off process can be seen in Figure 2. Other methods using a two steps process have

parameter as Si. The system is supposed to be coherent and to be described by linear isotropic elasticity in the different layers. Because of small experimental differences and of a negligible influence on the following results,34 we neglect the differences in Poisson’s ratio ν for the three materials. In contrast, we account for the difference in Young’s modulus, which proves to have a significant impact.35,36 While the SiGe and Si Young’s modulus are similar (equal to Y), the CS stiffness is YCS = sY, with 0 ≤ s ≤ 1 for a relatively soft CS. We also account for a possible prestrain of the CS measured in experiments prior to the deposition of the film.29 It is associated with the strain η and, thence, the condition ux → ηx, uy → ηy when z → −∞ (with respect to the Si reference state), which corresponds to a biaxial strain. The displacement vector is solution of the equilibrium equation ∇·σ = 0 where σ is the stress tensor, with the boundary condition of a stress-free film surface σ·n = 0 where n is the normal to the surface. In the case of a flat film (with a free surface defined by z = h̅ ≡ e + h), the forces, the stress tensor, the displacement gradients, etc., are independent of x and y and the general solution for the Navier equation is merely u0 = a·R + b, with a constant tensor a and vector b. It is associated with an energy density in the film ,̅ 0 = , 0(1 − η /m)2 with the typical density , 0 = Ym2 /(1 − ν). When the film surface is corrugated, it is convenient to search for u in Fourier space along r = (x,y). We thence consider a free surface defined by z = h̅ + h1 eik·r with the wavevector k. The solution of the Navier equation is u = u0 + u1, where u1 = h1 eik·r û̂1 may be found exactly in the small-slope approximation, see Supporting Information. We eventually find that the elastic energy density on the surface is at first order , = ,̅ 0 − 2(1 + ν),̅ 0A(kh ̅ )kh1, where

Figure 2. SEM image of the (HT-PSi/Si buffer layer/SiGe layer) membrane after lift-off from the Si(001) substrate. also been developed with a first step of nanopatterning by focused ion beam (FIB) of holes (with depth larger than the total membrane thickness) and a second step of chemical etching. Here, the lift-off is obtained by a faster rate of etching of HT-PSi compared with Si(001) bulk. Easy methods of PSi lift-off have been reported in the literature. For instance, a final electropolishing step is shown to remove the silicon atoms layer by layer and to separate the PSi film from the wafer. To switch from PSi formation to electropolishing, it is sufficient to increase the current density.32,33 Samples Characterization. The RMS roughness of the samples is measured by a PSIA XE-100 AFM in air, using a silicon tip in tapping mode. The TEM observations are performed using a Jeol2010F microscope working at 200 keV on lamellae prepared by the Tripod technique.

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A (x ) =

THEORETICAL SECTION Elasticity. We modeled the effect of the mechanical softness and strain state of a CS on the dynamics of the strained SiGe layers.29 We considered a three-layer system with a thick semiinfinite CS, a thin silicon buffer layer (of thickness e), and an epitaxial SiGe layer (of thickness h), see Figure 3. The

1 {[3 − 4ν + (3 − 4ν)s 2 γ (x )

+ 2(8ν 2 − 12ν + 5)s]e 4x + 4(s − 1)(3 − 4ν + s)x e 2x + (4ν − 3)(s − 1)2 } (1)

with γ(x) = [(3 − 4ν)(1 − s) − (3 − 4ν + s) e 2x] [1 − s + (4νs − 3s − 1) e 2x] + 4x 2(s − 1)(3 − 4ν + s) e 2x

(2)

The elastic energy density depends both on the Young’s modulus ratio, s, and on the total film or buffer thickness h̅. The latter dependence is due to finite size effects, which are associated here with the Young’s modulus difference, which generates buried dipoles.37−40 In the small wavevector limit, kh̅ ≪ 1, A(kh̅) may be expanded as A(x) = 1/s + (s − 1)(2 − 2ν + s)x/[(1 − ν)s2] + ... where the effect of the substrate stiffness is clearly visible in the lowest order 1/s term. For a soft substrate, s < 1 and A(x) >1 for thin enough films so that the relaxation is enhanced compared with the case of equal stiffness. In contrast, for a hard substrate with s > 1, A is lowered compared with the equal stiffness case, leading to the slow-down of the instability, see below. This effect is rather counterintuitive and was also derived in ref 41. In fact, it may be rationalized by noticing that the driving force for the morphological instability is the strain relaxation in the film. However, the energy gain due to the elastic relaxation in the film δEfilm < 0 due to a film corrugation δh(r) is accompanied by an energetic cost in the substrate δEsub

Figure 3. System under modeling: a SiGe film deposited on a Si buffer layer deposited on a compliant substrate. The two parameters considered are YCS different from the one of the buffer and film Y (assumed equal for simplification) and the strain state of the substrate, which is included in the zero-order reference state and is equivalent to a biaxial stress.

hypothesis of a semi-infinite CS is accurate because the CS is commonly several micrometers thick, several orders of magnitude thicker than the film and buffer. The substrate/ buffer interface is located at z = 0, and the buffer/film interface is at z = e. The SiGe film has a lattice parameter aSiGe different from Si, aSi, with the misfit m = (aSiGe − aSi)/aSi. For simplification, we consider that the CS has the same lattice C



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Figure 4. AFM images of the SiGe layer (x = 0.15, h = 45 nm) deposited at 550 °C on (left) PSi and (right) bulk Si(001) substrate (scan size is 5 × 5 μm2). The height scale is 57 nm.

Figure 5. Plot of the growth rate, σ, of the morphological instability of a strained SiGe film on a Si buffer on a soft substrate with s varying as 0.05 (solid line), 0.1 (dashed line), 0.5 (dotted line) and classical case 1 (red solid line) for (a) h̅/l0 = 0.3, (b) h̅/l0 = 1.25 (corresponding to Figure 4), and (c) h̅/l0 = 3.

> 0, which is lower than |δEfilm|. Hence, the global balance is favorable. But the energetic cost in the substrate δEsub is proportional to its Young’s modulus. As a consequence, it is diminished in a soft substrate and the global energetic balance is all the more favorable on a soft substrate, leading to the instability enhancement. Dynamics. The evolution by surface diffusion of the film surface h(x,y,t) is dictated by the general diffusion equation ∂h/ (∂t) = DΔμ, with the diffusion coefficient D and the chemical potential μ on the surface.41 The latter is the sum of the elastic energy density on the surface and the capillarity energy cost − γΔh at first order, with the surface energy γ. With this set of equations, an harmonic initial condition, z = h̅ + h1 eik·r evolves as h1(t) = h1(0) eσt where the growth rate is σ(k ; h ̅ , s , η /m) = A(kh ̅ )(1 − η /m)2 k3 − k 4

If the k4-term is only affected by corrections due to the stiffness, the k3-term, which drives the instability, is multiplied by (i) 1/s, which is related to the CS softness, and (ii) (1 − η/m)2, related to the CS prestrain. The first effect clearly enhances the instability when s < 1, while the second slows down the instability when a tensile prestrain (η > 0) is present, that is, when the instability-driving strain decreases.

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RESULTS AND DISCUSSION Effect of the CS Softness Alone. The Youngs modulus of porous silicon is dramatically dependent on the porosity as explained by theory.43 Calculations showed that by varying the volume fraction of pores, one can design voided materials with a tailored Young’s modulus with ΔY/YSi between 0 and 1.44 It was shown that the ratio of the Young’s moduli of the porous material over those of the bulk material (Y/YCS) varies with the square of the density of pores.45 The elastic properties of the PSi layer can then be engineered by varying the density of pores in the PSi layer.46 Moreover, the doping level may also greatly influence the PSi Young’s modulus.43 We first investigate the experimental results obtained during the epitaxy of SiGe layers on as-grown PSi at low temperature. In this case, the substrate is not prestrained (η = 0) and we investigate the effect of its softness. Epitaxy of Si1−xGex was performed on a thick (7 μm) PSi and compared with the evolution on a Si substrate with otherwise similar parameters. We considered a low-strained system (x = 0.15, h = 45 nm) and find an evolution on PSi similar to the evolution on Si, see Figure 4. The AFM observation of the SiGe surface shows a corrugated layer with a RMS roughness similar to the one

(3)

We work from now on with the characteristic space and time scales l0 = γ /[2(1 + ν), 0] and t0 = l04/(Dγ). In the case of equal stiffness (s = 1) and absence of prestrain (η = 0), one finds the usual spectrum of the Asaro−Tiller−Grinfel’d instability,23,24,42 σATG = k3 − k4, which is positive for 0 ≤ k ≤ 1. In the general case, however, for small wavevector, the growth rate is σ=

η ⎞2 k3 ⎛⎜ 1− ⎟ s ⎝ m⎠ ⎡ (s − 1)(2 − 2ν + s)(1 − η /m)2 h ̅ ⎤ 4 − ⎢1 − ⎥k ⎦ ⎣ (1 − ν)s 2 + 6(k5)

(4) D



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Figure 6. TEM cross-section images of Si1−xGex layers. From left to right: x = 0.35, h = 27 nm; x = 0.20, h = 150 nm; x = 0.15, h = 250 nm; high resolution image of the Si0.85Ge0.15 surface (corresponding to the square inset of the nearby micrograph).

of the 2D system (under investigation here) is quite different from what could be obtained on a finite substrate (such as mesas). In the latter case, a significant effect of the softness is observed.48 The analysis proved that the residual elastic strain is much lower on PSi/Si mesas than on bulk Si even if the Si buffer layer decreases the elastic relaxation in the pseudomorphic layer. Another interesting effect of the compliance of the substrate is depicted in the Supporting Information. When the PSi compliant substrate is sufficiently thin compared with the SiGe epitaxial layer, the compliant substrate is distorted under the epitaxial stress and cracks periodically while the SiGe layer remains flat. Combined Effect of the CS Softness and Prestrain. The PSi strain state may be monitored either by varying the porous density49 or by heating at high-T (HT-PSi).50 During heating, HT-PSi undergoes a significant morphological transformation where the ultrasmall pores (mean diameter ≈ 20 nm) coalesce into large holes (0.5−1 μm).51 Such enlargement processes were developed to increase the penetration of the epitaxial layers inside the pores.50,52,53 The porous morphological change is assisted by hydrogen desorption and the resultant change of the dangling bond, which is expected to modify the silicon crystalline lattice54 While desorption of hydrogen from the PSi layer proceeds at 400 °C, since it is encapsulated by an almost nonporous layer, the hydrocarbons are probably trapped in the top PSi layer and expected to decorate the pore surfaces. Such behavior has been demonstrated to produce an expansion of the lattice parameter during dry thermal oxidation of PSi.22 Various studies investigated the evolution of the PSi lattice parameter during annealing in different atmospheres. Different results (expansion or contraction of the lattice parameter) depending on the atmosphere were reported.26,55 The strain state of the PSi could then be adjusted by varying either the porous density or the annealing conditions. The preparation conditions of HT-PSi and the presence of the bilayer are then crucial to produce a tensilely strained porous layer. In our experimental conditions, during heating, the morphological change is accompanied by a tensile distortion of the HT-PSi crystalline lattice, which was measured by X-ray diffraction.29 We found on the samples used in this study that the PSi lattice spacing after thermal treatment is aPSi ∥ = 0.5465 Å, while the free-standing PSi is characterized by aPSi = aSi = 0.5431 Å. This measure characterizes an effective dilatation η = 0.62%. This tensile strain diminishes the effective misfit experienced by the deposited SiGe layers, which corresponds to a relative effective misfit decrease (m − η)/m

obtained on a Si (RMS = 13 and 12 nm, respectively). Hence, the effect of the softness alone could correspond to a small enhancement of the instability but not measurable experimentally. The theoretical evolution of the Asaro−Tiller−Grinfel’d (ATG) instability growth rate with s for η = 0 is given in Figure 5. The evolution is plotted for three values of s that can be easily obtained by varying the density of pores: (i) s = 0.05; (ii) s = 0.1; (iii) s = 0.5. The instability is enhanced when s decreases, that is, for a softer CS (smaller Young’s modulus). However, the amplitude of this effect is function of the total thickness of the system (Si buffer + SiGe layer) h̅ and is all the more important as h̅/l0 is small. The influence of h̅ is quantified for three different Si buffer thicknesses (e = 0, 20, and 50 nm) leading to h̅ = 45, 65, and 95 nm, respectively (Figure 5). When the film + buffer thickness is on the order of the ATG characteristic length, the coupling between the strain generated by the undulated surface and the CS relaxation is important and the effect of the CS softness results in a clear increase in the instability growth rate. It is noticeable that this effect generates a dependence on the rather large ATG wavelength, l0, in the zdirection. For h̅/l0 = 1.25, see Figure 5b, the effect of s is already negligible for usual values of s, while it is clearly already crucial for h̅/l0 ≃ 1. When h̅/l0 is large, the coupling between the strain generated by the undulated surface and the CS relaxation is damped by the film + buffer system and vanishes. For the experimental conditions used in Figure 4, one gets for x = 0.15, h = 45 nm, and e = 20 nm, the dimensionless total thickness h̅/ l0 ≃ 1.25 as l0(x = 0.3) = 13 nm,47 while l0 is expected to scale as 1/x2. The evolution corresponding to these parameters is plotted in Figure 5b. In this case (h̅/l0 ≃ 1), the effect of the softness on σ is expected to be small (see Figure 5b), with a small increase in σ even for a quite soft substrate s = 0.05 where max(σ) ≃ 0.33 while max(σ) ≃ 0.11 for s = 1. While this single experimental data cannot confirm by itself the theoretical modeling, it is still in good agreement with it. We evidence here two very important results that clarify the effect of the compliance of the substrate. The first result is that the softness of the substrate should amplify the growth of the instability. The second result is that the film + buffer layer may inhibit the effect of the softness depending on its thickness. Indeed, Figure 5c shows that a film + buffer layer 180 nm thick for x = 0.15 is sufficient to inhibit the effect of a factor 20 smaller Young’s modulus, s = 0.05. Such effects are key parameters to consider when the softness of the substrate is used for instance to accommodate a 2D heterogeneous epitaxial layer. The situation E



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≃ 54% for x = 0.35 (where m = 1.47%). During the thermal treatment, the HT-PSi pores are closed at the top surface, and there is no penetration of the epitaxial layers inside the pores and the usual (Si buffer layer/SiGe epilayer) structure can be deposited in standard experimental conditions. When thick Ge layers are deposited onto such a HT-PSi covered by a thin Si buffer layer, we find the striking suppression of the usual morphological instability of a strained film, see Figure 6. This suppression occurs for different values of the Ge concentration from x = 0.15 up to x = 0.35 and for different film thickness, even up to 250 nm. In this situation, thick Ge layers totally flat and fully relaxed are obtained. This contrasts significantly with the deposition on either (i) a Si substrate47,56 or (ii) an {unstrained PSi substrate, Si buffer} system (see previous section), which leads to the full development of the usual ATG morphological instability, see, for example, Figure 4, upper. The striking strain accommodation provided by HT-PSi may thence be rationalized by the effect of the tensile strain resulting from the high temperature flash, which outweighs the enhancement due to the softness. Indeed, we plot in Figure 7 the resulting growth rate σ for the

nm (x = 0.15). The AFM or TEM images of the morphology of the different SiGe epilayers are superimposed in Figure 7. The porosity was measured to be ϕ = 50% so that s= (1 − ϕ) 2 = 0.25,36 while ν = 0.279. The prestrain was measured to be η = 0.62%. In all the experimental conditions, we clearly see that the growth rate is mainly negative when both the opposite softness and strain effects are accounted for, see Figure 7 (negligible positive values are present at very small k but correspond to a completely negligible dynamical evolution given that t0 = 270 s for x = 0.3, while it should behave as 1/x8). For comparison, we plot in Figure 7, the growth rate of the usual ATG instability corresponding to the absence of a prestrain and equal stiffness, which does develop a clear maximum and a wide range of growing wavevectors. For the typical experimental parameters, the inhibition effect of the tensile prestrain clearly overcomes the enhancement due to the CS softness. The inhibition of the morphological instability on a HT-PSi substrate is thence consistent with the common description of the morphological evolution of a strained film when accounting for the prestrain built in the porous substrate during the thermal treatment. In these conditions, the small tensile strain (η = 0.62%) is expected to provide a sufficiently large elastic relaxation of the SiGe layers to inhibit the development of the morphological instability. Dislocations. Another possible route to relax the misfit strain at work in such heteroepitaxial films is the nucleation of dislocations, which can occur either before or after the morphological evolution. It is strongly dependent on the whole system elastic response and is thence again function of the substrate elastic properties. It is then also crucial to determine the effects of the substrate softness and tensile strain on the nucleation mechanism. For this purpose, we compare the morphology and microstructure of SiGe epitaxial layers [typically Si0.8 Ge 0.2 (h = 200 nm)] grown in similar experimental conditions either on HT-PSi or on nominal Si(001) substrate. The two samples are investigated by TEM cross-section analyses. The dramatic difference between the microstructures is immediately visible on the TEM crosssection images, see Figure 8. When the layer is deposited on nominal Si(001), we can see a dense network of dislocations on the TEM images (Figure 8a). These threading dislocations are gliding along the (111) planes, at 54° from the interfacial Si0.8Ge0.2/Si(001) plane. They originate from the misfit dislocations located at the interface that relax the elastic strain. The presence of dislocations is also attested by the presence of a square lattice of grooves visible on the SiGe surface and

Figure 7. Plot of the growth rate, σ, of the morphological instability of a strained SiGe film on a Si buffer on a tensile and soft porous substrate (typically HT-PSi) with (i) x = 0.35, h = 27 nm (solid line), (ii) x = 0.2, h = 150 nm (dashed line), (iii) x = 0.15, h = 250 nm (dotted line) and (iv) a substrate with equal stiffness and without prestrain (red line), corresponding to the parameters of Figure 6. The space and time scales are l0 and t0 given by the instability parameters. The three first curves are hardly distinguishable. The TEM and AFM images of the corresponding SiGe epilayers are superimposed on the schemas for the different situations. In all cases, we obtain a perfect agreement between the morphology observed and the theoretical results.

parameters relevant to the experiments described in Figure 6 on HT-PSi, with h = 27 nm (x = 0.35), 150 nm (x = 0.2), and 250

Figure 8. TEM cross-section images of the SiGe epitaxial layers Si0.8Ge0.2 (h = 200 nm) grown in similar experimental conditions: (a) on nominal Si(001) substrate (AFM image is in the inset with a 12 × 12 μm2 scan size); (b) on HT-PSi. F


Crystal Growth & Design oriented along [110] directions, which are representative of the threading dislocations. These dislocations have been longstudied in the literature and are already well-documented [see ref 57 for a review]. In the same experimental conditions, when the layer was deposited on HT-PSi, no dislocation could be observed on the TEM cross-section imaqes (Figure 8b). In addition, the SiGe surface is totally flat and does not present the grooves observed previously. It can then be concluded that HTPSi pseudosubstrate inhibits the nucleation of dislocations in the experimental conditions used here. The effect of HT-PSi on the nucleation of dislocations could be attributed either to its softness or to the tensile strain built-in the layer. The effect of the softness can be easily ruled out since it affects equally both the epitaxial strain energy and the relaxation energy resulting from the dislocation. To rationalize the absence of nucleation of dislocations even in thick films on a HT-PSi substrate, we consider the strain state of such systems and analyze the driving force for dislocation. In the geometry under study, the displacement vector in a flat film is given by uf0 = {ηx,ηy,[−2νηz + m(1 + ν)(z − e)]/(1 − ν)}. The stress tensor in the film associated with this displacement field is biaxial σ0ij = σel∥ (δi,x + δi,y)δi,j with σ el μ

= − (m − η)

1+ν 1−ν

μ 1 − ν cos2 β log(4h/b) 2π 1−ν h/b

CONCLUSION

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ASSOCIATED CONTENT

We investigated the influence of a compliant substrate on the morphological evolution of an heteroepitaxial system made of (SiGe/Si buffer layer/porous silicon) layers. The study is focused on the two major behaviors commonly observed in heteroepitaxial systems: the development of the ATG growth instability and the nucleation of misfit dislocations. We analyzed quantitatively the effect of the softness (small Young’s modulus) and of a tensile strain. We have demonstrated that the softness of the substrate can dramatically enhance the development of the ATG growth instability until the formation of nanoribbons, while it has almost no effect on the nucleation of dislocations. However, this enhancement effect is controlled by the total thickness h̅ of the (SiGe layer + Si Buffer) and can only take place when h̅ is small compared with the wavelength of the instability. At large thicknesses, however, that is, when h̅ is larger than the wavelength of the instability, the effect of the softness is damped. Quantitative data are given in realistic conditions to guide the experimental work. An experimental proof of the latter effect is given when SiGe layers are deposited on Si buffer layer on porous silicon unstrained and soft. In a second part, we have shown both theoretically and experimentally that a tensilely strained substrate could fully inhibit both the development of the ATG instability and the nucleation of misfit dislocations. Experimental evidence is given for the heteroepitaxial growth of SiGe on a Si buffer on PSi double layer annealed at high temperature. The conditions to obtain tensilely strained or soft porous silicon are provided. The results exemplify the growth of thick lattice matched Ge rich SiGe layers, coherently strained to the Si buffer underlayer, using the HT-PSi configurable compliant substrate. The procedure developed can efficiently tune the SiGe epitaxial strain and is expected to produce new optoelectronic properties resulting from the change of the fundamental energy band gap from indirect to direct. It is fully compatible with the microelectronic industry and is easily extendable to many other systems without any risk of contamination. The use of low cost and reliable HT-PSi compliant pseudosubstrate could provide an efficient way to tune the strain of heteroepitaxial systems and is best suited to the growth of pseudomorphic heterogeneous layers elastically partially relaxed and free of dislocations.

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with the shear modulus μ = Y/2(1 + ν). The equilibrium analysis of dislocations leads to the existence of the Matthews’ length58 above which dislocations are favorable from an energetic point of view. It is achieved when the excess stress59 σexc = |σel∥ | − σdislo with σdislo =

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vanishes, σexc eq = 0, where b is the Burgers vector modulus of the dislocation and β the angle between the dislocation line and the Burgers vector. This excess stress is a measure of the driving force for strain relief though dislocation. During growth, however, it is well-known that metastable films can be grown with thicknesses much larger than the equilibrium Matthews’ length59 because nucleation is an activated process. Hence, the maximum thickness that can be grown may be characterized by exc a maximal excess stress σmax /μ, which depends on the temperature T.59 This excess stress was measured experimentally in SiGe systems and estimated to be σexc max/μ = 0.024 at T = 534 °C, while it is only 0.0085 at 568 °C. We use this analysis to rationalize the absence of dislocations in the thick films described above when deposited on HT-PSi. These films are characterized by a mean Ge concentration x = 0.2, so that the strain field is |σel∥ |/μ = 0.0045. Hence, the thickness performed experimentally (h = 150 nm) is already above the Matthews’ length as σdislo/μ = 0.0038 when considering β = 60° and b = 0.54/√2 nm.59 However, from a kinetic point of view, the strain is not high enough in the system. Indeed, the strain exc satisfies |σel∥ | < σexc max even for T up to 568 °C where data for σ exc are available. Hence, σ will all the more satisfy the kinetic condition σexc < σexc max for the inhibition of dislocations. In our experiments where T = 550 °C, we clearly expect dislocations not to occur even for such thick films, and the experimental result is fully consistent with the kinetic analysis of the dislocation nucleation.

S Supporting Information *

Details of the elastic calculation and description of the case of an ultrathin porous silicon, including TEM cross-section of the SiGe layer. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acs.cgd.5b00485.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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Configurable Compliant Substrates for SiGe Nanomembrane

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