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Critical conditions for SiGe island formation during Ge deposition on Si(100) at high temperatures
Materials Science in Semiconductor Processing 57 (2017) 18–23
Contents lists available at ScienceDirect
Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp
Critical conditions for SiGe island formation during Ge deposition on Si(100) at high temperatures
crossmark
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A.A. Shklyaeva,b, , A.E. Budazhapovac a b c
A.V. Rzhanov Institute of Semiconductor Physics, SB RAS, Novosibirsk 630090, Russia Novosibirsk State University, Novosibirsk 630090, Russia Novosibirsk State Technical University, Novosibirsk 630055, Russia
A R T I C L E I N F O
A BS T RAC T
Keywords: Ge MBE on Si(100) High-temperature growth Self-organization Strain relaxation Dynamic equilibrium
The strain relaxation during the Ge growth on Si(100) occurs vikia surface diffusion and Si-Ge intermixing at temperatures below 800 °C. The Ge diffusion into the Si substrate is an additional process at higher temperatures. We found that, if its rate is higher than the Ge deposition rate, the island formation is not realized. We determined the critical Ge deposition rate as a function of the temperature in the range of 840– 960 °C, at which the dynamic equilibrium between the growth of islands and their decay through the diffusion takes place. The islands grown in the conditions close to the dynamic equilibrium are ordered with a distance between them of about 1 µm and they form a smoothed surface morphology. These are indicative of the surface layer strain uniformity. The islands have a SiGe composition which, in the direction parallel to the sample surface, is more uniform in comparison with the islands grown at lower temperatures. The results show that the use of high temperatures essentially improves the conditions for the heterostructure self-organization.
1. Introduction Self-organization during heteroepitaxial growth provides the possibility for the fabrication of semiconductor heterostructures with quantum dot arrays that exhibit unique optoelectronic properties. In order to obtain their best performance, they should be prepared on the base of the ordered three-dimension (3D) islands of identical sizes. Since the self-organization occurs to reduce the lattice strain, the formation of ordered island arrays provides the most exhaustive strain relaxation. It was found that the island ordering can be realized when the nucleation of islands does not occur randomly along the surface, but their locations are governed by the elastic strain distribution generated by underlying patterned structures [1–5]. The surface morphology formation usually takes place via surface processes which can limit the realization of strain relaxation. The facilitated strain relaxation is suggested to occur in the conditions close to thermodynamic equilibrium, which can be realized, for example, in liquid phase epitaxy [6,7]. In this Letter, it is shown that the conditions for island ordering can be implemented during Ge molecular beam epitaxy (MBE) on Si(100) at high temperatures, when the islands are formed by means of the nucleationless process via gradual changes in the surface morphology in the conditions close to the dynamic equilibrium between the growth of islands and their decay through the Ge diffusion
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into the substrate. At temperatures up to 500 °C, the 3D island formation during the Ge deposition on Si(100) is realized via the surface diffusion and incorporation of deposited Ge atoms into energetically favorable surface sites [8–11]. At 500–750 °C, the island growth is accompanied by the additional process, i.e. by the intermixing of deposited Ge atoms with Si atoms of surface layers [12–15]. When the temperature increases above 800 °C, the diffusion of deposited Ge atoms into the bulk of Si substrates becomes significant. If the Ge deposition rate is not sufficiently high, deposited Ge entirely diffuses into the substrate and the island formation does not occur [16]. Therefore, at each temperature there is a minimal Ge deposition rate at which the islands can grow. We obtained here the experimental data to describe the dependence of the minimal Ge deposition rate on temperature. It represents the boundary in coordinates of the Ge deposition rate and the temperature, along which the dynamical equilibrium between the island growth and their decay due to the Ge diffusion into the substrate takes place. The boundary can be referred to as the critical conditions for the island growth at high temperatures using the analogy with the case of oxygen interaction with Si surfaces in which the critical conditions describe the dependence of the minimal oxygen pressure on the temperature for the transition from the Si etching by oxygen to the silicon oxide growth
Corresponding aauthor at: A.V. Rzhanov Institute of Semiconductor Physics, SB RAS, Novosibirsk 630090, Russia. E-mail address: [email protected] (A.A. Shklyaev).
http://dx.doi.org/10.1016/j.mssp.2016.09.033 Received 26 July 2016; Received in revised form 21 September 2016; Accepted 27 September 2016 1369-8001/ © 2016 Elsevier Ltd. All rights reserved.
Materials Science in Semiconductor Processing 57 (2017) 18–23
A.A. Shklyaev, A.E. Budazhapova
tures of about 900°С leads to the increase in the monolayer step density and to the trenches formation of dimer vacancies that form the (2×N) reconstruction [Fig. 2(a)]. The N value was in the range from 5 to 10. The trenches provide the lattice strain reduction. Such surface morphologies are typical of the SiGe layer growth on Si(100) in the middle temperature range from about 500–650 °С [25–27]. In this aspect, the Ge deposition on Si(100) at high temperatures appears to produce similar effects.. The monolayer step density increase was observed through the 2D island nucleation preferably on Si(100) terraces of smaller sizes. This occurs inhomogeneously along the surface, leading to the gradual 3D formation in the places where the terrace size decreases faster. At the same time, the correlation in their lateral locations, which can then provide their development into the ordered island arrays during the further Ge deposition [16], is observed (Fig. 2). Such behavior shows that the 3D island formation occurs not via the spontaneous island nucleation stage, but through the gradual changes in the surface morphology, i.e. through a nucleationless process. It should be mentioned that some island ordering can also occur under long-time postgrowth annealing [28,29]. The island formation at high temperatures occurs in the conditions when a significant amount of deposited Ge diffuses into the substrate [16]. There is the Ge deposition rate (Rdep) at which the dynamic equilibrium between the growth of islands on the surface and their decay due to the Ge diffusion into the substrate is realized. This rate can be referred to as the critical rate (Rc) for the island formation, similar to the critical oxygen pressure at which the quasi-equilibrium conditions between the silicon oxide growth and decomposition on Si surfaces appear [17–19]. The Rc value can be determined by obtaining the island height dependence on Rdep. The island height appears to have a strong dependence on Rdep clearly indicating the Rc value [Fig. 3(a)]. The island height dependences on the Ge deposition rate and on the amount of deposited Ge are similar in the range of the critical conditions studied here.. The Ge deposition and Ge diffusion into the substrate form a strained SiGe layer on the surface. The 3D island formation begins, when the SiGe layer thickness reaches a certain value depending on the Si-Ge composition [30,31]. In the conditions of Ge diffusion into the substrate, if after the deposition of a certain Ge amount at a given temperature and Rdep the formation of islands is not observed, they can appear when the deposited Ge amount increases, as shown in Fig. 3(b). For the same growth temperature, this dependence means that the critical conditions are realized at a smaller Ge deposition rate when they are determined for a larger amount of deposited Ge. Since Rc depends on the amount of deposited Ge, its temperature dependence is reasonable to be obtained for several given amounts of deposited Ge. These temperature dependences show, in particular, that
[17–19]. We found that the growing islands have a tendency to ordering when the growth conditions are close to the dynamic equilibrium. These islands form the smooth surface morphology indicating the strain distribution homogeneity in the surface layer. The islands are also characterized by the homogeneity in the SiGe alloy composition in the direction along the surface. It is expected that SiGe heterostructures, made on the base of such island arrays, can have narrow electronic state spectra. 2. Experimental details The growth experiments were carried out in an ultrahigh-vacuum chamber with a base pressure of about 1×10−10 Torr. The chamber was equipped with a scanning tunneling microscope (STM) manufactured by Omicron. A 10×2×0.3 mm3 sample was cut from an n-type Si(100) wafer with a miscut angle of < 10´ and a resistivity of 5–20 Ω cm. Clean Si surfaces were prepared by flash direct-current heating at 1250–1300 °C. A Knudsen cell with a BN crucible was used for Ge deposition at the rate up to 1.1 nm/min. The Ge growth on Si(100) surfaces was carried out at temperatures from 700 to 960 °C. The sample temperature was measured using an IMPAC IGA 12 pyrometer. After the removal of the samples from the growth chamber, their scanning electron microscope (SEM) images were obtained using a Pioneer microscope manufactured by Raith. The grown layer chemical composition was measured using energy-dispersive X-ray spectroscopy (EDX) of SEM SU8220 made by Hitachi. To improve the spatial resolution in EDX measurements of chemical compositions along a certain line on a sample cleavage, the incident e-beam energy was reduced to 3 keV. The EDX for such low e-beam energy was calibrated using the samples with the known SiGe compositions. This provided obtaining the spatial resolution of 25 nm for 95% changes in chemical composition which was determined using the sample cleavages with sharp Si/Ge interfaces. In order to obtain the critical Ge deposition rate for the island formation, the measurement of the Ge deposition rate dependence on the K-cell temperature was required. The Ge deposition rate is proportional to the Ge vapor pressure in the K-cell. When the aperture size of a K-cell is much smaller than its sidewalls total areas, the vapor pressure is governed by the equilibrium between the gaseous and condensed Ge phases. The simplified equilibrium gas pressure is (o ) described as Peq = Peq exp(−ΔH / kT ), where ΔH=ΔHo+aT is the vaporization heat, ΔHo is a constant and a is the difference in the heat capacity between the gaseous and condensed phases [20,21]. Assuming Rdep (T )~Peq (T ), that the Ge deposition rate is we (o ) (o ) exp(−ΔH /kT ), where Rdep is the pre-exponential factor obtainRdep = Rdep depending on the K-cell aperture and the distance between the K-cell and the substrate. The deposition rate was obtained with the STM by measuring the Ge coverage of submonolayer thick Ge wetting layers on Si(111) deposited at about 450 °C for different K-cell temperatures (Fig. 1). The Ge growth on Si(111) proceeds through the formation of two-dimensional (2D) islands which can be of three heights, i.e. 1, 2 or 3 bilayer (BL), where 1 BL ≈0.327 nm is the distance between adjacent (111) planes (inset in Fig. 1) [22,23]. The Ge coverage was derived by accounting the size of islands and their thickness.. By this technique, the Ge deposition rates can be measured with the accuracy within 5% for each K-cell temperature. The obtained experimental data can be well described by the exponential function, as shown in Fig. 1. The value of ΔHo≈3.5 eV is in agreement with the previously obtained data for the Ge evaporation [20,24] and, thereby, this confirms that the Ge vapor pressure in the K-cell used in our experiments is governed by the equilibrium between the gaseous and condensed Ge phases. 3. Critical conditions for island formation
Fig. 1. Temperature dependence of the Ge deposition rate. The STM image of the Si(111) surface covered with 2D islands with heights 1, 2 and 3 BL, obtained by about 0.5 BL Ge deposition at 450°С, is shown in the inset.
The initial stage of the Ge deposition on Si(100) at high tempera19
Materials Science in Semiconductor Processing 57 (2017) 18–23
A.A. Shklyaev, A.E. Budazhapova
Fig. 4. Critical conditions for the island formation during 5 (data A) and 100 nm (data B) Ge depositions on Si(100) at high temperatures. The solid and open symbols represent the conditions at which the islands appear or not on the surface, respectively.
required for the gradual surface morphology evolution to the 3D growth.. The critical conditions presented in Fig. 4 allow them to be well approximated by the exponential function Rc(T)=Roexp(-Ea/kT), where Ro is the pre-exponential factor and Ea is the effective activation energy. The obtained Ea was found to be about 4.5 and 5.0 eV for the Ge depositions of 5 and 100 nm, respectively. As expected, these values are in agreement with the activation energy of Ge diffusion in Si [32,33]. This, thereby, confirms that the main process, which is responsible for the island decay, is the Si-Ge intermixing with the Ge diffusion in the Si substrate. The fact that the island growth does not occur at the high temperatures and the low Ge deposition rates can not be only the result of Ge diffusion into the substrate, but it can also be due to the Ge desorption from the surface. The Ge evaporation rate can be estimated by extrapolating of higher temperature data obtained by Lehovec et al. [24]. This gives the Ge evaporation rate of 0.04 nm/min at 940 °C at which the critical Ge deposition rate is much greater, being 1.05 nm/ min in the case of the Ge deposition in the amount of 5 nm (Fig. 4). That the Ge desorption rate is relatively low is in agreement with the rapid increase of the height of islands after their formation (Fig. 3), and with the possibility of a description of the critical conditions by an exponential function with the effective activation energy which coin-
Fig. 2. (a) STM and (b) SEM images of the surfaces obtained by 5 and 100 nm Ge depositions on Si(100) with the Ge deposition rates of 0.14 and 1.00 nm/min at 890 and 940 °С, respectively. The inset in (a) shows that the surfaces are composed of 2×N reconstructed (100) terraces.
Rc is about 2.5 times bigger for the 5 nm Ge deposition than that for 100 nm (Fig. 4). It can be noted that, in order to prepare ordered island arrays, rather large Ge depositions of about 20 nm or larger must be carried out in the conditions close to the dynamic equilibrium. It is
Fig. 3. Island height dependences (a) on the Ge deposition rate for the deposited Ge amount of 20 nm and (b) on the deposited Ge amount for the Ge deposition rate of 0.39 nm/min at 940 °С.
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Materials Science in Semiconductor Processing 57 (2017) 18–23
A.A. Shklyaev, A.E. Budazhapova
faceting planes. The numerical simulations showed that essential changes in the surface morphology profile can be obtained by long time annealing of strained heteroepitaxial structures [32,45,46]. In the models, the lateral island ordering is governed by the lattice strain anisotropy and the obtained results clearly reflect the substrate crystal symmetry. However, considerable progress in the ordered 3D structure preparation by long time annealing was not achieved experimentally [28,29]. It is, probably, due to the necessity for using rather high annealing temperature, since the ordering requires an intensive mass transport along the surface. As shown here and in [16], the hightemperature annealing initiates the atom diffusion from epitaxial layers into substrates. This diffusion significantly restricts the temperature and duration of annealing. The results of this study show that the limitations on the annealing temperature and on its duration can be overcome if the epitaxial layer composition is restored during annealing by the material deposition on its surface.
cides with the activation energy of Ge diffusion in Si. These arguments indicate that the probability of Ge sticking to the SiGe surfaces is not essentially less than one in the range of critical conditions. However, there is no evidence that the Ge sticking probability is close to one for the Si surface at the initial Ge deposition stage. The size, shape and spatial distribution of islands on the surface strongly depend on ΔR (Fig. 5). The islands grown in the conditions close to the dynamic equilibrium have an oval shape and a tendency to lateral ordering [16]. Moreover, they form a smooth surface shape at their base [Fig. 5(a)]. The height profile measured along an island array can be well approximated by the sinusoidal function [Fig. 5(c)]. This surface morphology shape indicates that the strain distribution along the surface is homogeneous, since the highest strain inhomogeneity is usually formed along island perimeters where the surface morphology has the sharpest edges [34,35].. 4. Island chemical composion
5. Conclusion The islands grown by the Ge deposition on Si(100) at 450–750 °С are characterized by the bimodal island size distribution [36]. The distribution of the islands grown at 800–900 °С becomes monomodal [16]. The islands grown at different temperatures have different SiGe compositions. The Si-Ge intermixing, taking place at temperatures above 500 °С, leads to the formation of the trenches along the island perimeter, where the lattice strain is the strongest [15,37]. The different rate of Si-Ge intermixing in different surface layer areas results in inhomogeneous SiGe composition distributions [38]. The trenches around islands are not formed at temperatures of 850–900 °С [16]. The EDX data for SiGe compositions of the structures grown in this work were obtained for cleaved samples from the areas where cleaving planes crossed island centers (Fig. 6).. The Ge content is higher in the centers than near the edges of the islands grown at 700 °C [Fig. 6(d) and (e)]. In the island surface layers it is about 25%, whereas in the island central areas it reaches 33%, i.e. in agreement with the data obtained previously [38]. The greater Ge content in the island central areas reflects the fact that Si enters an island from its perimeter by means of diffusion on the island surface. It can be noted that the Ge content in islands depends on the Ge deposition rate, and it is higher when higher deposition rates are used [39–41]. The Ge content in the grown islands decreases with the increasing growth temperature and it becomes about 6% at 900 °C [Fig. 6(с)]. The SiGe content distribution in the islands measured in the direction along the sample surface is uniform for the structures grown at temperatures in the range of 800–900 °С [Fig. 6(d) and (e)]. At the same time, the Ge content decreases as a function of the distance in the direction from the surface [Fig. 6(e)]. The obtained data indicate that the Si-Ge intermixing occurs uniformly in the whole surface layer, thereby, confirming the important role of Ge diffusion into the Si substrate at temperatures above 800 °C. The results of Ge deposition on Si(100) at high temperatures are different from those on Si(111) [42,43] in several aspects. The Si-Ge intermixing on Si(111) occurs with the essentially lower rate and, at 800 °C, it leads to the formation of large 3D structures with the Ge content of about 30% [40], that is about two times higher than that in the islands grown on Si(100) [Fig. 6(d)]. The other difference consists in the interface between the grown structures and substrates, which is sharp on Si(111), whereas the Ge content changes gradually in the SiGe surface layers grown on Si(100) [Fig. 6(e)]. The sharp interface and the shapes of 3D SiGe structures on Si(111) gave the evidences of that SiGe segregates on Si(111) at 800 °С due to dewetting [42–44]. Self-organization during heteroepitaxial growth occurs due to the strain relaxation whose potential for the surface morphology transformation is restricted by the kinetics of surface processes, such as the island nucleation with its random spatial nature, elastic strain anisotropy and surface diffusion, as well as different growth rates of different
We obtained the critical rates for Ge depositions on Si(100) at temperatures in the range of 840–960 °C at which the dynamic equilibrium between the growth of islands and their decay by means of the Si-Ge intermixing with the Ge diffusion into the substrate is realized. It depends on the deposited Ge amount that reflects the Ge accumulation in surface layers. The SiGe islands grown in the conditions close to the dynamic equilibrium are formed via a nucleationless process, exhibiting a tendency to ordering. The island arrays are characterized by homogeneous lattice strain distributions and SiGe compositions in the direction along the surface. It is expected that the SiGe/Si heterostructures, fabricated on the base of such island arrays,
Fig. 5. (a) and (b) STM images of the surfaces obtained by the 20 nm Ge deposition on Si(100) at 925 °С with the deposition rate of 0.39 and 0.57 nm/min, respectively. (c) The solid line represents the height profile along the island array indicated by the arrow in (a). The dotted line is the experimental height profile approximation by the sinusoidal function.
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Fig. 6. (a) and (b) SEM cleavage images of the samples prepared by (a) the 40 nm Ge deposition with the rate of about 0.23 nm/min at 900 °C (that is slightly above the critical conditions) and (b) 10 nm Ge deposition with the rate of 0.5 nm/min at 800 °C. (c)-(e) EDX data for the atomic composition of the surface layers as a function of (c) the growth temperature and the distance across the islands along the A and B lines marked in (b) for (d) and (e), respectively, for the layers growth by the Ge deposition at the temperatures marked at the corresponding curves. [6] M. Schmidbauer, T. Wiebach, H. Raidt, M. Hanke, R. Köhler, H. Wawra, Phys. Rev. B 58 (1998) 10523. [7] C.L. Zheng, K. Scheerschmidt, H. Kirmse, I. Häusler, W. Neumann, Ultramicroscopy 124 (2013) 108. [8 Y.-W. Mo, D.E. Savage, B.S. Swartzentruber, M.G. Lagally, Phys. Rev. Lett. 65 (1990) 1020. [9] M.W. Dashiell, U. Denker, C. Muller, G. Costantini, C. Muzano, K. Kern, O.G. Schmidt, Appl. Phys. Lett. 80 (2002) 1279. [10] S.A. Chaparro, Y. Zhang, J. Drucker, D. Chandrasekhar, D.J. Smith, J. Appl. Phys. 87 (2000) 2245. [11] A.B. Talochkin, A.A. Shklyaev, V.I. Mashanov, J. Appl. Phys. 115 (2014) 144306. [12] K. Nakajima, A. Konishi, K. Kimura, ., Phys. Rev. Lett. 83 (1999) 1802. [13] G. Capellini, M. De Seta, F. Evangelisti, Appl. Phys. Lett. 78 (2001) 303. [14] V.A. Baranov, A.V. Fedorov, T.S. Perova, R.A. Moore, V. Yam, D. Boucher, V. Le Thanh, K. Berwick, Phys. Rev. B 73 (2006) 075322. [15] A.A. Shklyaev, K.N. Romanyuk, S.S. Kosolobov, Surf. Sci. 625 (2014) 50. [16] A.A. Shklyaev, A.E. Budazhapova, Appl. Surf. Sci. 360 (2016) 1023. [17] J.J. Lander, J. Morrison, J. Appl. Phys. 33 (1962) 2089. [18] F.W. Smith, G. Ghidini, J. Electrochem. Soc. 129 (1982) 1300. [19] A.A. Shklyaev, T. Suzuki, Phys. Rev. Lett. 75 (1995) 272. [20] A.W. Searcy, J. Am. Chem. Soc. 74 (1952) 4789. [21] B.E. Poling, J.M. Prausnitz, O.C. John Paul, R.C. Reid, The properties of gases and liquids 5, McGraw-Hill, New York, 2001, pp. 7.1–7.33. [22] B. Voigtländer, Surf. Sci. Rep. 43 (2001) 127. [23] S.A. Teys, A.B. Talochkin, B.Z. Olshanetsky, J. Cryst. Growth 311 (2009) 3898. [24] K. Lehovec, J. Rosen, A. MacDonald, J. Broder, J. Appl. Phys. 24 (1953) 513.
may have narrow electronic state spectra which are required for the realization of electronic and optical resonances. Acknowledgment The financial support by Russian Science Foundation Grant 14-1201037 is gratefully acknowledged. The experiments were partly carried out using the equipment of and supported by CKP “NANOSTRUKTURY”, Ministry of Education and Science of the Russian Federation. References [1] C. Teichert, M.G. Lagally, L.J. Peticolas, J.C. Bean, J. Tersoff, Phys. Rev. B 53 (1996) 16334. [3] V. Holý, J. Stangl, S. Zerlauth, G. Bauer, N. Darowski, D. Luebbert, U. Pietsch, J. Phys. D. 32 (1999) A234. [3] O.G. Schmidt, N.Y. Jin-Phillipp, C. Lange, U. Denker, K. Eberl, R. Schreiner, H. Gräbeldinger, H. Schweizer, Appl. Phys. Lett. 77 (2000) 4139. [4] H. Omi, D.J. Bottomley, T. Ogino, Appl. Phys. Lett. 80 (2002) 1073. [5] V.A. Zinovyev, A.V. Dvurechenskii, P.A. Kuchinskaya, V.A. Armbrister, S.A. Teys, A.A. Shklyaev, A.V. Mudryi, Semiconductors 49 (2015) 149.
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Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp
Critical conditions for SiGe island formation during Ge deposition on Si(100) at high temperatures
crossmark
⁎
A.A. Shklyaeva,b, , A.E. Budazhapovac a b c
A.V. Rzhanov Institute of Semiconductor Physics, SB RAS, Novosibirsk 630090, Russia Novosibirsk State University, Novosibirsk 630090, Russia Novosibirsk State Technical University, Novosibirsk 630055, Russia
A R T I C L E I N F O
A BS T RAC T
Keywords: Ge MBE on Si(100) High-temperature growth Self-organization Strain relaxation Dynamic equilibrium
The strain relaxation during the Ge growth on Si(100) occurs vikia surface diffusion and Si-Ge intermixing at temperatures below 800 °C. The Ge diffusion into the Si substrate is an additional process at higher temperatures. We found that, if its rate is higher than the Ge deposition rate, the island formation is not realized. We determined the critical Ge deposition rate as a function of the temperature in the range of 840– 960 °C, at which the dynamic equilibrium between the growth of islands and their decay through the diffusion takes place. The islands grown in the conditions close to the dynamic equilibrium are ordered with a distance between them of about 1 µm and they form a smoothed surface morphology. These are indicative of the surface layer strain uniformity. The islands have a SiGe composition which, in the direction parallel to the sample surface, is more uniform in comparison with the islands grown at lower temperatures. The results show that the use of high temperatures essentially improves the conditions for the heterostructure self-organization.
1. Introduction Self-organization during heteroepitaxial growth provides the possibility for the fabrication of semiconductor heterostructures with quantum dot arrays that exhibit unique optoelectronic properties. In order to obtain their best performance, they should be prepared on the base of the ordered three-dimension (3D) islands of identical sizes. Since the self-organization occurs to reduce the lattice strain, the formation of ordered island arrays provides the most exhaustive strain relaxation. It was found that the island ordering can be realized when the nucleation of islands does not occur randomly along the surface, but their locations are governed by the elastic strain distribution generated by underlying patterned structures [1–5]. The surface morphology formation usually takes place via surface processes which can limit the realization of strain relaxation. The facilitated strain relaxation is suggested to occur in the conditions close to thermodynamic equilibrium, which can be realized, for example, in liquid phase epitaxy [6,7]. In this Letter, it is shown that the conditions for island ordering can be implemented during Ge molecular beam epitaxy (MBE) on Si(100) at high temperatures, when the islands are formed by means of the nucleationless process via gradual changes in the surface morphology in the conditions close to the dynamic equilibrium between the growth of islands and their decay through the Ge diffusion
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into the substrate. At temperatures up to 500 °C, the 3D island formation during the Ge deposition on Si(100) is realized via the surface diffusion and incorporation of deposited Ge atoms into energetically favorable surface sites [8–11]. At 500–750 °C, the island growth is accompanied by the additional process, i.e. by the intermixing of deposited Ge atoms with Si atoms of surface layers [12–15]. When the temperature increases above 800 °C, the diffusion of deposited Ge atoms into the bulk of Si substrates becomes significant. If the Ge deposition rate is not sufficiently high, deposited Ge entirely diffuses into the substrate and the island formation does not occur [16]. Therefore, at each temperature there is a minimal Ge deposition rate at which the islands can grow. We obtained here the experimental data to describe the dependence of the minimal Ge deposition rate on temperature. It represents the boundary in coordinates of the Ge deposition rate and the temperature, along which the dynamical equilibrium between the island growth and their decay due to the Ge diffusion into the substrate takes place. The boundary can be referred to as the critical conditions for the island growth at high temperatures using the analogy with the case of oxygen interaction with Si surfaces in which the critical conditions describe the dependence of the minimal oxygen pressure on the temperature for the transition from the Si etching by oxygen to the silicon oxide growth
Corresponding aauthor at: A.V. Rzhanov Institute of Semiconductor Physics, SB RAS, Novosibirsk 630090, Russia. E-mail address: [email protected] (A.A. Shklyaev).
http://dx.doi.org/10.1016/j.mssp.2016.09.033 Received 26 July 2016; Received in revised form 21 September 2016; Accepted 27 September 2016 1369-8001/ © 2016 Elsevier Ltd. All rights reserved.
Materials Science in Semiconductor Processing 57 (2017) 18–23
A.A. Shklyaev, A.E. Budazhapova
tures of about 900°С leads to the increase in the monolayer step density and to the trenches formation of dimer vacancies that form the (2×N) reconstruction [Fig. 2(a)]. The N value was in the range from 5 to 10. The trenches provide the lattice strain reduction. Such surface morphologies are typical of the SiGe layer growth on Si(100) in the middle temperature range from about 500–650 °С [25–27]. In this aspect, the Ge deposition on Si(100) at high temperatures appears to produce similar effects.. The monolayer step density increase was observed through the 2D island nucleation preferably on Si(100) terraces of smaller sizes. This occurs inhomogeneously along the surface, leading to the gradual 3D formation in the places where the terrace size decreases faster. At the same time, the correlation in their lateral locations, which can then provide their development into the ordered island arrays during the further Ge deposition [16], is observed (Fig. 2). Such behavior shows that the 3D island formation occurs not via the spontaneous island nucleation stage, but through the gradual changes in the surface morphology, i.e. through a nucleationless process. It should be mentioned that some island ordering can also occur under long-time postgrowth annealing [28,29]. The island formation at high temperatures occurs in the conditions when a significant amount of deposited Ge diffuses into the substrate [16]. There is the Ge deposition rate (Rdep) at which the dynamic equilibrium between the growth of islands on the surface and their decay due to the Ge diffusion into the substrate is realized. This rate can be referred to as the critical rate (Rc) for the island formation, similar to the critical oxygen pressure at which the quasi-equilibrium conditions between the silicon oxide growth and decomposition on Si surfaces appear [17–19]. The Rc value can be determined by obtaining the island height dependence on Rdep. The island height appears to have a strong dependence on Rdep clearly indicating the Rc value [Fig. 3(a)]. The island height dependences on the Ge deposition rate and on the amount of deposited Ge are similar in the range of the critical conditions studied here.. The Ge deposition and Ge diffusion into the substrate form a strained SiGe layer on the surface. The 3D island formation begins, when the SiGe layer thickness reaches a certain value depending on the Si-Ge composition [30,31]. In the conditions of Ge diffusion into the substrate, if after the deposition of a certain Ge amount at a given temperature and Rdep the formation of islands is not observed, they can appear when the deposited Ge amount increases, as shown in Fig. 3(b). For the same growth temperature, this dependence means that the critical conditions are realized at a smaller Ge deposition rate when they are determined for a larger amount of deposited Ge. Since Rc depends on the amount of deposited Ge, its temperature dependence is reasonable to be obtained for several given amounts of deposited Ge. These temperature dependences show, in particular, that
[17–19]. We found that the growing islands have a tendency to ordering when the growth conditions are close to the dynamic equilibrium. These islands form the smooth surface morphology indicating the strain distribution homogeneity in the surface layer. The islands are also characterized by the homogeneity in the SiGe alloy composition in the direction along the surface. It is expected that SiGe heterostructures, made on the base of such island arrays, can have narrow electronic state spectra. 2. Experimental details The growth experiments were carried out in an ultrahigh-vacuum chamber with a base pressure of about 1×10−10 Torr. The chamber was equipped with a scanning tunneling microscope (STM) manufactured by Omicron. A 10×2×0.3 mm3 sample was cut from an n-type Si(100) wafer with a miscut angle of < 10´ and a resistivity of 5–20 Ω cm. Clean Si surfaces were prepared by flash direct-current heating at 1250–1300 °C. A Knudsen cell with a BN crucible was used for Ge deposition at the rate up to 1.1 nm/min. The Ge growth on Si(100) surfaces was carried out at temperatures from 700 to 960 °C. The sample temperature was measured using an IMPAC IGA 12 pyrometer. After the removal of the samples from the growth chamber, their scanning electron microscope (SEM) images were obtained using a Pioneer microscope manufactured by Raith. The grown layer chemical composition was measured using energy-dispersive X-ray spectroscopy (EDX) of SEM SU8220 made by Hitachi. To improve the spatial resolution in EDX measurements of chemical compositions along a certain line on a sample cleavage, the incident e-beam energy was reduced to 3 keV. The EDX for such low e-beam energy was calibrated using the samples with the known SiGe compositions. This provided obtaining the spatial resolution of 25 nm for 95% changes in chemical composition which was determined using the sample cleavages with sharp Si/Ge interfaces. In order to obtain the critical Ge deposition rate for the island formation, the measurement of the Ge deposition rate dependence on the K-cell temperature was required. The Ge deposition rate is proportional to the Ge vapor pressure in the K-cell. When the aperture size of a K-cell is much smaller than its sidewalls total areas, the vapor pressure is governed by the equilibrium between the gaseous and condensed Ge phases. The simplified equilibrium gas pressure is (o ) described as Peq = Peq exp(−ΔH / kT ), where ΔH=ΔHo+aT is the vaporization heat, ΔHo is a constant and a is the difference in the heat capacity between the gaseous and condensed phases [20,21]. Assuming Rdep (T )~Peq (T ), that the Ge deposition rate is we (o ) (o ) exp(−ΔH /kT ), where Rdep is the pre-exponential factor obtainRdep = Rdep depending on the K-cell aperture and the distance between the K-cell and the substrate. The deposition rate was obtained with the STM by measuring the Ge coverage of submonolayer thick Ge wetting layers on Si(111) deposited at about 450 °C for different K-cell temperatures (Fig. 1). The Ge growth on Si(111) proceeds through the formation of two-dimensional (2D) islands which can be of three heights, i.e. 1, 2 or 3 bilayer (BL), where 1 BL ≈0.327 nm is the distance between adjacent (111) planes (inset in Fig. 1) [22,23]. The Ge coverage was derived by accounting the size of islands and their thickness.. By this technique, the Ge deposition rates can be measured with the accuracy within 5% for each K-cell temperature. The obtained experimental data can be well described by the exponential function, as shown in Fig. 1. The value of ΔHo≈3.5 eV is in agreement with the previously obtained data for the Ge evaporation [20,24] and, thereby, this confirms that the Ge vapor pressure in the K-cell used in our experiments is governed by the equilibrium between the gaseous and condensed Ge phases. 3. Critical conditions for island formation
Fig. 1. Temperature dependence of the Ge deposition rate. The STM image of the Si(111) surface covered with 2D islands with heights 1, 2 and 3 BL, obtained by about 0.5 BL Ge deposition at 450°С, is shown in the inset.
The initial stage of the Ge deposition on Si(100) at high tempera19
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Fig. 4. Critical conditions for the island formation during 5 (data A) and 100 nm (data B) Ge depositions on Si(100) at high temperatures. The solid and open symbols represent the conditions at which the islands appear or not on the surface, respectively.
required for the gradual surface morphology evolution to the 3D growth.. The critical conditions presented in Fig. 4 allow them to be well approximated by the exponential function Rc(T)=Roexp(-Ea/kT), where Ro is the pre-exponential factor and Ea is the effective activation energy. The obtained Ea was found to be about 4.5 and 5.0 eV for the Ge depositions of 5 and 100 nm, respectively. As expected, these values are in agreement with the activation energy of Ge diffusion in Si [32,33]. This, thereby, confirms that the main process, which is responsible for the island decay, is the Si-Ge intermixing with the Ge diffusion in the Si substrate. The fact that the island growth does not occur at the high temperatures and the low Ge deposition rates can not be only the result of Ge diffusion into the substrate, but it can also be due to the Ge desorption from the surface. The Ge evaporation rate can be estimated by extrapolating of higher temperature data obtained by Lehovec et al. [24]. This gives the Ge evaporation rate of 0.04 nm/min at 940 °C at which the critical Ge deposition rate is much greater, being 1.05 nm/ min in the case of the Ge deposition in the amount of 5 nm (Fig. 4). That the Ge desorption rate is relatively low is in agreement with the rapid increase of the height of islands after their formation (Fig. 3), and with the possibility of a description of the critical conditions by an exponential function with the effective activation energy which coin-
Fig. 2. (a) STM and (b) SEM images of the surfaces obtained by 5 and 100 nm Ge depositions on Si(100) with the Ge deposition rates of 0.14 and 1.00 nm/min at 890 and 940 °С, respectively. The inset in (a) shows that the surfaces are composed of 2×N reconstructed (100) terraces.
Rc is about 2.5 times bigger for the 5 nm Ge deposition than that for 100 nm (Fig. 4). It can be noted that, in order to prepare ordered island arrays, rather large Ge depositions of about 20 nm or larger must be carried out in the conditions close to the dynamic equilibrium. It is
Fig. 3. Island height dependences (a) on the Ge deposition rate for the deposited Ge amount of 20 nm and (b) on the deposited Ge amount for the Ge deposition rate of 0.39 nm/min at 940 °С.
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faceting planes. The numerical simulations showed that essential changes in the surface morphology profile can be obtained by long time annealing of strained heteroepitaxial structures [32,45,46]. In the models, the lateral island ordering is governed by the lattice strain anisotropy and the obtained results clearly reflect the substrate crystal symmetry. However, considerable progress in the ordered 3D structure preparation by long time annealing was not achieved experimentally [28,29]. It is, probably, due to the necessity for using rather high annealing temperature, since the ordering requires an intensive mass transport along the surface. As shown here and in [16], the hightemperature annealing initiates the atom diffusion from epitaxial layers into substrates. This diffusion significantly restricts the temperature and duration of annealing. The results of this study show that the limitations on the annealing temperature and on its duration can be overcome if the epitaxial layer composition is restored during annealing by the material deposition on its surface.
cides with the activation energy of Ge diffusion in Si. These arguments indicate that the probability of Ge sticking to the SiGe surfaces is not essentially less than one in the range of critical conditions. However, there is no evidence that the Ge sticking probability is close to one for the Si surface at the initial Ge deposition stage. The size, shape and spatial distribution of islands on the surface strongly depend on ΔR (Fig. 5). The islands grown in the conditions close to the dynamic equilibrium have an oval shape and a tendency to lateral ordering [16]. Moreover, they form a smooth surface shape at their base [Fig. 5(a)]. The height profile measured along an island array can be well approximated by the sinusoidal function [Fig. 5(c)]. This surface morphology shape indicates that the strain distribution along the surface is homogeneous, since the highest strain inhomogeneity is usually formed along island perimeters where the surface morphology has the sharpest edges [34,35].. 4. Island chemical composion
5. Conclusion The islands grown by the Ge deposition on Si(100) at 450–750 °С are characterized by the bimodal island size distribution [36]. The distribution of the islands grown at 800–900 °С becomes monomodal [16]. The islands grown at different temperatures have different SiGe compositions. The Si-Ge intermixing, taking place at temperatures above 500 °С, leads to the formation of the trenches along the island perimeter, where the lattice strain is the strongest [15,37]. The different rate of Si-Ge intermixing in different surface layer areas results in inhomogeneous SiGe composition distributions [38]. The trenches around islands are not formed at temperatures of 850–900 °С [16]. The EDX data for SiGe compositions of the structures grown in this work were obtained for cleaved samples from the areas where cleaving planes crossed island centers (Fig. 6).. The Ge content is higher in the centers than near the edges of the islands grown at 700 °C [Fig. 6(d) and (e)]. In the island surface layers it is about 25%, whereas in the island central areas it reaches 33%, i.e. in agreement with the data obtained previously [38]. The greater Ge content in the island central areas reflects the fact that Si enters an island from its perimeter by means of diffusion on the island surface. It can be noted that the Ge content in islands depends on the Ge deposition rate, and it is higher when higher deposition rates are used [39–41]. The Ge content in the grown islands decreases with the increasing growth temperature and it becomes about 6% at 900 °C [Fig. 6(с)]. The SiGe content distribution in the islands measured in the direction along the sample surface is uniform for the structures grown at temperatures in the range of 800–900 °С [Fig. 6(d) and (e)]. At the same time, the Ge content decreases as a function of the distance in the direction from the surface [Fig. 6(e)]. The obtained data indicate that the Si-Ge intermixing occurs uniformly in the whole surface layer, thereby, confirming the important role of Ge diffusion into the Si substrate at temperatures above 800 °C. The results of Ge deposition on Si(100) at high temperatures are different from those on Si(111) [42,43] in several aspects. The Si-Ge intermixing on Si(111) occurs with the essentially lower rate and, at 800 °C, it leads to the formation of large 3D structures with the Ge content of about 30% [40], that is about two times higher than that in the islands grown on Si(100) [Fig. 6(d)]. The other difference consists in the interface between the grown structures and substrates, which is sharp on Si(111), whereas the Ge content changes gradually in the SiGe surface layers grown on Si(100) [Fig. 6(e)]. The sharp interface and the shapes of 3D SiGe structures on Si(111) gave the evidences of that SiGe segregates on Si(111) at 800 °С due to dewetting [42–44]. Self-organization during heteroepitaxial growth occurs due to the strain relaxation whose potential for the surface morphology transformation is restricted by the kinetics of surface processes, such as the island nucleation with its random spatial nature, elastic strain anisotropy and surface diffusion, as well as different growth rates of different
We obtained the critical rates for Ge depositions on Si(100) at temperatures in the range of 840–960 °C at which the dynamic equilibrium between the growth of islands and their decay by means of the Si-Ge intermixing with the Ge diffusion into the substrate is realized. It depends on the deposited Ge amount that reflects the Ge accumulation in surface layers. The SiGe islands grown in the conditions close to the dynamic equilibrium are formed via a nucleationless process, exhibiting a tendency to ordering. The island arrays are characterized by homogeneous lattice strain distributions and SiGe compositions in the direction along the surface. It is expected that the SiGe/Si heterostructures, fabricated on the base of such island arrays,
Fig. 5. (a) and (b) STM images of the surfaces obtained by the 20 nm Ge deposition on Si(100) at 925 °С with the deposition rate of 0.39 and 0.57 nm/min, respectively. (c) The solid line represents the height profile along the island array indicated by the arrow in (a). The dotted line is the experimental height profile approximation by the sinusoidal function.
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