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Microscopic parameters of heterostructures containing nanoclusters and thin layers of Ge in Si matrix
Nuclear Instruments and Methods in Physics Research A 470 (2001) 283–289
Microscopic parameters of heterostructures containing nanoclusters and thin layers of Ge in Si matrix S.B. Erenburga,*, N.V. Bauska, N.P. Stepinab, A.I. Nikiforovb, A.V. Nenashevb, L.N. Mazalova a
Chemical Bonds Study Laboratory, Institute of Inorganic Chemistry of SB RAS, Lavrentyeva avenue 3, Novosibirsk 630090, Russia b Institute of Semiconductors Physics SB RAS, Lavrentyeva avenue 13, Novosibirsk 630090, Russia
Abstract GeK XAFS measurements have been performed using the total electron yield detection mode for pseudomorphous Ge films deposited on Si(0 0 1) substrate via molecular beam epitaxy at 3001C. The samples have been produced by thrice repeating the growing procedure separated by deposition of blocking Si layers at 5001C. The local microstructure parameters (interatomic distances, Ge coordination numbers) are linked to nanostructure morphology and adequate models are suggested and discussed. It was established that pseudomorphous 4-monolayer Ge films contain 50% of Si atoms on the average. Pyramid-like, pure Ge islands formed in the Stranski–Krastanov growth are characterized by ( (by 0.04 A ( less than in bulk Ge) and the Ge–Si distances of 2.37 A ( . It was the interatomic Ge–Ge distances of 2.41 A revealed that the pure Ge nanoclusters are covered by a 1–2-monolayer film with admixture on the average of a 50% Si atom impurity from blocking Si layers. r 2001 Elsevier Science B.V. All rights reserved. PACS: 61.10.Ht Keywords: XAFS; Local structure; Ge films; Quantum dots
1. Introduction The phenomenon of self-organization in the process of heteroepitaxial semiconductor system growth allows fabrication of dense, extended, wellordered structures containing islands of uniform shape and size. Such structures are especially important for high-technology applications [1,2]. The possible use of these structures includes both the traditional trends towards miniaturization in semiconductor technologies and new ideas relating *Corresponding author. Tel.: +7-3832-333166; fax: +73832-344489. E-mail address: [email protected] (S.B. Erenburg).
to element engineering for quantum computer [2]. In semiconductor nanostructures with spontaneously ordered inclusions of a narrower bandgap material within a broader bandgap matrix, under appropriate conditions, a potential appears at the island boundaries preventing motion of charge carriers (electrons and holes) in all three dimensions. Thus, the limiting case of the dimensional quantization is realized within a certain interval of microinclusion sizes with the formation of the so-called quantum dots (QDs) characterized by discrete electronic spectra. In a heteroepitaxial system, in the presence of a difference of the lattice constants, the initial growth may occur by layers. When the layers
0168-9002/01/$ - see front matter r 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 1 0 8 0 - 4
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grow thicker, there appears the trend to elastic strain relaxation and elastic energy decreases by disturbing the two-dimensional growth and forming isolated islands, the so-called Stranski–Krastanov growth. The main characteristics of QDs, determining their electrophysical, optical and some other properties, are given by the energy spectrum of their charge carriers. In a series of comparatively recent studies, it was shown by different experimental methods (capacitance spectroscopy [3], hopping transport [4], admittance spectroscopy [5]) that at a certain thickness of the epitaxial Ge film on Si(0 0 1) in the electronic spectra of the heterostructures there appear features associated with the zero-dimensional density of the states. These features are due to the dimensional quantization of the hole spectrum in the Ge islands appearing during disturbed two-dimensional growth. The spectrum of states in the self-organizing nanoclusters may be largely influenced by the elastic deformation at the boundaries arising from a mismatch of the lattice parameters of the nanocluster and substrate. In the Ge/Si system, the lattice mismatch amounts to 4.2%. This will cause changes in the local structure: local distortions of the symmetry, changes in the valence angles and interatomic distances. Such structural changes may change the energy spectrum by a magnitude of the order of 0.1 eV [6], which is comparable with the dimensional quantization energy in a QD. The local structural changes in the thin layers and nanoclusters are not detectable by the traditional X-ray structural analysis or electron diffraction, because such systems have no long-range ordering. Extended X-ray absorption fine structure (EXAFS) and an X-ray absorption near-edge structure (XANES) spectroscopy provides a unique possibility for solving such problems [7]. These methods allow the determination of parameters of the local environment of atoms: interatomic distances, coordination numbers, the symmetry of the environment, the types of atoms of the environment, the Debye–Waller factors. They also allow the determination of shifts of the electronic levels and estimation of the charge states of atoms. Thus in Ref. [8], using XANES spectro-
scopy, a broadening of the forbidden gap with decreasing size of the CVD grown germanium nanoclusters in silicon was found. In Refs. [9,10], using EXAFS spectroscopy, the local environment of Ge adatoms on Si(0 0 1), the structure of thin Ge layers on Si(0 0 1) and a superlattice with strained (Ge4/Si4)5 layers were studied. In particular, in Ref. [10], a lattice contraction was revealed as the interatomic distances decreased from 0.245 nm for R(Ge–Ge) (in massive germanium) and 2.40 nm for R(Ge–Si) (the sum of the covalent radii of Ge and Si atoms) to R(Ge–Ge)=243 nm and R(Ge–Si)=2.38 nm, respectively, in strained (Ge4/Si4)5 layers. However, we do not know about an EXAFS study of the local structure in a QD. During the growth of the self-organizing islands of Ge and then of the blocking layer of Si a temperature-dependent diffusion of atoms of Si and Ge, respectively, may take place, which has an influence on the wetting layer composition and the composition and width of the transitional layer at the Si–Ge boundaries. These characteristics of the transitional layers should have a substantial influence on the features in the QD energy spectrum. Such information about the local structure is also obtainable from EXAFS data. Thus in Ref. [10], a high degree of interlayer mixing of Ge and Si in strained (Ge4/Si4)5 layers was found. Therefore, when calculating QD energy spectra or interpreting peculiarities of their experimental energy spectra as well as when engineering elements with given electronic properties, the changes in the QD local structure should be taken into account. In this work, to study such peculiarities of Ge/Si structures a surface-probing technique of EXAFS measurements was used, which is based on full electron yield detection.
2. Experimental Two structures prepared by molecular beam epitaxy on two halves of a (0 0 1) Si substrate were studied experimentally. Both structures contained layers of Ge separated by 10 nm thick blocking
S.B. Erenburg et al. / Nuclear Instruments and Methods in Physics Research A 470 (2001) 283–289
layers of Si and differed from each other only in the thickness of their Ge layers. In one structure, each Ge layer had a thickness of 4 monolayers, and in the other, this thickness was equal to 10 monolayers. It was suggested that in the structure of the first type a pseudomorphous film of Ge would be formed, and in the second type structure disturbances of the two-dimensional growth after thickness of 4 monolayers will occur with the formation of pyramidal Ge nanoclusters with the lateral dimensions of B15 nm, a height of B1.5 nm and the separations between the islands of B5 nm. Such a nanocluster is shown schematically in Fig. 1. The wetting layer thickness and the size of the Ge nanoclusters on Si grown under disturbed growth conditions were determined by electron diffraction, high-resolution electron microscopy and scanning tunneling electron microscopy [4]. The Ge film growth temperature was equal to 3001C, the growth rate was 0.035 nm/s, the deposition temperature of the blocking layer was 5001C. For using as reference compounds, thick films (300 nm) of solid solutions of a different composition (30% Ge, 50% Ge and 75% Ge) were prepared by molecular beam epitaxy under the same conditions. The GeK EXAFS and XANES spectra in the Ge/Si (1 0 0) heterostructures were measured using the synchrotron radiation (SR) of the VEPP-3 storage ring at the Budker Institute of Nuclear Physics, Novosibirsk. The electron-beam energy was 2 GeV, with the stored current between 50 and 100 mA during the measurements. An Ar/He ionization chamber was used as the monitoring
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detector. The X-ray energy was defined by a double crystal monochromator with a channel-cut Si (1 1 1) single crystal. The spectra were recorded using the surface-sensitive EXAFS technique based on the measurements of the flux of electrons of the whole energy spectrum (total electron yield technique). The photocurrent was measured in a special vacuum chamber with a precision electrometer with a direct current amplifier. To avoid diffraction artifacts from the substrate the table with the sample was rotated at a frequency of about 10–15 Hz. For anisotropy study of the Ge atom environment in heterostructures the GeK spectra have been measured at the parallel ð8Þ and perpendicular ð>Þ Si(0 0 1) orientations relative to the electric field vector E of the linearly polarized SR beam. The obtained data were processed using the EXCURV92 software package [11]. In the data processing, the phase and amplitude characteristics were calculated in the Xa -DW approximation, using the procedures of the package [11]. For the analysis of the Ge local environment, the Fourier-filtered data were fitted using the k and k2 weighing procedure in the photoelectron wave ( @1. The error of vector interval from 2.5 to 13 A determining of interatomic distances with the ( . The amplitudefitting procedure was 70.01 A damping factor S02 was determined by data fitting for massive Ge and was equal to 0.8. Fig. 2 shows the experimental function kwðkÞ of GeK EXAFS, where wðkÞ is the normalized oscillating part of the absorption coefficient, for the sample with the 4-monolayer pseudomorphous film on Si(0 0 1).
3. Results and discussion
Fig. 1. Circuit of Ge nanocluster on Si(0 0 1).
Since the objects under study are essentially anisotropic with respect to the shape of the boundaries (especially, the two-dimensional layers), to obtain information about the boundaries, we have compared the GeK EXAFS and XANES spectra of the samples at two different orientations of the Si (0 0 1) plane relative to the electric field vector, E, of the SR beam. Fig. 3 shows the experimental functions kwðkÞ of the GeK EXAFS spectra for the sample with the
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4-monolayer pseudomorphous film in the parallel ð8Þ and perpendicular ð>Þ orientations of the Si(0 0 1) plane and the E vector. As is seen from the figure, there is a slight difference in the amplitude and practically no difference in the phase. For the samples with nanoclusters, the differences between the spectra at different orientations are also so slight that they are not interpretable. In the latter case, the absence of any appreciable anisotropy may be explained by the
Fig. 2. Experimental GeK EXAFS spectrum for pseudomorphous 4-monolayer (2D) film on Si(0 0 1) (E 8 ð0 0 1Þ, EFthe electric field vector).
Fig. 3. GeK EXAFS spectra for pseudomorphous 4-monolayer films on Si(0 0 1) (E 8 ð0 0 1ÞFthe solid line, E > ð0 0 1ÞFthe dashed line).
surface to bulk atom ratio in the QDs being equal to about 1/4. In samples containing only 4monolayer films, this ratio is 1/1 and the explanation may be the absence of a sharp Si–Ge boundary. It should be noted that the model of the 4-monolayer germanium film in silicon with sharp boundaries between the phases gives for Ge the mean coordination numbers n(Ge)=3 and n(Si)=1, i.e. a conventional stoichiometry Ge0.75Si0.25. The structure of the experimental GeK XANES spectra for the same samples is practically unchanged at different orientations, and the structure above the GeK edge resembles that in the spectrum of a film of the solid GexSi1@x solution with values of x close to 0.5. Indeed, while the amplitude and phase characteristics of kwðkÞ for the spectra of the GexSi1@x films with different stoichiometries are significantly different (Fig. 4 ), comparison of kwðkÞ of the EXAFS spectra of a film of the solid Ge0.50Si0.50 solution and the 4-monolayer film show their complete similarity both in the amplitude and phase. It does not mean that the 4 monolayers that grew are a uniform solid solution; but this fact establishes the presence of an appreciable exchange of atoms between the phases, which decreases the elastic strain in the system during the deposition of the blocking Si layer (5001C). Thus the monolayers forming the so-called pseudomorphous Ge films embedded in a
Fig. 4. GeK EXAFS spectra for solid Ge–Si solutions films: (1) 30% Ge; (2) 50% Ge; (3) 75% Ge.
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Fig. 5. Fourier transform magnitude of k3 wðkÞ GeK EXAFS data for pseudomorphous 4-monolayer (2D) films on Si(0 0 1): (1) E8 ð0 0 1Þ; (2) E> ð0 0 1Þ; and for a thick solid Ge–Si solution film (50% Ge) (3).
Si matrix contain up to 50% of Si atoms. The same conclusion was made by the authors of Ref. [10], who studied strained (Ge4/Si4)5 structures on Si(0 0 1) obtained by molecular beam epitaxy at 4001C. In their study, a model of ordered boundary in these structures involving substantial Ge and Si mixing was proposed. This model is not the only one possible. It is essential that both this model and our results (see below) show that only the atoms in the immediate vicinity to the boundary are really participating in the exchange. Fig. 5 shows the modules of the Fourier transforms of the function k3 wðkÞ of GeK EXAFS (the radial structural function without phase corrections) for the 4-monolyer film at different E orientations relative to Si(0 0 1) and for a thick (300 nm) film of the solid Ge0.50Si0.50 solution. As it is seen from the figure the structural functions are very similar. However, we can note the shift of the main maximum of the function towards smaller interatomic distances for the 4-monolayer film at both orientations. Taking into account the substantial exchange of atoms between the phases at the germanium layernanocluster–Si matrix boundary, let us consider the already available local structure data determined from the analysis of EXAFS spectra for films of solid GexSi1@x solutions with different compositions. The results for such films synthe-
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sized by different methods and obtained by different authors in the last several years are consistent with each other. This includes both MBE [12,13] and CVD grown films [14]. It was found that with the changing stoichiometry there is change in the bond lengths and apparently in the bond angles. The magnitude of such changes does ( for the Ge–Ge distances and not exceed 0.02 A ( 0.01 A for the Ge–Si distances in thick (relaxed) films as compared with pure Ge(R(Ge– ( ) and the sum of the covalent radii Ge)=2.450 A ( , respectively, at practically all R(Ge–Si)=2.401 A solid solution concentrations which allowed the authors to obtain sufficiently accurate bond lengths (for R(Ge–Ge) to 30% Ge concentration). According to the data of these studies, for the solid GexSi1@x solutions at x ¼ 0:320:5 the intera( , R(Ge– tomic distances R(Ge–Ge)=2.4370.01 A ( Si)=2.3970.01 A, which is in agreement with our data. According to the results of Ref. [13], the film with the stoichiometry close to GeSi3 is an exception. In the authors’ opinion, this film is a ( . For a special compound with R(Ge–Ge)=2.395 A thin film (presumably, with a thickness of about 40 monolayers) of the solid Ge0.50Si0.50 solution grown by molecular beam epitaxy at 4001C [10] (, the bond length R(Ge–Ge)=2.4270.01 A ( , which is by 0.01 A ( smalR(Ge–Si)=2.3870.01 A ler than in the thick relaxed films grown at 5501C and 5001C in Refs. [12] and [13], respectively. In Table 1, the results of the fitting of theoretical and experimental data within different structural models using the EXCURV92 software package are shown. The fitting was performed using the experimental data Fourier-filtered in the interval ( oRo2.6 A ( . The values of the Debye–Waller 1.5 A ( 2) and of the energy factor (s2 ¼ 0:0034 A Eo =10.6 eV were determined as a result of fitting for pure Ge with interatomic distances ( and the coordination number RðGe–Ge)=2.450 A n ¼ 4 and were fixed in all other cases. Goodness of fit is determined by the fit index FEXAFS [11]: X kni jwexp ðki Þ FEXAFS ¼ 104 X @wtheory ðki Þj2 = kni jwexp ðKi Þ: Simplest models No. 2, 3, 4 included one averaged variant of the environment for the Ge atoms with
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Table 1 Parameters obtained by the fitting procedure for pseudomorphous Ge films and structures with pyramid-like Ge islands on Si(0 0 1). R1(Ge–Ge)and R2(Ge–Si)Finteratomic distances; n1(Ge) and n2(Si)Fthe coordination numbers of Ge as to germanium atoms and to silicon atoms; goodness of fit is defined by the fit index F [11] No.
Sample
1. 2. 3. 3"a.
c-Ge Film ðE8 Þ QD ðE8 Þ QD ðE8 Þ
4. 5.
Film ðE> Þ QD ðE> Þ
() R1(Ge–Ge) (A
() R2(Ge–Si) (A
n1(Ge)
n2(Si)
2.45 2.41 2.40 2.41 2.40 2.41 2.41 2.41
2.37 2.38 2.37 2.38 2.36 2.36 2.38
4 1.70 3.16 1.70 4.14 1.78 1.78 4.5
2.35 1.67 2.34 0.54 2.00 2.00 0.10
the distances R1(Ge–Ge), R2(Ge–Si) and the coordination numbers of Ge as to germanium atoms (n1(Ge)) and to silicon atoms (n2(Si)). To a certain degree, such models are correct for the 4-monolayer films but for heterostructures with QDs the models should include at least two types of absorbing Ge atoms: the atoms at the boundary and those within the bulk of Ge nanoclusters. For the samples with QD the models included two types of absorbing Ge atoms: (1) Ge atoms at the boundary in the 2-monolayer thick transition layerFsuch atoms account for about one half of all the Ge atoms, (2) the atoms inside the QDs accounting for the other half of the Ge atoms. The thickness of the transition layer was estimated using the conclusion of this work that the pseudomorphous 4-monolayer Ge films embedded in the Si matrix and having the thickness of two transition layers contain about 50% of Si atoms. This assumption turned out to be true, since with the use of the QDs, of the same transition layer parameters (of the interatomic distances R1(Ge–Ge), R2(Ge–Si) and the coordination numbers n1(Ge) in germanium and n2(Si) in silicon) as in the 4-monolayer films, the Ge atoms in the QDs have practically no silicon atoms in the first sphere of their environment. As is seen from the table, the interatomic distances R1(Ge–Ge) decrease in the thin films ( as compared and structures with QD by 0.04 A ( . The with pure Ge and are equal to 2.41 A ( as comR2(Ge–Si) distances decrease by 0.03 A pared with the sum of the covalent radii of Ge and
F 0.8 0.6 1.0 1.7 3.9 1.1
Fig. 6. Bar chart of interatomic bond lengths distributions in Ge QD on Si(0 0 1) obtained by the VFF method calculation. NFthe number of interatomic bonds; RFthe interatomic distances.
( . Further refinement does Si and are equal to 2.37 A not appear correct at this stage because of the assumptions and suggestion made. In conclusion, the interatomic distances R1(Ge–Ge) and R2(Ge–Si) obtained by us from the EXAFS data are in agreement with the interatomic distances derived from the spatial distribution of elastic deformation calculated within the valence force field model. The calculation was performed by the procedure based on the use of the Green function of the ‘‘atomistic’’ elastic problem, which was further developed in Ref. [15]. Fig. 6 shows a histogram of the Ge–Ge and Ge–Si bond length distribution in a pyramidal germa( 15 A ( , see Fig. 1) nium quantum dot (150 A embedded in silicon on the Si(0 0 1) plane. The
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calculation was performed for the QD model with sharp Ge/Si boundaries. Financial support from the Russian State Scientific and Engineering Program on Physics of Surface Atomic Structures (grant 1-14-99) is greatly appreciated.
References [1] V.A. Shchukin, D. Bimberg, Appl. Phys. A 67 (1998) 687. [2] A. Barenco, D. Deutsch, A. Ekert, R. Jozsa, Phys. Rev. Lett. 74 (1995) 4083. [3] A.I. Yakimov, A.V. Dwurechenskii, A.I. Nikiforov, O.P. Pchelyakov, JETP Lett. 68 (1998) 125. [4] A.I. Yakimov, A.V. Dwurechenskii, A.I. Nikiforov, O.P. Pchelyakov, Phys. Low-Dimensional Struct. 3/4 (1999) 99. [5] A.I. Yakimov, C.J. Adkins, R. Boucher, A.V. Dvurechenskii, A.I. Nikiforov, O.P. Pchelyakov, G. Biskupskii, Phys. Rev. B 59 (1999) 12598. [6] M.M. Rieger, P. Vogl, Phys. Rev. B 48 (1993) 14276.
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[7] D.C. Koninsberger, R. Prins, X-ray Absorption: Principles, Applications, Techniques of EXAFS, SEXAFS and XANES, Wiley, New York, 1988, p. 710. [8] S. Kakar, T. van Buuren, R. Treusch, C. Heske, F.J. Himpsel, L.L. Chase, L.J. Terminello, Abstracts MRS 1998 Spring Meeting, V2.5, San Francisco, California, CA, 1998, p. 350. [9] H. Oyanagi, K. Sakamoto, R. Shioda, J. Phys. IV (France) 7 (C2) (1997) 669. [10] S. Wei, H. Oyanagi, K. Sakamoto, Y. Takeda, T.P. Pearsall, J. Synchrotron Radiat. 6 (1999) 790. [11] N. Binsted, J.W. Campbell, S.J. Gurman, P.C. Stephenson, SERC Daresbury Laboratory Report, 1991. [12] D.B. Aldrich, R.J. Nemanich, D.E. Sayers, Phys. Rev. B 50 (1994) 15026. [13] J.C. Aubry, T. Tyliszczak, A.P. Hitchcock, J.-M. Baribeau, T.E. Jackman, Phys. Rev. B 59 (1999) 12872. [14] J.C. Woicik, K.E. Miyano, C.A. King, R.W. Johnson, J.G. Pellegrino, T.-L. Lee, Z.H. Lu, Phys. Rev. B 57 (1998) 14592. [15] A.V. Nenashev, A.V. Dvurechenskii, JETP 117 (9) (2000) 570.
Microscopic parameters of heterostructures containing nanoclusters and thin layers of Ge in Si matrix S.B. Erenburga,*, N.V. Bauska, N.P. Stepinab, A.I. Nikiforovb, A.V. Nenashevb, L.N. Mazalova a
Chemical Bonds Study Laboratory, Institute of Inorganic Chemistry of SB RAS, Lavrentyeva avenue 3, Novosibirsk 630090, Russia b Institute of Semiconductors Physics SB RAS, Lavrentyeva avenue 13, Novosibirsk 630090, Russia
Abstract GeK XAFS measurements have been performed using the total electron yield detection mode for pseudomorphous Ge films deposited on Si(0 0 1) substrate via molecular beam epitaxy at 3001C. The samples have been produced by thrice repeating the growing procedure separated by deposition of blocking Si layers at 5001C. The local microstructure parameters (interatomic distances, Ge coordination numbers) are linked to nanostructure morphology and adequate models are suggested and discussed. It was established that pseudomorphous 4-monolayer Ge films contain 50% of Si atoms on the average. Pyramid-like, pure Ge islands formed in the Stranski–Krastanov growth are characterized by ( (by 0.04 A ( less than in bulk Ge) and the Ge–Si distances of 2.37 A ( . It was the interatomic Ge–Ge distances of 2.41 A revealed that the pure Ge nanoclusters are covered by a 1–2-monolayer film with admixture on the average of a 50% Si atom impurity from blocking Si layers. r 2001 Elsevier Science B.V. All rights reserved. PACS: 61.10.Ht Keywords: XAFS; Local structure; Ge films; Quantum dots
1. Introduction The phenomenon of self-organization in the process of heteroepitaxial semiconductor system growth allows fabrication of dense, extended, wellordered structures containing islands of uniform shape and size. Such structures are especially important for high-technology applications [1,2]. The possible use of these structures includes both the traditional trends towards miniaturization in semiconductor technologies and new ideas relating *Corresponding author. Tel.: +7-3832-333166; fax: +73832-344489. E-mail address: [email protected] (S.B. Erenburg).
to element engineering for quantum computer [2]. In semiconductor nanostructures with spontaneously ordered inclusions of a narrower bandgap material within a broader bandgap matrix, under appropriate conditions, a potential appears at the island boundaries preventing motion of charge carriers (electrons and holes) in all three dimensions. Thus, the limiting case of the dimensional quantization is realized within a certain interval of microinclusion sizes with the formation of the so-called quantum dots (QDs) characterized by discrete electronic spectra. In a heteroepitaxial system, in the presence of a difference of the lattice constants, the initial growth may occur by layers. When the layers
0168-9002/01/$ - see front matter r 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 1 0 8 0 - 4
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grow thicker, there appears the trend to elastic strain relaxation and elastic energy decreases by disturbing the two-dimensional growth and forming isolated islands, the so-called Stranski–Krastanov growth. The main characteristics of QDs, determining their electrophysical, optical and some other properties, are given by the energy spectrum of their charge carriers. In a series of comparatively recent studies, it was shown by different experimental methods (capacitance spectroscopy [3], hopping transport [4], admittance spectroscopy [5]) that at a certain thickness of the epitaxial Ge film on Si(0 0 1) in the electronic spectra of the heterostructures there appear features associated with the zero-dimensional density of the states. These features are due to the dimensional quantization of the hole spectrum in the Ge islands appearing during disturbed two-dimensional growth. The spectrum of states in the self-organizing nanoclusters may be largely influenced by the elastic deformation at the boundaries arising from a mismatch of the lattice parameters of the nanocluster and substrate. In the Ge/Si system, the lattice mismatch amounts to 4.2%. This will cause changes in the local structure: local distortions of the symmetry, changes in the valence angles and interatomic distances. Such structural changes may change the energy spectrum by a magnitude of the order of 0.1 eV [6], which is comparable with the dimensional quantization energy in a QD. The local structural changes in the thin layers and nanoclusters are not detectable by the traditional X-ray structural analysis or electron diffraction, because such systems have no long-range ordering. Extended X-ray absorption fine structure (EXAFS) and an X-ray absorption near-edge structure (XANES) spectroscopy provides a unique possibility for solving such problems [7]. These methods allow the determination of parameters of the local environment of atoms: interatomic distances, coordination numbers, the symmetry of the environment, the types of atoms of the environment, the Debye–Waller factors. They also allow the determination of shifts of the electronic levels and estimation of the charge states of atoms. Thus in Ref. [8], using XANES spectro-
scopy, a broadening of the forbidden gap with decreasing size of the CVD grown germanium nanoclusters in silicon was found. In Refs. [9,10], using EXAFS spectroscopy, the local environment of Ge adatoms on Si(0 0 1), the structure of thin Ge layers on Si(0 0 1) and a superlattice with strained (Ge4/Si4)5 layers were studied. In particular, in Ref. [10], a lattice contraction was revealed as the interatomic distances decreased from 0.245 nm for R(Ge–Ge) (in massive germanium) and 2.40 nm for R(Ge–Si) (the sum of the covalent radii of Ge and Si atoms) to R(Ge–Ge)=243 nm and R(Ge–Si)=2.38 nm, respectively, in strained (Ge4/Si4)5 layers. However, we do not know about an EXAFS study of the local structure in a QD. During the growth of the self-organizing islands of Ge and then of the blocking layer of Si a temperature-dependent diffusion of atoms of Si and Ge, respectively, may take place, which has an influence on the wetting layer composition and the composition and width of the transitional layer at the Si–Ge boundaries. These characteristics of the transitional layers should have a substantial influence on the features in the QD energy spectrum. Such information about the local structure is also obtainable from EXAFS data. Thus in Ref. [10], a high degree of interlayer mixing of Ge and Si in strained (Ge4/Si4)5 layers was found. Therefore, when calculating QD energy spectra or interpreting peculiarities of their experimental energy spectra as well as when engineering elements with given electronic properties, the changes in the QD local structure should be taken into account. In this work, to study such peculiarities of Ge/Si structures a surface-probing technique of EXAFS measurements was used, which is based on full electron yield detection.
2. Experimental Two structures prepared by molecular beam epitaxy on two halves of a (0 0 1) Si substrate were studied experimentally. Both structures contained layers of Ge separated by 10 nm thick blocking
S.B. Erenburg et al. / Nuclear Instruments and Methods in Physics Research A 470 (2001) 283–289
layers of Si and differed from each other only in the thickness of their Ge layers. In one structure, each Ge layer had a thickness of 4 monolayers, and in the other, this thickness was equal to 10 monolayers. It was suggested that in the structure of the first type a pseudomorphous film of Ge would be formed, and in the second type structure disturbances of the two-dimensional growth after thickness of 4 monolayers will occur with the formation of pyramidal Ge nanoclusters with the lateral dimensions of B15 nm, a height of B1.5 nm and the separations between the islands of B5 nm. Such a nanocluster is shown schematically in Fig. 1. The wetting layer thickness and the size of the Ge nanoclusters on Si grown under disturbed growth conditions were determined by electron diffraction, high-resolution electron microscopy and scanning tunneling electron microscopy [4]. The Ge film growth temperature was equal to 3001C, the growth rate was 0.035 nm/s, the deposition temperature of the blocking layer was 5001C. For using as reference compounds, thick films (300 nm) of solid solutions of a different composition (30% Ge, 50% Ge and 75% Ge) were prepared by molecular beam epitaxy under the same conditions. The GeK EXAFS and XANES spectra in the Ge/Si (1 0 0) heterostructures were measured using the synchrotron radiation (SR) of the VEPP-3 storage ring at the Budker Institute of Nuclear Physics, Novosibirsk. The electron-beam energy was 2 GeV, with the stored current between 50 and 100 mA during the measurements. An Ar/He ionization chamber was used as the monitoring
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detector. The X-ray energy was defined by a double crystal monochromator with a channel-cut Si (1 1 1) single crystal. The spectra were recorded using the surface-sensitive EXAFS technique based on the measurements of the flux of electrons of the whole energy spectrum (total electron yield technique). The photocurrent was measured in a special vacuum chamber with a precision electrometer with a direct current amplifier. To avoid diffraction artifacts from the substrate the table with the sample was rotated at a frequency of about 10–15 Hz. For anisotropy study of the Ge atom environment in heterostructures the GeK spectra have been measured at the parallel ð8Þ and perpendicular ð>Þ Si(0 0 1) orientations relative to the electric field vector E of the linearly polarized SR beam. The obtained data were processed using the EXCURV92 software package [11]. In the data processing, the phase and amplitude characteristics were calculated in the Xa -DW approximation, using the procedures of the package [11]. For the analysis of the Ge local environment, the Fourier-filtered data were fitted using the k and k2 weighing procedure in the photoelectron wave ( @1. The error of vector interval from 2.5 to 13 A determining of interatomic distances with the ( . The amplitudefitting procedure was 70.01 A damping factor S02 was determined by data fitting for massive Ge and was equal to 0.8. Fig. 2 shows the experimental function kwðkÞ of GeK EXAFS, where wðkÞ is the normalized oscillating part of the absorption coefficient, for the sample with the 4-monolayer pseudomorphous film on Si(0 0 1).
3. Results and discussion
Fig. 1. Circuit of Ge nanocluster on Si(0 0 1).
Since the objects under study are essentially anisotropic with respect to the shape of the boundaries (especially, the two-dimensional layers), to obtain information about the boundaries, we have compared the GeK EXAFS and XANES spectra of the samples at two different orientations of the Si (0 0 1) plane relative to the electric field vector, E, of the SR beam. Fig. 3 shows the experimental functions kwðkÞ of the GeK EXAFS spectra for the sample with the
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4-monolayer pseudomorphous film in the parallel ð8Þ and perpendicular ð>Þ orientations of the Si(0 0 1) plane and the E vector. As is seen from the figure, there is a slight difference in the amplitude and practically no difference in the phase. For the samples with nanoclusters, the differences between the spectra at different orientations are also so slight that they are not interpretable. In the latter case, the absence of any appreciable anisotropy may be explained by the
Fig. 2. Experimental GeK EXAFS spectrum for pseudomorphous 4-monolayer (2D) film on Si(0 0 1) (E 8 ð0 0 1Þ, EFthe electric field vector).
Fig. 3. GeK EXAFS spectra for pseudomorphous 4-monolayer films on Si(0 0 1) (E 8 ð0 0 1ÞFthe solid line, E > ð0 0 1ÞFthe dashed line).
surface to bulk atom ratio in the QDs being equal to about 1/4. In samples containing only 4monolayer films, this ratio is 1/1 and the explanation may be the absence of a sharp Si–Ge boundary. It should be noted that the model of the 4-monolayer germanium film in silicon with sharp boundaries between the phases gives for Ge the mean coordination numbers n(Ge)=3 and n(Si)=1, i.e. a conventional stoichiometry Ge0.75Si0.25. The structure of the experimental GeK XANES spectra for the same samples is practically unchanged at different orientations, and the structure above the GeK edge resembles that in the spectrum of a film of the solid GexSi1@x solution with values of x close to 0.5. Indeed, while the amplitude and phase characteristics of kwðkÞ for the spectra of the GexSi1@x films with different stoichiometries are significantly different (Fig. 4 ), comparison of kwðkÞ of the EXAFS spectra of a film of the solid Ge0.50Si0.50 solution and the 4-monolayer film show their complete similarity both in the amplitude and phase. It does not mean that the 4 monolayers that grew are a uniform solid solution; but this fact establishes the presence of an appreciable exchange of atoms between the phases, which decreases the elastic strain in the system during the deposition of the blocking Si layer (5001C). Thus the monolayers forming the so-called pseudomorphous Ge films embedded in a
Fig. 4. GeK EXAFS spectra for solid Ge–Si solutions films: (1) 30% Ge; (2) 50% Ge; (3) 75% Ge.
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Fig. 5. Fourier transform magnitude of k3 wðkÞ GeK EXAFS data for pseudomorphous 4-monolayer (2D) films on Si(0 0 1): (1) E8 ð0 0 1Þ; (2) E> ð0 0 1Þ; and for a thick solid Ge–Si solution film (50% Ge) (3).
Si matrix contain up to 50% of Si atoms. The same conclusion was made by the authors of Ref. [10], who studied strained (Ge4/Si4)5 structures on Si(0 0 1) obtained by molecular beam epitaxy at 4001C. In their study, a model of ordered boundary in these structures involving substantial Ge and Si mixing was proposed. This model is not the only one possible. It is essential that both this model and our results (see below) show that only the atoms in the immediate vicinity to the boundary are really participating in the exchange. Fig. 5 shows the modules of the Fourier transforms of the function k3 wðkÞ of GeK EXAFS (the radial structural function without phase corrections) for the 4-monolyer film at different E orientations relative to Si(0 0 1) and for a thick (300 nm) film of the solid Ge0.50Si0.50 solution. As it is seen from the figure the structural functions are very similar. However, we can note the shift of the main maximum of the function towards smaller interatomic distances for the 4-monolayer film at both orientations. Taking into account the substantial exchange of atoms between the phases at the germanium layernanocluster–Si matrix boundary, let us consider the already available local structure data determined from the analysis of EXAFS spectra for films of solid GexSi1@x solutions with different compositions. The results for such films synthe-
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sized by different methods and obtained by different authors in the last several years are consistent with each other. This includes both MBE [12,13] and CVD grown films [14]. It was found that with the changing stoichiometry there is change in the bond lengths and apparently in the bond angles. The magnitude of such changes does ( for the Ge–Ge distances and not exceed 0.02 A ( 0.01 A for the Ge–Si distances in thick (relaxed) films as compared with pure Ge(R(Ge– ( ) and the sum of the covalent radii Ge)=2.450 A ( , respectively, at practically all R(Ge–Si)=2.401 A solid solution concentrations which allowed the authors to obtain sufficiently accurate bond lengths (for R(Ge–Ge) to 30% Ge concentration). According to the data of these studies, for the solid GexSi1@x solutions at x ¼ 0:320:5 the intera( , R(Ge– tomic distances R(Ge–Ge)=2.4370.01 A ( Si)=2.3970.01 A, which is in agreement with our data. According to the results of Ref. [13], the film with the stoichiometry close to GeSi3 is an exception. In the authors’ opinion, this film is a ( . For a special compound with R(Ge–Ge)=2.395 A thin film (presumably, with a thickness of about 40 monolayers) of the solid Ge0.50Si0.50 solution grown by molecular beam epitaxy at 4001C [10] (, the bond length R(Ge–Ge)=2.4270.01 A ( , which is by 0.01 A ( smalR(Ge–Si)=2.3870.01 A ler than in the thick relaxed films grown at 5501C and 5001C in Refs. [12] and [13], respectively. In Table 1, the results of the fitting of theoretical and experimental data within different structural models using the EXCURV92 software package are shown. The fitting was performed using the experimental data Fourier-filtered in the interval ( oRo2.6 A ( . The values of the Debye–Waller 1.5 A ( 2) and of the energy factor (s2 ¼ 0:0034 A Eo =10.6 eV were determined as a result of fitting for pure Ge with interatomic distances ( and the coordination number RðGe–Ge)=2.450 A n ¼ 4 and were fixed in all other cases. Goodness of fit is determined by the fit index FEXAFS [11]: X kni jwexp ðki Þ FEXAFS ¼ 104 X @wtheory ðki Þj2 = kni jwexp ðKi Þ: Simplest models No. 2, 3, 4 included one averaged variant of the environment for the Ge atoms with
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Table 1 Parameters obtained by the fitting procedure for pseudomorphous Ge films and structures with pyramid-like Ge islands on Si(0 0 1). R1(Ge–Ge)and R2(Ge–Si)Finteratomic distances; n1(Ge) and n2(Si)Fthe coordination numbers of Ge as to germanium atoms and to silicon atoms; goodness of fit is defined by the fit index F [11] No.
Sample
1. 2. 3. 3"a.
c-Ge Film ðE8 Þ QD ðE8 Þ QD ðE8 Þ
4. 5.
Film ðE> Þ QD ðE> Þ
() R1(Ge–Ge) (A
() R2(Ge–Si) (A
n1(Ge)
n2(Si)
2.45 2.41 2.40 2.41 2.40 2.41 2.41 2.41
2.37 2.38 2.37 2.38 2.36 2.36 2.38
4 1.70 3.16 1.70 4.14 1.78 1.78 4.5
2.35 1.67 2.34 0.54 2.00 2.00 0.10
the distances R1(Ge–Ge), R2(Ge–Si) and the coordination numbers of Ge as to germanium atoms (n1(Ge)) and to silicon atoms (n2(Si)). To a certain degree, such models are correct for the 4-monolayer films but for heterostructures with QDs the models should include at least two types of absorbing Ge atoms: the atoms at the boundary and those within the bulk of Ge nanoclusters. For the samples with QD the models included two types of absorbing Ge atoms: (1) Ge atoms at the boundary in the 2-monolayer thick transition layerFsuch atoms account for about one half of all the Ge atoms, (2) the atoms inside the QDs accounting for the other half of the Ge atoms. The thickness of the transition layer was estimated using the conclusion of this work that the pseudomorphous 4-monolayer Ge films embedded in the Si matrix and having the thickness of two transition layers contain about 50% of Si atoms. This assumption turned out to be true, since with the use of the QDs, of the same transition layer parameters (of the interatomic distances R1(Ge–Ge), R2(Ge–Si) and the coordination numbers n1(Ge) in germanium and n2(Si) in silicon) as in the 4-monolayer films, the Ge atoms in the QDs have practically no silicon atoms in the first sphere of their environment. As is seen from the table, the interatomic distances R1(Ge–Ge) decrease in the thin films ( as compared and structures with QD by 0.04 A ( . The with pure Ge and are equal to 2.41 A ( as comR2(Ge–Si) distances decrease by 0.03 A pared with the sum of the covalent radii of Ge and
F 0.8 0.6 1.0 1.7 3.9 1.1
Fig. 6. Bar chart of interatomic bond lengths distributions in Ge QD on Si(0 0 1) obtained by the VFF method calculation. NFthe number of interatomic bonds; RFthe interatomic distances.
( . Further refinement does Si and are equal to 2.37 A not appear correct at this stage because of the assumptions and suggestion made. In conclusion, the interatomic distances R1(Ge–Ge) and R2(Ge–Si) obtained by us from the EXAFS data are in agreement with the interatomic distances derived from the spatial distribution of elastic deformation calculated within the valence force field model. The calculation was performed by the procedure based on the use of the Green function of the ‘‘atomistic’’ elastic problem, which was further developed in Ref. [15]. Fig. 6 shows a histogram of the Ge–Ge and Ge–Si bond length distribution in a pyramidal germa( 15 A ( , see Fig. 1) nium quantum dot (150 A embedded in silicon on the Si(0 0 1) plane. The
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calculation was performed for the QD model with sharp Ge/Si boundaries. Financial support from the Russian State Scientific and Engineering Program on Physics of Surface Atomic Structures (grant 1-14-99) is greatly appreciated.
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