ISSN 1063-7826, Semiconductors, 2006, Vol. 40, No. 7, pp. 829–833. © Pleiades Publishing, Inc., 2006. Original Russian Text © S.G. Yastrebov, S.K. Gordeev, M. Garriga, I.A. Alonso, V.I. Ivanov-Omskiœ, 2006, published in Fizika i Tekhnika Poluprovodnikov, 2006, Vol. 40, No. 7, pp. 850–854.
AMORPHOUS, VITREOUS, POROUS, ORGANIC, AND MICROCRYSTALLINE SEMICONDUCTORS; SEMICONDUCTOR COMPOSITES
Spectral Ellipsometry of a Nanodiamond Composite S. G. Yastrebova^, S. K. Gordeevb, M. Garrigac, I. A. Alonsoc, and V. I. Ivanov-Omskiœa aIoffe
Physicotechnical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 26, St. Petersburg, 194021 Russia ^e-mail:
[email protected] bCentral Research Institute for Materials, St. Petersburg, 191014 Russia cInstitute de Ciencia de Materials de Barcelona, CSIC 08193 Bellaterra, Spain Submitted November 22, 2005; accepted for publication December 7, 2005
Abstract—Optical properties of a nanodiamond composite were analyzed by methods of spectral ellipsometry in the range of photon energies 1.4–5 eV, which are characteristic of π–π* transitions in amorphous carbon. The nanocomposite was synthesized by molding nanodiamond powder with subsequent binding of diamond nanoparticles by pyrocarbon formed as a result of the heterogeneous chemical reaction of methane decomposition. The dispersion curves of the imaginary and real parts of the dielectric function were reconstructed. It is shown that the imaginary part of the dielectric function can be represented as the sum of two components generated by the two types of π–π* optical transitions. The maximum contribution of the transitions of the first and second types manifests itself at energies of 2.6 and 5.6 eV, respectively, which correspond to peaks in optical density at 2.9 and 6.11 eV. It was established that the main specific features of the normalized optical density of the nanodiamond composite almost coincide with those for poly(para-phenylenevinylene). It was found that the energy of a σ + π plasmon of the pyrocarbon component of the nanodiamond composite is 24.2 eV. On the basis on this value, the pyrocarbon density matrix was estimated to be 2 g/cm3. Within the concepts of optimum filling of an elementary volume by carbon atoms in an amorphous material with such a density, the allotropic composition of the pyrocarbon matrix was restored. PACS numbers: 78.20.Ci, 78.66.Sq, 77.84.Df DOI: 10.1134/S1063782606070177
1. INTRODUCTION In recent years, great interest has been shown in the development and investigation of carbon nanomaterials. One of the directions in this field is the fabrication and analysis of nanocomposites. Carbon nanocomposites can be prepared using nanodiamond powders. The technique of preparation is as follows: a billet molded from nanodiamond powder is treated in a hydrocarbon medium to synthesize a pyrocarbon matrix, which binds nanodiamond particles into a unified composite [1, 2]. Such materials are referred to as nanodiamond composites (NDCs) [3, 4]. They have a high porosity (50–65%), which actively manifests itself in the processes of sorption of low-molecular materials. NDCs have semiconductor type of conductivity, which depends on the content of pyrocarbon. The properties of these materials were described in [3, 4]. In this paper, we report the results of the investigation of optical constants of NDC. The problem of reconstruction of optical constants from experimental data can be solved using ellipsometric methods [5]. In this study, we reconstructed the optical constants of bulk samples of nanodiamond composite from ellipsometric data. Taking into account the fact that the material under study contains pyrocarbon, whose structure is formed
to a large extent by carbon atoms in the sp2 hybridization state, measurements were performed in the region of optical transitions characteristic of graphitelike carbon (1–5 eV). 2. EXPERIMENTAL Experiments were performed with samples of NDC-30 [3, 4]. This material is characterized by volume contents of nanodiamond and pyrocarbon of 28 and 15%, respectively, and porosity of 57%. The average thickness of the pyrocarbon layer on the surface of nanodiamond particles is 0.6 nm, and the average size of nanodiamond grains is 4 nm. The relatively high strength of NDC-30 (more than 10 MPa for bending) allowed us to polish the surface of the sample (diameter 20 mm, thickness 1 mm) to the level necessary for ellipsometric measurements. Polarization angles were measured on an ellipsometer with a rotating polarizer. A 75-W xenon lamp was used as a light source. An optical signal was detected by a multichannel photomultiplier located at the exit slit of a grating-prism monochromator with a focal length of 750 mm. This setup makes it possible to perform investigations in the spectral range 1.4–5.1 eV with a resolution better than 1 meV. The spectral dependences of the ellipsometric angles Ψ and ∆ were measured in the
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830 tanΨ 0.14
cos∆
κ''
κ' 3.7
1.0 1.0
0.12
3.6
0.8
0.10
3.5 0.5 3.4
0.08 0.06
0.6 0 2
4 Photon energy, eV
6
2
3.3 6
4 Photon energy, eV
Fig. 1. Ellipsometric angles Ψ and ∆ for a sample of nanodiamond composite.
Fig. 2. Dispersion curves of the real and imaginary parts of the dielectric function for a sample of nanodiamond composite.
above-mentioned spectral range with a step of 20 meV at an angle of incidence of 65°.
In this case, the total dielectric response of a-C can be written as n
κ'' =
3. RESULTS AND DISCUSSION Figure 1 shows the spectra of ellipsometric angles of the samples studied. Figure 2 shows the dispersion curves of the imaginary (κ'') and real (κ') parts of the dielectric function, reconstructed in the approximation of light reflection from an interface between two media [5]. It can be seen in Fig. 1 that the maximum experimentally accessible energy does not exceed the photon energy corresponding to the optical absorption edge of diamond and is equal to 5.25 eV [6]. Since optical transitions in nanodiamond should not be observed in the accessible spectral range, the approach proposed here is based on the comparison of the experimental data with the spectral dependence of the imaginary part of the dielectric function of pyrocarbon. To this end, we will assume that the pyrocarbon structure is similar in many respects to the structure of amorphous carbon a-C. It is well known that the electrons of two subsystems (π and σ) determine the contribution to the absorption of a-C [7]. Furthermore, we will use the following simplifying assumption (made for the first time in [7]) concerning the symmetry of optical transitions in a-C. We will assume that the transitions from occupied states to free states of π (π–π*) and σ (σ–σ*) electrons determine the dependence of the imaginary part of the dielectric function on the photon energy. It is well known [7] that π−π* and σ–σ* transitions occur in the spectral ranges that overlap each other only partially: at energies 0 ε 8 eV and ε 8 eV, respectively. This circumstance gives grounds to consider the experimentally observed spectrum of the imaginary part of the dielectric function as a superposition of the spectra of several transitions of the πj– π *j type (j = 1, …, n).
∑ κ'' .
(1)
j
j=1
Here, κ ''j is the contribution of j-type transitions to the imaginary part of the dielectric function. As was shown by us previously [8], the dependence of the imaginary part of the dielectric function κj on the photon energy ε for a-C has the form A ε – E gj⎞ ( 2E Gj + E gj – ε ) , - erf ⎛ --------------κ ''j ( ε ) = ----2-j exp – --------------------------------------2 ⎝ 2s j ⎠ ε 4s j 2
ε ≥ E gj , κ ''j ( ε ) = 0,
(2)
ε < E gj .
Here, Aj is a constant, EGj is the value of the energy at which the electron density of states reaches maximum, sj is the value characterizing the spread of the density of states, and Egj is the energy gap between the occupied and free states of the electronic spectrum [9]. Expressions (1) and (2) can be used to estimate the contribution of transitions of different types to the dielectric response of diamond nanocomposite. The results of this estimation performed by the least-squares method are shown in Fig. 3. Using this method, we determined the numerical values of the variables Aj, EGj, sj, and Egj ( j = 1, …, n), which enter expressions (1) and (2). In other words, we minimized the functional residual F ( n; A 1, …, A n ; E Gj, …, E Gn ; s j, …, s n ; E g1, …, E gn ) ⎛ ⎞ κ ''j ( ε i ) – κ ''i ⎟ ⎜ ⎝j = 1 ⎠ n
=
∑∑ i
2
(3)
with respect to these parameters. SEMICONDUCTORS
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SPECTRAL ELLIPSOMETRY OF A NANODIAMOND COMPOSITE
Here, i is the number of an experimental point on the curve κ''(ε), i = 0, …, 181. The results of the calculation performed on the assumption that only one type of transitions (n = 1) makes a contribution to the dielectric response of the material under study are shown in Fig. 3. The numerical values of the variables whose indices are omitted in this case are given in the figure caption. It can be seen in Fig. 3 that, in the energy range ε = 1.4–3 eV, the calculated curve obtained by substitution of the fitting parameters into expressions (1) and (2) deviates significantly from the experimental data. Therefore, we also performed calculation for n = 2. The values of the desired parameters calculated in this case are listed in the table. The result of the calculation carried out using expressions (1) and (2) with substituted parameters for j = 1 and j = 2 from the table is shown by a solid line in Fig. 4. There is good agreement between the experimental and calculated data. Figure 4 indicates that the contribution of the optical transitions with j = 1 is maximum at an energy of 2.6 eV. For j = 2, the corresponding energy is 5.62 eV. Let us compare the spectral dependence of the optical density for the two types of optical transitions in NDC with the corresponding experimental dependence for a layer of unsubstituted poly(para-phenylenevinylene) (PPV)—a polymer containing pairwise bound graphene rings. To this end, we will reconstruct the optical density of NDC using the data listed in the table and the well-known expression relating the optical density αj to κ ''j :
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κ''
1.0
0.5
0
2
3
4
5 ε, eV
Fig. 3. Experimental data from Fig. 2 (crosses) in comparison with the calculation according to (1) and (2). The calculation parameters are n = 1, Eg = 0 eV, EG = 3.9 eV, A = 67 eV2, and s = 1.55 eV.
κ'' 1.5
1.0 5.62 eV 0.5
α j ∝ εκ ''j . The thus-reconstructed dependences, along with the experimental absorption spectrum for PPV [10], are shown in Fig. 5. It can be seen that the main specific features of the normalized optical density of PPV and NDC, lying near 3 and 6 eV, coincide. Moreover, isolated contributions of different optical transitions in NDC not only demonstrate coincidence of the frequencies of the main specific features, but also correspond to the tendency of increasing intensity of the main peaks of PPV with increasing energy of absorbed photons. The significant broadening of the observed spectral lines of NDC in comparison with PPV may be related to the amorphous state of the matrix binding diamond grains. Apparently, the matrix, as well as PPV, contains pairwise bound graphene rings. Amorphization of the structure of amorphous carbon in pyrocarbon can be related not only to the break of neighboring bonds but also to fluctuations of interatomic distances in the short-range order of the atomic arrangement. For further analysis, it is reasonable to compare the photon energy at which the strongest peak in Fig. 4 is obtained, εma = 5.62 eV, with the known dependence (Fig. 6) obtained by treating the data in the literature [7]. Figure 6 shows the relation between the strongest peak of εm on the dependences of the imaginary part of SEMICONDUCTORS
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0 2.6 eV 2
4
6
ε, eV
Fig. 4. Experimental data from Fig. 2 (crosses) in comparison with the calculation according to (1) and (2) taking into account two types of optical transitions with substitution of the parameters listed in the table (solid line). The dotdashed and dashed lines represent separate contributions to κ'' from the transitions of the first (j = 1) and second (j = 2) types.
the dielectric function in the region of π–π* transitions on the energy of a σ + π plasmon, Eσ + π, in samples of amorphous carbon of different density. It can be seen in Fig. 6 that the energy εma corresponds to that of a σ + π Parameters of calculation of κ'' j
Aj, eV2
Egj, eV
EGj, eV
sj, eV
1 2
1.95 47.56
0.5 0
1.33 3.25
0.67 1.09
YASTREBOV et al.
832 Normalized optical density 1.0
Volume fraction 100 3
6.105 eV 50
0.5
2 2.89 eV 1
0 2
4
6 ε, eV
1
Fig. 5. Reconstructed optical density for two types of optical transitions in NDC: j = 1 (dot-dashed line) and 2 (dashed line). Crosses show the experimental data for a layer of unsubstituted poly(para-phenylenevinylene) [10]. The arrows indicate the maxima of the optical density of the transitions in the nanodiamond composite.
εma
Fig. 7. Dependence of the most probable allotropic composition of a-C on the density: symbols indicate the volume fractions of the (1) sp1, (2) sp2, and (3) sp3 components according to the data of [12]; the solid lines show the result of polynomial interpolation. The arrow indicates the experimental result obtained in this study. The intersection of the dashed vertical line with the solid lines gives the most likely allotropic composition of the amorphous phase in the sample studied.
εm, eV
(Eσ + π)a = 24.18 eV
5
4
3
2
20
22
24 Eσ + π, eV
Fig. 6. Dependence of the position of the peak in the spectrum of the imaginary part of the dielectric function, formed by the π–π* transitions on the energy of a σ + π plasmon in amorphous carbon samples of different densities (the data of [7]). The solid line is plotted using the least-squares method. The arrow shows the energy of a σ + π plasmon corresponding to the peak energy of the π–π* transitions: εma = 5.62 eV (see Fig. 4).
plasmon: (Eσ + π)a ≈ 24 eV. Furthermore, we will use the well-known relation for the plasmon energy 2 1/2
ne e ⎞ E σ + π = ⎛ --------⎝ m* ⎠
,
3 Density, g/cm3
2
(4)
where e is the elementary charge, m* ≈ 0.87m0 is the effective electron mass [11], and ne is the electron density. Assuming that each carbon atom supplies four electrons to the ensemble involved in plasma oscilla-
tions, we can estimate the pyrocarbon density from (5); it turned out to be 2 g/cm3 in the case under consideration. This value coincides with the pyrocarbon density determined from the dependence of the change in the porosity of the material on the mass of the synthesized pyrocarbon matrix [3]. Using these values, one can estimate the fractions of the sp1-, sp2-, and sp3-hybridized atoms forming the framework of a-C. Estimation can be performed by comparing the densities obtained with the published data. In [12], the most likely configurations of atoms forming the framework of a-C in the density range from 1.2 to 3.5 g/cm3 were modeled by the molecular-dynamics method. On the basis of these data, a diagram relating the density of a-C and its most likely allotropic composition was constructed (Fig. 7). The value of the density ρ = 2 g/cm3 is shown in Fig. 7 by the arrow. It can be seen from Fig. 7 that the volume contents of the sp1, sp2, and sp3 components in the pyrocarbon phase are, respectively, 8, 55, and 37%. 4. CONCLUSIONS The analysis of the optical properties of nanodiamond composite performed here indicates that the pyrocarbon binding nanodiamond grains is an amorphous carbon compound characterized by some degree of order. The amorphous state of this material is evidenced by the similarity of its optical properties to the corresponding properties of a-C. The presence of ordering is confirmed by two inhomogeneously broadened spectral lines at ~3 and ~6 eV. SEMICONDUCTORS
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SPECTRAL ELLIPSOMETRY OF A NANODIAMOND COMPOSITE
Analysis of the optical properties of the nanodiamond composite studied made it possible to reconstruct the density and allotropic composition of the pyrocarbon matrix binding nanodiamond grains. ACKNOWLEDGMENTS This study was supported in part by the Russian Foundation for Basic Research (project no. 03-02-16289), the program of the Presidium of the Russian Academy of Sciences “Effect of Atomic and Electronic Structure on the Properties of Condensed Matter,” and grant no. DGI MAT2001-1873. REFERENCES 1. S. K. Gordeev, S. G. Zhukov, P. I. Belobrov, et al., US Patent No. 6,083,614 (4 July 2000). 2. S. K. Gordeev, S. G. Zhukov, Yu. I. Nikitin, and V. G. Poltoratskiœ, Neorg. Mater. 31, 470 (1995). 3. S. K. Gordeev, in Nanostructured Carbon for Advanced Applications, Ed. by G. Benedek et al. (Kluwer Academic, Dordrecht, 2001), p. 71.
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4. S. K. Gordeev, Sverkhtverd. Mater., No. 6, 60 (2002). 5. R. M. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977; Mir, Moscow, 1981). 6. C. D. Clark, P. J. Dean, and P. V. Harris, Proc. R. Soc. London, Ser. A 277, 312 (1964). 7. J. Fink, Th. Müller-Heinzerling, J. Pflüger, et al., Phys. Rev. B 30, 4713 (1984). 8. V. I. Ivanov-Omskiœ, A. Tagliaferro, G. Fanchini, and S. G. Yastrebov, Fiz. Tekh. Poluprovodn. (St. Petersburg) 36, 117 (2002) [Semiconductors 36, 110 (2002)]. 9. J. Robertson and E. P. O’Reilly, Phys. Rev. B 35, 2946 (1987). 10. M. Chandross, S. Mazumdar, M. Liess, et al., Phys. Rev. B 55, 1486 (1997). 11. J. T. Titantah and D. Lamoen, Phys. Rev. B 70, 033101 (2004). 12. C. Mathioudakis, G. Kopidakis, and P. C. Kelires, Phys. Rev. B 70, 125202 (2004).
Translated by Yu. Sin’kov
