ISSN 1063-7826, Semiconductors, 2009, Vol. 43, No. 5, pp. 594–598. © Pleiades Publishing, Ltd., 2009. Original Russian Text © S.N. Samsonenko, N.D. Samsonenko, 2009, published in Fizika i Tekhnika Poluprovodnikov, 2009, Vol. 43, No. 5, pp. 621–626.

SEMICONDUCTOR STRUCTURES, INTERFACES, AND SURFACES

Dislocation Electrical Conductivity of Synthetic Diamond Films S. N. Samsonenko^ and N. D. Samsonenko Donbass National Academy of Civil Engineering and Architecture, Makeevka, 86123 Ukraine ^e-mail: [email protected] Submitted June 10, 2008; accepted for publication June 25, 2008

Abstract—A relationship between the electric resistance of single-crystal homoepitaxial and polycrystalline diamond films and their internal structure has been investigated. It is established that the electrical conductivity of undoped homoepitaxial and polycrystalline diamond films is directly related to the dislocation density in them. A relation linking the resistivity ρ (~1013–1015 Ω cm) with the dislocation density Γ (~1014–4 × 1016 m–2) is obtained. The character of this correlation is similar for both groups of homoepitaxial and polycrystalline diamond films. Thin (~1–8 µm) homoepitaxial and polycrystalline diamond films with small-angle dislocation boundaries between mosaic blocks exhibit dislocation conductivity. The activation energy of dislocation acceptor centers was calculated from the temperature dependence of the conductivity and was found to be ~0.3 eV. The conduction of thick diamond films (h > 10 µm) with the resistivity ρ ≈ 108 Ω cm is determined by the conduction of intercrystallite boundaries, which have a nondiamond hydrogenated structure. The electronic properties of the diamond films are compared with those of natural semiconductor diamonds of types IIb and Ic, in which dislocation acceptor centers have activation energies in the range 0.2–0.35 eV and are responsible for hole conduction. PACS numbers: 61.72.Dd, 61.72.Hh, 61.72.Lk, 72.80.-r DOI: 10.1134/S1063782609050091

1. INTRODUCTION The development of the method of gas-phase synthesis of diamond films and coatings at low pressures and temperatures makes diamond available for systematic study [1]. Since this material has a very wide band gap (~5.6 eV), its physical properties are very difficult to analyze. Most researchers disregard two important circumstances. First, impurity atoms in wide-gap materials form an inverted system of energy levels in the band gap: donor impurities form deep donor levels, lying at the top of the valence band, while acceptor impurities form acceptor levels closer to the bottom of the conduction band. Such a situation has been known for long time by the researchers dealing with surface centers in conventional semiconductors. Second, semiconductor diamonds of type IIb have a mosaic structure with a large number of dislocations. Lang et al., [2] showed that IIb-type diamonds are the result of plastic deformation of nitrogen-free diamonds of type IIa under natural conditions. We also investigated in detail, the electronic properties of nitrogencontaining diamonds of type I subjected to plastic deformation under natural conditions; such diamonds were assigned to type Ic [3]. It was found that, independent of the type of initial diamonds, plastic deformation under natural conditions leads to the same unusual electronic properties (peculiar absorption bands in the visible and IR spectral

regions; peculiar photoconductivity; hole conduction with close activation energies (0.2–0.36 eV) of acceptor centers, which are paramagnetic; etc.). The difference between diamonds of types IIb and Ic [3] is only quantitative. Our further studies of Ic-type diamonds showed that their electrical conductivity and other electronic properties are related to extended structural defects (dislocations). Unsaturated carbon bonds in a dislocation core form dislocation acceptor centers (DACs), provide hole conduction, and are simultaneously paramagnetic centers [4]. We formed dislocations under laboratory conditions in natural and synthetic diamonds [5–7]. The results of our experiments confirmed that the semiconductor conductivity of diamonds is due to dislocations. In this paper, we report the results of a detailed study of the relationship between the complex internal structure of undoped single-crystal and polycrystalline diamond films and their electrical conductivity. 2. INTERNAL STRUCTURE OF UNDOPED SYNTHETIC DIAMOND FILMS Our previous study of undoped synthetic diamond films showed that they have a very complicated internal structure, which is based on small-angle dislocation boundaries between mosaic blocks and intercrystallite boundaries; the latter form a hydrogenated nondiamond carbon phase [4, 8].

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2.1. Single-Crystal and Polycrystalline Homoepitaxial Diamond Films The samples of homoepitaxial diamond films (HEDFs), which had been grown at the Institute of Physical Chemistry, Russian Academy of Sciences, for our studies, had a thickness from 1.65 to 100 µm. Thin (below 10 µm) HEDF samples were single-crystal and had an internal structure very similar to that of natural semiconductor diamonds of type IIb. The difference is as follows. Chemically active hydrogen from the medium of the diamond film synthesis reacts with unsaturated carbon bonds in dislocation cores, thus decreasing the number of DACs. The HEDF resistivities measured by us indicate a very low concentration of hydrogen-free DACs (4.5 × 102–2 × 10–6 cm–3). Such low DAC concentrations cannot be studied by electron spin resonance (ESR). However, thin HEDFs and polycrystalline diamond films (PDFs) exhibit another ESR spectrum, consisting of a single line with g ≅ 2.0028 and width ∆H = 2–6 Oe, which, according to [9], is due to complex paramagnetic defects H1, formed by vacancies and hydrogen in the form of paramagnetic centers, such as (V + H)*. Note that at synthesis temperatures (about 1273 K), simultaneously with dislocations, forming small-angle dislocation boundaries between mosaic blocks, thermodynamically equilibrium vacancies also arise. These vacancies are mainly located near dislocations because the binding energy of the carbon atoms near dislocations is lower than that far from the dislocations. Our previous analysis [10] suggests that the weight density of mosaic diamonds is smaller due to the increase in their total volume. This increase is caused by the expansion of the diamond lattice in the dislocation boundaries between mosaic blocks. Approximate estimation of this relative expansion for mosaic diamonds gave values from 1 to 10%. Thus, we could estimate the average binding energy of carbon atoms in the extended boundaries between mosaic blocks in HEDFs and approximately determine the number of thermodynamically equilibrium vacancies in them at synthesis temperatures. Since Schottky defects (carbon vacancies) are mainly formed in the growth planes of diamond films due to their proximity to the surface, it is assumed that the binding energy of carbon atoms with neighboring atoms makes the main contribution to the formation energy of these defects. In the conventional diamond lattice, this energy is ~5 eV, while in the extended lattice of boundaries, according to our estimates, it is about 4.56 eV. The calculations showed also that about 90% of vacancies are located in the extended boundaries between the mosaic blocks and only 10% are in the bulk of blocks. Reacting with chemically active hydrogen from the gaseous HEDF growth medium, vacancies form paramagnetic H1 centers. We established experimentally that their concentration almost linearly increases with an increase in the film’s thickness in the range from 1 to 10 µm; this behavior is SEMICONDUCTORS

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Ns, 1018 cm–3 30 25 20 15 10 5

0

5

10

15

20

25

30

35 40 h, µm

Fig. 1. Dependence of the concentration of paramagnetic centers H1 on the thickness of undoped HEDF samples.

in good agreement with the decrease in the size of mosaic blocks with an increase in their thickness. Hence, the density of dislocations forming mosaic blocks also increases with increasing the concentration of paramagnetic centers. This correlation can be an alternative to X-ray diffraction for estimating dislocation density in HEDFs, because it is very difficult to separate the X-ray reflections from synthesized diamond films from the corresponding reflections from diamond substrates. Special nonstandard X-ray diffraction systems are developed to solve these problems. Therefore, to estimate the dislocation density in relatively thin HEDF samples, we applied an indirect method for evaluating this parameter from the intensity of the ESR spectrum of paramagnetic H1 centers. To implement this method, we plotted the dependence of the ESR center concentration Ns(h) on the HEDF thickness (Fig. 1). It can be seen in Fig. 1 that in the range of HEDF thicknesses from 0 to 10 µm, with allowance for the error in measuring the concentration of the paramagnetic center (±35%), this dependence can be linearized in the form N s ( h ) = Bh,

(1)

where B ≈ 1.54 × 1022 cm–4 is the proportionality factor and h is the HEDF thickness in centimeters. Since the vacancy concentration and dislocation density depend on the HEDF thickness, to estimate the dislocation density in thin samples, one has to know the dislocation density for at least one sample (the second point is the reference point, where h = 0; Ns(h) = 0; and, correspondingly, Γ = 0) and experimental values of concentrations of paramagnetic centers H1 in the sam-

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Table 1. Structural and electronic parameters of diamond films Film type

Sample

HEDF HEDF-1 HEDF-2 HEDF-3 HEDF-4 HEDF-5 PDF PDF-11 PDF-17 PDF-13 PDF-23 PDF-17

Thickness h, µm

Block sizes D, nm

Microstrains ε × 103

1.65 3.7 7.8 35 100 5.8 5.1 5.8 5.2 4.0

– – 1000 – – 57 49 34 22 19

– – – – – 1.6 2.5 1.8 2.1 2.0

ples under study. In our experiments, the reference was sample HEDF-3, for which the average size D of mosaic blocks was determined by scanning electron microscopy to be about 1 µm. The size of the mosaic block was used to estimate the dislocation density, which was then recalculated to the local dislocation density Γ, introduced to characterize the interfaces between two crystals with similar unit-cell parameters [10]. For HEDFs, Γ is determined by the difference in the unit-cell parameters of mosaic blocks and extended diamond lattice between blocks. For HEDF-3, Γ was found to be 7.5 × 1014 cm–2. 2.2. Polycrystalline Diamond Films Undoped PDFs were grown by the method of highgradient chemical transport reaction [1] from the gas phase on single-crystal silicon substrates [10]. In this experiment, PDF samples were obtained from a hydrogen–methane mixture (98% hydrogen, 2% methane). The substrate temperatures were 1073, 1173, and 1273 K. The working pressures of the gas mixture were 80, 160, and 240 Torr. A graphite activator was heated to ~2273 K. The diamond films had thicknesses from 4 to 6 µm. We investigated previously the internal PDF structure in several studies [8]. In accordance with the results of [8], we consider crystallites to be large diamond grains with linear sizes, close to the thickness of the diamond film (several micrometers). The crystallites consist of smaller blocks (substructure) with sizes from 20 to 100 nm, which can be coherent-scattering regions or mosaic blocks. Since diamond has small anisotropy, coherent-scattering regions and mosaic blocks have similar sizes. X-ray diffraction analysis allowed us to estimate the dislocation density in the PDF samples from the sizes of these blocks and microstrains. The corresponding procedure was described by

Spin concen- Local dislotration Ns, cation density Γ, m–2 cm–3 3.1 × 1018 5.7 × 1018 1.2 × 1019 – – – – – – –

0.6 × 1014 3.5 × 1014 7.5 × 1014 – – 1.3 × 1016 1.7 × 1016 2.1 × 1016 3.4 × 1016 4.2 × 1016

Resistivity ρ, Ω cm

References

3 × 1013 3.7 × 1010 1.6 × 109 2 × 108 1.3 × 108 6.5 × 107 2 × 1017 5.5 × 105 3.3 × 105 9.8 × 104

[4] [4] [4] [4] [4] [11] [11] In this study [11] In this study

us in detail in [10, 11]. The parameters of the internal PDF structure are listed in Table 1. 3. ELECTRICAL CONDUCTIVITY OF HEDF AND PDF SAMPLES On the basis of the results of studying the dislocation structure of HEDFs and PDFs, we investigated its effect on the conductivity of relatively thin (1–10 µm) HEDF and PDF samples. 3.1. Homoepitaxial Diamond Films We measured the room temperature resistivity of HEDFs using an U2-7 electrometer and a V7-40/5 voltmeter. The films were connected to the measuring scheme through aquadag (ohmic) contacts. The measurement results are listed in Table 1, and they were used to plot the dependence of resistivity on the dislocation density (Fig. 2, curve 1). Using phenomenological parameterization of the experimental dependence of resistivity, we derived the resistivity ρ as a function of the local dislocation density: ρ0 -, ρ = ----------------n ( Γ/Γ 0 )

(2)

where ρ0 ≈ 3 × 1013 Ω cm is the resistivity of sample HEDF-1 at Γ = Γ0. The value Γ0 ≈ 1.6 × 1014 m–2 was determined by the ESR method on the hydrogenrelated vacancies located near dislocations [4], Γ is the local dislocation density in the samples, and n = 6.5. We believe the numerical values of ρ0 and n to be determined by current transport in diamond films. In addition, we measured the temperature dependences of the conductivity of HEDF-2, HEDF-3, and HEDF-5 samples and used them to find the activation energies of electrically active centers in them. SEMICONDUCTORS

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DISLOCATION ELECTRICAL CONDUCTIVITY OF SYNTHETIC DIAMOND FILMS ρ, Ω cm 1014

σ, Ω–1 cm–1 10–4

1012

10–5

ε5

1 1010

10–6

108

10–7

ε4 ε3

2 10–8

106

104

597

1.5 1014

1015

1016

1017 ΓL, m –2

Fig. 2. Dependences of the resistivity of thin (1) HEDF and (2) PDF samples on dislocation density.

The measurements were performed in the temperature range from 293 to 673 K. Figure 3 shows the dependence of the conductivity on the inverse temperature for sample HEDF-5. In this case, we obtained the following energies for the levels of electrically active centers: ε3 = 0.27 eV for dislocation centers, a value close to ε3 for bulky natural semiconductor diamond crystals, and ε4 = 1.24 eV and ε5 = 2.22 eV, values corresponding to ε4 and ε5 for natural and synthetic diamond crystals. Levels with energy ε3 arise in diamonds as a result of their plastic deformation, both under natural and laboratory conditions. This group includes levels in the range approximately from 0.2 to 0.36 eV. Note also that the energies ε3–ε5 decrease with decreasing the thickness of the HEDF sample. We believe this effect to be due to the decrease in the binding energy of atoms near the surface. This decrease is caused by the elongation of these bonds, which can be related to the reconstruction of the surface structure (Table 2). In addition, our analysis of the temperature dependence of the activation energy of electrically active centers showed that the thickness range 10–100 µm is characterized by not only the change in the HEDF internal structure but also the transition from the purely dislocation conduction to the mixed one. Thus, beginning with ~10 µm, the resistivity becomes a constant, which is not related to the increase in the dislocation density but is determined by the resistance of hydrogenated diamondSEMICONDUCTORS

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2.0

2.5

3.0 3.5 1000/T, K

Fig. 3. Dependence of the conductivity of undoped sample HEDF-5 on inverse temperature.

like intercrystallite boundaries (~108 Ω cm [12]). However, the charge accumulation at crystallite boundaries is controlled by their dislocation conductivity. 3.2. Polycrystalline Diamond Films Contacts to PDFs were prepared as follows. A titanium layer was deposited by an electron beam onto a substrate through a mask. This layer was covered with a gold layer by thermal vacuum sputtering. Heating at 703 K for 30 min led to carbidization of the titanium layer’s surface, and the contacts became ohmic. The gold layer prevents titanium from oxidizing. The PDF resistivity was found from current and voltage measurements using V7-40/5 and V7-49 digital meters. The obtained values of ρ are listed in Table 1. These data were used to plot the dependence of the PDF resistivity on dislocation density (Fig. 2, curve 2). For PDF-II, ρ0 ≈ 6.5 × 107 Ω cm and n = 5.84. Figure 2 shows that Table 2. Activation energies of levels in HEDFs Parameters h, µm ε3, eV ε4, eV ε5, eV

HEDF samples HEDF-2

HEDF-3

HEDF-5

3.7 0.21 0.96 1.30

7.8 0.24 1.12 1.96

100 0.27 1.24 2.22

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the dependences of resistivity on the dislocation density in relatively thin HEDF and PDF samples are similar. However, the dependence of ρ on Γ for PDFs is shifted to larger Γ. This can be explained by the decrease in the mobility of the integral carrier in PDFs, since holes overcome diamond-like boundaries between crystallites with lower drift mobility in comparison with their mobility in dislocation regions along dislocations. Concerning the dislocation conduction of diamond films, we should add the following. Conducting dislocation lines are not straight, because dislocations generally wind between neighboring slip planes, and charge carriers have to hop from one dislocation portion to another during motion. Such conduction is described by the Mott hopping mechanism [13]. In this case, the factor 2 in the denominator of the exponential factor is absent, according to the theory of hopping conduction in disordered semiconductors. We believe this to be true for only the ε3 levels, which are related to the diamond film dislocation structure. 4. CONCLUSIONS On the basis of the results obtained, we can draw several conclusions. It is established that the electrical conductivity of undoped single-crystal diamond films is determined by the dislocations generated during film synthesis and forming dislocation boundaries between mosaic blocks. It is shown that the dependences of electrical conductivity on the dislocation density in single-crystal HEDFs and thin polycrystalline samples are similar. Chemically active hydrogen from the zone of diamond film synthesis reduces the number of DACs to 102– 106 cm–3 in comparison with semiconductor diamonds of type IIb, where the DAC concentration can be as high as 1013–1014 cm–3. At the same time, hydrogen, being involved in single bonding with diamagnetic vacancies, transforms them into the paramagnetic state. The concentration of paramagnetic vacancies in thin (1–10 µm) HEDFs is proportional to the density of dislocations forming boundaries between mosaic blocks. The temperature dependences for the HEDF and PDF samples were used to determine the level energies ε3–ε5. In HEDF samples, the energies ε3–ε5 decrease with a decrease in the sample thickness. This decrease is believed to be related to the lattice expansion in the surface layers of thin films. Since dislocations wind between neighboring atomic planes, charge carriers are involved in conduction via hops between linear dislocation portions, as in disordered semiconductors. Thus, consideration of the role of dislocations in the formation of electronic properties of diamond materials opens a new approach in studying control of their elec-

tronic properties, which is very urgent for modern microelectronics, power electronics, and electric power engineering. ACKNOWLEDGMENTS We are grateful to B.V. Spitsyn (Institute of Physical Chemistry, Russian Academy of Sciences) for supplying HEDF samples, to A.G. Gontar (Institute of Superhard Materials, National Academy of Sciences of Ukraine) and V.I. Timchenko (Donbass National Academy of Civil Engineering and Architecture, Ukraine) for their help. The study was supported by the Ministry of Education and Science of Ukraine. REFERENCES 1. B. V. Spitsyn, L. L. Bouilov, and A. E. Alexenko, Braz. J. Phys. 30, 471 (2000). 2. A. R. Lang, in The Properties of Diamond, Ed. by J. E. Field (Academic, London, 1979), p. 425. 3. N. D. Samsonenko, G. B. Bokii, N. A. Shul’ga, and V. I. Timchenko, Dokl. Akad. Nauk SSSR 218, 1336 (1974) [Sov. Phys. Dokl. 19, 710 (1974)]. 4. N. D. Samsonenko and S. N. Samsonenko, Vestn. DonGu., Ser. A: Estestv. Nauki, vyp. 1, 78 (2001). 5. V. N. Varyukhin, N. D. Samsonenko, S. N. Samsonenko, and I. V. Sel’skaya, Fiz. Tekh. Vysok. Davl. 11 (2), 7 (2001). 6. V. N. Varyukhin, N. D. Samsonenko, S. N. Samsonenko, and I. V. Sel’skaya, Fiz. Tekh. Vysok. Davl. 11 (4), 30 (2001). 7. N. D. Samsonenko, V. I. Timchenko, V. A. Emets, and G. B. Bokii, Kristallografiya 25, 1300 (1980) [Sov. Phys. Crystallogr. 25, 741 (1980)]. 8. N. D. Samsonenko, S. N. Samsonenko, and G. S. Oleinik, Vestn. DonGu., Ser. A: Estestv. Nauki, vyp. 2, 104 (2001). 9. K. M. McNamara Rutledge, G. D. Wotkins, X. Zhou, and K. K. Gleason, in Diamond Based Composites and Related Materials, Ed. by M. A. Prelas, A. Benedictus, L. S. Lin, G. Popovici, and P. Gielisse (Kluwer, Dordrecht, 1997). 10. N. D. Samsonenko, S. N. Samsonenko, V. N. Varyukhin, and Z. I. Kolupaeva. J. Phys.: Condens. Matter 18, 5303 (2006). 11. S. N. Samsonenko, N. D. Samsonenko, and Z. I. Kolupaeva, Function. Mater. 14 (2), 212 (2007). 12. V. I. Ivanov-Omskii, in Diamond Based Composites and Related Materials, Ed. by M. A. Prelas, A. Benedictus, L. S. Lin, G. Popovici, and P. Gielisse (Kluwer, Dordrecht, 1997), p. 171. 13. N. Mott and E. Davis, Electron Processes in Noncrystalline Materials (Clarendon, Oxford, 1971; Mir, Moscow, 1974).

Translated by Yu. Sin’kov

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