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Electrical properties of 3D-polymeric crystalline and disordered C60 and C70 fullerites
Diamond & Related Materials 14 (2005) 896 – 901 www.elsevier.com/locate/diamond
Electrical properties of 3D-polymeric crystalline and disordered C60 and C70 fullerites S.G. Bugaa,*, V.D. Blanka, N.R. Serebryanayaa, A. Dzwilewskib, T. Makarovab, B. Sundqvistb a
Department of Nanoelectronics, Technological Institute for Superhard and Novel Carbon Materials, 7a Centralnaya St., Troitsk, Moscow Region, 142190, Russia b Department of Physics, Umea University, SE-901 87, Umea, Sweden Available online 17 February 2005
Abstract Crystalline and disordered 3D-polymeric C60 and C70 with different lattice parameters and with densities in the range of 2.2H3.25 g cm1 were obtained by high-pressure-high-temperature treatment at P=11.5H15 GPa, T=670H1800 K. Their d.c. electrical conductivity was investigated at temperatures 30H350 K. The variable range hopping mechanism dominates in all samples up to room temperature. A temperature activated conductivity via delocalized states was observed at TN160H260 K in crystalline C60 samples and in some samples with disordered structure. The evaluated band gap value is E g=0.28H0.54 eV for different crystalline structures and 0.06H0.25 eV for disordered ones. D 2005 Elsevier B.V. All rights reserved. Keywords: Fullerenes; High pressure high temperature; Amorphous; Electrical conductivity
1. Introduction Polymeric fullerenes are new carbon solids obtained from either pure or doped fullerenes by UV illumination, charge transfer or high-pressure high-temperature treatment (HPHT) [1–14]. We created 3D-polymeric (bulk polymer) C60 and C70 solids for the first time by static HPHT at P=9.5–15 GPa and investigated their structure and physical properties [2–12]. Of particular interest are the crystalline 3D-polymeric fullerenes, because their structures represent absolutely new carbon solids of the zeolite type with combined sp 2–sp 3 interatomic bonding and various bond lengths [9,10,14]. Physical properties of these new carbon solids strongly depend on the actual structures obtained at certain pressure-temperature conditions from either solid C60 or C70. Crystalline 3D-polymeric fullerites are formed in a narrow range of synthesis temperatures (670–1000 K) at pressures in the range of about 10–15 GPa. At higher
* Corresponding author. E-mail address: [email protected] (S.G. Buga). 0925-9635/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2005.01.018
treatment temperatures disordered structures have been obtained. We obtained and investigated for the first time crystalline 3D-polymers of C60 with densities in the range of 2.3–2.65 g cm3 and C70 with densities 2.0–2.2 g cm3 [2–5,9–12]. Their structures have been investigated by X-ray powder diffraction and Raman scattering. The thermal stability of the new materials obtained have been studied by DSC in the range 240–640 K [11]. The densest crystal polymers as well as the disordered ones were stable up to temperatures of about 500–550 K, while low-density structures started to dissociate at about 380–400 K. Electrical transport in 3D-polymeric fullerenes attracts great attention, because due to a large fraction of sp 2 bonds they represent intrinsic pure carbon semiconductors. Our earlier study of such materials with disordered structures revealed variable range hopping (VRH) conductivity and power r(T) functions in the temperature range of 2–300 K [8]. Power factors of 3/2, 2, 4 was observed. In this work we continued the investigations of disordered structures and also focused on crystalline 3D-polymer samples, obtained both from C60 and C70 fullerenes. The d.c. resistivity versus
S.G. Buga et al. / Diamond & Related Materials 14 (2005) 896–901
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Table 1 The P,T-parameters of synthesis, density q, unit-cell parameters, Mott parameters A for VRH approximation of conductivity, the room temperature part of delocalized charge carriers d 300 K=(r a/r)d 100%, the activation energy E a and the localisation–delocalisation temperature edge Ta Samples, No. P, GPa T, K q, g cm3 unit cell, 2 Immm A 1, K 1/4 A 2, K 1/4 A 3, K 1/4 d 300 K, % E a , eV Ta , K
a b c
1
2
3
4
5
6
13 670 2.3 9.07 9.47 12.87 – 36.0 – 3.6 0.215 256
11.5 850 2.45 8.73 9.16 12.94 – 46 89.5 25 0.14 200
12 820 2.5 8.69 8.88 12.70 – 21.5 58.9 34.6 0.145 163
12 900 2.55 8.68 8.84 12.65 – – 78.2 50 0.18 220
12 950 2.65 8.67 8.81 12.60 – – 91.1 22.4 0.27 220
12 1000 2.7 8.65 8.78 12.55 4 21 73.0 23.5 0.23 240
temperature function was measured in the range 30–350 K. The activation law of conductivity, indicating electrical transport via delocalized states in semiconductor materials was observed in some investigated samples above 160H260 K. The estimated band gap values are E g=0.28H0.54 eV for different crystalline structures and 0.06H0.25 eV in samples with disordered structures.
2. Experimental procedure Twenty samples were synthesized from commercially available pure C60 (99.98%, C70: 0.01%) and C70 (99,8%, 0.2%-C60) fullerenes in btoroidQ-type high pressure apparatus under pressure of 11.5–15 GPa and temperature in the range of 670–1800 K. The details of the synthesis procedure can be found elsewhere [2]. The actual parameters of synthesis, structural data and experimentally obtained parameters of electrical conductivity for the 11 most interesting samples are presented in Table 1. Sample No.
7 12.5 (C70) 820 2.2 9.83 9.83 13.16 5.9 30 – 0 – –
8
9
10
11
9.5 950 2.6 cryst.+Am1
15 (C70) 1100 2.9 Am1+Am2
12.5 1500 3.05 Am1+Am2
15 1800 3.25 Am2
4 13.7 – 0 – –
3.15 20.5 73.3 0 – –
11.5 27 73.4 0 – –
– 25 125.3 64 0.22 220
1 was synthesized from rhombohedral 2D-polymer after pre-treatment at P=8 GPa, T=870 K. The dimensions of specimens were F33 mm3 after synthesis and small pieces were used for electrical measurements and X-ray structural analysis. X-ray powder diffraction using filtered Cu Ka radiation have been employed (Fig. 1). The diffraction patterns obtained are analogous to those of similar samples investigated earlier in [3–5,9,10] and recently in [12,14]. The crystalline structures of C60 polymers are body-centered orthorhombic, with 2 C60 molecules per unit cell and the Immm space group. The structure of crystalline C70 3D-polymer (sample No. 7) is body-centered tetragonal. Four types of disordered structures were investigated (samples No. 8–11). The densities of the samples were measured by the flotation method with an accuracy of F0.05 g cm3. The d.c. R(T) functions in the range of 30H350 K were studied by conventional 4-probe method using an Oxford Instruments MagLab 2000k cryostat system. Silver paste contacts were used.
Fig. 1. X-ray diffraction patterns of samples numbered according to Table 1.
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3. Electrical conductivity Arrhenius plots of electrical conductivity vs temperature were non-linear for all studied samples. Several examples of such graphs are shown in Fig. 2a. The best linear fits for all r(T) functions were found using a logarithmic relation, indicating a power law of conductivity vs temperature: log r=log r 0+Bd log T. Such plots for the same samples as in Fig. 2a are shown in Fig. 2b. A simple empirical linear relation covers a wide studied temperature range of 80H350 K: log Tc3.92–6.04d T 1/4. The deviations are below 4%. This means that any power law of conductivity vs temperature in this temperature range may indicate the variable range hopping (VRH) mechanism. Fig. 3 shows all r(T) functions in Mott’s coordinates, according to [15,16]. Indeed, this picture exhibits VRH conductivity: r ¼ r0 ðT Þexp AT 1=4 ; where r0 ðTÞ ¼ CT1=2 : ð1Þ Actually, in different samples the best fits were found with 1–3 VRH dependencies and Boltzmann activation law: r ¼ CI T 1=2 exp AI T 1=4 þ C2 T 1=2 exp A2 T 1=4 ð2Þ þ C3 T 1=2 exp A3 T 1=4 þ r1 expð Ea =kT Þ The examples of fitting are presented in Fig. 4. The simplest case among the selected samples is No. 8 (Fig. 4a). Its total conductivity contains two VRH parts— the low temperature below T 1c40 K and the high-temperature above. The structure of this sample has a small crystalline 3D-polymer component and a dominating dis-
ordered structure on the basis of intact and destroyed molecules. The mean interplane distance of 3.1 2 (Fig. 1b) is about 7% smaller than in graphite, but it still indicates the presence of graphite-like 2D-layers in this structure. This was also confirmed by HRTEM [6]. Therefore one can suppose mainly 2D-character of the electronic system. Weak localization of charge carriers in disordered 2D electronic systems leads to a T 1/2 behavior of conductivity. Indeed, r(T) in sample No. 8 follows this rule approximately, but again with a kink at T 1c35 K. Thus, the interplay between weak localization of charge carries in disordered 2D electronic system and VRH at 3D disorder affect strongly the conductivity of samples with such a structure. The value of parameter A increases by a factor of 3.5 at the crossover. In the other samples with such a layered structure the ratio of A 2 /A 1 =5F2 also. Typical values of A 1 and A 2 are 5 and 25 K1/4 respectively. The deviations in these parameters, as well as in critical temperature T 1, are relatively large, about 50%, nevertheless we suppose a similar dominating VRH mechanism in other samples with disordered layered structures (Fig. 3a,b). In the other group of samples (Fig. 3c,d) a higher mean value of parameter A was found: A 3=75F16 K1/4. Only in sample No. 11 it is significantly higher: 125.3 K1/4. The plots were fitted with 3 VRH parts. The next critical temperature was T 2=160F40 K. Another VRH conductivity dominates at TNT 2. We assume this part is intrinsic in such high-resistive samples, while the other mechanisms may take place due to a small fraction (less than bulk 1% ) of layered structures in these samples. Such an explanation is most evident for samples No. 6 and 10 (Fig. 4b,d) having distinctly three different VRH parts. A regular semiconductor conductivity appears at TNTa in samples Nos. 1–6 and 11. But its part (d 300 K in Table 1) does not exceed ~50% in total conductivity up to the room temperature.
Fig. 2. Logarithm of conductivity r vs inverse temperature T (a) and vs log T (b) for samples numbered according to Table 1. Data for sample No.8 in (a) are multiplied by 105.
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Fig. 3. log(rT 0.5) vs T 1/4 for some of the studied samples with different magnitudes of the increase in conductivity r at T= 30 350 K: (a) 1–2 orders of magnitude; (b) 2–3 orders; (c) 3–4 orders; (d) 4–5 orders. Numbers in left column indicate density q, g cm3.
In samples No. 2 and 9 r(T) functions even more complicated (Fig. 4e,f). They can not be fitted with Eq. (2) continuously. We fitted them separately in two temperature regions: TbT k and T NT k (Fig. 4 e,f). At T NT k the slope of the curves (parameter A) decreased with respect to TbT k almost twice. Parameters C and A account for the density of states close to the Fermi level N(E F) and the overlap distance R i of atomic wavefunctions in different phases with numbers i [15,16]: 1=4 Ai ¼ 2:1 1=R3i kNi ðEF Þ ;
Ci fni Ri Ni ðEF Þ1=2 ;
ð3Þ
here i=1, 2, 3; k=Boltzmann constant; n i =phase i fraction parameter for multiphase structure. It is difficult to estimate the value of n i , because real mixture of phases in samples may be not spatially uniform, thus besides the volume factor it may contain the geometrical ones. Therefore, the experimentally found values of C i can not be used for estimations of variations in the
density of states close to the Fermi level. We can use only the values of A i for this purpose. The maximum variation coefficient of R i in different phases can be roughly estimated ~1.5 in all studied temperature range. The observed changes in A 4 are much more significant:more than two orders of magnitude at each step. Since N i (E F) and A4i are related reciprocally, the total value of N(E F) increases at T NT 1 and at T NT 2 by an additive smaller than 0.01 part relatively to previous temperature range. In samples No. 2 and 9 we observed decrease in the value of A at T NT k. The N(E F ) values rise just by factors seven and five, respectively, but these are absolute increase in N(E F) above T k. The reason for such an effect may be electronic phase transitions at T k=21 K and 43 K in samples No. 9 and 2, respectively. The crystalline 3D-polymeric fullerene samples (Nos. 1– 7) have hopping conductivity like the disordered ones. This indicates strong atomic disorder in molecularly ordered structures. According to the models for crystalline 3D-
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Fig. 4. VRH and exponential fits of conductivity curves for samples Nos.8 (a), 10 (b), 5 (c), 6 (d), 2 (e) and 9 (f). T 1 , T 2 , T 3 , Ta and T k-particular temperature points discussed in the text.
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polymers [9,10,14], the unit cell contains 120 atoms occupying nine independent positions with 27 various interatomic distances. Both sp 2 and sp 3 type bonds occur. The temperature contraction (expansion) of the lattice may induce strong changes in the overlap of atomic wavefunctions. Such relatively small lattice transformations can cause electronic phase transitions. Above 160–240 K an onset of conductivity via delocalized states takes place in crystalline 3D-polymeric C60 samples (Nos. 1–6) with an activation energy of 0.14H0.27 eV. If the charge carriers originate from mid-gap states close to the Fermi level, the band gap value is E g=0.28H0.54 eV for different structures. Smaller values of 0.06H0.25 eV have been found in samples with disordered structures, possessing general semiconductor type conductivity.
4. Conclusion The d.c. electrical conductivity in seven types of crystalline and four types disordered 3D-polymeric C60 and C70 fullerites have been investigated in a wide temperature range. That was done for the first time in samples with crystalline structures and C70-derived materials. All samples exhibit variable range hopping conductivity. Despite the molecular crystalline lattice, the degree of atomic disorder is very high. Consequently, the electronic structure of crystalline 3D-polymers as well as disordered ones lacks long-range order. A step-like changes in the density of states close to the Fermi level have been evaluated from log (rT 1/2) versus T 1/4 plots. Such a step-like increase in N(E F) may take place both due to a) multiphase structure of some samples and b) complicated electronic structure. Conductivity via delocalized states was observed above 160H260 K in crystalline C60 samples and in some samples with disordered structure. The evaluated band gap value is E g=0.28H0.54 eV for different crystalline structures and 0.06H0.25 eV for disordered ones.
901
Acknowledgements The work was financially supported by the Royal Swedish Academy of Sciences and the Swedish Research Council VR, and by the Russian Ministry of Industry, Science and Technologies.
References [1] H. Kuzmany, J. Winter, B. Burger, Synth. Met. 85 (1997) 1173. [2] V.D. Blank, S.G. Buga, N.R. Serebryanaya, V.N. Denisov, G.A. Dubitsky, A.N. Ivlev, B.N. Mavrin, M.Yu Popov, Phys. Lett., A 205 (1995) 208. [3] V.D. Blank, S.G. Buga, N.R. Serebryanaya, G.A. Dubitsky, S.N. Sulyanov, M.Yu Popov, et al., Phys. Lett., A 220 (1996) 149. [4] V.D. Blank, S.G. Buga, N.R. Serebryanaya, G.A. Dubitsky, R.H. Bagramov, M.Yu Popov, et al., Appl. Phys., A 64 (1997) 247. [5] V.D. Blank, N.R. Serebryanaya, G.A. Dubitsky, S.G. Buga, V.N. Denisov, B.N. Mavrin, et al., Phys. Lett., A 248 (1998) 415. [6] V.D. Blank, S.G. Buga, G.A. Dubitsky, N.R. Serebryanaya, M.Yu Popov, B. Sundqvist, Carbon 36 (1998) 319. [7] B. Sundqvist, Adv. Phys. 48 (1999) 1. [8] S.G. Buga, V.D. Blank, G.A. Dubitsky, L. Edman, X.-M. Zhu, E.B. Nyeanchi, et al., J. Phys. Chem. Solids 61 (2000) 1009. [9] L.A. Chernozatonskii, N.R. Serebryanaya, B.N. Mavrin, Chem. Phys. Lett. 316 (2000) 199. [10] N.R. Serebryanaya, L.A. Chernozatonskii, Solid State Commun. 114 (2000) 537. [11] S. Buga, V. Blank, A. Fransson, N. Serebryanaya, B. Sundqvist, Phys. Chem. Solids 63 (2002) 331. [12] V.D. Blank, G.A. Dubitsky, N.R. Serebryanaya, B.N. Mavrin, V.N. Denisov, S.G. Buga, L.A. Chernozatonskii, Physica. B 339 (2003) 39. [13] T.L. Markova, P. Scharff, B. Sundqvist, M.E. Gaevski, V.A. Davydov, A.V. Rakhmanina, et al., Carbon 39 (2001) 2203. [14] D.H. Chi, Y. Iwasa, T. Takano, T. Watanuki, Y. Ohishi, S. Yamanaka, et al., Phys. Rev., B 68 (2003) 153402. [15] N.F. Mott, Phil. Mag. 19 (1969) 835. [16] P. Nagels, in: M.H. Brodsky (Ed.), Amorphous Semiconductors, Springer-Verlag, Berlin, NY, 1979.
Electrical properties of 3D-polymeric crystalline and disordered C60 and C70 fullerites S.G. Bugaa,*, V.D. Blanka, N.R. Serebryanayaa, A. Dzwilewskib, T. Makarovab, B. Sundqvistb a
Department of Nanoelectronics, Technological Institute for Superhard and Novel Carbon Materials, 7a Centralnaya St., Troitsk, Moscow Region, 142190, Russia b Department of Physics, Umea University, SE-901 87, Umea, Sweden Available online 17 February 2005
Abstract Crystalline and disordered 3D-polymeric C60 and C70 with different lattice parameters and with densities in the range of 2.2H3.25 g cm1 were obtained by high-pressure-high-temperature treatment at P=11.5H15 GPa, T=670H1800 K. Their d.c. electrical conductivity was investigated at temperatures 30H350 K. The variable range hopping mechanism dominates in all samples up to room temperature. A temperature activated conductivity via delocalized states was observed at TN160H260 K in crystalline C60 samples and in some samples with disordered structure. The evaluated band gap value is E g=0.28H0.54 eV for different crystalline structures and 0.06H0.25 eV for disordered ones. D 2005 Elsevier B.V. All rights reserved. Keywords: Fullerenes; High pressure high temperature; Amorphous; Electrical conductivity
1. Introduction Polymeric fullerenes are new carbon solids obtained from either pure or doped fullerenes by UV illumination, charge transfer or high-pressure high-temperature treatment (HPHT) [1–14]. We created 3D-polymeric (bulk polymer) C60 and C70 solids for the first time by static HPHT at P=9.5–15 GPa and investigated their structure and physical properties [2–12]. Of particular interest are the crystalline 3D-polymeric fullerenes, because their structures represent absolutely new carbon solids of the zeolite type with combined sp 2–sp 3 interatomic bonding and various bond lengths [9,10,14]. Physical properties of these new carbon solids strongly depend on the actual structures obtained at certain pressure-temperature conditions from either solid C60 or C70. Crystalline 3D-polymeric fullerites are formed in a narrow range of synthesis temperatures (670–1000 K) at pressures in the range of about 10–15 GPa. At higher
* Corresponding author. E-mail address: [email protected] (S.G. Buga). 0925-9635/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2005.01.018
treatment temperatures disordered structures have been obtained. We obtained and investigated for the first time crystalline 3D-polymers of C60 with densities in the range of 2.3–2.65 g cm3 and C70 with densities 2.0–2.2 g cm3 [2–5,9–12]. Their structures have been investigated by X-ray powder diffraction and Raman scattering. The thermal stability of the new materials obtained have been studied by DSC in the range 240–640 K [11]. The densest crystal polymers as well as the disordered ones were stable up to temperatures of about 500–550 K, while low-density structures started to dissociate at about 380–400 K. Electrical transport in 3D-polymeric fullerenes attracts great attention, because due to a large fraction of sp 2 bonds they represent intrinsic pure carbon semiconductors. Our earlier study of such materials with disordered structures revealed variable range hopping (VRH) conductivity and power r(T) functions in the temperature range of 2–300 K [8]. Power factors of 3/2, 2, 4 was observed. In this work we continued the investigations of disordered structures and also focused on crystalline 3D-polymer samples, obtained both from C60 and C70 fullerenes. The d.c. resistivity versus
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897
Table 1 The P,T-parameters of synthesis, density q, unit-cell parameters, Mott parameters A for VRH approximation of conductivity, the room temperature part of delocalized charge carriers d 300 K=(r a/r)d 100%, the activation energy E a and the localisation–delocalisation temperature edge Ta Samples, No. P, GPa T, K q, g cm3 unit cell, 2 Immm A 1, K 1/4 A 2, K 1/4 A 3, K 1/4 d 300 K, % E a , eV Ta , K
a b c
1
2
3
4
5
6
13 670 2.3 9.07 9.47 12.87 – 36.0 – 3.6 0.215 256
11.5 850 2.45 8.73 9.16 12.94 – 46 89.5 25 0.14 200
12 820 2.5 8.69 8.88 12.70 – 21.5 58.9 34.6 0.145 163
12 900 2.55 8.68 8.84 12.65 – – 78.2 50 0.18 220
12 950 2.65 8.67 8.81 12.60 – – 91.1 22.4 0.27 220
12 1000 2.7 8.65 8.78 12.55 4 21 73.0 23.5 0.23 240
temperature function was measured in the range 30–350 K. The activation law of conductivity, indicating electrical transport via delocalized states in semiconductor materials was observed in some investigated samples above 160H260 K. The estimated band gap values are E g=0.28H0.54 eV for different crystalline structures and 0.06H0.25 eV in samples with disordered structures.
2. Experimental procedure Twenty samples were synthesized from commercially available pure C60 (99.98%, C70: 0.01%) and C70 (99,8%, 0.2%-C60) fullerenes in btoroidQ-type high pressure apparatus under pressure of 11.5–15 GPa and temperature in the range of 670–1800 K. The details of the synthesis procedure can be found elsewhere [2]. The actual parameters of synthesis, structural data and experimentally obtained parameters of electrical conductivity for the 11 most interesting samples are presented in Table 1. Sample No.
7 12.5 (C70) 820 2.2 9.83 9.83 13.16 5.9 30 – 0 – –
8
9
10
11
9.5 950 2.6 cryst.+Am1
15 (C70) 1100 2.9 Am1+Am2
12.5 1500 3.05 Am1+Am2
15 1800 3.25 Am2
4 13.7 – 0 – –
3.15 20.5 73.3 0 – –
11.5 27 73.4 0 – –
– 25 125.3 64 0.22 220
1 was synthesized from rhombohedral 2D-polymer after pre-treatment at P=8 GPa, T=870 K. The dimensions of specimens were F33 mm3 after synthesis and small pieces were used for electrical measurements and X-ray structural analysis. X-ray powder diffraction using filtered Cu Ka radiation have been employed (Fig. 1). The diffraction patterns obtained are analogous to those of similar samples investigated earlier in [3–5,9,10] and recently in [12,14]. The crystalline structures of C60 polymers are body-centered orthorhombic, with 2 C60 molecules per unit cell and the Immm space group. The structure of crystalline C70 3D-polymer (sample No. 7) is body-centered tetragonal. Four types of disordered structures were investigated (samples No. 8–11). The densities of the samples were measured by the flotation method with an accuracy of F0.05 g cm3. The d.c. R(T) functions in the range of 30H350 K were studied by conventional 4-probe method using an Oxford Instruments MagLab 2000k cryostat system. Silver paste contacts were used.
Fig. 1. X-ray diffraction patterns of samples numbered according to Table 1.
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3. Electrical conductivity Arrhenius plots of electrical conductivity vs temperature were non-linear for all studied samples. Several examples of such graphs are shown in Fig. 2a. The best linear fits for all r(T) functions were found using a logarithmic relation, indicating a power law of conductivity vs temperature: log r=log r 0+Bd log T. Such plots for the same samples as in Fig. 2a are shown in Fig. 2b. A simple empirical linear relation covers a wide studied temperature range of 80H350 K: log Tc3.92–6.04d T 1/4. The deviations are below 4%. This means that any power law of conductivity vs temperature in this temperature range may indicate the variable range hopping (VRH) mechanism. Fig. 3 shows all r(T) functions in Mott’s coordinates, according to [15,16]. Indeed, this picture exhibits VRH conductivity: r ¼ r0 ðT Þexp AT 1=4 ; where r0 ðTÞ ¼ CT1=2 : ð1Þ Actually, in different samples the best fits were found with 1–3 VRH dependencies and Boltzmann activation law: r ¼ CI T 1=2 exp AI T 1=4 þ C2 T 1=2 exp A2 T 1=4 ð2Þ þ C3 T 1=2 exp A3 T 1=4 þ r1 expð Ea =kT Þ The examples of fitting are presented in Fig. 4. The simplest case among the selected samples is No. 8 (Fig. 4a). Its total conductivity contains two VRH parts— the low temperature below T 1c40 K and the high-temperature above. The structure of this sample has a small crystalline 3D-polymer component and a dominating dis-
ordered structure on the basis of intact and destroyed molecules. The mean interplane distance of 3.1 2 (Fig. 1b) is about 7% smaller than in graphite, but it still indicates the presence of graphite-like 2D-layers in this structure. This was also confirmed by HRTEM [6]. Therefore one can suppose mainly 2D-character of the electronic system. Weak localization of charge carriers in disordered 2D electronic systems leads to a T 1/2 behavior of conductivity. Indeed, r(T) in sample No. 8 follows this rule approximately, but again with a kink at T 1c35 K. Thus, the interplay between weak localization of charge carries in disordered 2D electronic system and VRH at 3D disorder affect strongly the conductivity of samples with such a structure. The value of parameter A increases by a factor of 3.5 at the crossover. In the other samples with such a layered structure the ratio of A 2 /A 1 =5F2 also. Typical values of A 1 and A 2 are 5 and 25 K1/4 respectively. The deviations in these parameters, as well as in critical temperature T 1, are relatively large, about 50%, nevertheless we suppose a similar dominating VRH mechanism in other samples with disordered layered structures (Fig. 3a,b). In the other group of samples (Fig. 3c,d) a higher mean value of parameter A was found: A 3=75F16 K1/4. Only in sample No. 11 it is significantly higher: 125.3 K1/4. The plots were fitted with 3 VRH parts. The next critical temperature was T 2=160F40 K. Another VRH conductivity dominates at TNT 2. We assume this part is intrinsic in such high-resistive samples, while the other mechanisms may take place due to a small fraction (less than bulk 1% ) of layered structures in these samples. Such an explanation is most evident for samples No. 6 and 10 (Fig. 4b,d) having distinctly three different VRH parts. A regular semiconductor conductivity appears at TNTa in samples Nos. 1–6 and 11. But its part (d 300 K in Table 1) does not exceed ~50% in total conductivity up to the room temperature.
Fig. 2. Logarithm of conductivity r vs inverse temperature T (a) and vs log T (b) for samples numbered according to Table 1. Data for sample No.8 in (a) are multiplied by 105.
S.G. Buga et al. / Diamond & Related Materials 14 (2005) 896–901
899
Fig. 3. log(rT 0.5) vs T 1/4 for some of the studied samples with different magnitudes of the increase in conductivity r at T= 30 350 K: (a) 1–2 orders of magnitude; (b) 2–3 orders; (c) 3–4 orders; (d) 4–5 orders. Numbers in left column indicate density q, g cm3.
In samples No. 2 and 9 r(T) functions even more complicated (Fig. 4e,f). They can not be fitted with Eq. (2) continuously. We fitted them separately in two temperature regions: TbT k and T NT k (Fig. 4 e,f). At T NT k the slope of the curves (parameter A) decreased with respect to TbT k almost twice. Parameters C and A account for the density of states close to the Fermi level N(E F) and the overlap distance R i of atomic wavefunctions in different phases with numbers i [15,16]: 1=4 Ai ¼ 2:1 1=R3i kNi ðEF Þ ;
Ci fni Ri Ni ðEF Þ1=2 ;
ð3Þ
here i=1, 2, 3; k=Boltzmann constant; n i =phase i fraction parameter for multiphase structure. It is difficult to estimate the value of n i , because real mixture of phases in samples may be not spatially uniform, thus besides the volume factor it may contain the geometrical ones. Therefore, the experimentally found values of C i can not be used for estimations of variations in the
density of states close to the Fermi level. We can use only the values of A i for this purpose. The maximum variation coefficient of R i in different phases can be roughly estimated ~1.5 in all studied temperature range. The observed changes in A 4 are much more significant:more than two orders of magnitude at each step. Since N i (E F) and A4i are related reciprocally, the total value of N(E F) increases at T NT 1 and at T NT 2 by an additive smaller than 0.01 part relatively to previous temperature range. In samples No. 2 and 9 we observed decrease in the value of A at T NT k. The N(E F ) values rise just by factors seven and five, respectively, but these are absolute increase in N(E F) above T k. The reason for such an effect may be electronic phase transitions at T k=21 K and 43 K in samples No. 9 and 2, respectively. The crystalline 3D-polymeric fullerene samples (Nos. 1– 7) have hopping conductivity like the disordered ones. This indicates strong atomic disorder in molecularly ordered structures. According to the models for crystalline 3D-
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Fig. 4. VRH and exponential fits of conductivity curves for samples Nos.8 (a), 10 (b), 5 (c), 6 (d), 2 (e) and 9 (f). T 1 , T 2 , T 3 , Ta and T k-particular temperature points discussed in the text.
S.G. Buga et al. / Diamond & Related Materials 14 (2005) 896–901
polymers [9,10,14], the unit cell contains 120 atoms occupying nine independent positions with 27 various interatomic distances. Both sp 2 and sp 3 type bonds occur. The temperature contraction (expansion) of the lattice may induce strong changes in the overlap of atomic wavefunctions. Such relatively small lattice transformations can cause electronic phase transitions. Above 160–240 K an onset of conductivity via delocalized states takes place in crystalline 3D-polymeric C60 samples (Nos. 1–6) with an activation energy of 0.14H0.27 eV. If the charge carriers originate from mid-gap states close to the Fermi level, the band gap value is E g=0.28H0.54 eV for different structures. Smaller values of 0.06H0.25 eV have been found in samples with disordered structures, possessing general semiconductor type conductivity.
4. Conclusion The d.c. electrical conductivity in seven types of crystalline and four types disordered 3D-polymeric C60 and C70 fullerites have been investigated in a wide temperature range. That was done for the first time in samples with crystalline structures and C70-derived materials. All samples exhibit variable range hopping conductivity. Despite the molecular crystalline lattice, the degree of atomic disorder is very high. Consequently, the electronic structure of crystalline 3D-polymers as well as disordered ones lacks long-range order. A step-like changes in the density of states close to the Fermi level have been evaluated from log (rT 1/2) versus T 1/4 plots. Such a step-like increase in N(E F) may take place both due to a) multiphase structure of some samples and b) complicated electronic structure. Conductivity via delocalized states was observed above 160H260 K in crystalline C60 samples and in some samples with disordered structure. The evaluated band gap value is E g=0.28H0.54 eV for different crystalline structures and 0.06H0.25 eV for disordered ones.
901
Acknowledgements The work was financially supported by the Royal Swedish Academy of Sciences and the Swedish Research Council VR, and by the Russian Ministry of Industry, Science and Technologies.
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