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Electrical conductivity of single polycrystalline-amorphous carbon nanocoils
Carbon 98 (2016) 285e290
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Carbon journal homepage: www.elsevier.com/locate/carbon
Electrical conductivity of single polycrystalline-amorphous carbon nanocoils Yanming Sun a, Chenwei Wang a, Lujun Pan a, *, Xin Fu a, Penghe Yin b, Helin Zou b a b
School of Physics and Optoelectronic Technology, Dalian University of Technology, No. 2 Linggong Road, Ganjingzi District, Dalian, 116024, PR China Key Laboratory for Micro/Nano Technology and Systems of Liaoning Province, Dalian University of Technology, Dalian, 116024, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 August 2015 Received in revised form 15 October 2015 Accepted 7 November 2015 Available online 11 November 2015
Polycrystalline-amorphous carbon nanocoils (CNCs) have been synthesized by thermal chemical vapor deposition. The electrical conductivity of a single CNC is investigated over a wide temperature range from 4 to 300 K by employing the four-probe method. It is found that the smaller the line diameter of the CNC, the bigger the size of the crystalline grain, which results in the better crystallinity and conductivity. Moreover, the temperature behavior of r(T) reveals that the intrinsic electric-transport mechanisms through a single helical CNC are mainly due to a combination conduction processes of the thermal activation, the nearest-neighbor hopping, and variable range hopping. Meanwhile, the dominate electron transport mechanisms crossover from one mode to another with the circumstance temperature. Notably, it follows Mott variable range hopping and EfroseShklovskii variable range hopping at low temperature. The model transition zones which are related to the crystallinity of the CNCs are also discussed in each temperature regime. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction The great development of nanoelectronic devices and mechanical miniaturization, is attracting more basic researches on how nanostructures affect the properties of these materials [1e4]. Carbon nanocoils (CNCs) have received much concern in recent years, as its peculiar helical morphology which consists of polycrystalline-amorphous structure. It shows potential applications in field-emission devices, electromagnetic wave absorbers and micro-electromechanical systems [5e7]. Therefore, it is a promising and valuable subject to develop a simple way to study the mechanism of conductance in this special spiral carbonaceous structure. There inevitably exist disordered factors, such as the state of impurities and defects, in the process of preparation of lowdimensional system of electronic materials and components. The electronic states of disordered systems are localized, which affects the electronic transport characteristics of low-dimensional materials and devices. The localization length of the wave-functions increases with increasing the degree of distortion, while
* Corresponding author. E-mail address: [email protected] (L. Pan). http://dx.doi.org/10.1016/j.carbon.2015.11.025 0008-6223/© 2015 Elsevier Ltd. All rights reserved.
decreases with increasing the crystalline grain size [8e10]. It indicates that the disorder degree of interfacial atoms and irregular crystalline grain size affect the distributions of electronic localization in low-dimensional nanometer materials. The helical polycrystalline-amorphous CNCs are a hybrid of sp2 grains and sp3 amorphous structures [11,12], the physical properties of CNCs may differ from both of sp2 structured carbon nanotubes (CNTs) and sp3 structured amorphous carbon nanofibers (CNFs). The electrical conductivity of CNCs is higher than that of amorphous CNFs at 300 K due to the better crystallinity of CNCs [13]. The optoelectronic applications of CNCs such as field-emission devices or infrared sensors relied strongly on electron transportation mechanism in the CNCs. Shen et al. measured the electrical properties of a single carbon microcoil with a double helix structure by a standard fourprobe technique [14]. The results revealed that the temperature dependence of the resistance above 13 K was in accordance with the Mott variable range hopping (VRH), whereas below 13 K, it obeyed the Efros-Shklovskii VRH. Chiu and Tang et al. measured the electrical properties of quasi one-dimensional disordered CNCs [15,16]. They analyzed the electric transport with an electron hopping length of about 5e50 nm inside the disordered carbon coils. Most recently, Ma et al. reported that the resistivity of carbon nanocoils annealed from 300 to 2900 K was decreased with increasing the annealing temperature [17]. The average activation
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energy for electron hopping in the annealed CNCs was decreased from 11 to 4.2 meV with the increase of annealing temperature because of the improvement of the crystallinity. To date, there are few studies addressing the systematic discussions on the resistivity behavior of the CNCs with a polycrystalline-amorphous structures over a broad range of low temperature. In this paper, therefore, we measured the temperature dependence of resistivity, r(T), of the single polycrystallineamorphous CNCs over the temperature from 4 to 300 K based on the designed four-probe method. An in-depth physical explanation for the temperature dependence of electrical conduction mechanism in this specifically polycrystalline-amorphous structure was studied. The results revealed that the conductivity of the CNCs increases with the crystalline grain size, and the mode of electron hopping changes with the circumstance temperature.
The length of the CNC was 130 mm, the line diameter of the CNC was 380 nm, and the screw pitch was 480 nm. The electrical measurement was performed by an Agilent B2902A source meter. Fig. 1(b) shows the partial enlarged SEM image of the four-electrode sample. The white arrow indicates the critical point, from which the CNC is fixed firmly by the multilayered electrodes. It is also obvious to see that the surface of the CNC between the two electrodes is clear so that there is no other factors to affect the electrical conductivity of the CNC. The IeV curves at fixed temperatures of 4 and 150 K were tested, as shown in Fig. 1(d). It is found that the IeV curves performed at different temperatures show a linear behavior and the resistance of the CNC at 4 K is larger than that at 150 K. The good linearity of the IeV curves reveals that the CNC contacts well with the electrodes. 3. Results and discussion
2. Experimental The CNCs used in the experiment were synthesized by the thermal chemical vapor deposition (CVD) using Fe/Sn as catalyst. Fe2(SO4)3/SnC solution was selected as precursor, the mole ratio of Sn to Fe was approximately 1:60. It is known that the melting point of Sn is 231.89 C. In order to prevent the Sn from vaporization during heating in Ar, the prepared Sn/Fe catalyst films were calcined at 710 C for 30 min in air. Finally, CNCs were synthesized in a thermal CVD system at 710 C for 30 min by introducing Ar and C2H2 gases. The flow rate ratio of Ar to C2H2 was maintained at 23:3 [18]. Fig. 1(c) shows the diagram of an interdigitated four-probe module. In a typical process, four-probe Ti/Pt/Cr multilayer electrodes were prepared on SiO2/Si wafers by combining lithography with magnetron sputtering technique. Firstly, the micron-sized Ti/ Pt (30/100 nm) electrodes were patterned on a Si substrate which was capped with a 500 nm thick SiO2 layer. Secondly, a drop of CNCs dispersed ethanol solution was deposited on the metallic electrodes, ensuring that one of CNCs was located across a fourelectrode unit. Finally, one more lithography and magnetron sputtering process was conducted to deposit another layer of Ti electrode (30 nm) exactly on the multilayer electrodes of Pt/Cr, insuring that the CNC was sandwiched between the two layers of Ti and Pt electrodes. In this way, the CNC could be fixed firmly and contacted well with multilayered electrodes, which greatly reduced the contact resistance. The measured resistivity was thus the intrinsic one of the individual CNC. Fig. 1(a) shows a typical SEM image of one complete fourelectrode sample. The gap between two electrodes was 10 mm.
Fig. 2(a) shows the measured resistivity of the CNC by ramping down the temperature from 300 to 4 K. It clearly demonstrates that the resistivity changes little with the temperature below 60 K. Notice that the resistivity decreases monotonically with increasing temperature between 300 and 60 K, as would be expected for semiconductors. The conductivity of polycrystalline-amorphous nanostructure are related to many factors. And different mechanisms have different activation energies, a model to analyze the conductive mechanism is established as following equation: 1 r1 ðTÞ ¼ r1 A þ rB ;
(1)
where r is the temperature-independent resistivity, rA is the resistivity with a combination of the thermal activation model and the nearest-neighbor hopping (NNH) model, and rB is the resistivity with VRH model. r1A can be expressed by
DE1 DE2 1 þ r1 r1 1 exp A ðTÞ ¼ r0 exp kT kT DE 3 þ r1 ; 2 exp kT
(2)
where k is the Boltzmann constant, and DE is the thermal activation energy describing the electronic conduction in three temperature regimes between 300 and 60 K DE1, DE2 and DE3 present three contributions given by equation (2) which are corresponding to the extended states of conduction bands, localized states conduction at band tails and NNH conduction processes, respectively. The electrons are thermally excited from the Fermi level to the conduction
Fig. 1. (a) SEM image of a single CNC in the four-probe electrode. (b) Partially enlarged SEM image of the single CNC. (c) Diagram of the four-electrode module. (d) IeV characteristics of the single CNC at 4 and 150 K.
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Fig. 2. (a) Resistivity r of a single CNC plotted against 1000/T between 300 and 4 K. The inset shows ln(r) as a function of 103/T to estimate the activation energy DE between 300 and 60 K. The Solid lines (bed) are three parts of the best-fit lines with the thermal activation equation. The details in three temperature regimes are shown in (bed).
bands, where a huge amount of unoccupied, extended states with high mobility are available [19]. lnr as a function of 1000/T for each temperature regime is plotted in Fig. 2(bed). From the slope values, DE1 z 29.7 meV, DE2 z 5.7 meV, and DE3 z 1.3 meV are obtained. With the reducing temperature, the thermal energy kBT becomes too small to excite the electrons. As a consequence, the NNH conduction of electrons eventually becomes the dominant charge transport process around 60 K. The electrons are excited from the occupied levels to nearby, or the nearest-neighbor, unoccupied levels. Therefore, the activation energy presents the following rule: DE3 < DE2 < DE1. The electrons transport in this special structure have two kinds of mechanisms: repeatedly trapped mechanism and hopping mechanism. The electrons not only have diffusion motion but also fall to the band tails of localized states. The trapped electrons need to be thermally excited again to participate in the transport. Therefore, in the process of the movement of electrons tend to experience multiple collapsing and re-exciting, and form the diffusion transport. At the higher temperature, the electrons can be excited to the energy states above the edge of the conduction band EC, which forms the extended states of conduction bands (DE1). When the temperature is low, the electrons can only be excited to the band tail states of the EC, and then transition from a localized state into another localized state by the help of phonons, which forms localized states conduction at band tails (DE2). At lower temperature, the electrons can only jump from the energy states below the Fermi level EF to the adjacent empty state above the EF with the help of phonons, forming the nearest-neighbor hopping conduction (DE3). As a consequence, the rule of the activation energy (DE3
conductive mechanism is no longer meet the equation (2). Hence, the transportation of internal electrons is analyzed with the theory of variable range hopping (VRH). The temperature dependence of CNCs can be fitted with the following equation:
r1 B ðTÞ
¼
r1 0
" # T0 1=d exp ; T
(3)
For disordered systems, when d ¼ 4, it can be explained by Mott VRH of (non-interacting) localized electrons, where T0 is the characteristic Mott temperature. When d ¼ 2, it can be explained by Efros-Shklovskii (EeS) VRH model, where T0 is the characteristic EeS temperature. Briefly, electrons would prefer to hop between non-nearest-neighboring localized states which have lower energy difference. The localized states correspond to the sp2 grains in CNCs. Fig. 3 shows the temperature dependence resistivity of a single CNC ranges from 46 to 4 K. There is a conductive mechanism transformation from the NNH conduction to the VRH conduction processes between 60 and 46 K. Notice that the electrons transportation in the CNCs through localized states exhibits a crossover from three-dimensional Mott VRH model to one-dimensional EeS VRH model. It can be attributed to the fact that the polycrystallineamorphous CNCs is highly disordered. Fig. 3(a) indicates the resistivity of a single CNC with the temperature region from 46 to 28 K. The result is agreed with the theory of Mott VRH. It can be explained by Mott VRH which is based on phonon-helped tunneling of carriers between localized states with energies near the Fermi level. With the increasing temperature, electrons obtain enough energy from phonons and the number of empty states between nearest neighbors for a certain occupied state leads, so that the electron hopping mechanism transfers from Mott VRH to NNH mode which is described by equation (2) [20,21]. Three-
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Fig. 3. The resistivity of a single CNC at low temperature (46 e 4 K) with different transmission regimes (a) Four-terminal resistances as a function of T1/4, and the solid curves are fit to the expression (3) with d ¼ 4. (b) Four-terminal resistances as a function of T1/2, and the solid curves are fit to the expression (3) with d ¼ 2.
dimensional Mott-David VRH model also observed in carbon material with similar helical structures, such as the single microcoiled carbon fiber [22,23]. The temperature ranged from 4 to 16 K, the resistivity in CNC follows the relation lnr ~ T1/2 which is based on the EeS VRH model, as shown in Fig. 3(b). It refers to that the electroneelectron interaction is an important issue dominating the electron transport processes in the CNC. The results above suggest that the model analysis elicits a basic understanding of the electric transport through localized states which exhibits a crossover from Mott to EeS VRH inside the disordered CNC. As the CNC used in experiment is polycrystalline-amorphous structure, it is inferred that the electron transportation is affected by the degree of disorder and the crystalline grain size of the system. And the electron transportation within the crystalline grain is unimpeded but impeded at the edge of the crystallines, which will be further discussed in the following. The depletion of the density of the states at low energy demonstrates a signature of eee interaction, which plays an important role in the electron transportation, as shown in Fig. 4. The curve is almost linear at 30 K, but it becomes nonlinear at 5 K which further validates the existence of a model transition between the two
regions [24,25]. As we know that Coulomb gap occurs in the localized states due to long-range Coulomb interactions between the electrons in different centers of localization near the Fermi energy. Therefore, the Coulomb gap DC ¼ 0.09 meV based on Efros and Shklovskii theory is calculated [26,27]. In the experiment, the resistivity of the CNCs have been measured over the temperature range from 4 to 300 K. For convenience, the samples used above is labeled as #1. And another three reference samples are labeled as #2 #3 #4. The morphologies of the four carbon nanocoils are shown in Fig. S1. The specific parameters of the four different CNCs, the line diameter, coil diameter, and screw pitch are shown in Table 1. The curves in Fig. 3(a) and (b) are linear, and this is agreed with the Mott VRH and EfrosShklovskii (EeS) VRH model theory, respectively. For the reference samples #2, #3 and #4, the results show similar behavior as #1. From approximately 300 to 60 K and 46 to 4 K, there presents a transition area with two conductive mechanisms in each temperature region. For the four CNCs #1, #2, #3 and #4, the lengths of the transition zone from Mott to EeS VRH model are 12 K, 16 K, 18 K and 19 K, and from NNH to VRH model are 14 K, 20 K, 23 K and 25 K, respectively. It indicates that the CNC with different nanostructure, shows different transmission mechanisms and the length of the transition zone in each transmission mechanism dominated area is different at low temperature. Fig. 5(a) is the Raman spectra of the four CNCs #1, #2, #3 and #4 used in the experiment to characterize the degree of disorder and graphitization. Two main peaks are observed in the Raman spectra: one at approximately 1322 cm1, known as the D-band, which originates from structural defects in carbon materials, and the other at approximately 1593 cm1, known as the G-band, which originates from the graphitic structure of carbon materials. Lorentz and BWF functions are adopted to fit the D and G peaks, respectively [28]. Fig. 5(b) is the value of ID/IG (the area ratio of the D to G peaks) with the diameter of the four CNCs. Smaller values of ID/IG indicates the larger graphite crystallites and a higher degree of graphitization [12]. The value of ID/IG increases with the increasing line diameter, as shown in Fig. 5(b). The results above suggest that the CNC with a
Table 1 The line diameter, screw pitch, length of the four CNCs.
Fig. 4. The differential conductance measurement of the CNC as a function of Bias voltage for 4 and 30 K.
Coil
Line diameter (nm)
Coil diameter (nm)
Screw pitch (mm)
#1 #2 #3 #4
280 470 500 520
537 886 876 752
2.05 1.55 1.25 0.9
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Fig. 5. (a) The Raman spectra of the four CNCs. (b) Values of ID/IG of the four CNCs.
larger diameter, the crystal lattice trends to be more irregular which means the degree of disorder is larger, so the degree of graphitization is smaller. For the CNCs with a smaller diameter, it has more regular crystal lattice and a higher degree of graphitization. Due to this, the CNC shows a better resistivity. In Fig. 5(b), among the four CNCs, the minimum value of ID/IG is about 1.9, and its diameter is about 0.28 mm; while the maximum value of ID/IG is approximately 2.6, and its diameter is about 0.55 mm. The ratio of ID to IG is inversely proportional to the average crystalline size according to the empirical formula of ID/IG ¼ C(l)/La, where C(l) is a constant at the certain laser wavelength (l) and La indicates the size of sp2 grains [28e30]. For the exciting laser of 632.8 nm used in our Raman system, C (632.8) can be calculated by the formula of C(l) ¼ 12.6 þ 0.033 l [29], which is equal to 8.28 nm. For the four samples, La is 4.35, 3.68, 3.35, 3.21 nm, respectively. Hence, with increasing the line diameter, the size of sp2 grain becomes small, and the orientation of the crystallite is disordered. The structures of the single CNCs is confirmed by TEM images shown in Fig. 6. Fig. 6(a) is the TEM image of a single CNC with a line diameter of 280 nm, which shows the graphitization of the CNC. From the TEM image, the lattice is partially orderly. The red square shows the size of the grain which is approximately 5 nm. It is in accordance with the La 4.35 nm. Fig. 6(b) shows the diameter of the CNC is approximately 520 nm. The red square shows the crystalline size is approximately 3.4 nm, which is in accordance with the La 3.35 nm. The electron diffraction patterns shown inset of Fig. 6 provide more visual representations of the degree of crystallinity. The inner and outer hallows near the innermost ring corresponds to the graphite (002) and (101) planes, respectively. The hallow
diffraction pattern (inset, Fig. 6(b)) indicates the poor crystallinity of the CNC. From the arc-shaped diffraction spots of the (002) plane (inset, Fig. 6(a)), the main orientation of the graphite (002) plane can be inferred to be perpendicular to the dashed line, which indicates the improved crystallinity. Based on large number of experiments, the statistical average electrical conductivities are calculated (the CNCs are regarded as ideal and untwisted) [31]. The resistivity of CNCs with the diameter of 520 and 280 nm are approximately 6.5 104 and 8 105Um, respectively. In summary, the TEM images prove that the structure of the CNCs used in our experiment is polycrystalline-amorphous, which is different from the Chiu's bidirectional CNCs and Tang's coin-in-coin CNCs [15,16]. Resistivity of the four CNCs with increasing temperature is shown in Fig. 7. The results demonstrate that the CNC has better crystallinity, the resistivity is smaller. The CNCs can be treated as a kind of material with short-range ordering while long-range disordering structure. This can be attributed to that the bigger crystalline size lead the short range periodic to be extended, and hence causes a trend to be an ordered system. However, for the disorder degree of interfacial atoms, the system presents the general disordered features. Electron transports within the crystalline grains without barrier, while at the edge of the grains, it has to overcome the energy barrier to hop to another site in the adjacent grain. The hopping mode is dependent on the circumstance temperature. When temperature is changed, the hopping mode is transferred from one to another, and the transition zone has a relation with the crystallinity. From transition zones of the four CNCs #1, #2, #3 and #4 we discussed above, the results demonstrate that when a CNC has a better crystallinity, the lattice
Fig. 6. TEM image of a single CNC with a line diameter of (a) 280 nm; (b) 520 nm. Insets are the corresponding Electron diffraction patterns.
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Acknowledgments This work was supported by the National Natural Science Foundation of China (Nos. 11274055 and 61137005) and the Program for Liaoning Excellent Talents in University.
Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.carbon.2015.11.025.
References
Fig. 7. The resistivity of four CNCs: #1, #2, #3, #4.
orientation trends to be regular and the hopping length becomes shorter, so that the model transition zone becomes narrower, meaning that electron hopping is easy to transform from one mode to another when the circumstance temperature is changed. 4. Conclusions We have carried out four-probe measurements over a wide range of temperature from 4 to 300 K to investigate the conductivity in a single polycrystalline-amorphous CNCs. It is observed that the temperature-dependent conductivity of single CNCs closely related to its crystallinity. The better crystallinity results in a better conductivity. Meanwhile, the resistivity data suggest that the dominant conduction mechanism is thermal activation, NNH and VRH conduction processes. From 300 to 60 K, the electrical conductivity of the investigated CNCs exhibits a combination of the thermal activation model and NNH model, while from 46 to 4 K it follows VRH model. Specifically, the transition mechanism changes from Mott VRH (46e30 K) to EeS VRH (20e4 K). The transition zones of transmission mechanisms are changed with the crystallinity of CNCs at different circumstance temperature. A better crystallinity of CNC results in a narrower transition zone, which makes electron hopping easy to transform from one mode to another. Finally, the polycrystalline-amorphous CNC shows a semiconductor characteristic which can be regarded as a promising semiconductor and are expected for being used in various electronic devices.
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Contents lists available at ScienceDirect
Carbon journal homepage: www.elsevier.com/locate/carbon
Electrical conductivity of single polycrystalline-amorphous carbon nanocoils Yanming Sun a, Chenwei Wang a, Lujun Pan a, *, Xin Fu a, Penghe Yin b, Helin Zou b a b
School of Physics and Optoelectronic Technology, Dalian University of Technology, No. 2 Linggong Road, Ganjingzi District, Dalian, 116024, PR China Key Laboratory for Micro/Nano Technology and Systems of Liaoning Province, Dalian University of Technology, Dalian, 116024, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 August 2015 Received in revised form 15 October 2015 Accepted 7 November 2015 Available online 11 November 2015
Polycrystalline-amorphous carbon nanocoils (CNCs) have been synthesized by thermal chemical vapor deposition. The electrical conductivity of a single CNC is investigated over a wide temperature range from 4 to 300 K by employing the four-probe method. It is found that the smaller the line diameter of the CNC, the bigger the size of the crystalline grain, which results in the better crystallinity and conductivity. Moreover, the temperature behavior of r(T) reveals that the intrinsic electric-transport mechanisms through a single helical CNC are mainly due to a combination conduction processes of the thermal activation, the nearest-neighbor hopping, and variable range hopping. Meanwhile, the dominate electron transport mechanisms crossover from one mode to another with the circumstance temperature. Notably, it follows Mott variable range hopping and EfroseShklovskii variable range hopping at low temperature. The model transition zones which are related to the crystallinity of the CNCs are also discussed in each temperature regime. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction The great development of nanoelectronic devices and mechanical miniaturization, is attracting more basic researches on how nanostructures affect the properties of these materials [1e4]. Carbon nanocoils (CNCs) have received much concern in recent years, as its peculiar helical morphology which consists of polycrystalline-amorphous structure. It shows potential applications in field-emission devices, electromagnetic wave absorbers and micro-electromechanical systems [5e7]. Therefore, it is a promising and valuable subject to develop a simple way to study the mechanism of conductance in this special spiral carbonaceous structure. There inevitably exist disordered factors, such as the state of impurities and defects, in the process of preparation of lowdimensional system of electronic materials and components. The electronic states of disordered systems are localized, which affects the electronic transport characteristics of low-dimensional materials and devices. The localization length of the wave-functions increases with increasing the degree of distortion, while
* Corresponding author. E-mail address: [email protected] (L. Pan). http://dx.doi.org/10.1016/j.carbon.2015.11.025 0008-6223/© 2015 Elsevier Ltd. All rights reserved.
decreases with increasing the crystalline grain size [8e10]. It indicates that the disorder degree of interfacial atoms and irregular crystalline grain size affect the distributions of electronic localization in low-dimensional nanometer materials. The helical polycrystalline-amorphous CNCs are a hybrid of sp2 grains and sp3 amorphous structures [11,12], the physical properties of CNCs may differ from both of sp2 structured carbon nanotubes (CNTs) and sp3 structured amorphous carbon nanofibers (CNFs). The electrical conductivity of CNCs is higher than that of amorphous CNFs at 300 K due to the better crystallinity of CNCs [13]. The optoelectronic applications of CNCs such as field-emission devices or infrared sensors relied strongly on electron transportation mechanism in the CNCs. Shen et al. measured the electrical properties of a single carbon microcoil with a double helix structure by a standard fourprobe technique [14]. The results revealed that the temperature dependence of the resistance above 13 K was in accordance with the Mott variable range hopping (VRH), whereas below 13 K, it obeyed the Efros-Shklovskii VRH. Chiu and Tang et al. measured the electrical properties of quasi one-dimensional disordered CNCs [15,16]. They analyzed the electric transport with an electron hopping length of about 5e50 nm inside the disordered carbon coils. Most recently, Ma et al. reported that the resistivity of carbon nanocoils annealed from 300 to 2900 K was decreased with increasing the annealing temperature [17]. The average activation
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energy for electron hopping in the annealed CNCs was decreased from 11 to 4.2 meV with the increase of annealing temperature because of the improvement of the crystallinity. To date, there are few studies addressing the systematic discussions on the resistivity behavior of the CNCs with a polycrystalline-amorphous structures over a broad range of low temperature. In this paper, therefore, we measured the temperature dependence of resistivity, r(T), of the single polycrystallineamorphous CNCs over the temperature from 4 to 300 K based on the designed four-probe method. An in-depth physical explanation for the temperature dependence of electrical conduction mechanism in this specifically polycrystalline-amorphous structure was studied. The results revealed that the conductivity of the CNCs increases with the crystalline grain size, and the mode of electron hopping changes with the circumstance temperature.
The length of the CNC was 130 mm, the line diameter of the CNC was 380 nm, and the screw pitch was 480 nm. The electrical measurement was performed by an Agilent B2902A source meter. Fig. 1(b) shows the partial enlarged SEM image of the four-electrode sample. The white arrow indicates the critical point, from which the CNC is fixed firmly by the multilayered electrodes. It is also obvious to see that the surface of the CNC between the two electrodes is clear so that there is no other factors to affect the electrical conductivity of the CNC. The IeV curves at fixed temperatures of 4 and 150 K were tested, as shown in Fig. 1(d). It is found that the IeV curves performed at different temperatures show a linear behavior and the resistance of the CNC at 4 K is larger than that at 150 K. The good linearity of the IeV curves reveals that the CNC contacts well with the electrodes. 3. Results and discussion
2. Experimental The CNCs used in the experiment were synthesized by the thermal chemical vapor deposition (CVD) using Fe/Sn as catalyst. Fe2(SO4)3/SnC solution was selected as precursor, the mole ratio of Sn to Fe was approximately 1:60. It is known that the melting point of Sn is 231.89 C. In order to prevent the Sn from vaporization during heating in Ar, the prepared Sn/Fe catalyst films were calcined at 710 C for 30 min in air. Finally, CNCs were synthesized in a thermal CVD system at 710 C for 30 min by introducing Ar and C2H2 gases. The flow rate ratio of Ar to C2H2 was maintained at 23:3 [18]. Fig. 1(c) shows the diagram of an interdigitated four-probe module. In a typical process, four-probe Ti/Pt/Cr multilayer electrodes were prepared on SiO2/Si wafers by combining lithography with magnetron sputtering technique. Firstly, the micron-sized Ti/ Pt (30/100 nm) electrodes were patterned on a Si substrate which was capped with a 500 nm thick SiO2 layer. Secondly, a drop of CNCs dispersed ethanol solution was deposited on the metallic electrodes, ensuring that one of CNCs was located across a fourelectrode unit. Finally, one more lithography and magnetron sputtering process was conducted to deposit another layer of Ti electrode (30 nm) exactly on the multilayer electrodes of Pt/Cr, insuring that the CNC was sandwiched between the two layers of Ti and Pt electrodes. In this way, the CNC could be fixed firmly and contacted well with multilayered electrodes, which greatly reduced the contact resistance. The measured resistivity was thus the intrinsic one of the individual CNC. Fig. 1(a) shows a typical SEM image of one complete fourelectrode sample. The gap between two electrodes was 10 mm.
Fig. 2(a) shows the measured resistivity of the CNC by ramping down the temperature from 300 to 4 K. It clearly demonstrates that the resistivity changes little with the temperature below 60 K. Notice that the resistivity decreases monotonically with increasing temperature between 300 and 60 K, as would be expected for semiconductors. The conductivity of polycrystalline-amorphous nanostructure are related to many factors. And different mechanisms have different activation energies, a model to analyze the conductive mechanism is established as following equation: 1 r1 ðTÞ ¼ r1 A þ rB ;
(1)
where r is the temperature-independent resistivity, rA is the resistivity with a combination of the thermal activation model and the nearest-neighbor hopping (NNH) model, and rB is the resistivity with VRH model. r1A can be expressed by
DE1 DE2 1 þ r1 r1 1 exp A ðTÞ ¼ r0 exp kT kT DE 3 þ r1 ; 2 exp kT
(2)
where k is the Boltzmann constant, and DE is the thermal activation energy describing the electronic conduction in three temperature regimes between 300 and 60 K DE1, DE2 and DE3 present three contributions given by equation (2) which are corresponding to the extended states of conduction bands, localized states conduction at band tails and NNH conduction processes, respectively. The electrons are thermally excited from the Fermi level to the conduction
Fig. 1. (a) SEM image of a single CNC in the four-probe electrode. (b) Partially enlarged SEM image of the single CNC. (c) Diagram of the four-electrode module. (d) IeV characteristics of the single CNC at 4 and 150 K.
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Fig. 2. (a) Resistivity r of a single CNC plotted against 1000/T between 300 and 4 K. The inset shows ln(r) as a function of 103/T to estimate the activation energy DE between 300 and 60 K. The Solid lines (bed) are three parts of the best-fit lines with the thermal activation equation. The details in three temperature regimes are shown in (bed).
bands, where a huge amount of unoccupied, extended states with high mobility are available [19]. lnr as a function of 1000/T for each temperature regime is plotted in Fig. 2(bed). From the slope values, DE1 z 29.7 meV, DE2 z 5.7 meV, and DE3 z 1.3 meV are obtained. With the reducing temperature, the thermal energy kBT becomes too small to excite the electrons. As a consequence, the NNH conduction of electrons eventually becomes the dominant charge transport process around 60 K. The electrons are excited from the occupied levels to nearby, or the nearest-neighbor, unoccupied levels. Therefore, the activation energy presents the following rule: DE3 < DE2 < DE1. The electrons transport in this special structure have two kinds of mechanisms: repeatedly trapped mechanism and hopping mechanism. The electrons not only have diffusion motion but also fall to the band tails of localized states. The trapped electrons need to be thermally excited again to participate in the transport. Therefore, in the process of the movement of electrons tend to experience multiple collapsing and re-exciting, and form the diffusion transport. At the higher temperature, the electrons can be excited to the energy states above the edge of the conduction band EC, which forms the extended states of conduction bands (DE1). When the temperature is low, the electrons can only be excited to the band tail states of the EC, and then transition from a localized state into another localized state by the help of phonons, which forms localized states conduction at band tails (DE2). At lower temperature, the electrons can only jump from the energy states below the Fermi level EF to the adjacent empty state above the EF with the help of phonons, forming the nearest-neighbor hopping conduction (DE3). As a consequence, the rule of the activation energy (DE3
conductive mechanism is no longer meet the equation (2). Hence, the transportation of internal electrons is analyzed with the theory of variable range hopping (VRH). The temperature dependence of CNCs can be fitted with the following equation:
r1 B ðTÞ
¼
r1 0
" # T0 1=d exp ; T
(3)
For disordered systems, when d ¼ 4, it can be explained by Mott VRH of (non-interacting) localized electrons, where T0 is the characteristic Mott temperature. When d ¼ 2, it can be explained by Efros-Shklovskii (EeS) VRH model, where T0 is the characteristic EeS temperature. Briefly, electrons would prefer to hop between non-nearest-neighboring localized states which have lower energy difference. The localized states correspond to the sp2 grains in CNCs. Fig. 3 shows the temperature dependence resistivity of a single CNC ranges from 46 to 4 K. There is a conductive mechanism transformation from the NNH conduction to the VRH conduction processes between 60 and 46 K. Notice that the electrons transportation in the CNCs through localized states exhibits a crossover from three-dimensional Mott VRH model to one-dimensional EeS VRH model. It can be attributed to the fact that the polycrystallineamorphous CNCs is highly disordered. Fig. 3(a) indicates the resistivity of a single CNC with the temperature region from 46 to 28 K. The result is agreed with the theory of Mott VRH. It can be explained by Mott VRH which is based on phonon-helped tunneling of carriers between localized states with energies near the Fermi level. With the increasing temperature, electrons obtain enough energy from phonons and the number of empty states between nearest neighbors for a certain occupied state leads, so that the electron hopping mechanism transfers from Mott VRH to NNH mode which is described by equation (2) [20,21]. Three-
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Fig. 3. The resistivity of a single CNC at low temperature (46 e 4 K) with different transmission regimes (a) Four-terminal resistances as a function of T1/4, and the solid curves are fit to the expression (3) with d ¼ 4. (b) Four-terminal resistances as a function of T1/2, and the solid curves are fit to the expression (3) with d ¼ 2.
dimensional Mott-David VRH model also observed in carbon material with similar helical structures, such as the single microcoiled carbon fiber [22,23]. The temperature ranged from 4 to 16 K, the resistivity in CNC follows the relation lnr ~ T1/2 which is based on the EeS VRH model, as shown in Fig. 3(b). It refers to that the electroneelectron interaction is an important issue dominating the electron transport processes in the CNC. The results above suggest that the model analysis elicits a basic understanding of the electric transport through localized states which exhibits a crossover from Mott to EeS VRH inside the disordered CNC. As the CNC used in experiment is polycrystalline-amorphous structure, it is inferred that the electron transportation is affected by the degree of disorder and the crystalline grain size of the system. And the electron transportation within the crystalline grain is unimpeded but impeded at the edge of the crystallines, which will be further discussed in the following. The depletion of the density of the states at low energy demonstrates a signature of eee interaction, which plays an important role in the electron transportation, as shown in Fig. 4. The curve is almost linear at 30 K, but it becomes nonlinear at 5 K which further validates the existence of a model transition between the two
regions [24,25]. As we know that Coulomb gap occurs in the localized states due to long-range Coulomb interactions between the electrons in different centers of localization near the Fermi energy. Therefore, the Coulomb gap DC ¼ 0.09 meV based on Efros and Shklovskii theory is calculated [26,27]. In the experiment, the resistivity of the CNCs have been measured over the temperature range from 4 to 300 K. For convenience, the samples used above is labeled as #1. And another three reference samples are labeled as #2 #3 #4. The morphologies of the four carbon nanocoils are shown in Fig. S1. The specific parameters of the four different CNCs, the line diameter, coil diameter, and screw pitch are shown in Table 1. The curves in Fig. 3(a) and (b) are linear, and this is agreed with the Mott VRH and EfrosShklovskii (EeS) VRH model theory, respectively. For the reference samples #2, #3 and #4, the results show similar behavior as #1. From approximately 300 to 60 K and 46 to 4 K, there presents a transition area with two conductive mechanisms in each temperature region. For the four CNCs #1, #2, #3 and #4, the lengths of the transition zone from Mott to EeS VRH model are 12 K, 16 K, 18 K and 19 K, and from NNH to VRH model are 14 K, 20 K, 23 K and 25 K, respectively. It indicates that the CNC with different nanostructure, shows different transmission mechanisms and the length of the transition zone in each transmission mechanism dominated area is different at low temperature. Fig. 5(a) is the Raman spectra of the four CNCs #1, #2, #3 and #4 used in the experiment to characterize the degree of disorder and graphitization. Two main peaks are observed in the Raman spectra: one at approximately 1322 cm1, known as the D-band, which originates from structural defects in carbon materials, and the other at approximately 1593 cm1, known as the G-band, which originates from the graphitic structure of carbon materials. Lorentz and BWF functions are adopted to fit the D and G peaks, respectively [28]. Fig. 5(b) is the value of ID/IG (the area ratio of the D to G peaks) with the diameter of the four CNCs. Smaller values of ID/IG indicates the larger graphite crystallites and a higher degree of graphitization [12]. The value of ID/IG increases with the increasing line diameter, as shown in Fig. 5(b). The results above suggest that the CNC with a
Table 1 The line diameter, screw pitch, length of the four CNCs.
Fig. 4. The differential conductance measurement of the CNC as a function of Bias voltage for 4 and 30 K.
Coil
Line diameter (nm)
Coil diameter (nm)
Screw pitch (mm)
#1 #2 #3 #4
280 470 500 520
537 886 876 752
2.05 1.55 1.25 0.9
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Fig. 5. (a) The Raman spectra of the four CNCs. (b) Values of ID/IG of the four CNCs.
larger diameter, the crystal lattice trends to be more irregular which means the degree of disorder is larger, so the degree of graphitization is smaller. For the CNCs with a smaller diameter, it has more regular crystal lattice and a higher degree of graphitization. Due to this, the CNC shows a better resistivity. In Fig. 5(b), among the four CNCs, the minimum value of ID/IG is about 1.9, and its diameter is about 0.28 mm; while the maximum value of ID/IG is approximately 2.6, and its diameter is about 0.55 mm. The ratio of ID to IG is inversely proportional to the average crystalline size according to the empirical formula of ID/IG ¼ C(l)/La, where C(l) is a constant at the certain laser wavelength (l) and La indicates the size of sp2 grains [28e30]. For the exciting laser of 632.8 nm used in our Raman system, C (632.8) can be calculated by the formula of C(l) ¼ 12.6 þ 0.033 l [29], which is equal to 8.28 nm. For the four samples, La is 4.35, 3.68, 3.35, 3.21 nm, respectively. Hence, with increasing the line diameter, the size of sp2 grain becomes small, and the orientation of the crystallite is disordered. The structures of the single CNCs is confirmed by TEM images shown in Fig. 6. Fig. 6(a) is the TEM image of a single CNC with a line diameter of 280 nm, which shows the graphitization of the CNC. From the TEM image, the lattice is partially orderly. The red square shows the size of the grain which is approximately 5 nm. It is in accordance with the La 4.35 nm. Fig. 6(b) shows the diameter of the CNC is approximately 520 nm. The red square shows the crystalline size is approximately 3.4 nm, which is in accordance with the La 3.35 nm. The electron diffraction patterns shown inset of Fig. 6 provide more visual representations of the degree of crystallinity. The inner and outer hallows near the innermost ring corresponds to the graphite (002) and (101) planes, respectively. The hallow
diffraction pattern (inset, Fig. 6(b)) indicates the poor crystallinity of the CNC. From the arc-shaped diffraction spots of the (002) plane (inset, Fig. 6(a)), the main orientation of the graphite (002) plane can be inferred to be perpendicular to the dashed line, which indicates the improved crystallinity. Based on large number of experiments, the statistical average electrical conductivities are calculated (the CNCs are regarded as ideal and untwisted) [31]. The resistivity of CNCs with the diameter of 520 and 280 nm are approximately 6.5 104 and 8 105Um, respectively. In summary, the TEM images prove that the structure of the CNCs used in our experiment is polycrystalline-amorphous, which is different from the Chiu's bidirectional CNCs and Tang's coin-in-coin CNCs [15,16]. Resistivity of the four CNCs with increasing temperature is shown in Fig. 7. The results demonstrate that the CNC has better crystallinity, the resistivity is smaller. The CNCs can be treated as a kind of material with short-range ordering while long-range disordering structure. This can be attributed to that the bigger crystalline size lead the short range periodic to be extended, and hence causes a trend to be an ordered system. However, for the disorder degree of interfacial atoms, the system presents the general disordered features. Electron transports within the crystalline grains without barrier, while at the edge of the grains, it has to overcome the energy barrier to hop to another site in the adjacent grain. The hopping mode is dependent on the circumstance temperature. When temperature is changed, the hopping mode is transferred from one to another, and the transition zone has a relation with the crystallinity. From transition zones of the four CNCs #1, #2, #3 and #4 we discussed above, the results demonstrate that when a CNC has a better crystallinity, the lattice
Fig. 6. TEM image of a single CNC with a line diameter of (a) 280 nm; (b) 520 nm. Insets are the corresponding Electron diffraction patterns.
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Acknowledgments This work was supported by the National Natural Science Foundation of China (Nos. 11274055 and 61137005) and the Program for Liaoning Excellent Talents in University.
Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.carbon.2015.11.025.
References
Fig. 7. The resistivity of four CNCs: #1, #2, #3, #4.
orientation trends to be regular and the hopping length becomes shorter, so that the model transition zone becomes narrower, meaning that electron hopping is easy to transform from one mode to another when the circumstance temperature is changed. 4. Conclusions We have carried out four-probe measurements over a wide range of temperature from 4 to 300 K to investigate the conductivity in a single polycrystalline-amorphous CNCs. It is observed that the temperature-dependent conductivity of single CNCs closely related to its crystallinity. The better crystallinity results in a better conductivity. Meanwhile, the resistivity data suggest that the dominant conduction mechanism is thermal activation, NNH and VRH conduction processes. From 300 to 60 K, the electrical conductivity of the investigated CNCs exhibits a combination of the thermal activation model and NNH model, while from 46 to 4 K it follows VRH model. Specifically, the transition mechanism changes from Mott VRH (46e30 K) to EeS VRH (20e4 K). The transition zones of transmission mechanisms are changed with the crystallinity of CNCs at different circumstance temperature. A better crystallinity of CNC results in a narrower transition zone, which makes electron hopping easy to transform from one mode to another. Finally, the polycrystalline-amorphous CNC shows a semiconductor characteristic which can be regarded as a promising semiconductor and are expected for being used in various electronic devices.
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