Electric field-dependent conductivity achieved for carbon nanotube-introduced ZnO matrix

Abstract

In contrast to the carbon nanotube (CNT)-introduced insulating matrix, the electric conductivity of CNT-introduced ZnO matrix is not only dependent on the CNT content, but is also dependent on the applied electric field when the CNT content approaches the electrical percolation threshold. From the viewpoint of circuit interconnections in a microscope, there are two conductor–semiconductor contact structures equivalent to Schottky junctions being series connected between the adjacent CNTs, forming electrical field-dependent impedances between adjacent CNTs in the CNT-introduced ZnO matrix. Based on the electrical percolation theory, the CNT-introduced ZnO matrix may be seen to be a comprehensive circuit composed of a large amount of electrical field-dependent impedances connected in series and in parallel. On increasing the applied electric field, these impedances would be decreased, leading to an inevitable decrease in the resistivity of the CNT-introduced ZnO matrix. In essence, the electric field-dependent conductivity for a CNT-introduced ZnO matrix is a macroscopic quantum tunneling effect. From a practical perspective in electronic technologies, such a distinctive performance in electrical conductivity would have promising applications.

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1. Introduction

In conventional composite conductive materials, the electrically conductive components, including metal powders, semiconductor powders and carbon derivatives of different morphologies, achieve electrical conductivity in the insulating composite matrixes (polymers in general).^1–3 As indicated in the electrical percolation theory, with increases in the amount of conductive component approaching the electrical percolation threshold, a three-dimensional conductive network begins to form in the composite matrix and the resistivity of the composite conductive material decreases dramatically.^2,4,5 In contrast to conventional conductive components, carbon nanotube (CNT) is distinctive due to its unique properties.^6–8 The conductive characteristics of CNT-introduced insulating matrixes have no differences in contrast to those of conventional composite conductive materials, except that a lower electrical percolation threshold is achieved.

In our research, based on the electrical percolation theory of composite conductive materials and related theories in solid state physics, multi-walled CNTs of a certain amount were introduced into zinc oxide (ZnO, a typical semiconductor material) and the electric field-dependent conductivity for the CNT-introduced ZnO matrix was identified to have been achieved. Moreover, the physical mechanisms of the distinctive performances have been theoretically investigated for the CNT-introduced ZnO matrix. From the practical perspective of electronic technologies, the electric field-dependent conductivity of a CNT-introduced ZnO matrix would have promising applications and our research work is of significant importance.

2. Experimental section

2.1. Preparation of material samples

Y₂O₃ sample was synthesized using the sol–gel method. 35 g of Y(NO₃)₃·6H₂O was dissolved in dilute nitric acid to form an aqueous solution; 170 g of citric acid (C₆H₈O₇·H₂O), 200 ml of glycol (C₂H₆O₂) and 10 g of polyethylene glycol (HO(CH₂CH₂O)_nH, molecular weight > 20 000) were then added into the aqueous solution. The turbid suspension was stirred and heated at 90 °C for 5 h to form a gel, the gel was preheated at 300 °C for 2 h and then sintered at 600 °C for 2 h to obtain a Y₂O₃ sample in micrometer magnitude.

The micron-sized Y₂O₃ sample was attached to In₂O₃ by the hydrolysis of indium isopropoxide (In[OCH(CH₃)₂]₃). Y₂O₃ sample, distilled water and isopropyl alcohol were added to the alkoxide solution of In. During churning of these reactants at 80 °C, hydrolysis and condensation occurred. After the solution was dried and sintered at 600 °C for 8 h, In₂O₃-introduced Y₂O₃ sample was formed.

In the preparation of multi-walled CNT-introduced Y₂O₃ sample, a certain amount of ethanol solution of multi-walled CNTs, which had been sufficiently dispersed by powerful ultrasonic oscillation, was added in the aqueous solution during the preparation of the Y₂O₃ sample in the sol–gel method. The final sintering process was performed at 800 °C for 6 h in a nitrogen atmosphere.

In the preparation of multi-walled CNT-introduced ZnO sample, 16.5 g of zinc acetate (Zn(Ac)₂·H₂O) was dissolved in 75 ml of deionized water to form an aqueous solution, and then 10 g of ammonium citrate ((NH₄)₃C₆H₅O₇) was added to the solution. The solution was heated to 70 °C, and then 125 ml of ethanolic solution of multi-walled CNTs, which had been sufficiently dispersed by powerful ultrasonic oscillation, was added in the solution with stirring and heating. After 2 h, a certain amount of peptizing agent (NH₃·H₂O) was added, and Zn(OH)₂ gel was formed after a long time. After the gel was dried and sintered at 800 °C for 5 h in a nitrogen atmosphere, multi-walled CNT-introduced ZnO sample was formed.

The adopted multi-walled CNTs have diameters of ∼8 nm and lengths of 10–30 μm with an electrical conductivity of ∼1.5 × 10⁴ S m⁻¹ and a specific surface area of ∼500 m² g⁻¹.

2.2. XRD characterization and resistivity measurements

The crystalline phase of multi-walled CNT-introduced ZnO samples was identified using a Rigaku-D/max 2500 X-ray diffractometer using Cu Kα radiation (λ = 0.15405 nm).

In the resistivity measurements, each sample was made into a cylindrical shape with diameter 2r = 13 mm and thickness d = 2 mm under a pressure of 1.5 × 10² MPa. Electrodes were made by Al deposition on both the sides of each sample. The resistance was measured with a 769YP-24B megohmmeter and the resistivity was calculated using the following formula:

3. Results and discussion

3.1. General features of conventional composite conductive materials

According to the electrical percolation theory of composite conductive materials, suitable conductive filler, as a separate component, may be introduced to improve the conductivity of a composite matrix. In this experiment, yttrium oxide (Y₂O₃) was adopted as the typical composite matrix with high resistivity, and indium oxide (In₂O₃) was adopted as the conventional conductive component owing to its favorable compatibility in the preparation of composite conductive materials with inorganic matrixes.⁹ The experiment indicated that the resistivity of the In₂O₃-introduced Y₂O₃ matrix decreases gradually with increasing In₂O₃ content when the In₂O₃ content is relatively lower, and decreases dramatically above the electrical percolation threshold P_th (P_th ≈ 25 wt% for In₂O₃-introduced Y₂O₃ matrix), and then decreases slightly with further increasing of In₂O₃ content, as shown in Fig. 1. The characteristics of resistivity–conductive content relation for the In₂O₃-introduced Y₂O₃ matrix are typical for the conventional composite conductive materials.^9,10 The electrical percolation theory indicates that when the conductive content increases to the electrical percolation threshold, a three-dimensional conductive network begins to form in the matrix.^10–13 As for the formation of a conductive network, the dominant mechanisms lie in the physical contacts between the conductive fillers. Moreover, the quantum tunneling effect would play a role in the formation of a conductive network, especially when the size of the conductive component is in nanometer magnitude.¹⁰ For a certain composite conductive material, the electrical percolation threshold P_th is nearly independent of the composite matrix and largely determined by parameters such as the conductivity, size and morphology of the conductive component.¹⁰

Fig. 1 Resistivity–In₂O₃ content relation for In₂O₃-introduced Y₂O₃ matrix.

3.2. Low electrical percolation threshold and weak tunneling effect in the CNT-introduced insulating matrix

In contrast to the conventional conductive components, CNT is distinctive due to its unique properties. Consequently, distinctive performances may be expected for CNT-introduced composite materials. CNTs are rolled graphite sheets with diameters in nanometer magnitude and lengths in micrometer magnitude, possessing a one-dimensional morphology of rather larger aspect ratios. CNTs can be classified as single-walled CNTs and multi-walled CNTs possessing remarkable mechanical strength, reliable chemical stability, high melting point and excellent electrical conductivity.^6–8 In contrast to the single layer structure of single-walled CNTs, the structure of multi-walled CNTs is cylinders inside cylinders. The resistivity–conductive content relation for multi-walled CNT-introduced Y₂O₃ matrix is similar to those of conventional composite conductive materials, as shown in Fig. 2. However, the electrical percolation threshold, i.e., the CNT content at which the three-dimensional conductive network begins forming in the composite matrix, is rather low (P_th ≈ 1.5 wt% in the experiment), being at least an order of magnitude lower than conventional conductive components. In theory, the electrical percolation threshold of CNTs in the composite matrix may be lower, as reported in the literature.^3,14,15 The low electrical percolation threshold of CNTs originates from the unique structure and excellent conductivity of CNTs (>150 s cm⁻¹). The one-dimensional morphology of CNTs with large aspect ratios (>1000) would make them an excellent conductive component in the composite matrix. Although the directions of CNTs would be distributed randomly in the matrix, each has a component parallel to the applied electric field. Consequently, from the viewpoint of charge transmission, the one-dimensional morphology of CNTs is apparently a merit.^16–18 As an excellent conductive component, multi-walled CNTs are more suitable to be introduced into a composite matrix than single-walled CNTs. The reason lies in the fact that if the electric conductivity of the outer layer of a multi-walled CNT deteriorates on combining with composite matrixes owing to the ultra-large specific surface area of the CNT (>500 m² g⁻¹), the inner layer would conduct independently, ensuring the conductive function of the CNT.

Fig. 2 Resistivity–CNT content relation for multi-walled CNT-introduced Y₂O₃ matrix.

As pointed out in the literature, the quantum tunneling effect may play a role in the formation of a conductive network when the size of the conductive component is in nanometer magnitude.¹⁰ In principle, for a certain conductive component and a certain composite matrix, the tunneling effect would be apparent when the average distance of adjacent conductive fillers is decreased and the applied electric field is increased in the composite conductive material. Moreover, the tunneling currents between the adjacent conductive fillers would increase super-linearly with the increasing of the applied electric field, leading to the current nonlinearity in the composite conductive material. However, in the experiments, the electric field–current relation for the multi-walled CNT-introduced Y₂O₃ matrix has been identified to be linear. The electric field–current linear relation is different for different CNT contents, corresponding to different resistivity of multi-walled CNT-introduced Y₂O₃ matrix. The linearity in the electric field–current relation indicates that the tunneling effect is negligibly weak, and the physical contacts between the conductive fillers should be the dominant mechanisms in the formation of a conductive network. In principle, the weak tunneling effect, which is independent of CNT content in CNT-introduced Y₂O₃ matrix, originates from the high potential barriers between the CNTs and the insulating matrix, and the height of the potential barriers should be adjustable by the application of different composite matrices.¹⁹

3.3. Electric field-dependent conductivity for a CNT-introduced ZnO matrix

To improve the quantum tunneling effect in conductive mechanisms in CNT-introduced composite material, the CNT-matrix potential barriers should be lowered. In the experiments, the insulating matrix was substituted by a ZnO semiconductor. ZnO is a traditional semiconductor material; it has important and promising applications in electronic technology.^20–22 Fig. 3 shows the XRD patterns of the ZnO sample and the CNT-introduced ZnO sample formed in the sol–gel processes. The XRD patterns were all indexed to the typical hexagonal wurtzite phase of ZnO, indicating that the introduction of CNTs has not affected the lattice structure of ZnO. Based on the XRD data and Scherrer's equation, the size of the CNT-introduced ZnO monocrystal in the CNT-introduced ZnO sample can be determined to be in the nanometer magnitude. However, the scanning electron microscopy data indicated that the sizes of the CNT-introduced ZnO sample were in micrometer magnitude. Consequently, it can be inferred that the as-formed CNT-introduced ZnO sample has a polycrystalline structure.

Fig. 3 XRD patterns of ZnO sample and CNT-introduced ZnO sample formed using sol–gel processes.

In contrast to the CNT-introduced insulating matrix, the conductive performance of the CNT-introduced ZnO matrix is distinctive because its conductivity (or resistivity) is not only dependent on CNT content, but it is also dependent on the applied electric field when the CNT content is in a certain range. As shown in Fig. 4, when the CNT content in multi-walled CNT-introduced ZnO matrix is far below the electrical percolation threshold (P_th ≈ 1.5%), the electric field dependence of the resistivity may be neglected; the CNT-introduced ZnO matrix has a relatively higher resistivity, which is independent of the applied electric field. However, for a CNT content approaching the electric percolation threshold P_th, the resistivity of the CNT-introduced ZnO matrix is decreased and the decrease in resistivity becomes progressively drastic (dR/dE is enlarged) with the increasing applied electric field, until ultimately the resistivity tends to be a constant of a rather lower value (dR/dE decreases to 0). Moreover, for a higher CNT content near the electrical percolation threshold, the resistivity of the multi-walled CNT-introduced ZnO matrix decreases more rapidly (dR/dE is larger) with an increasing applied electric field, and the variation range of the electric field corresponding to the drastic decrease of resistivity is reduced. In addition, when the CNT content is higher, exceeding the electric percolation threshold, the resistivity of the CNT-introduced ZnO matrix begins to be rather lower, reverting to a constant that is independent of the applied electric field.

Fig. 4 Electric field–resistivity relations for different CNT contents in multi-walled CNT-introduced ZnO matrix.

So far, the electric field-dependent conductivity for the CNT-introduced ZnO matrix was identified to have been achieved owing to the distinctive performances, proper content of CNTs and the irreplaceable functions of the semiconductor matrix.

3.4. Related mechanisms in the electric field-dependent conductivity for CNT-introduced ZnO matrix

In general, when a high electric field is applied, forming a negative electrical potential on a conductor surface, the electrons inside the conductor may penetrate the conductor-vacuum potential barrier, emitting out into the vacuum by the quantum tunneling effect.^23–26 As shown in Fig. 5, the electric field on the conductor surface is E_local; the work function of the conductor is ϕ₀ = E₀ − E_F, where E₀ is the vacuum level and E_F is the Fermi level of the conductor. Taking into account the image potential relative to the conductor surface, the conductor-vacuum potential barrier may be formulated to be

Fig. 5 Conductor-vacuum potential barrier in the local electric field.

The field emission current density can be quantitatively investigated using the Fowler–Nordheim formula, which may be given in a simple and approximate form as follows:

where ϕ is the height (maximum of E_barrier(x)) of the potential barrier.^24,25 It can be seen in formula (2) that J would be larger when ϕ is lower and E_local is higher. It has been reported that to achieve a considerable field emission current density, the electric field on the conductor surface should be in the order of 10⁷ V cm⁻¹. This is a rather higher electric field and is difficult to achieve.²⁵

CNTs have diameters in nanometer magnitude and lengths in micrometer magnitude, possessing one-dimensional morphology of rather larger aspect ratios in the order of 10³ and conductivity in the order of 10⁴ S m⁻¹. The work function of CNT is 4.6 eV. Owing to the unique structure, lower work function and excellent conductivity, CNT has distinctive field emission properties, which originate from the remarkable field enhancement effect.^27–30 Under the stimulation of the applied macroscopic electric field E_macro, a much higher local electric field E_local would be initiated on the top of the CNT. A field enhancement factor is involved, defined as

In general, β is the function of aspect ratio, the larger the aspect ratio, the higher the factor β. The previous research indicated that β may be considerably higher (e.g., in the order of 10³), and as a result the CNTs are capable of exhibiting a considerable current density up to 1 A cm⁻² under a lower macroscopic electric field in the order of 10⁴ V cm⁻¹.

In the CNT-introduced composite matrix, the orientations of CNTs should be distributed randomly and the configurations of the adjacent CNTs form noncoplanar lines predominantly. When the macroscopic electric field E_macro is applied in the matrix, the body electric potential is different for different positions in the direction of E_macro. However, owing to the high electrical conductivity of CNTs (∼1.5 × 10⁴ S m⁻¹), the space occupied by a CNT is an equipotential body in the matrix and the corresponding electric potential is a constant. The constant electric potential of a CNT should be equal to the body electric potential at the middle point of the CNT when the CNT is not presented in the matrix. As shown in Fig. 6, a and b stand for two adjacent CNTs with different orientations in the matrix, and oo′ is their common perpendicular with the length d; d represents the average distance of adjacent CNTs in the matrix. The middle points of a and b are A and B, respectively. The component of AB in the direction of E_macro is l. Consequently, the electric potential difference between a and b should be

ΔV_ab = E_macrol (4)

Fig. 6 Two adjacent CNTs in the applied macroscopic electric field. The illustration shows the electric field lines between adjacent CNTs.

The average electric field between these two adjacent CNTs (i.e., between o and o′) should be

The local electric field E_local at the sidewalls of CNTs (o or o′) may be considerably higher than Ē_oo′, as indicated by the electric field lines in the illustration in Fig. 6, and this originates from the thin sizes of CNTs. Consequently, a local field enhancement factor is involved having the following relation:

It is apparent that relative to the macroscopic electric field E_macro, the field enhancement factor for the two adjacent CNTs is .

According to solid state physics, a conductor–semiconductor contact structure is a Schottky junction with a certain potential barrier. Taking into account the image potential relative to the conductor surface, the conductor–semiconductor (n-type) potential barrier should be formulated to be

where ϕ₀ is the work function of the conductor, x′ is the electron affinity of the semiconductor, N_D is the donator concentration in the semiconductor and x_d is the width of the potential barrier, as shown in Fig. 7. Owing to the presence of intrinsic defects, ZnO is an n-type semiconductor. The energy gap of ZnO is 3.37 eV and the electron affinity energy of ZnO is 2.1 eV.^20,21 In the CNT-introduced ZnO matrix, from the viewpoint of circuit interconnections in the microscope, there are two equivalent conductor–semiconductor contact structures with equivalent potential barriers connected in series between the adjacent CNTs with a small distance. In Fig. 6, the two conductor–semiconductor contact structures and their potential barriers are located at o on the sidewall of b and o′ on the sidewall of a. However, when the macroscopic electric field is applied in the CNT-introduced ZnO matrix, the impedance characteristics of these two conductor–semiconductor contact structures should be different. In view of the direction of the macroscopic electric field in Fig. 6, the contact structure at o′ on the sidewall of a is under forward bias, while the contact structure at o on the sidewall of b is under reverse bias. As a result, higher impedance is dominant for the conductor–semiconductor contact structure at o, largely determining the series impedance characteristic between the two adjacent CNTs.

Fig. 7 Potential barrier of conductor–semiconductor (n-type) contact structure in the equilibrium state.

For a Schottky junction under forward bias, such as the conductor–semiconductor (n-type) contact structure at o′ on the sidewall of a, the impedance characteristic should be in accordance with diffusion theory or thermionic emission theory. The alternative applicability of these two theories lies in whether or not the mean free path of an electron in the semiconductor is larger than the width of the potential barrier.¹⁹ However, for a Schottky junction under reverse bias, such as the conductor–semiconductor (n-type) contact structure at o on the sidewall of b, the impedance characteristic should be in accordance with field emission theory. Consequently, the impedance characteristic of the conductor–semiconductor contact structure under reverse bias should be qualitatively investigated using the Fowler–Nordheim formula. It should be noted that when the local electric fields are same, the conductor–semiconductor (n-type) potential barrier should be lower and narrower than the conductor-vacuum potential barrier due to the electron affinity energy of the semiconductor, while they should have the same characteristics in field emission.¹⁹

From the viewpoint of statistics, when the CNT content is increased near the electric percolation threshold P_th in the CNT-introduced composite matrix, the average distance d between the adjacent CNTs is decreased, tending toward 0 (i.e., the adjacent CNTs tend to contact each other). Consequently, the field enhancement factor may be very large. In this case, the local electric field E_local on the sidewalls of CNTs (at o and o′), given in formula (6), would increase swiftly with the increasing E_macro. Owing to the increase of E_local at o, the field emission current of the conductor–semiconductor contact structure (under reverse bias) at o on the sidewall of b would increase. Based on the Fowler–Nordheim formula, the derivative of the field emission current density may be given as

It can be seen in formula (8) that the field emission current at o, i.e., the current between the adjacent CNTs, should increase super-linearly (increase of J becomes progressively drastic) with the increasing E_local. Herein, it should be noted that the super-linear increase of J means the tunneling impedance at o on the sidewall of b is not a constant; it is decreasing with the increasing E_local. Moreover, the relatively lower impedance of the conductor–semiconductor contact structure (under forward bias) at o′ on the sidewall of a is simultaneously decreased owing to the increase of E_local at o′. It can be expected that when the applied macroscopic electric field E_macro is high, leading to a rather higher E_local, then the impedance between a and b, i.e., the series impedance of the two conductor–semiconductor contact structures between the adjacent CNTs, should be substantially decreased.

So far, the related mechanisms in the electric field-dependent conductivity for CNT-introduced ZnO matrix may be clarified. In essence, the electric field-dependent conductivity for the CNT-introduced ZnO matrix is a macroscopic quantum tunneling effect. The CNT-introduced ZnO matrix with CNT content approaching the electrical percolation threshold may be seen as a three-dimensional disconnected network of CNTs interacting with a semiconductor matrix. The CNTs with excellent electrical conductivity and large aspect ratios act as conductive channels and the close areas of adjacent CNTs in the matrix are equivalent to electric field-dependent impedances. In fact, there must be a large amount of adjacent CNTs in contact or apart from each other in the matrix; in these cases, the impedances between the adjacent CNTs should be seen as infinitesimal and infinite, respectively. The CNT-introduced ZnO matrix may be treated as a comprehensive circuit composed of a large amount of electrical field-dependent impedances connected in series and in parallel. With the increasing applied macroscopic electric field in the CNT-introduced ZnO matrix, these impedances would be decreased, leading to the inevitable decrease in the resistivity of the CNT-introduced matrix. Moreover, the higher the CNT content (around the electric percolation threshold) in the matrix, the smaller the average distance between the adjacent CNTs, and the larger the field enhancement factor. As a result, the range of the electric field corresponding to the decreasing resistivity of the CNT-introduced ZnO matrix is reduced, as indicated in the experiments. In addition, with respect to the preparation of the CNT-introduced ZnO matrix, the sufficient dispersibilities of multi-walled CNTs in the ZnO matrix and the sufficient combination between multi-walled CNTs and ZnO matrix should be prerequisites for the stable and distinctive performances of a CNT-introduced ZnO matrix.

4. Conclusion

The electric field-dependent conductivity was achieved for a multi-walled CNT-introduced ZnO matrix with CNT content approaching the electrical percolation threshold. The CNT-introduced ZnO matrix may be seen as a three-dimensional disconnected network of CNTs interacting with a semiconductor matrix. From the viewpoint of circuit interconnections in the microscope, there are two conductor–semiconductor contact structures being connected in series between adjacent CNTs, and the corresponding impedance between the adjacent CNTs is decreased with the increasing applied electric field. The CNT-introduced ZnO matrix may be treated as a comprehensive circuit composed of a large amount of electrical field-dependent impedances connected in series and in parallel. With the increasing applied macroscopic electric field in the CNT-introduced ZnO matrix, these impedances connected in series and parallel would be decreased, leading to the inevitable decrease in resistivity of the CNT-introduced matrix.

Acknowledgements

This work was supported by the Program of Educational Department in Heilongjiang Province of China (no. 12543070). We thank XiaoHua Tian and Qian Cheng (School of Materials Science and Engineering, Harbin Institute of Technology) for their warm-hearted help in the experiments.

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