Electrical characteristics of multiwalled carbon nanotube arrays and influence of pressure

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It has been shown recently that the resistance of array decreases with increasing array diameter and temperature, 15,16 and NT arrays can be suitable for low resistance interconnects.8][19][20] NT arrays can be suitable for low resistance interconnects as the resistance decreases as the diameter of the arrays is increased. 15Here, we have reported two-probe measured transport properties of millimeter long arrays of multiwalled NTs (MWNTs) in the view point of technological applications and fundamental understandings.The current increase rapidly with voltage before the breakdown occurs.No current saturation is observed.Simultaneous measurements of current and temperature at one end of the arrays suggest that the rapid increase of current is due to Joule heating.The current through the array, the threshold voltage and the breakdown temperature are found to increase with decreasing pressure.

II. EXPERIMENT
Millimeter long MWNTs with an average diameter of 70 nm are prepared by a simple pyrolysis technique as described elsewhere. 21A pyrolysis temperature of 1100 NTs.Taking the advantage of the long NTs, the electrical contact has been made to the array using conventional method.Different arrays are taken on oxidized silicon or glass substrates and thin copper wires were connected to either side of the array with the help of conducting silver epoxy.Schematic of the device used for the IV characteristic studies is shown in Fig. 1(a).Shown in Fig. 1(b) is the scanning electron microscopy (SEM) micrograph of a suspended array device.The IV characteristics have been recorded at ambient and vacuum conditions using Keithley 237 source measurement unit.Further more, the temperature at the end of the array at ambient condition is measured by a thermocouple.Fig. 1(c) shows the SEM micrographs of NTs taken at a higher magnification.Transmission electron microscope (TEM) and high resolution TEM (HRTEM) micrographs are shown in Figs.1(d)-1(f) that confirms the multiwalled nature of NTs with an outer diameter of 70 nm.SEM images of a different MWNT arrays are shown in Figs.1(g) and 1(h).It is evident that MWNT arrays stretch without any apparent interruption the entire length of the array.
We have investigated more than 30 supported and suspended arrays of different diameter in between 10 and 500 μm and length between 700 and 1000 μm.We have also investigated few arrays of length 1600 μm and the results are almost identical.Thin copper wires were connected on either side of the nanotube arrays with the help of conducting silver epoxy.The current (I) -voltage (V) characteristics have been recorded using Keithley 237.

III. RESULTS AND DISCUSSION
IV curve of an array in air ambient is shown in Fig. 2(a).The current increases rapidly with voltage, reaches a maximum followed by a gradual decrease of current.The gradual decrease of current is due to the sequential destruction of individual tubes.Similar results have also been observed for individual NTs. 4,11,13 Te rapid increase of current with voltage has also been observed for experiments performed at different pressures (10 -6 Torr range) as shown in Figs.2(b)-2(d).This indicates that the nature of the IV characteristics does not change with pressure or ambient.However, the current through the bundle increases with decreasing pressure and is believed to be due to the removal of the adsorbed gas on the surface of NTs.This observation is in contrast with the previous reports on short individual SWNTs, 22,23 but in accordance with the reports on SWNT array, 24 and on carbon nanofibers. 25With the lowering of pressure, the conductance increases due to releasing of electrons as the adsorbed oxygen is removed from the nanotube surface. 25One of the interesting observation is that the threshold voltage is 5.5-6.5 V for measurements carried out at low pressures as shown in Fig. 2(b), while it is 2.3-3.5 V at ambient.Measurements carried out at constant pressure (2x10 -5 mbar) at different time interval are almost independent as shown in Fig. 2(d).
As the measurement of temperature at the middle is not easy, we measured the temperature at one end of the arrays during the experiments at ambient and found that not only the current but also temperature T rises with applied voltage.The rise in temperature (T-T 0 ) measured at one end of the array is plotted as a function of VI as shown in Fig. 3 for both supported and suspended arrays.Here, T 0 is the room temperature and is 298 K in our case.It has been established that the rise in temperature (T-T 0 ) at the middle of a conductor is related to VI through the thermal conductivity κ as: 26 where L is length and A is area of the array.Similar relation is expected at the end as well.It is evident from Fig. 3 that the rise in temperature is found to be linear with VI which demonstrates the Joule's law.It may be noted that the rise in temperature with voltage is almost identical for both supported and suspended arrays.Most of the NTs are above the surface even for the supported arrays and as a result, a small difference is observed for supported and suspended arrays.As (T-T 0 ) varies linearly with VI, T is expected to vary with voltage as V 2 .It is found that T versus V 2 is linear in most of the cases and a typical plot is shown in the inset of Fig. 3.The temperature at either end of the arrays is represented by T(V)=300+aV 2 .Similar variation is also expected at the middle of the arrays for different pressures.It is evident from Fig. 2(a) that breakdown occurs at a voltage of 2.35 V and it is well known that the temperature required for the breakdown to occur in air is 900 K. Therefore, the variation of temperature at the middle is assumed to be T=300+108V 2 .Similary, a=49 for a threshold voltage of 3.5 V. Taking these values of a and the observed threshold voltage is 5.5-6.5 V in vacuum, the breakdown temperature is estimated to be more than 2000 K which is in good agreement with reported results. 27o ensure that the current enhancement is due to the temperature, we have measured the temperature (T) at one end of the contact and current (I) through the array as a function of time (t) simultaneously.Typical I-t and T-t curves are shown in Fig. 4. It may be noted that the current as well as the temperature is higher for higher biases.Furthermore, the variation of I and T with t is  identical that indicates that the non-linear variation of current with voltage [Fig.2] is a temperature effect.
In our case, the length of the arrays is much larger than the mean free path of electrons suggesting diffusive conduction.The absence of current saturation suggests that electron-phonon scattering might be reduced or irrelevant.Moon et al. 13 have argued that the reduced electron-phonon scattering could be the existence of the intershell coupling.It is known that more number of shells in NTs contribute as the applied field is increased. 6Zener tunneling is also known to result in high current 11 in NTs with large diameter/voltage.The other possibility is the Joule heating.Joule heating is shown to be responsible for the current saturation as well as for the negative differential conductance in supported and suspended metallic NTs, respectively. 28,29 t is evident from Fig. 3 that temperature increases with increasing applied voltage.The increase in current might be due to the thermionic emission. 30,31 he advantage of Joule heating is that the device performance as gas sensor, flow sensor, pressure sensor, etc. can be improved without external heating.It can also be used as a heater material for localized heating.
SEM image of a device used for transport studies is shown in Fig. 5(a).A crack in the array which is a consequence of partial breakdown is seen that occurs when a high voltage is applied to the device and causes the current to decrease as evident from Fig. 2(a).SEM images taken at higher magnification are also shown in Figs.5(b) and 5(c).Shown in Figs.5(d) and 5(e) are the SEM images of broken arrays which indicates that breakdown does not occur at the middle.Some researchers believe that Joule heating is responsible for the catastrophic breakdown of NTs, 32,33 while other researchers believe that Joule heating alone cannot explain the breakdown of NTs. 4,34 er all, breakdown occurs when the voltage is increased.Breakdown away from the middle has also been reported. 27,35 e temperature profile is shown to be dependent on the length as well as on the type of NTs. 26,29,36,37 Th temperature is maximum at the middle of short metallic NTs and therefore, the breakdown is expected at the midpoint as shown in Fig. 6(a). 15,16 he temperature distribution is almost uniform along the length of long metallic NTs as heat removal mainly takes place through the electrodes [Fig.6(a)].It has been shown recently that the temperature distribution is asymmetric for semiconducting NTs as shown in Fig. 6(b) and the breakdown is highly probable in this maximum temperature region. 36,37 owever, the maximum temperature region shifts toward the middle as the tube diameter increases and the breakdown was expected accordingly [Fig.6(b)].As the average tube diameter is 70 nm in our case, the breakdown was expected to occur at the middle.In contrast, the breakdown occurs near one end, especially the end with narrower array diameter [Figs.5(d)

IV. CONCLUSION
In conclusion, we have reported that the current increases rapidly with applied voltage for NT arrays and no current saturation is observed before the breakdown.The current through the array, the threshold voltage and the breakdown temperature are found to increase with decreasing pressure.

FIG. 1 .
FIG. 1.(a) Schematic of the device used for the IV characteristic studies.(b) SEM micrograph of a suspended NT array device with an array diameter of ∼50 μm and length ∼600 μm.(c) SEM micrograph of the array taken at higher magnification.(d) TEM micrograph of an NT.(e) HRTEM micrograph of an NT and (f) is the magnified image of the region marked by a rectangular box in (e).(g,h) SEM images showing that MWNT arrays stretch without apparent interruption.

FIG. 2 . 2 )FIG. 3 .
FIG. 2. (a) Typical I-V characteristic of an array in ambient.(b) Typical I-V characteristic of an array at 2x10 -5 mbar.(c) I-V characteristics at different pressures.(d) I-V characteristics of a different array at ambient and repeated measurements at 2x10 -5 mbar.Lines are the guide to the eye.

FIG. 4 .
FIG. 4. (a) I-t and (b) T-t curves at 1.8 V. (c) I-t and (d) T-t curves at 2.0 V.The solid lines are guide to the eye.

FIG. 5 .FIG. 6 .
FIG. 5. (a-c) SEM image of a suspended NT array device with an array diameter of 450 μm and length 700 μm taken after the partial breakdown and different regions.(d) SEM image of a broken array of length 1.6 mm and diameter 50 μm.(e) SEM image of another broken array.