Effect of different vacuum on field emission of carbon nanotube arrays

Abstract

In this paper, the electron-molecule collision ionization is added to field emission under non-vacuum conditions, and the change of emission current caused by vacuum adjustment in field emission of carbon nanotubes is explained. The field emission current density equation under non-vacuum conditions is established. Through the theoretical analysis and the processing of experimental data, it can be concluded that when other variables are controlled unchanged, the change of pressure will affect the concentration of gas molecules in the air and the collision probability with electrons, then the density of emission current is changed. The study has a certain reference value for the application of field emission in low vacuum and atmospheric pressure.

Keywords

Field emission carbon nanotube arrays vacuum degree

1. Introduction

With the development of AC speed regulation technology, the application of variable frequency motor is more and more extensive. But at the same time, the bearing current of the variable frequency drive motor will cause the bearing abnormal and damage. Bearing current will cause electrical corrosion on the inner raceway of bearings, and long-term electrical corrosion will cause strip corrosion marks on the inner raceway of bearings [1,2].

Installing carbon brush on the bearing and grounding the connecting wire is an effective method to eliminate the bearing current (Fig. 1). However, factors such as temperature and humidity in the working environment will destroy the good contact between the carbon brush and the bearing when the motor runs for a long time, and then reduce the life of the motor.

Fig. 1.

Motor and grounding brush.

According to the above questions, the idea of using field emission non-contact discharges to relieve bearing current is proposed. The carbon nanotube arrays is fixed on the electrode fixing ring instead of carbon brushes, and the metal anode is fixed on the bearing. The bearing current will be eliminated by field emission.

Carbon nanotube, also known as Bucky Tube, is a new type of carbon structure, which can be seen as a seamless, hollow tube made of graphite sheets curled in one direction [3]. Carbon nanotubes are generally divided into single-walled carbon nanotubes (SWNTs) and multi-walled carbon nanotubes (MWNTs). They have the characteristics of small diameter and large aspect ratio which can be regarded as quasi-one-dimensional materials [4,5]. It has special electronic band structure, different configurations have different band gaps. In addition, it also has obvious quantum effect, low emission threshold, high emission current density and high field stability.

Therefore, the field emission characteristics of carbon nanotube arrays under different vacuum conditions are studied. The influence of collision ionization between electrons and gaseous molecules on field emission characteristics is proposed. The field emission characteristics of carbon nanotube arrays under non-vacuum condition and the feasibility of applying field emission technology to non-vacuum environment is discussed.

2. Field emission principle

Field emission refers to the phenomenon that electrons are released from the cathode material due to the change of the height and width of the barrier on the material surface under the action of strong electric field. When a large amount of electrons are continuously released from the cathode surface to the anode, we can obtain a continuous field emission current [6,7]: $\begin{eqnarray}\displaystyle J=aE^{2}\exp \left(-\frac{b}{E}\right). & & \displaystyle\end{eqnarray}$ (1) And in the upper part, $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle a=1.42\times 10^{-6}{\varphi}^{-1}\exp (9.89{\varphi}^{-1/2})\end{eqnarray}$ (2) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle b=6.53\times 10^{7}{\varphi}^{-3/2}.\end{eqnarray}$ (3) Among them φ is the work function of the emitter.

Fig. 2.

Field emission schematic diagram.

It can be seen from this law that the field emission current density is related to the work function of the material itself and the electric field intensity, that is, these two variables will determine the field emission current density.

3. Study on different distance and vacuum

3.1. Influence of distance on field emission

According to the field emission theory, the field emission current density is not only related to the work function of the conductor material, but also to the electric field intensity of the emitter. The distance between the emitter tip and the anode becomes the main factor affecting the constant voltage field emission because the size of carbon nanotubes reaches the quantum level [8–10].

At the same voltage, the potential distribution and electric field intensity distribution between carbon nanotube fibers and anode metal plates in air with distances of 20, 15, 10 and 5 microns were simulated by software (Fig. 3). The voltage is 200 V. The simulation results are compared and analyzed.

Fig. 3.

Electric potential and electric field intensity at different distances.

The simulation results show that the electric field strength increases with the decrease of the gap due to the existence of carbon nanotubes. At a distance of 20 microns, the maximum electric field is concentrated at the tip. With the decrease of the gap, the region where the maximum electric field intensity is located gradually extends to the anode until the “path” of the maximum electric field intensity is formed when the carbon nanotubes are connected to the end plate [11].

Fig. 4.

Comparison of three distances.

The comparison of the volt-ampere characteristics of carbon nano fiber clusters obtained from field emission experiments at different distances is shown in Fig. 4.

However, the premise of the formula is that the air density in the launch zone is low and the gas molecule content is low under high vacuum [12]. When electrons are emitted from the cathode, they will basically move directly to the anode without colliding with gas molecules, thus forming a stable current [13,14].

3.2. Influence of vacuum on field emission

In order to calculate the emission current under low vacuum, we need to consider the collision between electrons and gas molecules. Therefore, the electrons emitted from cathode are divided into three types:

No collision, directly moving to the anode.

Collision ionization with molecules.

Collision with molecules, but no ionization.

Firstly, the average collision frequency of electron and gas molecule is calculated. In formula (4), r_m is the diameter of gas molecule, r_e is the electron diameter, n_m is the molecular number density, v_e is the average velocity [14]. $\begin{eqnarray}\displaystyle Z=n_{m}\cdot {\pi}(r_{m}+r_{e})^{2}\cdot v_{e}. & & \displaystyle\end{eqnarray}$ (4)

The diameter of the electron (10⁻¹⁵ m) is smaller than that of the gas molecule (The molecular diameter of oxygen is 2.96 ×10⁻¹⁰ m, and the molecular diameter of nitrogen is 3.04 ×10⁻¹⁰ m.). According to the ideal gas equation of state P = nkT, the formula (4) could be simplified as follows in formula (5). $\begin{eqnarray}\displaystyle Z\approx {\pi}r_{m}^{2}v_{e}n_{m}={\pi}r_{m}^{2}v_{e}\frac{P}{kT}. & & \displaystyle\end{eqnarray}$ (5)

And the mean free path of electrons can be calculated: $\begin{eqnarray}\displaystyle {\lambda}=\frac{v_{e}}{Z}=1/[{\pi}(r_{m}+r_{e})^{2}n_{m}]\approx 1/[{\pi}r_{m}^{2}n_{m}]=1\hspace{-2.0pt}\left/\left[{\pi}r_{m}^{2}\frac{P}{kT}\right]\right.. & & \displaystyle\end{eqnarray}$ (6)

It can be seen that the average free path of electrons is infinite when P is close to 0 (near vacuum), so collision ionization will not occur basically.

However, the average free path of electrons can be calculated by formula (6) under standard atmospheric conditions (1 ×10⁵ pa) and room temperature (300 K), which is 1.46 ×10⁻⁶ m, much less than the distance from stable field emission (1 ×10⁻⁴ m). Therefore, the collision between electron and gas molecule can’t be neglected in the air.

The electron density of the electrons emitted from the cathode without collision is shown in formula (7): $\begin{eqnarray}\displaystyle n_{d}=n_{e}\cdot e^{-d/{\lambda}}. & & \displaystyle\end{eqnarray}$ (7)

In the formula (7), n_e is the electron density emitted by the cathode and d is the distance between the cathode and the anode. Since current is defined as the velocity of directional charge flows, the current density can be written as: $\begin{eqnarray}\displaystyle J=e\cdot n_{e}\cdot v_{e}. & & \displaystyle\end{eqnarray}$ (8)

Therefore, the current density formed by the movement of collision-free electrons to the anode are as follows: $\begin{eqnarray}\displaystyle J_{1}=aE^{2}\exp \left(-\frac{b}{E}\right)\cdot e^{-d/{\lambda}}. & & \displaystyle\end{eqnarray}$ (9)

The electron density (free path less than d) of the collision is shown in formula (10): $\begin{eqnarray}\displaystyle n_{b1}=n_{e}\cdot (1-e^{-d/{\lambda}}). & & \displaystyle\end{eqnarray}$ (10)

The necessary condition for collision ionization is: $\begin{eqnarray}\displaystyle Eqx\geq W_{i}. & & \displaystyle\end{eqnarray}$ (11)

In formula (11), W_i is the ionization energy of gas molecules.

The ionization energies of the main components (nitrogen and oxygen) in the air are 15.6 ev (nitrogen) and 12.5 ev (oxygen). The average ionization energy is W_i =14.79 ev. The experimental distance is 100 μm and the voltage is 200 V. Under these conditions, x_i can be calculated as: $\begin{eqnarray}\displaystyle x_{i}=\frac{W_{i}}{Eq}=7.4\times 10^{-6}∼\text{m}. & & \displaystyle\end{eqnarray}$ (12)

The electron density of collision ionization is in formula (13): $\begin{eqnarray}\displaystyle n_{b2}=n_{b1}\cdot e^{-x_{i}/{\lambda}}=n_{e}\cdot (1-e^{-d/{\lambda}})\cdot e^{-x_{i}/{\lambda}}. & & \displaystyle\end{eqnarray}$ (13)

When the electrons reach the anode, the electron density will increase to n_b3 in formula (14): $\begin{eqnarray}\displaystyle n_{b3}=n_{b2}\cdot e^{{\alpha}d}=n_{e}\cdot (1-e^{-d/{\lambda}})\cdot e^{-x_{i}/{\lambda}}\cdot e^{{\alpha}d}. & & \displaystyle\end{eqnarray}$ (14)

In the formula (14), 𝛼 is the ionization coefficient. $\begin{eqnarray}\displaystyle {\alpha}=(1/{\lambda})\cdot e^{-x_{i}/{\lambda}}. & & \displaystyle\end{eqnarray}$ (15)

Only the electrons with a free path greater than x_i can collide and ionize.

Therefore, the current density of electrons formed by collision ionization can be obtained as follows: $\begin{eqnarray}\displaystyle J_{2}=aE^{2}\exp \left(-\frac{b}{E}\right)\cdot (1-e^{-d/{\lambda}})\cdot e^{-x_{i}/{\lambda}}\cdot e^{{\alpha}d}. & & \displaystyle\end{eqnarray}$ (16)

Since field emission is the main cause of the ionization of cathode surface, we assume that the ionization of cathode surface caused by colliding positive ions is not considered. In summary, the emission current in the air is: $\begin{eqnarray}\displaystyle J=J_{1}+J_{2}=aE^{2}\exp \left(-\frac{b}{E}\right)\cdot [e^{-d/{\lambda}}+(1-e^{-d/{\lambda}})\cdot e^{-x_{i}/{\lambda}}\cdot e^{{\alpha}d}]. & & \displaystyle\end{eqnarray}$ (17)

4. Field emission experiment

In order to investigate the effect of vacuum on field emission performance, a field emission experiment platform was established, as shown in Fig. 5.

Carbon nanotube arrays were selected as emission materials, and polished copper sheets were used as anode materials. Field emission characteristics of different cathode materials were compared by adjusting the degree of vacuum.

Fig. 5.

Field emission vacuum device.

Field emission charges were obtained in the air, 0.07 MPa, 0.04 MPa, 0.02 MPa and 0.005 MPa conditions under the condition of keeping the distance between anode and cathode about 0.1 mm.

The experimental data were input to MATLAB and the volt ampere characteristic curve was obtained. We found that the field emission current amplitude of carbon nanotube arrays can reach about 0.6 mA, the switching-on voltage is about 90 V, and the emission current can maintain a relatively stable value when the air pressure reaches 0.005 MPa, as shown in Fig. 6.

Fig. 6.

Air pressure 0.005 MPa.

Fig. 7.

Air pressure 0.02 MPa.

After adjusting the air pressure to 0.02 MPa, the emission current amplitude is reduced to nano-ampere level, the maximum is 2 nA, and the switching-on voltage rises to about 150 V, as shown in Fig. 7. Compared with 0.005 MPa, the emission effect is reduced by three orders of magnitude.

When the air pressure is adjusted to 0.04 MPa, as shown in Fig. 8, the field emission current amplitude decreases by an order of magnitude compared with 0.02 MPa, and the starting voltage of the emission current is delayed to about 170 V.

Fig. 8.

Air pressure 0.04 MPa.

Fig. 9.

Air pressure 0.07 MPa.

Fig. 10.

Air pressure 0.1 MPa (Air).

The air pressure was again adjusted to 0.07 MPa, the current amplitude was found to be about 0.2 pA, and the volt-ampere characteristic curve was not stable, so it was speculated that the field emission does not end when the voltage reached 200 V, as shown in Fig. 9.

Finally, when the vacuum chamber is opened and exposed to air, the current amplitude increases slightly relative to 0.07 MPa, and sparks are generated between carbon nanotube arrays and copper sheets after several field emission experiments. It is concluded that the spark discharge is due to the field evaporation effect of the tip of carbon nanotube arrays under strong electric field after a series of experiments. The volt-ampere characteristic curve is linear in the range of 70 V to 170 V, as shown in Fig. 10, and the field emission effect is not as good as that in vacuum.

Under the same working conditions, the experimental results obtained by repeated experiments under air conditions are basically the same, and spark discharges eventually occur. After consulting the data, we believe that the spark discharge is due to the field evaporation effect of the tip of nanotube arrays under strong electric field, which changes the emission distance and promotes the field emission.

In view of this problem, we will continue to explore it in the future research.

5. Conclusion

Aiming at the field emission problem of carbon nanotubes, a method to study the field emission characteristics of carbon nanotube arrays under low vacuum by changing the vacuum condition is proposed. The following conclusions are drawn:

(1) By introducing free path into the theory of gas ionization, the formula for calculating the current density of field emission under non-vacuum conditions is obtained. The formula shows that in the field emission process, the emission distance, the electric field intensity, the emitter work function, the gas pressure and the temperature will all affect the field emission current under non-vacuum conditions.

(2) For the carbon nanotube arrays, when the environment is close to the vacuum, the field emission results obtained by the experiment are the best. As the air pressure increases, the initial voltage of the field emission gradually increases, the current of field emission decreases from 8 ×10⁻⁷ A at 0.005 MPa to 2.5 ×10⁻¹⁰ A in the air, and the effect of field emission decreases gradually.

(3) In view of the fact that the field emission can occur in non-vacuum state, this experiment has a high reference value for the application of field emission in non-vacuum state.

Footnotes

Acknowledgements

This work was supported by National Natural Science Foundation of China (No. 51577122).

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