1. Introduction

Direct current (DC) discharge and laser-induced breakdown (LIB) are two established methods of generating artificial plasmas. Historically, William Crookes invented his DC discharge-based tubes in 1875, and studies on LIB go back to at least 1960s [1]. However, microplasma, which typically refers to a nonthermal plasma confined to submillimeter dimensions, began to appear in the literature in the mid-90s and has been used in biological and environmental applications, gas and surface analysis, and ultraviolet radiation sources [2, 3]. In a DC discharge system, a gas is energized by applying high DC voltage between two conductive electrodes to create plasma. In such systems, the breakdown voltage is usually defined as the voltage at which the current between the electrodes rapidly increases. On the other hand, in a laser-induced plasma (LIP) system, the nonlinear interaction between a high power focused pulsed laser with gases creates an opaque conducting plasma. Since typically there is no current measurement in an LIP system, the breakdown due to LIB is usually defined as a certain concentration of electrons (e.g. greater than 10¹⁵cm⁻³) or a certain degree of fractional ionization (e.g. 0.1 %) [1]. For self-consistency, some information about DC discharge, LIP, plasma sustainment, and plasma characterization has been provided in the appendix.

DC discharge and LIB have been separately studied extensively. Also, studying the interaction between pulsed lasers (ranged from long pulses to the state of the art 10 fs pulses) and plasmas is not new [4, 5]. However, in this work, our focus was on CW laser and its effects on microplasma’s V_BD and V_Q. In some applications, such as switching, V_Q becomes as important as V_BD. We envision using the results of this work in designing practical electro-optically activated microplasma devices, in which the electron-hole plasma (solid state) is replaced with electron-ion plasma (gas phase). These devices will benefit from the advantages of both vacuum and semiconductor electronics. An ideal device in this approach is activated by a combination of low-power CW laser illumination and small DC bias [6].

2. The measurement setup

The measurement setup, shown in Fig. 1, was designed to measure V_BD and V_Q of 3-D microplasmas, as well as their emission spectra. Plasma parameters such as electron density, temperature, and degree of ionization can be obtained from its emission spectrum. A proper imaging system was also included to visualize the experiments and to control the laser spot location during the study. V_BD and V_Q of the microplasma were measured using the relaxation oscillator technique as in [7]. In the relaxation oscillator technique, the microplasma was driven by the circuit shown in Fig. 1(a), which created a sawtooth voltage waveform across the microplasma due to the difference between V_BD and V_Q. Clearly, the extremes of the sawtooth waveform were V_BD and V_Q of the microplasma. Figure 2 shows a sample of the sawtooth waveform across the microplasma. Besides simplicity, accuracy, and repeatability, the main advantage of using such a relaxation oscillator technique is the simultaneous measurement of V_BD and V_Q. The electrodes of the microplasma had tip diameters comparable to the gap size in order to implement 3-D microplasmas as opposed to the more studied 1-D microplasmas in which the electrodes’ dimensions are much larger than the gap size. It was discussed in [7] that, unlike a 1-D configuration (also known as plate-plate structure), Paschen’s law does not apply to a 3-D microplasma (also known as point-point geometry).

 

Fig. 1 a) relaxation oscillator circuit, b) the 3-D printed plastic fixture to focus the laser beam onto the microgap, c) the measurement setup.

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Fig. 2 The sawtooth voltage waveform across the microplasma with the gap size of 1000 µm and at pressure 0.5Torr. V_BD and V_Q are extremums of the sawtooth as specified.

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Two different electrodes were used during the study: 1) cylindrical tungsten electrodes with a diameter of 635 microns, and 2) conical, gold plated tungsten electrodes with tip diameters of 10 microns. The electrodes were mounted on two nanopositioners and a plastic 3-D printed fixture was used to align the gap between the two electrodes into the focal point of a parabolic reflector, as shown in Fig. 1(b). The groove in the center of the fixture (see the appendix) accommodated a gauge sheet metal with a thickness of 700 microns for the initial alignment of the electrodes. The nanopositioners then moved the electrodes to the desired gap size. The parabolic reflector in Fig. 1(b) had focal length of 2 inches, which could focus the applied laser beam (diameter 1 mm) onto a spot in the gap with a focal diameter of 52 microns (at wavelength 800 nm), using the approximate wave optics equation (after numerous assumptions regarding the perfect wavefront quality, near-field intensity distribution, and alignment accuracy) d = 4λ f/(πD), where f is the focal length, λ is the wavelength, and D and d are the beam diameters before and after focusing, respectively. Throughout the experiments, the laser power is set to be p = 1Watt which leads to irradiance of 50kW/cm² at the focal point. The fixture was exposed to argon gas with different pressures inside a chamber, and the applied DC voltage was transmitted to the fixture using a coaxial cable to prevent any plasma formation around the feed wires inside the chamber. Two pieces of hookup wires with equal lengths fed the electrodes from the coaxial terminal on the fixture to keep the geometry as symmetrical as possible.

Figure 1(c) depicts the measurement setup schematically. The input laser beam was generated by a tunable (700 – 1000nm) continuous wave Ti:Sapphire laser pumped optically by a 10Watts green diode laser. The laser beam was successively transmitted through a beam sampler (for power measurement/adjustment), a laser chopper, a 50-50 beam splitter, and a series of mirrors (for adjusting the laser spot location) before it became focused on the microplasma using the parabolic reflector. At the same time, as indicated in Fig. 1(c), a second parabolic reflector collected the emission spectrum of the microplasma from the 50-50 beam splitter and fed it to a spectrometer through an optical fiber. The microplasma was being imaged through an optical viewport on the chamber using a 0.5X Telecentric lens (170mm working distance) with inline illumination and a camera. Some pictures of the measurement setup, as well as the 3D printed fixture, have also been included in the appendix.

3. Results and discussions

Figure 3(a) shows the gold and the tungsten electrodes inside the chamber both before and after applying voltage across them. The voltage and the pressure in Fig. 3(a) were 1000V and 100Torr, respectively, which kept the plasma in the oscillatory state range of argon plasma. In the oscillatory state, as described in [7], due to the high intensity of metastable atoms, V_BD and V_Q are different, and a relaxation oscillator circuit can create a sawtooth voltage across the microplasma. Before we proceeded to study the laser effect, the microplasma parameters, such as electron temperature and density and the degree of ionization were approximated from the measured emission spectrum shown in Fig. 3(b). Note that the emission spectrum varied as the pressure, the applied voltage, and the relaxation oscillator circuit changed. However, we only intend to present a rough approximation of the studied microplasma parameters, which will not affect our conclusions.

 

Fig. 3 a) gold plated tungsten electrodes with a tip diameter of 10µm (top), and tungsten electrodes with a tip diameter of 635µm (bottom), before and after plasma ignition, b) emission spectrum of the microplasma at p = 100Torr for the relaxation oscillator circuit parameters V_DC = 1kV, R = 2MΩ, and C = 70nF.

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The electron’s temperature can be obtained using the two-line comparison method as [8, 9] (see also the appendix)

The electron density can be approximated using [10]

The calculated plasma parameters were only approximations, and no curve fitting has been applied to the emission line (usually a voigt distribution profile is fitted on the emission line in order to obtain the line width). Knowing the electron density, the degree of ionization can be easily found using α = n_i/(n_i + n₀), in which n_i and n₀ are the number of ions and neutral atoms, respectively. Assuming the plasma had only singly ionized atoms, and therefore n_i = n_e, we could use the equation of state for an ideal gas to find n₀ as n₀ = P/(k_BT), in which P is the pressure in Pascal units. Using the temperature 300K and the pressure P = 100Torr≃ 13kPa led to n₀ = 3.2 × 10¹⁸ cm⁻³ and the degree of ionization α = 13%, which is highly ionized.

The average conductivity of the argon microplasma could also be easily found from the average current. Considering the applied voltage V_DC = 1kV, the oscilloscope (including the used voltage isolator) resistance R = 2MΩ, and the measured average current I_DC = 340 µA, the resistance of the microplasma was R_plasma = 940kΩ. The current measurement was performed using a source-meter unit (Keithly 2410), which also provided V_DC.

As the first experiment, the laser spot was swept from the anode to the cathode with a constant pace, and the plasma threshold voltages were plotted in Fig. 4. The experiment was repeated using two different electrodes and gap sizes: a) the gold electrodes with a gap size of 200 µm and b) the tungsten electrodes with a gap size of 400 µm. It can be seen from Fig. 4 that the laser reduced both V_DC and V_Q if the electrodes were at least partially illuminated (note that the laser spot was 50 µm). In fact, when the laser was spotted only inside the gap, V_BD and V_Q remained unchanged even after switching the laser off. This suggests the CW laser can only interact with metals, rather than the plasma species, even at relatively high pressures. It was obvious that the CW laser could not cause any multiphoton or tunnel ionization due to the lack of sufficient power. However, it is rather interesting that the 1W laser could not participate in the plasma ionization even through inverse Bremsstrahlung absorption [12]. Changing the pressure and the laser frequency did not change the results either. The irradiance of the focused laser spot on the gold electrode is not enough for plasma generation either. Because, the roughness of the electrode’s surface can enhance the incoming electric field with a factor on the order of 50 (due to surface enhanced Raman scattering). Therefore, the resulting enhanced irradiance is still far below the required intensities for LIB (i.e. 10¹¹W/cm²). From Fig. 4, it appears that V_BD and V_Q were affected more when the laser illuminated the anode. However, we are convinced that the reason simply was the better focusing of the laser on the anode due to the measurement setup. Also, since the laser photons had lower energy than the work function of the electrodes, the thermal absorption remained as the dominant mechanism by which the laser interacted with the electrodes. Another evidence for the heating effect was the asymmetrical pattern of the laser effect on V_BD and V_Q as the laser was swept from the anode to the cathode. A simple explanation was that the plasma cooling down was slower than its heating up. As a confirmation, Fig. 5 shows the timing of the plasma V_BD transitions as the laser was switched on and off. The cooling down process was almost five times slower than the heating up one.

 

Fig. 4 V_Q and V_BD as a function of laser spot location at p = 100Torr using the gold electrodes with a gap size of 200 µm (left), and the tungsten electrodes with a gap size of 400 µm (right).

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Fig. 5 Time evolution of V_BD and V_Q as the laser is switched on and off. The laser with p = 1W, and λ = 800nm was focused on the anode (left). The relaxation oscillator circuit parameters were V_DC = 0.6kV, R = 32MΩ, and C = 70nF.

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The CW laser-plasma interaction could only occur indirectly through thermal exchange with the electrodes. It is reasonable to expect this thermal exchange to depend on the plasma pressure for at least two reasons. First, at higher pressures, the heat exchange was more efficient since there were more plasma species around the electrodes. Second, the field emission, which dominated at low pressures, and the cascade ionization, which dominated at higher pressures, had different temperature dependencies. Figure 6 shows V_BD and V_Q of microplasmas with different gap sizes with and without laser. It can be seen from Fig. 6 that the laser had almost no effect at pressures below 10Torr, independent of the gap size. At higher pressures, the heating effect in most gap sizes decreased V_BD. This has been summarized in Fig. 7 by plotting the laser effect on V_BD for different gap sizes. It is worth mentioning that for some combinations of pressure, gap size, and laser spot location, the laser caused an increase in V_BD, the reason for which is sill unclear to us.

 

Fig. 6 V_BD and V_Q as a function of pressure using the gold plated electrodes with gap sizes of 20 µm (left), 500 µm (center), and 1000 µm (right). The laser and the relaxation oscillator parameters were the same as Fig. 5.

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Fig. 7 Laser effect on V_BD of microplasmas using the gold electrodes with different gap sizes, and as a function of pressure. The laser with a spot size of 50µm, p = 1W, and λ = 800nm was focused on the cathode (left). The relaxation oscillator circuit parameters were V_DC = 0.6kV, R = 32MΩ, and C = 70nF.

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4. Conclusion

In summary, a 1W CW laser can only affect argon microplasmas through the heat exchange with the electrodes, rather than the gas atoms. In other words, neither multiphoton ionization nor inverse Bremsstrahlung absorption are observable. The heat exchange is very slow, has different speeds when the laser is switched on and off, and is noticeable at pressures above 10Torr. Possible approaches for changing plasma conductivity using CW lasers are eclectic field enhancement by a designed resonant surface (similar to surface enhanced Raman Scattering), lowering the pressure so that electron field emission from the the electrodes can take part, or using electrodes with lower work function materials than the laser photons (to benefit from the photo-electric effect). The results are particularly useful in designing optical microplasma devices.

5. Appendix

5.1. DC discharge breakdown

DC plasma is mainly sustained via electrons impact on gas atoms/molecules and secondary electron emissions [13, 14, 15]. Townsend’s theorem quantifies these two processes and provides a criterion for DC breakdown in a 1-D geometry. One of the most important outcomes of Townsend’s theorem is the well-known traditional Paschen curve for V_BD as a function of pressure-gap product (pd) which has a minimum and two upturn arms (approximately V-shaped [16, 17]). In order to generalize Townsends theorem, electron field emission effect, which is the dominant process sustaining plasma in small dimensions, has been added to describe small gap sizes, below 5 µm in atmospheric pressure. Electron field emission, also called Fowler-Nordheim tunneling, is the process whereby electrons tunnel through a potential barrier (e.g. a metal surface) in the presence of a high electric field [18, 19]. For 1-D microplasmas with small gap sizes, combination of Townsend and Fowler-Nordheim theorems leads to a modified Paschen curve in which the left upturn of the pure Paschen curve is replaced with a plateau and a decline to zero [20, 21]. However, it has been shown in [7] that the existing Townsend and Fowler-Nordheim theorems may not be applied to practical microplasmas with 3-D geometries, readily.

5.2. Laser induced breakdown

In an LIP, the transfer of energy from lasers to gas atoms can happen via three main mechanisms: multiphoton ionization, tunnel ionization, and cascade collisions ionization [12]. In the multiphoton ionization process, the outer layer electrons of gas atoms gain the liberation energy by absorbing several photons, consecutively. This process demands high photon intensities (which necessitates short pulsed lasers) as the probability of absorbing several photons by an electron is extremely small. In fact, large laser power intensities and high photon energies are desired to increase the number of the incident photons and to decrease the number of the required photons for ionization, respectively. Typical required laser powers to initiate this process are in the range GW/cm². Note that a single photon cannot initiate this process as the energy band gap of typical gases (usually over 10 eV) are several times larger than laser photon energies even in the UV wavelength range. If the electric field intensity (photon number) is very high, tunnel ionization can also occur, in which an electron can be freed up with only one oscillation of the electric field. These two processes are almost independent from the pressure and neither of them are important in our experiments as the required beam intensities are far beyond a CW laser capability. In the cascade or avalanche ionization, energy is transferred from photons to the existing free electrons in the gas (e.g. electrons liberated via multiphoton ionization) through the inverse Bremsstrahlung absorption mechanism (in Bremsstrahlung process, high speed electrons are decelerated by atoms/ions and the energy difference is emitted as photons). This process is in fact inelastic collisions between electrons and atoms in which the interaction energy from light wave (or photon) is also considered. Consequently, the electrons gain enough energy through this process to ionize other atoms and add more free electrons to the system. Cascade collisions strongly depend on pressure and are most effective at a certain pressure range. It is not as affective at very low and very high pressures due to the lack of enough species and room for acceleration, respectively. Since LIB is typically implemented by pulsed lasers (due to their high power capability), four separate stages can be considered as the LIB scheme [22]. In the first stage, initiation, multiphoton ionization is the dominant process liberating some free electrons from gas atoms [23]. During the second stage, growth, the cascade ionization rapidly grows the number of free electrons until it reaches to the breakdown (these two steps typically happen within less than a few nanoseconds). During the third stage, laser-plasma interactions occur, leading to absorption and scattering of the laser radiation. In the final stage, extinction, the plasma gradually dies by transferring its energy to radiation, diffusion, attachment and recombination. This stage typically lasts several orders of magnitude longer than the first two stages (e.g. 50 µs). Figure 3 of [4] shows the dependence of the breakdown intensity to pressure and pulse duration. Note that the required intensity is above 10¹¹W/cm².

5.3. Plasma sustainment and extinction

As soon as plasma is ignited, its ionization will be balanced by the competing processes of ionization, recombination, and various excitation/de-excitation collisions, as well as radiative decays of excited states. The recombination of electrons and ions takes place in different ways including the radiative, and three-body recombination. Radiative recombination is the inverse of the direct photo-ionization, while the three body recombination is the inverse of the electron collisional ionization. At very low pressures, where collisions are infrequent, radiative recombination becomes the dominant mode, while in denser plasmas, the three-body electron-ion and electron-atom recombination dominates. In the three body recombination [24]

(3)$$\begin{array}{l}Ar+M\iff A{r}^{*}+M\\ A{r}^{*}+M\iff A{r}^{+}+e^{-}+M\end{array}$$

where M is an energetic catalyst (either Ar or e⁻) and Ar^* is excited Ar atom.

5.4. Plasma characterization

Three parameters of plasma are of special importance: the electron density, the electron temperature, and the degree of ionization. The most straight forward method to measure the above three parameters is to use a Langmuir probe. However, for microplasmas, the optical emission spectroscopy is preferred as a Langmuir probe’s dimensions might even exceed the size of a microplasma. In the optical emission spectroscopy, the emission lines of plasma are used to determine the temperature and the density of electrons [25, 26, 27, 9] by comparing the intensities and measuring the width of emission lines, respectively.

In the two line comparison method, the ratio of the integrated intensities (I) of the two lines having common lower state is used [10]. After some simplifications, Boltzmann and Saha equations lead to [8, 9]

(4)$$\frac{I_1}{I_2}=\frac{g_1}{g_2}\frac{A_1}{A_2}\frac{{\lambda }_2}{{\lambda }_1}\mathit{exp}\left[-\left(\frac{E_1-E_2}{k_{B}T}\right)\right]$$

where E_k is the energy level of the excited level k, A_k is the transition probability, g_k is the statistical weight, k_B is the Boltzmann constant, and T is the temperature in Kelvin. Boltzmann equation describes the ratio of level populations in an atom as a function of temperature, and Saha equation describes the similar ratio but for the ionization states of the atom. We use (4) to find the electron temperature of the argon plasma in our experiments.

Broadening of emission lines in a plasma happens due to different (and sometimes competing) mechanisms such as: Stark broadening, Doppler broadening, instrumental broadening, and pressure broadening. The Stark broadening, which appears due to collisions of charged species, is the primary mechanism responsible for the width of Ar emission lines [11, 28]. As a result of the Stark broadening effect, the Full Width Half Maximum (FWHM) of an emission line, ∆λ, is given by

(5)$$\mathrm{\Delta }\lambda =2w\left(n_e/{10}^{16}\right)+3.5A{\left(n_e/{10}^{16}\right)}^{5/4}\times \left(1-\frac{3}{4}{N}_D^{-1/3}\right)\times w$$

in which w [nm] is the electron impact width parameter, A is the ion broadening parameter, N_D is the number of particles in Debye sphere, and n_e [cm⁻³] is the electron density. The second term in (5) is the ion broadening contribution which is negligible in Ar. Therefore, we use the simplified equation

(6)$$\mathrm{\Delta }\lambda =2w\left(n_e/{10}^{16}\right)$$

as in [10]. The parameter w is obtained from [11]. It is worth mentioning that the Stark broadening, without ion impact, has symmetrical Lorentzian distribution. Ar II ions lines dominate in range from 350 – 520nm and Ar I neutral lines dominate in range from 690 – 860nm.

The degree of ionization is defined as the ratio of the ionized atoms to the total number of atoms. Interestingly, a gas achieves an electrical conductivity of about half of its possible maximum at about 0.1% ionization and has a conductivity nearly equal to that of a full ionized gas at about 1% ionization [29].

5.5. Pictures of the measurement setup

Figure 8 shows the 3-D printed fixture used for the alignment of electrodes. Figure 9 shows inside of the vacuum chamber. Figures 10 and 11 are pictures from the measurement setup.

 

Fig. 8 The 3-D printed fixture for electrodes alignment and their symmetrical feed. a) front view, b) side view. The indicated groove at the center can accommodate a 700 µm thick gauge sheet for the initial adjustment of the electrodes.

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Fig. 9 The 3-D printed fixture inside the chamber. There are two view-ports on the right side and top of the chamber for laser entrance and imaging, respectively. The green arrow indicates the laser path. The blue coaxial cable, carrying high voltage to the electrodes, is specified as well.

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Fig. 10 The measurement setup including the laser, optics section (elaborated in the next figure), vacuum chamber, and the camera with a lens mounted on an x-y manual micropositioner.

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Fig. 11 Top view of the optics section in Fig. 10. A: beam sampler, B: beam chopper, C: beam splitter with an attached fiber coupled parabolic collimator, D: spectrometer, E: photo detector, and F: periscope for beam elevation.

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Acknowledgments

This work was funded by Defense Advanced Research Projects Agency (DARPA) through grant N00014-13-1-0618.

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