**3.3. How small atmospheric-pressure microplasmas can be made?**

A plasma (**Figure 7**, regardless of its size) consists of two plasma sheaths (located in the vicinity of two electrodes bathed in a gas-of-interest in a gas-tight container) and a bulk plasma [133–137]. Shielding (or damping or screening) of the electric field arises from the presence of charged species in the plasma and from the unequal mobility of ions and electrons in the vicinity of the electrodes. Inside the plasma sheath, macroscopic electrical neutrality is likely not maintained. But outside of it (labeled bulk plasma in **Figure 7**), macroscopic neutrality is maintained and (time-averaged) electron and ion fluxes are roughly equal. Thus (on a timeaverage and per unit-volume), n<sup>e</sup> ≈n<sup>i</sup> (for singly charged species). The distance (or thickness) a sheath screens electric fields is called the *Debye length* (λD), given by Eq. 1.

$$
\lambda\_D = \left[\frac{\epsilon\_o kT}{n\_e e^2}\right]^{1/2} \tag{1}
$$

is mainly due to a reduced interaction-time between an analyte and a microplasma. Thus, from an elemental analysis viewpoint, decreasing the length of a microplasma (e.g., by fabricating microplasmas in μm cavities) may not necessarily be beneficial in terms of signal intensity. This is significant because as signal intensity worsens, signal-to-noise ratio (SNR) degrades, thus degrading the detection limit (defined as the minimum amount or concentration that can be detected with a stated statistical confidence). The detection limit is a key figure of merit in chemical analysis. From the foregoing it can be concluded that mm-long microplasmas formed inside microfluidic channels (e.g., **Figure 8**) will likely be beneficial for

**Figure 8.** (a) Simplified diagram of a microplasma and (b) microplasma formed at the end of a needle electrode (OD: 470 μm, ID: 130 μm) inside a microfluidic channel on a microfluidic chip. A Canadian 1 cent coin (about the same

Microfluidics and Nanofluidics: Science, Fabrication Technology (From Cleanrooms to 3D...

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13

diameter as that of a US one-cent coin, or UK's one-pence, or a one-cent euro) has been included for size.

Conceptually, there are two steps involved in forming and sustaining a continuouslyoperated atmospheric-pressure microplasma. For instance, a microplasma must be first initiated (or "ignited") and then it must be sustained. The minimum "ignition" (or spark-

when a uniform electric field is applied between two flat electrodes at a distance or gap (d) immersed in a gas of interest under pressure (p) can be determined using Paschen's

> In[ Apd \_\_\_\_\_\_\_\_\_\_\_ In (1/γ)]

A and B are constants that depend on the properties of the gas in which the electrodes are immersed in (not accounting for any ionization due to background radiation). The values of A and B are either determined experimentally or they are calculated from literature values [139]. The coefficient γ (also known as Townsend's coefficient) incorporates properties of the

) for which the entire discharge gap is fully formed (often called "bridged")

(2)

**3.5. Igniting and sustaining a microplasma at atmospheric pressure**

<sup>V</sup><sup>b</sup> <sup>=</sup> Bpd \_\_\_\_\_\_\_\_\_\_\_\_\_

elemental chemical analysis.

ing) voltage (V<sup>b</sup>

law (Eq. 2).

where k is the Boltzmann constant, T is the electron temperature, ε0 is the permeability in vacuum, n<sup>e</sup> is the electron number density and e is the charge of an electron.

To generalize, a key assumption is that sheath thickness is about the same magnitude as the Debye length. A few, what-if type thought-experiments will be used to obtain an indication on how λD changes as T and n<sup>e</sup> vary. For example, for an atmospheric pressure plasma when T = 10,000 K (with 1 eV = 11,600 K) and n<sup>e</sup> = 1016 m−3, then λ*<sup>D</sup>* <sup>=</sup> 110 μm. But when T = 5000 K and assuming that there is no thermal ionization (thus the degree of ionization is constant and the same as in the example above) with n<sup>e</sup> = 1016 m−3, then λ*<sup>D</sup>* <sup>=</sup> 80 μm. For less than atmospheric pressure operation and assuming that n<sup>e</sup> = 5 x 1014 m−3 and (for simplicity, assuming that the degree of ionization is unchanged) and that T = 5000 K, then λ*<sup>D</sup>* <sup>=</sup> 350 μm. Because plasmas cannot be made smaller than their boundary layers (per conditions outlined in Section 3.1), plasma sheaths (and Debye length) set a **fundamental limit** as to how small the inter-electrode distance d (**Figure 7**) can become, in other words, **how small a microplasma can be made**.

Since inter-electrode distance d must be >> λD, and for the example with λD = 110 μm and for a two-electrode operation, then the microplasma must be larger (or much larger) than 2 times λD or (for this example) it must be >> 220 μm). As d becomes ~2 times the length of the sheath, the sheath-bulk plasma structure must disappear and thus the plasma must become devoid of a bulk plasma (**Figure 7**), that is to become a sheath-only plasma. But in a strict interpretation of the definition of a plasma, can such an ionized gas still be called a *"plasma"* [134]? There are published reports of microplasmas formed in constrained cavities that are smaller than 10 μm by 10 μm [133–137]. This has been explained by considering that sheath-thickness scales as inter-electrode distance decreases. Several open-ended questions in this research area still remain unanswered for instance, would microplasmas the size of 10's of μm be useful for chemical analysis? To obtain insights, perhaps this question must be re-phrased to read *"how small analytical, atmospheric pressure microplasmas* **should** *be made"?*

### **3.4. How small analytical, ambient-pressure plasmas should be made?**

There are two answers to this question. One is that microchannels can be 10's of mm long ([48–51] and cited literature). Since there does not seem to be a fundamental reason why microplasmas should be constrained in μm-size cavities, microplasmas can occupy part of mm-long microchannels (**Figure 8**). Therefore, such microplasmas are not limited by Debye length or by plasma sheaths.

The other answer involves residence time of an analyte in a microplasma (**analyte = the chemical species of interest in a sample to be used for chemical analysis**). Residence time (important in elemental chemical analysis) is defined as the time an analyte resides in, or is in contact with or it interacts with a microplasma. In general, as microplasma length (dictated by the inter-electrode distance or gap) decreases, so does residence time. But as residence time decreases, so does signal intensity from an analyte introduced into a microplasma. This Microfluidics and Nanofluidics: Science, Fabrication Technology (From Cleanrooms to 3D... http://dx.doi.org/10.5772/intechopen.74426 13

*λ<sup>D</sup>* = [

vacuum, n<sup>e</sup>

12 Microfluidics and Nanofluidics

on how λD changes as T and n<sup>e</sup>

length or by plasma sheaths.

where k is the Boltzmann constant, T is the electron temperature, ε0

*small analytical, atmospheric pressure microplasmas* **should** *be made"?*

**3.4. How small analytical, ambient-pressure plasmas should be made?**

<sup>ϵ</sup><sup>0</sup> *kT* \_\_\_\_ *ne <sup>e</sup>* <sup>2</sup> ]

is the electron number density and e is the charge of an electron.

To generalize, a key assumption is that sheath thickness is about the same magnitude as the Debye length. A few, what-if type thought-experiments will be used to obtain an indication

T = 10,000 K (with 1 eV = 11,600 K) and n<sup>e</sup> = 1016 m−3, then λ*<sup>D</sup>* <sup>=</sup> 110 μm. But when T = 5000 K and assuming that there is no thermal ionization (thus the degree of ionization is constant and the same as in the example above) with n<sup>e</sup> = 1016 m−3, then λ*<sup>D</sup>* <sup>=</sup> 80 μm. For less than atmospheric pressure operation and assuming that n<sup>e</sup> = 5 x 1014 m−3 and (for simplicity, assuming that the degree of ionization is unchanged) and that T = 5000 K, then λ*<sup>D</sup>* <sup>=</sup> 350 μm. Because plasmas cannot be made smaller than their boundary layers (per conditions outlined in Section 3.1), plasma sheaths (and Debye length) set a **fundamental limit** as to how small the inter-electrode distance d (**Figure 7**) can become, in other words, **how small a microplasma can be made**.

Since inter-electrode distance d must be >> λD, and for the example with λD = 110 μm and for a two-electrode operation, then the microplasma must be larger (or much larger) than 2 times λD or (for this example) it must be >> 220 μm). As d becomes ~2 times the length of the sheath, the sheath-bulk plasma structure must disappear and thus the plasma must become devoid of a bulk plasma (**Figure 7**), that is to become a sheath-only plasma. But in a strict interpretation of the definition of a plasma, can such an ionized gas still be called a *"plasma"* [134]? There are published reports of microplasmas formed in constrained cavities that are smaller than 10 μm by 10 μm [133–137]. This has been explained by considering that sheath-thickness scales as inter-electrode distance decreases. Several open-ended questions in this research area still remain unanswered for instance, would microplasmas the size of 10's of μm be useful for chemical analysis? To obtain insights, perhaps this question must be re-phrased to read *"how* 

There are two answers to this question. One is that microchannels can be 10's of mm long ([48–51] and cited literature). Since there does not seem to be a fundamental reason why microplasmas should be constrained in μm-size cavities, microplasmas can occupy part of mm-long microchannels (**Figure 8**). Therefore, such microplasmas are not limited by Debye

The other answer involves residence time of an analyte in a microplasma (**analyte = the chemical species of interest in a sample to be used for chemical analysis**). Residence time (important in elemental chemical analysis) is defined as the time an analyte resides in, or is in contact with or it interacts with a microplasma. In general, as microplasma length (dictated by the inter-electrode distance or gap) decreases, so does residence time. But as residence time decreases, so does signal intensity from an analyte introduced into a microplasma. This

1/2

vary. For example, for an atmospheric pressure plasma when

(1)

is the permeability in

**Figure 8.** (a) Simplified diagram of a microplasma and (b) microplasma formed at the end of a needle electrode (OD: 470 μm, ID: 130 μm) inside a microfluidic channel on a microfluidic chip. A Canadian 1 cent coin (about the same diameter as that of a US one-cent coin, or UK's one-pence, or a one-cent euro) has been included for size.

is mainly due to a reduced interaction-time between an analyte and a microplasma. Thus, from an elemental analysis viewpoint, decreasing the length of a microplasma (e.g., by fabricating microplasmas in μm cavities) may not necessarily be beneficial in terms of signal intensity. This is significant because as signal intensity worsens, signal-to-noise ratio (SNR) degrades, thus degrading the detection limit (defined as the minimum amount or concentration that can be detected with a stated statistical confidence). The detection limit is a key figure of merit in chemical analysis. From the foregoing it can be concluded that mm-long microplasmas formed inside microfluidic channels (e.g., **Figure 8**) will likely be beneficial for elemental chemical analysis.

#### **3.5. Igniting and sustaining a microplasma at atmospheric pressure**

Conceptually, there are two steps involved in forming and sustaining a continuouslyoperated atmospheric-pressure microplasma. For instance, a microplasma must be first initiated (or "ignited") and then it must be sustained. The minimum "ignition" (or sparking) voltage (V<sup>b</sup> ) for which the entire discharge gap is fully formed (often called "bridged") when a uniform electric field is applied between two flat electrodes at a distance or gap (d) immersed in a gas of interest under pressure (p) can be determined using Paschen's law (Eq. 2).

$$\mathbf{V}\_{\rm b} = \frac{\text{Bpd}}{\ln\left[\frac{\text{Apd}}{\ln\left(1/\gamma\right)}\right]} \tag{2}$$

A and B are constants that depend on the properties of the gas in which the electrodes are immersed in (not accounting for any ionization due to background radiation). The values of A and B are either determined experimentally or they are calculated from literature values [139]. The coefficient γ (also known as Townsend's coefficient) incorporates properties of the

Based on these ideas, we fabricated and tested a variety of battery-operated, atmospheric pressure, self-igniting, mm-length microplasmas in fluidic channels [143–156]. Due to their mm-length, plasma sheath and Debye length are not of a concern. In addition to being "cold", their high surface area-to-volume ratio further facilitates heat dissipation, thus facilitating use of polymeric substrates and 3D-printing fabrication methods. Example microplasmas fabri-

Microfluidics and Nanofluidics: Science, Fabrication Technology (From Cleanrooms to 3D...

For microplasmas formed inside a **microfluidic channel on a chip**, a dual substrate approach was used (**Figure 10**). Briefly, cleanroom-technologies (**Figure 2**) were employed to define and to sputter-deposit Au electrodes E1 and E2 (**Figure 10a**). Holes were drilled for the inlet and the outlet. On the bottom wafer, a chemically etched microchannel was formed. The top and bottom wafers (**Figure 10a** and **b**) were aligned so that the central part of the etched channel matched the protruding part of electrodes E1 and E2. Then the wafers were bonded together (**Figure 10c**) [143] and glass-tubes were affixed to the inlet and outlet holes (**Figure 10d**).

the sample-introduction carrier-gas. Upon application of electrical power, the microplasma selfignited, it was formed between electrodes E1 and E2 and was sustained by continuous application of electrical power (~10 W). To avoid electrode breakage, a high-voltage ac [143] was used.

**Figure 10.** (a) Top chip showing electrodes E1 and E2, (b) bottom chip showing the etched microchannel, (c) the top and bottom chips bonded together (the microplasma was formed between electrodes E1 and E2, and (d) an *"angle"* view of

) that was used as the microplasma gas and as

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15

cated in a variety of substrates will be discussed next.

The inlet was connected to a gas-supply (Ar-3%H2

the two bonded chips.

**4.1. Microplasmas in fluidic channels on amorphous substrates**

**Figure 9.** Paschen curve for argon gas and for a 2.8 mm inter-electrode gap (d) as a function of pd.

electrode material (e.g., work function) and it assumes that gas breakdown is predominantly a function of electron emission from the electrodes. In short, the two key variables in this equation are pressure (p) and inter-electrode distance (d). The product of p times d is often called "**pd scaling**." An example of a Paschen curve is shown in **Figure 9**.

Paschen's law applies to electrical discharges formed at low-pressures. In high-vacuum or at high pressures (e.g., atmospheric), Paschen's law fails ([139] and references herein). There are also deviations from the behavior predicted by Eq. 2 when kHz or MHz ac voltages are used or when μm inter-electrode distances (or gaps d) are employed [139]. Undeniably, there are limits to applicability of Paschen's law. Despite of these limitations, Paschen's law **(presumably, the only choice**) can be used to obtain rough estimates of the magnitude of the voltage required to ignite (or initiate) an atmospheric pressure plasma. Thus it can be used as an aid in the design of appropriate power supplies. For instance, when the electrodes are made from Iron (Fe) and the inter-electrode distance d is 2.8 mm, and the discharge gas is Argon (Ar) at (or near) atmospheric pressure, the minimum voltage (V<sup>b</sup> ) required for gas breakdown (or for microplasma ignition) is about 6000 V. As the inter-electrode distance d decreases from 2.8 to 1 mm (and by keeping all else constant), V<sup>b</sup> drops to about 2400 V, and when d further decreases to 0.5 mm, V<sup>b</sup> drops to about 1400 V. It should be emphasized that gas breakdown at the minimum voltage V<sup>b</sup> is not always necessary and that (once ignited), to sustain a microplasma lower voltages are typically required. An example is the ballast used in fluorescent lights.
