Ion expansion dynamics of laser induced multi-elemental plasmas

Ablation of multi-elemental materials by nanosecond lasers is often used to deposit oxide thin films. Understanding the ablation plume dynamics is of utmost importance to gain a detailed insight into thin film growth of materials with a complex composition. In this study, the plume expansion dynamics of several compound materials (AuCu, La0.33Ca0.67MnO3, and LiMn2O4) were characterized by measuring the angular-dependent kinetic energy (KE) distributions of ionic plasma species produced by KrF- and XeCl-excimer laser ablation in vacuum. The distributions of the lightest plume ions were found to differ fundamentally from those of other ions. The latter are similar to the energy distributions observed in single-component plumes and represent a low-energy peak and high-energy tail, while those for the lightest ions consist of at least two distinct peaks. These observations can be explained by assuming the formation of a dynamic double layer (DL) at the front of the plasma giving rise to different acceleration rates for light and heavier ions. As a consequence, heavier elements stay longer within the dynamic DL and gain larger KEs that leads to the observed ion separation. Extending these considerations into three dimensions yields an anisotropic acceleration concept for the plasma ions with high acceleration rates and longer presence within the DL normal to the target surface and lower acceleration rates and shorter time in the parallel direction.


Introduction
The expansion dynamics of laser-induced plasmas has received considerable attention in the last 30 years due to its importance for the basic understanding of materials removal * Authors to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. by laser ablation as well as laser-materials processing and thin film deposition [1][2][3][4][5][6]. To identify and untangle mechanisms governing the expansion of the plume is non-trivial due to the transient and complex nature of materials removal from the target taking place on a very short time scale (ps to 10's of ns). However, the entire plasma dynamics on a time scale of µs covering distances of the order of mm to cm. The latter is experimentally better accessible and some modeling can be done using quasi-stationary models. One major point is the origin of hyperthermal plasma species (atoms, ions, molecular species), in particular if the ablation is done using nanosecond pulses and the removal of material is considered to be largely a thermally governed process [7][8][9]. It has been long discussed that gas dynamic acceleration results in energetic species and several models have been proposed to describe the adiabatic expansion of the plume [4,[10][11][12][13][14][15]. Even though descriptions like Anisimov's model [10] can provide a relatively good explanation of the angular distribution of plume species, they do not treat the multi-elemental plume expansion dynamics.
In a multi-component plasma plume, a direct relationship between the ion mass and its maximum kinetic energy (KE) is reported with heavy ions having larger maximum KEs as compared to light ions [16]. This relationship can be explained by assuming the formation of a dynamic electrostatic double layer (DL) at the plume front since the laser-generated electrons have much higher thermal velocities than ions [4]. As a result, electrons move ahead of the main plasma body thus forming at the border of the plasma an electron-rich outer layer ('electron layer') and an inner positive-ion-rich region ('ion layer'). This charge separation region is called a 'double layer'. We would like to emphasize that the DL is formed at the front of the plasma plume while the plume core can remain quasi-neutral until its density drops to a level when the Debye length becomes comparable to the plume core size [17].
The thickness of the charge separation layer is governed by the potential φ described by the Poisson equation ε 0 ∂ 2 φ /∂x 2 = e (n e − Zn i ) [18]. Here e is the elementary charge, n e and n i are the electron and ion density, Z is the ion charge number (below we consider a relatively low laser fluences and hence singly ionized ions only), ε 0 is the dielectric constant, and x is the distance. In the expanding plasmas, the densities of charged particles are dynamically evolving, resulting in a dynamic evolution of the potential and hence, of the electric field distribution. The electric field of this dynamic DL prevents the electrons to escape far beyond the plasma border and at the same time accelerates the ions within the DL region. We note that, at the border between the expanding plume and vacuum, the collision frequency between plasma species is small compared to the main plasma body. Therefore, lighter plasma species are typically expanding considerably faster than heavy species. Hence, they move to the external part of the DL where the electric field strength is smaller. As a result, heavier ions remain longer within the DL with the highest electric field and gain more KE. Upon the axial and lateral plume expansion, which corresponds to a decreasing density of charged particles, the electric field becomes weaker and the electric field inside the DL is gradually degrading. For nanosecond laser pulses, the plasma is formed at an early stage of the laser action and has sufficient time during the pulse to absorb laser light. As a result, energetic ions and electrons are efficiently generated via photo-and collisional ionization [7,19]. Thus, the charge separation at the plume front can be stronger and DL acceleration effects are more pronounced as compared to femto-or pico-second laser pulses. The dynamic DL model addresses the difference in acceleration between light and heavy ions as shown in figure 1. Due to different masses, the light and heavy ions have different The separation between the light and heavy ions occurs because of the different acceleration rate for the different plasma species. Light ions move to the front of the DL while heavy ions stay at the center of the DL where the electric field is larger. As a consequence, a stronger acceleration for the heavy ions takes place [16]. acceleration rates and thus separate spatially during the expansion. Light ions move preferentially towards the front of the DL where the electric field is small or zero, while heavy ions stay inside the DL until the DL has degraded. Heavy ions are therefore accelerated longer and hence gain more energy than light ions that explains the observed relationship between the ion mass and the maximum ion KE [16].
In this paper, we explore the ion expansion dynamics in multi-elemental plasma plumes using nanosecond laser ablation. Based on measuring the angular ion energy distributions (IEDs) as well as analyzing the ion energy distribution in detail, the dynamic DL model is extended to explain characteristic features of the IED as well as the ion acceleration in three dimensions.

Pulsed laser ablation
The laser-induced plasma was generated and characterized in vacuum with a base pressure of <1 × 10 −6 mbar as shown in figure 2(a). For the ablation, four disk targets (Cu, AuCu, La 0.33 Ca 0.67 MnO 3 , and LiMn 2 O 4 ) and two different laser wavelengths were used: a KrF excimer laser (Lambda Physik LPX 300, 20 ns, λ = 248 nm) and a XeCl excimer laser (Lambda Physik LPX 205, 20 ns, λ = 308 nm), both with a flat-top beam profile. The two different wavelength will provide different maximum kinetic energies for the same fluence as well as significant differences in the species composition of a plasma. The increase in the number of elements in the targets increases the complexity of the plume dynamics and the relative mass difference for the different elements investigated [20] will help to study the reciprocal species interaction during the plume expansion. The imaged aperture of the laser beam profile on the target surface is 1 × 1 mm 2 and the beam incidence angle to the target surface normal was 45 • in most experiments. During the ablation, the target was rotated and displaced parallel to its surface to avoid groove and hole formation [21]. To measure the angular KE dependence of plume species, there are two alternatives which can be realized. For one, the measurement angle of the mass spectrometer (MS) with respect to the target surface normal can be changed. Alternatively, the laser and MS angle are fixed and the target plane is tilted. To realize proper the second approach, the imaged beam cross section and fluence on the target have to be adopted and verified for each angle to maintain a constant area and fluence [21,22]. The latter approach is shown schematically in figure 2(b) and realized for the presented experiments. When changing the beam incident angle, the beam spot size at the target and pulse energy were adjusted with a set of masks and an attenuator, respectively, to keep the same irradiation conditions.

KE measurement set-up
An energy dispersive quadrupole mass spectrometer (EQP-MS, Hiden Analytical) was used to study the expansion dynamics of ionized plasma species at a distance of 4 cm from the target, a typical target-substrate distance. The EQP-MS is a high transmission 45 • sector field ion energy analyzer and quadrupole mass spectrometer, which can measure the IED for a specific mass-charge ratio up to 1000 eV. Due to the high flux per pulse, a 30 µm diameter sampling orifice was used. In addition, an appropriate tuning of the lenses was done to avoid chromatic aberration and to ensure a stable ion transmission of the EQP [23]. In order to capture the transient plasma plume dynamics, the mass spectrometer was triggered and gated by a pulse generator connected to a photodiode. The pulse generator provides a TTL pulse to the mass spectrometer with a pulse width of 1 ms, which is much longer than the time the plume species require to reach the mass spectrometer. Thus, the mass spectrometer collects all the required species per trigger pulse.

The one-dimensional ion expansion
To examine the ion expansion dynamics in multi-elemental plasma plumes, we first compare the ion energy distributions of Cu + ablated from a Cu target and an alloyed AuCu target with λ = 308 nm and a fluence of 4 J cm −2 . The respective IEDs for Cu + and Cu + /Au + are shown in figures 3(a) and (b). Cu has two isotopes ( 63 Cu 69.2%; 65 Cu 30.8%) and the IEDs of the two isotopes are very similar so that only the distribution for 63 Cu + is shown. For the Cu target, the IED shows a one intensity maximum at around 6.5 eV and an energetic tail up to 110 eV. Deconvoluting the Cu + -IED, it consists of two low energy distributions with a maximum of the kinetic energies (E kin,max ) at 6 and 11.4 eV and a broad, flat distribution extending up to 110 eV. A similar IED with a lowenergy peak and a high-energy tail was previously observed in time-of-flight measurements in a copper plasma plume produced under similar ablation conditions [24]. With respect to the IEDs for the alloyed AuCu target, a low energy peak and an energetic tail are identified for Au + , but the IED of Cu + is different. It consists of a low energy peak at around 3 eV and an additional broad peak at higher energies instead of an energetic tail. On closer inspection, the Au + -IED can be perfectly described by two low energy distributions with E kin,max = 7.2 and 11 eV, and one broad distribution starting at ∼37 eV. The corresponding Cu + -IED is described by two low energy maxima (E kin,max = 3.1 and 4.8 eV) and one broad peak centered around 54 eV (see insert figure 3(a)). For further discussion, the two components of these distributions are termed 'low energy peak' and 'high energy peak'. Certainly, the optical properties of Cu and AuCu targets are different, which leads to a difference in the ablation rate. However, the change of the IED type for Cu + from a single peak with a high-energy tail to a double peak one is remarkable and needs a special consideration that is provided below. Note that the additional highenergy peak is unlikely to originate from the ablation itself but should be attributed to the plasma expansion dynamics since the initial ablation process is thermal in nature. As for plasma heating, it takes place at the initial formation stage due to the shielding of the laser light and the partial absorption of the laser energy. This results in relatively low plasma temperatures, not higher than a few eV, as demonstrated in spectroscopic studies under similar irradiation conditions and even at several times higher laser fluences [25,26].
To explore the ion expansion dynamics in multi-elemental plumes further, two oxide targets, La 0. 33   La 0.33 Ca 0.67 MnO 3 , the IEDs of La + , Mn + and Ca + show a low energy peak and an energetic tail while the O + distribution has a low and a high energy maximum. The IEDs of Mn + and O + for a LiMn 2 O 4 ablation show a low energy peak and an energetic tail while the IED of Li + has a low and a high energy peak. Here we note that O + shows two differently structured IEDs for the two different plumes. Table 1 gives a summary of the types of IEDs as well as the maximum detected energies for each ion ablated from the different targets. For further descriptions, the two types of IEDs are termed as • Type I: the distribution with a low energetic peak(s) and an energetic tail; • Type II: the distribution with low and high energy peaks.
Irrespective of the ablation conditions and target materials, one can infer from table 1 that a type I distribution can be measured for single-and multi-elemental plumes, while type II distributions exist for multi-elemental plumes only. Additionally, in a multi-elemental plume the IED of the lightest ion shows the type II distribution while that of the heaviest ion can be classified as type I. From these measurements we conclude, that E kin,max increases with increasing ion mass for multi-elemental plumes. However, the correlation is reversed when calculating the maximum velocity: The ion maximum velocity decreases with increasing mass.
As discussed in [16], the relationship between the ion mass and the ion maximum KE as well as the maximum velocity is the result of the acceleration within the dynamic double layer. According to the DL model, light and heavy ions separate during the expansion of the plasma due to different acceleration rates. Light ions have larger initial thermal velocities as compared to heavy ionic species. Thus, in the front part of the plume, where the density of species and hence the collision frequency are reduced compared to the plume core, light ions run ahead of the heavier ions. They separate from the light ions confined within the plume core and are at the leading edge of the DL where the ambipolar field is reduced [17,27]. As a result, the overall DL-induced acceleration is moderate. Due to the accumulation of these light ions with similar accelerated energies they would appear in the IED as a separate broad energy peak.
The heavier ions, which initially have lower thermal velocities compared to lighter species, are moving in the DL behind the lighter ions. Thus, they are subjected to the action of the electric field in the DL with different field intensities, which would explain why their IEDs have an energetic tail but not a high energy peak. Due to a semi-radial expansion of the plume and the associated drop of its density as ∼r −3 [17], where r is the plume size, the DL is gradually weakening and, as a result, the IED shapes for different species remain unchanged upon further expansion.

Three-dimensional expansion dynamics
The angular dependent IEDs of the LiMn 2 O 4 plasma plume is analyzed with the measurement configuration as described in figure 2(b). Such measurements provide useful information related to the plume expansion dynamics in two dimensions. Due to mirror and rotation symmetries of the plasma expansion geometry, these measurements also provide 3D information. The ablation conditions are the same as described previously. Figure 4(a) shows IEDs of Li + , O + and Mn + for an expansion direction between 0 • and 80 • off the target surface normal for the ablation of LiMn 2 O 4 . The ion intensity is plotted on a logarithmic scale in order to address the energetic tail in the distribution. A polar contour plot based on the measured IED's is presented in figure 4(b) to visualize the energy distributions at different angles.
The contour plots show, that with increasing angle the ion energies are reduced, which results in the typically observed anisotropic plasma plume expansion [19]. For Li + , the ion energy distribution remains type II at all angles. With increasing angle, the high energy peak becomes narrower and the maximum energy is significantly reduced while the intensity increases. In the polar contour plot, the Li + energetic peaks at different angles appear as curved bands of different intensities. For O + , its energy distribution is type I at low energies but contains, on closer inspection, a separate high energetic contribution. With increasing angles, the energetic tail becomes smaller, shifting towards lower energies, while its intensity and the high energy peak becomes visible. Therefore, with increasing angle the O + energy distributions turn from a type I into a  type II. For Mn + , the energy distributions remain type I at all angles. With increasing angle, the energetic tail becomes narrower and its intensity decreases as well.
The velocity distribution ( dN dv (v)) can be deduced from the ion energy distribution ( dN dε (ε)) as with ε the ion energy, v the velocity, m the mass, and N the total ion yield N =´d N dε dε =´d N dv dv. These distributions for different angles are shown in figure 4(c). The angular velocity distribution can reflect, to some extent, the spatial distribution of the plume at the late stages of plume expansion when the DL electric field becomes negligible and velocities constant.
From figure 4(c), it is seen that the intensity band, formed by the energetic Li + ions, is well pronounced also in the angular velocity distribution and most Li + ions are concentrated in this region. Projecting this two-dimensional representation onto the three-dimensional plume indicates that a shell of Li + ions is covering the plume. The outer and inner borders of the intensity bands are marked by the solid and dashed lines respectively. Regarding the velocities of O + and Mn + , the maximum velocities of O + at different angles are just above the inner border of the Li + band, and the maximum velocities of Mn + at different angles are overlapping with the inner border of the Li + band. Therefore, there is a spatial separation of Li + from the other ions in all directions. The expansion velocity of O + is slightly faster than Mn + in all directions, and its intensity is distributed more towards high velocities.
Combining the angular dependent IEDs and velocity distributions, one can see that the maximum ion kinetic energy, the maximum ion velocity, and the ion-mass dependent IED type are valid not only for the plume axis but also for all the measured directions, except the transformation of the O + IED from type I to type II at large angles. This indicates that the ion acceleration mechanism is the same for the ion expansion in different directions. Therefore, the proposed double layer model can be mapped into three dimensions to explain the angular dependent IEDs.
As already discussed, the formation of the double layer is due to the different velocities of ions and electrons in the plume that leads to a breaking of the quasi-neutrality at the leading edges of the plume of the order of the Debye length. At the initial stage of the plume expansion and before the laser pulse terminates, the plume can be considered to be onedimensional forming a disk-like layer above the laser irradiation spot. Its thickness can be estimated as L 0 ∼ v t τ [17], where τ is the laser pulse duration and v t is the thermal velocity given by v t = √ 8kTs π m with T s and m to be the surface temperature and an average mass of the plume species respectively. The thickness of this initial plume layer is usually a few µm for a nanosecond laser pulse.
In the meantime, the electrons can escape from the external plume layer with a thickness of approximately the Debye length λ D (typically from several to dozens of nanometers at the initial expansion stage [17]), and expand up to a distance from the plume boundary, both axially and radially, due to their much higher thermal velocities. The electrons can be considered in the early stages of expansion as isothermal due to the flat top laser beam profile and, hence, the layer of escaped electrons should be approximately equal in all directions from the plume body. The double layer at the initial stage of the plume expansion is composed of an electron outer layer, a positively charged layer with the thickness ∼λ D at the ablation plume boundaries depleted of the escaped electrons, and a slab of a quasi-neutral plasma core as schematically shown in figure 5. Considering the expansion geometry of the escaping electrons, one may state, that in the central part of the irradiation spot their average velocity is directed perpendicular away from the target ( figure 5(a)). The electric potential and the corresponding ambipolar field are illustrated in figure 5(b), left. However, at the plume edges, the electrons expand in a fan-like manner as shown in figure 5(a). As a result, the electric potential drops faster at the plume edges as compared to the central part of the plume. Although the electric field can locally be stronger at the plume edges due to fast drop of the potential, the distance for the initially thermal ions to pass through the DL field spike is shorter ( figure 5(b), right), which implies a weaker acceleration. Furthermore, lighter ions having higher thermal velocities are passing through the region of the electric field spike faster than heavier ions. The velocity gain upon acceleration can be evaluated as ∆v ≈ eE m ∆t with an approximate acceleration time ∆t ≈ mv t /eE. Assuming that the initial energies for light and heavy ions are the same and hence their ratio of the thermal velocities v l /v h is proportional to √ m h /m l , we obtain ∆t l /∆t h ≈ √ m l /m h that straightforwardly explains a larger energy gain for heavy ions and the appearance of the 'light ion bands'. At the same time, a shorter distance through the high-field DL region at the radial edges of the plume explains directly why the KE gain of the ions moving in the normal direction off the target is larger relative to ions moving parallel or at an angle with respect to the target surface. As a result, an anisotropic angular dependence for the IEDs is measured. At larger angles, the ions cross the high-field DL region faster and, after crossing, their further acceleration becomes insignificant. Thus, they are accumulated beyond the highfield DL and a larger amount of the accelerated ions is detected at larger angles. This gives rise to the increased intensity of the high energy peak at large angles as well as the transformation of the energetic tail to a high energy peak for the O + IEDs.
We note that, upon expansion in vacuum, the plume density at its boundary drops drastically while the temperature decrease is considerably lower [4]. Thus, the Debye length at the plume front is gradually increasing and more plume species become involved in acceleration. At the same time, the DL electric field is gradually degrading, both due to threedimensional plume expansion and ion recombination. From the above expression of the approximate acceleration time, we can roughly estimate that the dynamic DL is efficient up to a few µs after the laser pulse action depending on the ablation conditions. Beyond this time, the field strength drops to a level which cannot noticeably affect the ion energy distribution.
One more effect should be mentioned, which can contribute to the separation of light and heavy ions. Species are vaporized from the laser melted target dependent on their volatility and vapor pressure [28,29]. Thus, lithium atoms can leave the irradiated target earlier than Mn atoms [30]. Being vaporized, atoms can be easier ionized in the inverse Bremsstrahlung process with the first ionization energies of 5.39 and 7.34 eV for Li and Mn, respectively. As a result, a 'Li-ions DL prerequisite' can be formed leading to further separation of Li ions from the bulk of the plume. However, this effect is out of the scope of this paper and calls for further studies.
When analyzing the IED's in more detail, we note that the low energy peak can often be described best with two Maxwell distributions, likewise the intensities for the high energy region. For the heaviest element measured in a multicomponent plasma, the high energy part is usually not very distinct whereas for the lighter elements the low and high energy region is clearly separated. The signature of two energy maxima for both energy regions is maintained for the angular dependence. At the same time, the large kinetic energies are reduced with increasing angle, including that the low and high energy maxima move closer together with increasing angle. This indicates that the creation of species as a result of the ablation process does not have an intrinsic angular dependence. In addition, the reduction of the energy difference between these two energy maxima with increasing angle is the consequence of the preferentially forward directed momentum transfer of ablated species.
The anisotropic expansion of the plume is thus a result of the direction-dependence of the double layer structure. A 'thicker' DL region with a developed ambipolar electric field may lead to a weaker initial acceleration but the acceleration time is longer and hence the overall acceleration is larger as compared to a 'thinner' DL width. This phenomenological model provides an explanation for the renowned 'flip-over' effect, which refers to the fact that the lateral axis of the plume with the initial shortest dimension turns into the axis with the longest dimension during plume expansion when the laser spot is non-circular [31,32].
It should be noted that the double layer effect can be affected by the presence of a background gas as discussed in detail in [17]. At reduced background pressures, up to 0.1 mbar, the initial stage of the expanding laser plasma proceeds like in vacuum due to a large mean free path, of the order of hundreds of mm. Thus, the DL formation should not be influenced by the ambient gas. However, with plume expansion and developing a 'snowplowing' effect [33], the ion dynamics is expected to be considerably influenced. First, the high-energy DL-accelerated ions will penetrate into the 'snowplowed' ambient gas while low-energy ions will be confined in the plume core and can reach the detector only through diffusion. Second, for a multicomponent ablation plume, the heavier energetic ions will better preserve the velocity perpendicular to the target whereas lighter ions of the same energy are expected to be scattered to the plume peripheries (such an effect was observed in TOF MS measurements though for neutral plume species [14]). As a result, we can predict that the plume front and peripheries will be more enriched by heavy and light ions, respectively, as compared with the vacuum conditions, thus affecting the angular distribution of the plume species. We also expect to observe clear differences between a reactive gas environment like oxygen and a non-reactive background gas (Ar) [22] and that the separation in slow and fast species can still be measured [34]. But the general tendency will probably be a more hemispherical expansion with increasing pressure as known from time-resolved optical emission spectroscopy [22,35]. How the DL-model has to be adoped to these conditions is subject to further studies.

Conclusions
In this paper, the ion expansion dynamics of multi-component laser induced plasma plumes is analyzed based on kinetic energy distribution measurements of ionic plasma species. Regardless of the plume systems, a correlation of the ion energy and angular distributions with the ion mass is found namely: I. For all the expansion angles, heavier ions have a larger maximum KE but a smaller maximum velocity than light ions in a multicomponent plasma. II. Two types of energy distributions are found: a. Type I: a low energy peak and an energetic tail; b. Type II: a low energy peak and a high energy peak. III. For the lightest ions in a multi-elemental plume, the IED is of type II for all angles. For the heaviest ions, the IED is of type I for all angles. A transformation of the IED from type I to type II can be observed for ions with intermediate masses at large angles.
The measurement results can be explained by assuming the formation of a dynamic double layer at the plasma front. Ions in the double layer are accelerated by the electric field generated by the charge separation. The light and heavy ions, due to the different masses and thus the different acceleration rates, separate during the acceleration/expansion. Light ions having a larger acceleration rate move to the front of the double layer where the electric field is low and thus their further acceleration becomes insignificant. Contrarily, heavy ions stay in the double layer for a longer time and receive more energies from the DL acceleration. This gives a physical explanation for the observed correlation of the ion mass with its maximum energy as well as its maximum velocity. Our phenomenological analysis is expanded to three dimensions with the assumption of electrons escaping from a planar plasma core. With this geometry, the DL is inhomogeneous. Regions with a high electric field are created due to charge separation. They are thicker in the middle part of the expanding plume and thinner at the lateral edges. Therefore, in the direction normal to the target surface, the ion acceleration takes a longer time and ions gain more energy, while in the direction off the target surface normal, ions can cross the DL faster and their further acceleration becomes insignificant. This results in the anisotropic acceleration as observed in our MS measurements.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.

Acknowledgments
This work was partially supported by SNF (Project No 200021_134577) and the Paul Scherrer Institute. N M B and A V B acknowledge support of the European Regional Development Fund and the state budget of the Czech Republic (Project BIATRI: No. CZ.02.1.01/0.0/0.0/15_003/0000445).