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R. Srinivasan and V. Mayne-Banton of IBM Research first reported the laser ablation phenomenon to produce thin films in 198250. Laser ablation is a process whereby the short, intense burst of energy delivered by a laser pulse is used to vaporise a material that would often be impossible to vaporise by conventional methods51,52. Lasers are advantageous in many ways. Because of their high spatial coherence they may be focused onto a very small area and this can result in intense local heating without neighbouring areas being affected. The majority of the laser energy is deposited near the surface of the target, allowing surface regions to be ablated without affecting the bulk. It is also relatively easy to control a laser’s energy density or fluence53.

Fluence (Jcm-2) = laser pulse energy (J) / focal spot area (cm2) (3.1) Radiant Power or Flux (W) = pulse energy (J) / pulse duration (sec) (3.2) Intensity or Irradiance (Wcm-2) = peak power (W) / focal spot area (cm2) (3.3) It is almost impossibly complicated to carry out a detailed theoretical analysis of the ablation process, especially when the substrate melts or vaporises54. However it is possible, making simple assumptions, to adopt models that enable important parameters to be identified and orders of magnitude estimated. Appendix [C] lists some of the most representative theoretical models of the laser-solid interaction, and a brief description of each.

Laser intensity thresholds necessary to produce ablation are sensitive to surface parameters and the purity of the material. Typical reported34 threshold values for LIBS type plasmas on solids are in the range of 108-1010Wcm-2 . A paper by Semerok et al55discusses the thresholds and ablation rates of copper in air for a 532nm, 6ns, Nd:YAG laser.

Laser ablation results in heating and damage to the surrounding area, the degree of which is determined by the rate of energy absorption and the rate of energy loss through thermal conduction in the substrate. In general three types of absorption must be taken into account, volume absorption by the electrons and phonons in the lattice, free carrier absorption at the surface and absorption by the plume.

For ablation to take place there needs to be sufficient heating of the substrate to take it through to the vapour phase. The vaporised material will expand in the form of a plume, the plume being plasma-like, consisting of molecular fragments, neutral particles, free electrons and ions, and chemical reaction products53. The laser energy will continue to heat this partially ionised evaporated material while part of the energy continues to the substrate surface. As the energy increases the plume can become opaque and shield the surface. The ability of a material to absorb laser energy limits the depth to which that energy can perform useful ablation. Generally, reflectance decreases with decreasing wavelength48. This would tend to suggest that shorter wavelengths would be optimum for ablation, but the reflectance of most surfaces reduces during a laser pulse as the temperature rises. Therefore the initial advantage of a shorter wavelength is not necessarily maintained. For a more detailed study refer to Anisimov et al56 who have taken the reflection of light from substrates and the temperature dependence of the reflectance into consideration.

It should also be noted that after the initial pulse, subsequent laser pulses are incident upon a ‘new’ surface, which could have been melted, recondensed, have suffered surface reflectivity changes or be covered with re-deposited material of a composition that differs from that of the original substrate.

In general one can estimate the minimum power density needed to produce vaporisation using the Moenke-Blankenburg57 equation:

2 / 1 2 / 1 min t L I v ∆ = ρ κ (3.4) Where:

Imin = minimum power density (W.cm-2) ρ = density of substrate (kg.m-3)

Lv = latent heat of vaporisation (kJ.kg) ∆t = laser pulse length (s)

κ = thermal diffusivity of specimen (W.m-1.K-1)

The ablation depth per pulse can be calculated using equation34:

(

)

(

)

[

]

Ad = ablation depth per pulse (m) R = fractional surface reflectivity

Cp = specific heat (J.kg-1.K-1) Tb = boiling point (K)

f = fluence (J/m-2) T0 = room temperature (K)

There will be a significant change in ablation rate when working in different pressure environments, a decrease in pressure producing an increase in ablation rate, due to reduced shielding of the sample surface from the incident laser pulse. Work by Multari et al58, Vadillo et al59 and Semerok et al60, studied factors related to ablation rate, such as fluence, laser pulse length, pressure, lens to surface distance (LTSD) and angle of incidence.

Ionisation of the plume emitted from the sample can occur by multiphoton absorption or by avalanche (impact) ionisation. Breakdown thresholds for longer (ns) pulses are usually determined by avalanche ionisation61.

Multiphoton absorption62,63 is a process that was predicted theoretically by Maria Göppert-Mayer in 1929, but was unable to be experimentally verified until the advent of the laser in 1960. In this process an atom may absorb two or more photons simultaneously, (or within less than a nanosecond), in some cases allowing it to be ionized by photons with an energy less than that of the threshold energy due to possible transitions to virtual states.

Avalanche breakdown is the process whereby an energetic carrier creates a carrier pair after colliding with the lattice. These new carriers are then energised by photon absorption and accelerated until the process repeats and an avalanche develops. A study of avalanche breakdown in air has been completed by Kroll and Watson64.

Avalanche breakdown requires the presence of some “priming” free electrons which can be provided by dust particles, by multiphoton ionisation of a gas atom in the beam path or by absorbed impurities in the substrate which are evaporated and ionised below the bulk substrate threshold.

The vapour particles escaping the substrate surface have a Maxwell velocity distribution with vectors pointing away from the surface65. These vectors are changed by collisions with the vapour particles themselves producing a region known as the Knudsen layer66. Within this layer the plume reaches internal equilibrium and rapidly moves away from the sample surface. If the vapour pressure of the plume within this layer exceeds the ambient pressure, the flow velocity becomes supersonic and forms a shock front. Anisimov et al67 has produced a detailed discussion of vapour expansion and condensation.

At low irradiance most of the pulse energy is spent in heating the substrate surface. As the irradiance increases the energy and temperature of the plume increases, thus reducing the efficiency with which energy is imparted to the surface. This increase leads to more absorption creating a positive feedback loop; much of this energy goes into dissociation and ionisation of the plume particles. Thus the incident irradiance reflects the behaviour of the degree of absorption.

When the plume is partially ionised laser light is absorbed via two methods; by thermally excited atoms (bound-free absorption), and by ions (Bremsstrahlung absorption)61. The Bremsstrahlung phenomenon was discovered by Nikola Tesla in research between 1888 and 189768,69. Bremsstrahlung or ‘braking radiation’, also known as free-free radiation, is the process whereby electromagnetic radiation is produced by the deceleration of a charged particle, in this case an electron, when it has collided with another charged particle, in this case an ion. When this process is reversed, and produces an acceleration of the charged particle, is known as inverse-Bremsstrahlung.

Transitions, (radiation or absorption) that an atom or ion can undergo can be summarised using the following diagram:

Where, from left to right we have:

• bound-bound

• free-bound (Avalanche)

• free-free (Bremsstrahlung)

• Ionisation from the ground state

• Ionisation from an excited state

Figure 3.3: Illustration of possible transitions of electrons (Composite drawn from many sources)

Once the plume is fully ionised light absorption is dominated by Bremsstrahlung absorption. In this scenario the plume absorbs all or part of the incident radiation and the energy provided is converted into internal energy of the plume. This energy is consumed as hydrodynamic motion or radiated away as thermal radiation. As mentioned, the plume rapidly expands away from the surface, but this plume also remains confined to a channel formed by the incident light due to interaction of this light with the plume34. This phenomenon is commonly referred to as a Laser-Supported Absorption Wave (LSAW). This wave propagates in three zones, plume front, shock front and absorption front as shown in figure

3.334,70,71.

This LSAW can be divided into two classes depending on the incident irradiance, optical density and internal energy of the plume. The first class, known as a Laser-Supported Combustion Wave (LSCW), is a weakly absorbing subsonic wave, the theory of which was formulated by Raizer in 197072.

The layers of cold gas in the plume front are heated by conduction and thermal radiation from the absorption front until they themselves start producing their own radiation. In this regime a fraction of the light absorbed produces the chemical reaction and the propagation is limited to the laser beam channel, both towards and away from the laser source. The wave is also optically thin so the

laser radiation can still reach the surface. The velocity of the LSCW scales with the square root of the irradiance and vanishes at critical irradiance61.

The second class of an LSAW is known as a Laser-Supported Detonation Wave (LSDW). In this class the irradiance increases and in consequence there are increases in the temperature, pressure and velocity of the absorption front. The increased irradiance also results in a larger proportion of the beam flux being absorbed, which in turn contributes to preheating and ionization, and ultimately results in the dominating mechanism of plume expansion becoming compression rather than conduction so that the plume front becomes optically thick. The velocities increase and the wave becomes a supersonic shock wave. The plume is also shown to propagate cylindrically along the beam path due to its mechanism being supported by the laser beam.

At even higher irradiances the wave class changes to what is known as a Laser- Supported Radiation Wave (LSRW), or breakdown wave. In this regime the plasma itself is emitting enough radiation to enable the atmosphere in front of it to become absorbing34. This couples the absorption zone to the plasma front. The propagation of this wave relies on avalanche breakdown, with the avalanche first developing at the focal point (region of highest flux) and then transferring that propagation to areas of lower flux.

A one dimensional approximation study of velocities, pressure, temperature and densities for all classes of laser supported waves has been carried out by Root73 in 1989 and a further study modelling ablation mechanisms, rates and analytical considerations is reported by Bogaerts et al74.

All regimes will be altered with a change in ambient pressure producing a change in the plume size. A higher pressure will slow down and confine the plume whereas at low pressures there will be reduced trapping of the absorbed energy, and as such a plasma lifetime decrease, but there will also be an increase in ablation rate due to less plasma sheilding59.

Review papers have been written by Bogaerts et al74 and Russo et al75, which review the many models of the ablation process with varieties of laser and sample parameters. Papers by Aguilera and Aragon76, Wood et al77, Iriarte et al78, Capitelli et al79 and Gizzi et al80 also provide a good understanding of the ablation/plume process within a LIBS plasma.