Ablation depth

In non-highly focussed laser desorption ionisation, employing spot sizes in the range of 50-200 pm in diameter, the surface is deformed by an ablation volume of about 1 pm3 per pixel per laser pulse. But this ablated volume is spread over a large desorption area leading to ablation depths of the order of a few nanometres. In laser microprobing, the same ablation volume leads to ablation crater depths in the micrometer range. 

Figure 5. Yield of deposition as a function of ablation depth for various polymers. See Table I for acronyms.

The ablation depths are measured by profilometry (optical interferometer, mechanical stylus [59], atomic force microscopy [60]) and starts sharply at the threshold fluence. Similar conclusions can be drawn from reflectivity [61] or acoustic measurements [62]. The problem with these measurements is that either single- or multi-pulse experiments are used to determine the ablation depths and threshold which might give different results. 

Photochemical volume models [56, 57, 72-74], reveal sharp ablation thresholds and lead to logarithmic dependence of the ablated depths per pulse. Such models may also result in a linear dependence if the movement of the ablation front is taken into account, and if the screening by ablation products is ignored. These models cannot explain the previously described Arrhenius tails observed in mass loss measurements. 

One comment is appropriate here. The modeling of ablation depths at high fluences is not sensitive to the underlying mechanisms of ablation itself. At such fluences ablation rates of most polymers are quite similar [90] and are determined by screening of the radiation by the ablated products [80, 82] or generated plasma [91]. 

In recent studies of a photochemical model, attention was drawn to the absorption properties of the polymer during the laser pulse [132, 174]. These results were analyzed theoretically using a two-level model of chromophore absorption [175]. In this model, excited states of the chromophore are capable of photon absorption. The model is shown in Fig. 21. In Eqs. 2 and 3 the single photon absorption for ablation depth and transmission ratio is described,... 

Fig. 30 Ablation depth vs pulse fluence relationship for the 308-nm XeCl excimer laser irradiation of a 200-pm-thick polymer film. The experimental data are taken from [11]. The dash-dot curve indicates the predicted relationship based on Beer s law. The continuous curve uses n=4 to reach a satisfying fit. The dash curve shows the result of a different fit parameter, n=12, which must be used to reach a satisfying fit of the transmission ratio in Fig. 27. REPRINTED WITH PERMISSION OF [Ref. 60], COPYRIGHT (1996) Springer Verlag...

The majority of a series of shadowgraphs recorded at a laser fluence of 50 mj cm 2 are displayed in Fig. 38 and most of those from a series of experiments with a 250 mj cm 2 fluence laser are shown in Fig. 39. The time zero chosen for these photographs was at the peak of the excimer laser irradiation [209]. In this time zero reference, a photo was also taken at time=-4.8 ns for the 50 mj cm-2 fluence laser and at time=-7.2 ns for the 250 mj cm 2 fluence laser. Although both of these negative time photos were well after the beginning of the laser irradiation, neither showed any indication of shock wave formation or material expansion [94]. A depth profiler was used to measure a final ablation depth of 50 nm in one of the 50 mj cm 2 fluence case experiments and 650 nm in one of the 250 mj cm-2 fluence case experiments. 

Avalanche coefficient Linear absorption coefficient Effective absorption coefficient Ablation depth per pulse (=ablation rate) Diameter of ablated (modified) area Thermal diffusivity... 

A first ex situ inspection of the laser-generated structures on the different sample surfaces was performed by means of light microscopy (e.g., Reichert-Jung, Polyvar). The microscope featured the opportunity for a vertical and lateral measurement of various patterns with a resolution better than 1 pm. Therefore, absolute ablation depths and ablation depths per pulse d (for multipulse treatment) could be determined. Additionally, lateral cavity diameters D were measured in the case of hole drilling. 

From a physical point of view, but also in the context of the application of laser pulses for micromachining purposes, the determination of ablation rates d (=absolute ablation depth divided by the number of pulses per spot N) and ablation threshold fluences Fth is essential. 

Fig. 14 Absolute vertical precision of ablation Ad for different pulse durations r, derived from the 99% confidence interval of the slope of ablation curves (ablation depth vs number of pulses) for fused silica (FS) and barium aluminum borosilicate glass (BBS) [45]...

Additionally, Fig. 13 suggests a higher vertical and lateral ablation precision when shorter pulses are employed. Figure 14 depicts the absolute vertical ablation precision Ad vs pulse duration t. Ad describes the shot-to-shot deviation of the ablation depth per pulse d from its mean value for a 99% confidence interval [42]. The d-values were extracted from [24]. For both fused silica (FS) and barium aluminum borosilicate glass (BBS), a tendency of an increasing vertical ablation precision with decreasing pulse duration is clearly evident. This trend is expected to become even more pronounced if data obtained at F0/F = const rather than F0=const could be compared. Figure 14 visualizes that with pulses shorter than 10 fs, an absolute vertical ablation precision of the order of 10 nm can be achieved. 

Fig. 31 Ablation depth per pulse d vs laser fluence F0 for the treatment of human enamel ( ) and human dentine (A).r=300 fs, A=615 nm, N=100. The straight lines are fits using a d ln(F0/Fth) dependence. Solid line human enamel dashed line human dentine [81]...

The ablation depth per pulse d vs laser fluence F0 at enamel and dentine is depicted in Fig. 31. The data follow a logarithmic law according to Eq. 6. The ablation threshold fluence Fth was determined by extrapolating the d(F0)-cmve to Fth=F0(d=0). Ablation thresholds of Fth(N=100)=0.6 J cm-2 for healthy human enamel and Fth(N=l00)=03 J cm-2 for healthy human dentine can be derived. The lower threshold for dentine may be a result of preferential ablation at an increased number of structural defects. Human enamel consists mainly of hydroxyapatite. For comparison, a monocrystalline fluoroapatite was evaluated. The ablation threshold fluence amounts to Fth(N=100)=0.8 J cm-2 [81] which is slightly higher than the F of human enamel. 

Also, the method how the ablation parameters are acquired can have a pronounced influence on the results. The ablation rate can be defined either as the depth of the ablation crater after one pulse at a given fluence, or as the slope of a linear fit of a plot of the ablation depth versus the pulse number for a given fluence. Very different ablation rates can result from the two different measurement methods. This is especially the case for materials where ablation does not start with the first pulse, but after multiple pulses, or if the ablation crater depth after one pulse is too small to be measured. The process that occurs if ablation does not start with the first laser pulse is called incubation. It is related to physical or chemical modifications of the material by the first few laser pulses, which often results in an increase of the absorption at the irradiation wavelength [32,33], for example, the formation of double bonds in poly (methylmethacrylate) (PMMA). Incubation is normally observed only for polymers with low absorption coefficients at the irradiation wavelength. 

FIGURE 14.15 Interference measurement for TP1 during irradiation with 308 nm. The black curve represents the laser pulse, while the gray line corresponds to the phase shift, which is related to the ablation depth. 

The ablation is quantified by means of the ablation rate, i.e. the ablated depth per pulse. Generally, the ablation rate is insignificant at fluences below a threshold jhtence. Above this threshold, the ablation rate increases dramatically. This is demonstrated in Fig. 9.6 [51] for a commercial polyimide. It can also be seen in Fig. 9.6 that the threshold fluence decreases with shortening wavelength. 

For laser ablation of polymers, the key parameter is the laser fluence. Each combination of polymer material, laser wavelength, and pulse duration has a distinctive threshold fluence, below which no ablation takes place. The typical ablation depth vs. laser fluence is shown in Fig. 3. It plots the average ablation depth of poly(methyl methacrylate) at different fluences with a 193 nm excimer laser [4]. 

The drilling of anodically bondable Pyrex glass is demonstrated by Keiper et al. [272]. An excimer laser mask processing technique (248 and 193 nm wavelength, 10 ns pulse duration) was used. The average ablation depth per laser pulse between 150 and 260 nm depends on the laser fluence, the repetition rate and the diameter of the drilled holes ranging between 30 and 100 im. 

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