1. Introduction

Ultrashort laser pulses are utilized in a broad range of industrial applications such as surface modifications of solid materials and precise micromachining [1,2]. Compared to laser ablation of metals with ns pulses, ultrashort pulses have the advantage of a small heat affected zone [3,4].

Experimental studies on laser material processing of relevant industrial materials, such as stainless steel, aluminium and copper, focussed on the optimization of ablation rate [5] and surface quality [6] by varying the laser peak fluence F₀ [7] and the pulse duration τ_P [8,9]. It was demonstrated that the ablation process shows maximum efficiency at an optimum fluence of e² times the corresponding ablation threshold fluence [7,10]. The influence of the pulse duration on the laser ablation process was investigated for pulse durations ranging from a few tens of femtoseconds to a few nanoseconds. When a pulse duration of 3 ps to 5 ps is exceeded, a steep reduction of the removal rate and effective penetration depth was observed. For copper and stainless steel the removal rate and effective penetration depth δ_eff decreases to about 30% when increasing the pulse duration from 500 fs to 20 ps [11]. Most of these investigations were performed by irradiating the surface with multiple overlapping laser pulses, leading to heat accumulation [12] and incubation [13]. Both effects depend strongly on the pulse duration [14–16]. In order to determine pulse duration dependence without these effects, single-pulse ablation has to be studied [17–19]. In all these previous studies, laser parameters such as wavelength, laser spot diameter, pulse-overlap and repetition rate have been changed from study to study and were even inconsistent within an individual study. Therefore, the experimental findings cannot exclusively be attributed to a variation of the pulse duration. Thus, there is still a gap in the literature regarding a comparative study of pulse duration dependent single-pulse laser ablation.

In the field of theoretical research, a large number of studies focused on the understanding of single-pulse ablation from pulse absorption to material ejection. According to the current state of the art, a sequence of physical processes occurs after laser irradiation of a metal target with pulse durations of a few hundred femtoseconds.

Firstly, the laser pulse energy is deposited in the electronic system by the absorption of the ultrashort laser pulse, characterized by the pulse duration τ_P and an optical penetration depth δ_opt. The thermalization of electrons occurs on a faster time scale than the industrial relevant pulse durations considered here [20,21]. After absorption, a strong thermal non-equilibrium state is induced between the electron and lattice subsystems.

Secondly, the thermal energy is distributed by thermal diffusion within the electron system and to the lattice via electron-phonon coupling, whereby both are functions of the electron temperature [22]. In literature, two different diffusion regimes were observed: The first is attributed to the initial strong non-equilibrium (NE) between electrons and lattice. Here electron temperatures of a few 10,000 K are reached, resulting in a high thermal diffusion coefficient D_NE ≥ 10² cm²/s [22]. Secondly, after establishment of an electron-lattice equilibrium (EQ), temperatures of a few 1,000 K are established and the heat transport is governed by weaker heat diffusion with D_EQ ≈ 1 cm²/s [22]. The spatial extent of heat conduction is considered in this work with a heat diffusion length of δ_diff. The time of energy transfer from thermally heated electrons to the lattice is characterised by the electron-phonon interaction time τ_ep=C_e/G, where C_e is the electronic heat capacity and G is the electron-phonon coupling constant. The evolution of the electron- and lattice-temperatures is described in the framework of the two-temperature model (TTM) [23,24].

Thirdly, the unloading of the energy in the lattice, which is simplified by the idea of a sound wave, transporting the energy out of the heated lattice volume, characterized by a mechanical expansion time τ_mech temporally and a mechanical surface displacement d_disp spatially. When the characteristic time for lattice heating τ_heat - by laser pulse absorption and electron-phonon interaction - is shorter than the time for lattice expansion τ_mech of the heated volume, lattice heating occurs nearly isochorically, resulting in a build-up of high compressive stresses. This condition is referred to as “stress confinement” in literature and is expressed by the notation max {τ_P, τ_ep} ≈ τ_heat ≤ τ_mech [25,26]. The lattice heating time τ_heat is determined by either the laser pulse duration τ_P or the electron-phonon interaction time τ_ep, whichever is longer. The characteristic minimal time that is needed to initiate an expansion of the heated lattice is referred to as the mechanical expansion time τ_mech = δ_opt / c_s, where c_s denotes the sound velocity in the liquid material [25,26]. According to simulations, the interaction of the laser-induced compressive stresses with the free surface of the sample generates sufficiently high tensile stresses to cause an ejection of a liquid layer [27]. This so called spallation occurs at the ablation threshold and a factor of 1.5 higher, indicating a crater surface with a lower nanoscale surface roughness [28]. However, at higher fluences and thus higher temperatures the ablation process is mainly governed by a photothermal phase explosion [26,29], which is induced by homogeneous explosive boiling under a strong lattice overheating and rapid decomposition into vapour and liquid droplets. This occurs at temperatures of approximately 0.9·T_c, where T_c is the critical temperature [30,31], and may create a markedly rougher ablation crater surface [32].

Under irradiation with pulses, longer than τ_ep, the heating time τ_heat of the material is given by the pulse duration τ_P. When τ_P is shorter than the characteristic time of heat dissipation via heat conduction t_th = δ_eff²/D_EQ, the thermal energy remains confined in the deposited volume within the effective penetration depth δ_eff, where δ_eff is composed of the optical penetration depth δ_opt and the thermal diffusion length δ_diff as follows: δ_eff = δ_opt + δ_diff [18,33]. As a result, the condition of thermal confinement is fulfilled and the temperature near the surface is maximized [25]. The generated thermoelastic pressure build-up then causes a thermal expansion of the surface during laser pulse irradiation. Under this conditions the stress-confinement can be regarded as partly fulfilled (attenuated) near the material surface causing a mechanically driven spallation of molten material [34] accompanied by thermally dominated phase explosion of the expanded surface [35]. In fact, several studies have pointed out that phase explosion can occur simultaneously with relaxation of the laser-induced stresses under the condition of stress and thermal confinement [35,36]. From these theoretical studies, the high removal rates with ultrashort laser pulses were attributed to an efficient photomechanical spallation. For longer pulses with pulse durations of tens of picoseconds, the decreasing removal rate was ascribed to a transition from the photomechanical spallation to a less efficient photothermal phase explosion [34,35].

In this study, we carefully designed single-pulse experiments to investigate the pulse duration dependent laser ablation for three industrially relevant metals: stainless steel, aluminum and copper. The study was performed by solely varying the pulse duration from 525 fs to 20 ps and the incident peak fluence, while keeping all other laser and beam parameters constant.

The single-pulse laser ablation analysis starts with the pulse duration dependent ablation thresholds in sec. 3.1 to determine minimum energy density for the onset of material removal. The measurement of fluence and pulse duration dependent reflectivity in sec. 3.2 allows calculating the absorbed pulse energy for a later energetic consideration. The study of the crater morphology in sec. 3.3 indicates the photomechanical or –thermal ablation character. In sec. 3.4 the effective penetration depth δ_eff of the deposited pulse energy is observed for a later comparison to the optical penetration depth δ_opt and thermal diffusion length δ_diff. Finally, we assess the ablation energetics by determining the energy specific ablation volume (ESAV) and energy per volume ablated (EVA) in sec. 3.5 and 3.6, respectively. In Sec. 4 we discuss morphology, effective penetration depth and energetic efficiency in the context of stress confinement. Section 5 summarises the present work with evolved conclusions.

2. Material and methods

2.1. Laser ablation setup

Single-pulse laser ablation experiments were performed under in ambient air using a Nd:Glass laser source (Spectra Physics, FemtoREGEN). The laser source, operating at a constant repetition rate of f_rep = 500 Hz, emitted pulses with a full width half maximum (FWHM) duration of 600 fs at a wavelength λ = 1056 nm (spectral width of 5 nm (FWHM)). For the single-pulse ablation experiments, the laser pulse of 600 fs was varied with a pulse stretcher to obtain a set of six pulse durations (Supplement 1, Sec. 1).

Measurements of the reflectivity as a function of the applied fluence and pulse duration were performed under an incidence angle of 8° by an integrating sphere. The reflectivity measurements are based on the set-up and principle described in Ref. [37]. The single laser pulse was focused by a plano-convex lens with a focal length of f = 100 mm on the sample surface. The integrating sphere was located at a distance of Δz ≈ 1 mm above the sample. The individual single shot event was triggered by a delay generator, which directly receives a trigger signal from the laser source. The area A_sig below the recorded photocurrent curves is proportional to the reflected pulse energy. A Calibration was carried out for each applied fluence by illumination of 100% reflecting barium sulphate, which yielded the reference area A_ref. The total absorption is then given by A(F₀) = 1-[A_sig(F₀)/A_ref (F₀)], where F₀ = 2·$\overline P$ / (f_rep·πw₀²) denotes the incident laser peak fluence. A detailed description of the setup used for the single-pulse and integrating sphere experiments can be found in Supplement 1, Sec. 1.

In all performed experiments constant beam waist radii (measured at 1/e² intensity level) of w₀ = 15 ± 0.5 µm were prepared with the aid of a beam caustic measurement (PRIMES GmbH, MicroSpotMonitor). Single-pulse experiments were performed using six pulse durations: 525 fs, 1 ps, 3 ps, 5 ps, 10 ps and 20 ps. In order to ensure statistical significance and the suppression of outliers, all measurements were averaged over a sample size of five.

2.2. Sample preparation and analysis tools

Aluminium (Al) and copper (Cu) with a purity of 99.999% as well as the austenitic stainless steel AISI304 with a composition of 72 wt% Fe, 18 wt% Cr and 10 wt% Ni were obtained from Goodfellow GmbH. All samples were produced by a rolling process and have a diameter of 25 mm and a thickness of 1 mm. In order to achieve a flat optical surface, the samples were embedded in epoxy resin and subsequently sanded and polished with polycrystalline diamond suspensions with descending grain sizes ranging from 9 to 1 µm.

In the work at hand, we chose three different metals to cover a wide range of thermophysical properties. AISI304 represents alloys and Al elements with a high electron-phonon coupling resulting in a short electron-phonon interaction time τ_ep in the range of a few picoseconds (Table 1 in sec. 4.1). Cu was chosen as a representation of noble metals, such as silver (Ag) and gold (Au), which exhibit a weak electron-phonon coupling and thus a longer electron-phonon interaction time τ_ep in the range of tens of picoseconds [38]. The selected metals also differ in heat conduction and mechanical properties (Table 1 and Table 2).

Analysis of the ablation crater morphology was performed using a scanning electron microscope (SEM) (TESCAN, LYRA3). The crater diameters for the threshold determination were measured by using an optical microscope (Leica, Ergoplan) equipped with a 50x objective. The topography of the material surface was examined by a 3D optical profiler (Sensofar, Optical Imaging Profiler Plµ 2300). The 3D optical profiler is equipped with a phase shifting interferometer (PSI) unit in order to measure the surface height with 0.1 nm axial and 0.6 µm lateral resolution using a 50x objective.

The raw topography data was analysed with the open source software Gwyddion (Ver. 2.56, released 30 June 2020). Evaluating the 3D profiler images over an area of 250 µm x 180 µm yields an arithmetic average surface roughness of R_a = 1 nm, R_a = 13 nm and R_a = 12 nm for AISI304, Al and Cu, respectively. Note that R_a was derived from data collected with an optical profiler and is thus limited by the axial and lateral optical resolution. The remaining randomly distributed structures inside the ablation crater were also characterized by an average surface roughness, measured over a circular area with half the ablation crater diameter. For the laser wavelength of 1056 nm, the steady-state reflectivity R₀ was measured with an ellipsometer (Sentech, SE 850). The reflectivity values were 68.4% for AISI304, 95.2% for Al and 98.3% for Cu and the optical penetration depths δ_opt were 17 nm, 10 nm and 14.3 nm for AISI304, Al and Cu, respectively.

3. Results

3.1. Single-pulse ablation thresholds

The ablation threshold fluence F_thr was determined by the D²-method [39]. Figure 1 depicts the ablation threshold fluence in dependence of the pulse duration for AISI304, Al and Cu. Starting from a pulse duration of 3–5 ps, the threshold fluence of AISI304 (Fig. 1(a)) and Cu (Fig. 1(c)) shows an increase with increasing pulse duration, while the threshold fluence of Al exhibits a minimum at a pulse duration of about 3 ps.

 

Fig. 1. Ablation threshold fluence F_thr as a function of the pulse duration τ_P for AISI304 in (a), Al in (b) and Cu in (c). Coloured stars indicate comparative literature values in the wavelength range of 1030 nm to 1056 nm.

Download Full Size | PDF

For AISI304 and Cu the lowest respective threshold fluences of 0.27 ± 0.02 J/cm² and 1.80 ± 0.12 J/cm², were found at the shortest pulse duration of τ_P = 525 fs (Figs. 1(a) and (c)).

These values are in good agreement with reported literature values of 0.29 J/cm² for AISI304 (τ_P = 300 fs and λ = 1030 nm) [40] and 1.9 J/cm² (τ_P = 600 fs and λ = 1056 nm) for Cu [41], obtained at comparable laser parameters. For a pulse duration of 6.7 ps and a central wavelength of λ = 1030 nm, the reported values of 0.33 J/cm² for AISI304 and 2.78 J/cm² for Cu [42] (Fig. 1(a) and (c), green stars) also agree well with the presented threshold fluences. Note that the value of 0.33 J/cm² was obtained with a D²-Method fit to the diameter squared data points from Ref. [43] (Supplement 1, Fig. S3). At a pulse duration of 20 ps, an increase to a value of 0.44 ± 0.03 J/cm² for AISI304 and a value of 3.4 ± 0.2 J/cm² for Cu is observed.

For Al (Fig. 1(b)) the threshold fluence drops from a value of 0.62 ± 0.03 J/cm² at 525 fs to a minimum of 0.44 ± 0.02 J/cm² at about 3 ps. Up to a pulse duration of 20 ps, a gradual increase of F_thr to a value of 0.47 ± 0.03 J/cm² can be observed. This trend is in good agreement with the reported literature values (τ_P = 0.5 ps – 10 ps and λ = 1040 nm) in Ref. [44]. The observed minimum at a pulse durations of 3 ps was explained by a reduced heat conduction during the time of the electron-phonon interaction [45].

The F_thr rise above 3–5 ps pulse duration for all three metals was explained by the increase in heat deposition depth due to heat conduction [46]. Overall, the general evolution of threshold fluences is consistent with the works reported in Ref. [11,47].

3.2. Fluence dependent single-pulse reflectivity

To assess the absorbed energy in the materials, we measured the temporal and spatial integrated single-pulse reflectivity, as a function of the applied fluence for pulse durations of 525 fs (full circles) and 20 ps (empty triangles) (Fig. 2). Corresponding ablation threshold fluences are indicated by vertical solid (dotted) line for 525 fs (20 ps). Within the uncertainty of ±1%, the integrated reflectivity R(F₀) at the lowest applied fluence of 0.2–0.3 J/cm² agrees well with the corresponding steady-state ellipsometer values (horizontal dashed lines). When the fluence exceeds the corresponding ablation threshold fluences, a significant decrease of R(F₀) is observed for all three samples.

 

Fig. 2. Measured integrated reflectivity as a function of the incident fluence presented for AISI304 in (a), Al in (b) and Cu in (c). The pulse durations of 525 fs and 20 ps are presented by full circles and empty triangles, respectively. Reference values of R, recorded with a steady-state ellipsometer are depicted with horizontal dashed lines. Corresponding ablation threshold fluences are presented as a vertical solid line for 525 fs and dotted line for 20 ps.

Download Full Size | PDF

For AISI304 (Fig. 2 (a)), the decreasing trend can be divided into two regimes, which are similar for both pulse durations. The first regime, where the initial R(F₀) value of about 68.3% slightly drops to a value of about 65%, ranges from 0.3 J/cm² to about 2.5 J/cm². Above 2.5 J/cm² the second regime begins, which is characterized by a steep drop of R(F₀). Here a reflectivity value of 50% at the highest applied fluence of about 10 J/cm² was determined.

In the case of Al (Fig. 2(b)), the initial reflectivity of 95.2% drops nearly logarithmically for both pulse durations when the corresponding threshold fluence is exceeded. At a fluence of about 10 J/cm², this results in reflectivity values of 85% for a pulse duration of 525 fs and 72% for a pulse duration of 20 ps.

The starting point of the reflectivity decrease for Cu in Fig. 2(c) from the initial 98.3% occurs above ∼0.4 J/cm² at a pulse duration of 525 fs and above ∼3 J/cm² for 20 ps. Comparable values of about 86.5% for 525 fs and 88% for 20 ps pulse duration are achieved at the highest applied fluence.

Since transmission of the thick metallic samples can be neglected, the absorption can be calculated by A(F₀) = 1 – R(F₀), here specular reflected as well as scattered radiation contributes to R(F₀). All measured R(F₀) values for all pulse durations as a function of incident fluence can be found in Supplement 1, Fig. S2. A(F₀) represents spatial and temporal integrated absorption and thus can be used for the calibration of the source term in simulations.

3.3. Crater morphology

In this section, we observe the laser-induced material response in the final state to correlate crater morphology and surface roughness with electron-phonon interaction and thermal conductivity of the three metals. A detailed examination of the ablation craters by scanning electron microscopy is shown in Fig. 3 for AISI304 in (a), Al in (b) and Cu in(c). The surface roughness was determined by means of an optical 3D profiler (sec. 2.2). The left of each subfigure shows a comparison of the whole ablation crater for both pulse durations. On the right, close-ups of the ablation crater edges are depicted.

 

Fig. 3. SEM images of the laser processed surface for AISI304 in (a), Al in (b) and Cu in (c) for laser pulse durations of 525 fs and 20 ps (left). Optical magnification of the crater edge (right). The SEM images were recorded in top view at an applied fluence of 3·F_thr.

Download Full Size | PDF

The ablation crater of AISI304 with the shortest electron-phonon interaction time τ_ep < 3 ps and the lowest thermal conductivity (Table 1) generally appears smooth with sharp melt-induced edges for both pulse durations (Fig. 3(a)). After processing with 525 fs the smooth central part exhibits an average surface roughness R_a ≈ 2 nm, which is slightly higher compared to the pristine surface roughness of 1 nm. While the crater edge shows irregular microscopic patterns. At a pulse duration of 20 ps, the roughness of the central area decreases to R_a = 1 nm. The low crater surface roughness is a result of the slow re-solidification process of the laser-induced nanostructures due to AISI304´s low thermal conductivity [48].

The surface morphology of Al with τ_ep ≈ 3-4 ps and a higher thermal conductivity compared to AISI304 (Table 1) reveals a randomly distributed structure in the form of cellular nanostructures and nano-foams at a pulse duration of 525 fs, similar to those shown in Ref. [49] (Fig. 3(b)).

These nanostructures consist of filaments with a 50 - 100 nm droplet on the tip (Fig. 3(b), right), which are a result of quick solidification on the nanosecond timescale due to the high thermal conductivity of Al [49]. In addition, porous material is visible at the crater edge, containing voids and nano-cavities within a transition zone of about 2 µm, whereby the size and density of the pores decreases radially. At a pulse duration of 525 fs, a lower R_a value of about 9.5 nm was obtained in comparison to the pristine surface roughness of about 13 nm.

After irradiation with 20 ps, the crater surface of Al reveals some additional sub-micron features in the form of blurred circular rims. These remaining sub-micron rims with diameters of about 100–300 nm are more predominant near the crater edge, as depicted in Fig. 3(b) in top right sub-figure. Compared to 525 fs, at 20 ps a reduced transition area of the porous material can be seen at the crater edge. The surface roughness R_a in the central crater area with a value of about 10 nm is comparable to a pulse duration of 525 fs, whereby it remains below the R_a value of the pristine surface.

For Cu with the longest τ_ep ≈ 10 ps and the highest thermal conductivity, the crater surface displays a higher roughness, compared to AISI304 and Al. Similar structures are observed after irradiation with pulse duration of 525 fs and 20 ps (Fig. 3(c)). Traces of the rapid material re-solidification due to the strong heat conduction are visible as sub-micrometre to micrometre-sized structures. For a pulse duration of 525 fs, the ablation crater exhibits sub-micron bubbles randomly distributed throughout the ablation crater area with a diameter of about 300–500 nm. At 20 ps, However, the bubbles increase in size to about 2–3 µm. For both pulse durations, these structures radially decrease in size from the centre to the crater edge until they disappear completely. For a pulse duration of 20 ps, randomly distributed cellular micron structures with spherical tips are detected near the crater edge, whereby for 525 fs a sub-micron eruption structure is more pronounced (right sub-figure). The surface roughness R_a increases by a factor of 2.5 between pulse duration of 525 fs and 20 ps from about 16 nm to 40 nm. In total, both values of the surface roughness are clearly above the R_a value of the pristine surface.

The analysis of crater morphology for AISI304 and Al exhibits a predominantly photomechanical ablation character with low surface roughness, while Cu displays a more photothermal character with a higher surface roughness. A further discussion in the context of stress confinement is given in sec. 4.1 and 4.2.

3.4. Determination of the effective penetration depth

For the determination of the effective penetration depth δ_eff, the ablation depth d_abl was analysed as a function of the irradiated fluence for pulse durations of 525 fs (s. Figure 4, full circles) and 20 ps (Fig. 4, empty triangles). The ablation depths were determined by averaging the area in the central part of the ablation crater and are depicted for AISI304, Al and Cu in Fig. 4(a), (b) and (c), respectively.

 

Fig. 4. Average ablation depth as a function of incident fluence for AISI304 in black (a), Al in blue (b) and Cu in red (c) at a pulse duration of 525 fs (full circles) and 20 ps (empty triangles). The corresponding fit using Eq. (1) is plotted for 525 fs and 20 ps with a solid and dashed line, respectively.

Download Full Size | PDF

The effective penetration depth δ_eff is calculated from the ablation depth d_abl according to a model, which is based on two assumptions: (I) The fluence decays exponentially in the material according to Beer’s-law, introducing the effective penetration depth δ_eff. (II) A threshold behaviour with the meaning that above an ablation threshold fluence F_thr material is ablated and below no ablation occurs. Following these assumptions, the ablation depth d_abl in the low fluence regime [50] is described by

The evolution of the ablation depths with increasing fluences of AISI304 and Al exhibits two pronounced logarithmic dependencies, namely a low and high fluence regime [54]. For strongly heat conducting metals such as Al and Cu, δ_eff is usually larger than δ_opt [55]. Whereby weakly heat conducting transition metals such as iron, tungsten and molybdenum exhibit an δ_eff close to δ_opt [55,56].

For AISI304 (Fig. 4 (a)), the crater depth d_abl increases logarithmically from 5 nm at 0.3 J/cm² to 45 nm at 4 J/cm². At 20 ps pulse duration the crater depths are in the range of 12 nm to 18 nm up to a fluence of 3 J/cm². An effective penetration depth of δ_eff = 15 ± 1.5 nm was obtained at 525 fs. At 20 ps the penetration depth decreases to a value of δ_eff = 4 ± 1 nm.

In the case of Al, the crater depth shows a growth from about 45 nm to 120 nm at 525 fs (Fig. 4(b)). Slightly lower values of the crater depth, ranging from 45 nm to 80 nm are measured for 20 ps for fluences up to 3 J/cm². The determined effective penetration depth of δ_eff = 28 ± 2 nm at a pulse duration of 525 fs decreases to a value of δ_eff = 22 ± 3 nm at 20 ps.

When AISI304 and Al are irradiated with fluences higher than 5 J/cm², the crater depth increases significantly, indicating a second high fluence regime, as depicted in Fig. 4(a) and (b).

In contrast to AISI304 and Al, no second high fluence regime can be identified for Cu, as shown in Fig. 4(c). Since the fluence F₀ does not reach a sufficiently high value to enter the second fluence regime. The effective penetration depths are δ_eff = 63 ± 2 nm at a pulse duration of 525 fs and δ_eff = 50 ± 2 nm at a pulse duration of 20 ps.

In summary, we also can confirm a decrease of δ_eff with increasing pulse duration for single-pulse ablation. This trend of δ_eff has been previously reported for AISI304, Al and Cu, however, for multi-pulse ablation [11,46,52]. The drop of δ_eff is remarkable, since one would expect a higher δ_diff with increasing pulse duration. We will address this in section 4.3.

To gain a better understanding of the ablation process, cross sections of the ablation crater were recorded with a confocal microscope (s. Sec. 2.2). The cross sections are illustrated in Fig. 5 for AISI304 in (a), Al in (b) and Cu in (c) for a fluence of about 3·F_thr (green region in Fig. 6), where F_thr is the respective threshold fluence at 525 fs and 20 ps pulse duration. Solid lines display the cross-section for a pulse duration of 525 fs. The crater profiles for 20 ps pulse duration are presented by dashed lines. The corresponding effective penetration depths δ_eff at 525 fs (taken from Fig. 4) are depicted with a black dashed lines.

The cross-section of AISI304 in Fig. 5(a) exhibits for both pulse duration of 525 fs and 20 ps a nearly rectangular crater structure with a depth of 32 nm and 14 nm, respectively. For Al, a parabolic cross-section with depths of 78 nm for 525 fs and 67 nm for 20 ps is observed.

 

Fig. 5. Ablation crater cross-sections of AISI304 (a), Al (b) and Cu (c) for an applied fluence of about 3·F_thr (green region in Fig. 6). Areas below the solid lines display the cross-section for a pulse duration of 525 fs and the crater profiles for 20 ps are presented with dashed lines.

Download Full Size | PDF

In contrast to AISI304 and Al, the crater cross-section of Cu displays a randomly distributed spikes, which are elongated over about ± 50 nm. This is a manifestation of micro-eruptions (Fig. 3(c)). The estimated crater depth from the ablation crater cross-section is about 113 nm for 525 fs, while a value of 94 nm can be estimated for 20 ps.

3.5. Single-pulse energy specific ablation volume

To compare the single-pulse ablation efficiency with the state of the art of mostly multi-pulse experiments, the Energy Specific Ablation Volume (ESAV) was determined. The ESAV is defined as the ratio of the removed volume V_abl and the irradiated pulse energy E_p. The dependence of the ESAV on the irradiated fluence is visualized in Fig. 6 for AISI304 (a), for Al (b) and for Cu (c) at pulse durations of 525 fs (solid circles with dashed lines), 10 ps (transparent diamonds with dashed lines) and 20 ps (empty triangles with dashed lines). The green hatched areas denote the fluences F_opt where the ESAV is maximal.

Independent of the sample material, all ESAV values have a magnitude of a few µm³/µJ, which corresponds to 333 to 1000 J/mm³, as denoted by horizontal dashed black lines in Fig. 6. The maxima of the energy specific ablation volumes in Fig. 6 can be found in Supplement 1, Table S1.

For all materials, with the exception of Cu being irradiated with 20 ps pulses it can be observed that the general trend of the energy specific ablation volume ESAV exhibits an increase to a maximum (ESAV)_max at an optimum fluence F_opt. This is followed by a decrease of the ESAV with increasing applied fluence. For Cu at 20 ps no global maximum could be observed due to the fact that our set-up only was able to generate a maximum irradiated fluence of 11 J/cm². It might well be possible that Cu irradiated with 20 ps pulses also exhibits a maximum at higher fluences.

The smallest decrease of the ESAV to a level of about 67% is found for Al in Fig. 6 (b), when the pulse duration is increased from 525 fs to 20 ps (Fig. 6 and Supplement 1, Table S1). The ESAV maximum is reached at F_opt ≈ 2.6·F_thr for a pulse duration of 525 fs and at F_opt ≈ 3·F_thr for 10 ps and 20 ps pulse duration. We have normalized the irradiated fluence with the threshold fluence to enable a comparison of the three investigated metals, despite different absorption.

 

Fig. 6. Energy specific ablation volume ESAV as a function of the irradiated fluences in (a) for AISI304 with black symbols, in (b) for Al with blue symbols and in (c) for Cu with red symbols. Full circles with dashed lines at 525 fs, dashed lines with transparent diamonds at 10 ps and dashed lines with empty triangles at 20 ps.

Download Full Size | PDF

For AISI304 a decrease of the ESAV optimum to a level of about 50% is measured, as shown in Fig. 6(a). The energetic optimum of ESAV lies at F_opt ≈ 4.5·F_thr, 3·F_thr and 2.7·F_thr, for pulse durations of 525 fs, 10 ps and 20 ps, respectively.

The largest drop of ESAV to a level of 30% is visible in Fig. 6(c) and Supplement 1, Table S1 for Cu. The related ESAV optimum lies at F_opt ≈ 3.3·F_thr, 2.9·F_thr and 3.2·F_thr, for pulse durations of 525 fs, 10 ps and 20 ps, respectively.

It is remarkable that the presented single-pulse F_opt differ significantly from multi-pulse F_opt, which are located at about e²-times F_thr [10,57,58]. This issue is discussed in section 4.4.

3.6. Calculation of absorbed energy per removed volume

In a next step, we determined the absorbed Energy per Volume Ablated (EVA) to investigate how much energy is used to remove a specific volume from the material. Therefore, the reciprocal of the maximum ESAV at every pulse duration was corrected with the measured absorption from Fig. 2 and expressed in units of J/mm³. In this way, we are able to compare the energetics of the ablation with thermodynamic quantities such as the total energy density required for evaporation.

 Figure 7 illustrates the trend of absorbed EVA values at the respective optimum fluence as a function of the pulse duration for AISI304 (a), Al (b) and Cu (c). The empty circles with dash-dotted lines represent the absorption-corrected energy per volume calculated with steady-state absorption values A₀ (Supplement 1, Sec. 5.i)), which have been compared to the evaporation energy in multi-pulse measurements according to the state of the art [9,59]. In addition, we carried out the correction with the fluence dependent absorption coefficients at the optimal fluence A_IS(F_opt) for all pulse durations (Supplement 1 Sec. 3.ii)), which are depicted in Fig. 7 with full squares and dashed lines.

 

Fig. 7. Absorbed energy per removed volume at optimum fluence for AISI304 in (a) with black symbols and lines, for Al in (b) with blue symbols and lines and for Cu in (c) with red symbols and lines as a function of the pulse duration. The EVA values, corrected with R₀ are depicted by empty circles, while the EVA values corrected with fluence dependent R(F₀) from Fig. 2 are indicated by full squares.

Download Full Size | PDF

The calculation of the total evaporation energy density E_evap was performed using the thermal properties of the three metals (Supplement 1, Sec. 4), which leads values of 38 J/mm³ for Al, 55 J/mm³ for Cu and 68 J/mm³ for AISI304. These values are illustrated in Fig. 7 by black dashed lines.

A first observation from Fig. 7 is that Al and Cu undergo a stronger correction from Fig. 6 to Fig. 7 compared to AISI304, which has a high absorption value (Sec. 2.2). By comparing empty circles with full squares, the same trend can be seen: Al and Cu increase their fluence dependent absorption and thus their EVA stronger than AISI304, which stays almost at the same EVA level. At optimum fluence, however, the fluence dependent absorption coefficients are almost constant for all pulse durations: Thus the general trend of the absorbed EVA with pulse duration, as indicated by dashed lines with circles and squares, is very similar.

Secondly, we notice for all studied metals an increasing EVA with increasing pulse duration. The EVA rises for all samples by a factor of about two from pulse durations of 525 fs to 20 ps. AISI304 and Cu display a significant EVA increase from 10 ps to 20 ps. In Al, however, the significant change occurs up to a pulse duration of 10 ps.

All samples highlight a minimum and almost unchanged EVA below the mechanical expansion time (Fig. 7, vertical green dashed lines, and Table 1). The EVA values at a pulse duration of 525 fs are 176, 35 and 133 J/mm³ for AISI304, Al and Cu, respectively, below the corresponding mechanical expansion times of 5, 3 and 4 ps (s. Table 2).

Thirdly, we observe that the absorbed EVA values at 525 fs are of the same order of magnitude as the energy density for evaporation. With a value of about 35 J/mm³, Al displays the EVA closest to the evaporation energy density of 38 J/mm³. With an EVA of 176 J/mm³ and 133 J/mm² AISI304 and Cu indicate a factor of ∼2.5 higher values than the evaporation enthalpy of 68 J/mm³ and 55 J/mm³. We discuss this observation in sec. 4.4.

4. Discussion

For discussion, we consider the hypothesis of stress confinement (max {τ_P, τ_ep} ≈ τ_heat ≤ τ_mech) by varying the pulse duration τ_P and the electron-phonon interaction time τ_ep to point out the predominant ablation dynamics. To interpret the decrease in effective penetration depths we additionally have to take heat conduction and thermal expansion of the surface into account. Finally, we consider the energetics and discuss the influence of mechanical properties to a mainly thermodynamic process.

4.1. Ideally fulfilled stress confinement for AISI304 and Al: lattice heating is faster than lattice expansion (τ_heatbelow τ_mech)

For AISI304 and Al the mechanical expansion times are 5 ps and 3 ps, respectively. Thus, for an irradiation with a 525 fs pulse and respective τ_ep, of 1–3 ps and 3–4 ps, stress confinement is fulfilled ideally and material removal is primarily caused by photomechanical spallation.

Cu exhibits an electron-phonon interaction time of 10 ps, which exceeds the mechanical expansion time of 4 ps, thus stress confinement is attenuated (Sec. 4.2).

For the weakly heat conductive AISI304 we observe an effective penetration depth of δ_eff = 15 nm, which is comparable to the optical penetration depth δ_opt = 17 nm (Table 1). Here the laser pulse heats the target material within the optical penetration depth under the conditions of a neglectable electronic heat diffusion length δ_diff and a strong electron-phonon coupling, as reported in Ref. [62].

Table 1. The thermophysical parameters k_e, D_EQ and c_s were taken from Ref. [67] for Al and Cu and from Ref. [68] for AISI304.

View Table | View all tables in this article

For the highly thermally conductive Al, electronic heat conduction enlarges the effective penetration depth beyond the optical penetration depth, which is described by δ_eff = δ_opt + δ_diff [69]. We observe a δ_eff = 28 nm and δ_opt = 10 nm (Table 1), thus the contribution of thermal conduction to δ_eff can be determined to be δ_diff = 18 nm. With this value we are able to estimate the effective diffusion coefficient of 0.46 cm²/s (D_NE = δ_diff²/(2τ_ep))), which corresponds to a time and space averaged value during the ablation process of Al initiated with a 525 fs pulse. This is a factor ½ smaller than the literature value, determined at room temperature (Table 1).

The separation of the liquid layer during the spallation process under fulfilled stress-confinement is creating a smooth surface with a R_a of 2 nm for AISI304 and a rougher, cellular nanostructure with R_a = 9.5 nm for Al (Fig. 3). This spallation process in AISI304 and Al was also experimentally observed in our earlier work by spatially and temporally resolved pump-probe microscopy at comparable laser parameters [53].

4.2. Attenuated stress confinement for AISI304, Al and Cu: lattice heating is slower than lattice expansion (τ_heatabove τ_mech)

At 20 ps pulse duration, the thermal confinement is still satisfied, while the stress confinement is attenuated in all three metals. As mentioned before, for Cu this is also the case for 525 fs pulse duration, due to its long electron-phonon interaction time of about 10 ps (Table 1). For all samples in this case, the heating time defined by the pulse duration is longer than the mechanical expansion time: τ_{heat ≈} τ_p > τ_mech.

For AISI304 at 20 ps pulse duration, electron-lattice equilibration is achieved within a few picoseconds, but the heating of the laser pulse continues (Table 2).

As a result of the low heat conduction and high electron-phonon coupling, the absorbed laser energy is confined near the surface [34,62]. Consequently, the relaxation of the laser-induced stresses proceeds localized near the surface and the degree of thermoelastic stress is sufficient to cause a photomechanical spallation, as discussed in Ref. [35]. This is reflected in the morphology of AISI304 at 20 ps pulse duration by a smooth crater surface with R_a = 1 nm (Fig. 3(a) and Fig. 5(a) black dashed line).

For Al at 20 ps and Cu at 525 fs as well as 20 ps pulse duration, there is an almost homogenous distribution of the pulse energy into the depth of the material, due to higher electron heat conductivity compared to AISI304. This leads to the build-up of a lower pressure amplitude and thus to a weaker stress confinement [34]. For the leading edge of the 20 ps pulse, the stress confinement is still fulfilled and a part of the laser pulse energy can be utilized for spallation. The moderate pressure build-up in the laser irradiated region relaxes into a rarefaction wave on timescales given by the mechanical expansion time. When the tensile stress is strong enough during propagation of the rarefaction wave, void nucleation is initiated and bubbles are generated [70] (s. Figure 3(b, c)). As a matter of fact, for Al at a pulse duration of 20 ps we observe bubbles structures with a diameter of 100–300 nm, while in Cu those bubbles have a diameter of 300 nm to 500 nm [32,70] (s. Figure 3(c)) as characteristic traces of phase explosion of the superheated liquids [32].

When Cu is irradiated with a 20 ps pulse, lattice expansion occurs already during pulse absorption and stress confinement is further attenuated. Thereby, the ablation process proceeds through the transient formation of a foamy structure of interconnected liquid droplets accompanied by an even stronger vapour contribution in the form of phase explosion [71]. We measured a R_a value of about 40 nm for the surface structure, which is significantly larger than 16 nm at 525 fs (Fig. 3(c) and Fig. 5(c)). The cross section in Fig. 5(c) highlights significantly that the net ablation volume is reduced.

The morphology of Al at 20 ps pulse duration reveals a stronger vapour contribution during the material ablation than AISI304, but is comparable with Cu at 525 fs. In Cu, at 525 fs and 20 ps the photomechanical ablation process is always paralleled with a stronger contribution of vapour generation than in Al, which is the reason for strong particle shielding and re-deposition effects observed in literature [72–74].

For the attenuated stress confinement condition, it can be concluded that AISI304 shows a purely photomechanical spallation, while the spallation in Al and Cu is accompanied by a stronger contribution of photothermal phase explosion.

4.3. Interpretation of reduced effective penetration depth by early material motion

In the state of the art the decrease of ESAV with pulse duration has been addressed to a drop of the effective penetration depth, which was determined mainly in multi-pulse studies with the approach from section 3.3 (Eq. (1)) [11,14]. It was speculated that mechanical processes could also be the reason for an ESAV decrease with rising pulse duration [41,53]. In the following, we demonstrate that an early mechanical motion of the surface significantly reduces the single-pulse effective penetration depth at a pulse duration of 20 ps. The determined effective penetration depths δ_eff at the different pulse durations are summarized in Fig. 8 and highlight the decreasing trend with pulse duration for all three metals.

 

Fig. 8. Effective penetration depth δ_eff for AISI304 in (a) with black symbols and dashed lines, for Al in (b) with blue symbols and dashed lines and for Cu in (c) with red symbols and dashed lines as a function of the pulse duration lattice expansion time τ_mech taken from Table 1 is depicted with vertical green dashed line.

Download Full Size | PDF

Assuming an electron-lattice equilibrium, the expression δ_diff = (2·D_EQ·τ_P)^1/2 [75] is valid. For a pulse duration of 20 ps, this results in an increase of the heat diffusion length δ_diff compared to sec. 4.1 to 12 nm (AISI304), 62 nm (Al) and 68 nm (Cu).

For 20 ps long pulses and the thermal confinement condition, the surface has sufficient time to expand tens of nanometres above the initial height during the pulse absorption. The generated thermoelastic stress is eventually located in the vicinity of the material surface resulting in surface expansion during pulse irradiation, which consequently results in a reduction of the effective penetration depth, formulated as δ_eff = δ_opt + δ_diff - d_disp. The trailing edge of the laser pulse is absorbed by the expanded surface with a certain surface displacement d_disp during the 20 ps long irradiation. This is observable as a reduction of the effective penetration depth. Figure 8 illustrates that for pulse durations above the expansion time τ_mech (vertical green dashed line) the effective penetration depth δ_eff is gradually influenced by surface expansion, as indicated with black arrows.

From our measurements in Fig. 4 and the heat diffusion lengths, the surface displacements can be determined to 25 nm, 50 nm and 32 nm for AISI304, Al and Cu (s. Table 1), respectively. Such surface displacements correspond to respective expansion velocities of about 1250 m/s, 2500 m/s and 1600 m/s during 20 ps. This velocities agree with the predicted maximum surface expansion velocities of hydrodynamic and molecular dynamic simulations, which provide comparable values between 1000 m/s and 3000 m/s for pulse durations of 15 ps [76] and 6 ps [34]. The onset of the surface displacement of AISI304, Al and Cu starts already 3 - 5 ps after pulse impact due to an ultrafast density decrease, which was also experimentally demonstrated by transient ellipsometric measurements [53,64,77].

In summary, the reduction in effective penetration depth with pulse duration can also be observed with single-pulse ablation. The decrease of the effective penetration depth with rising pulse duration contradicts the expectations of heat diffusion, but reflects the early mechanical motion of the sample surface with a velocity of a few km/s.

4.4. Energetics and stress confinement

Energy specific ablation volume (ESAV): To compare the laser ablation of the investigated materials despite different laser parameters, the ESAV trends are compared at the same multiple of the ablation threshold fluence. We observe that the ESAV maximum for single-pulse ablation lies between 3–4.5 times the corresponding ablation threshold fluence (Fig. 7 and Sec. 3.5) and is consistent with previous studies [18,19]. This differs from previous multi-pulse processing literate findings, which predicted and measured the ESAV maximum at a fluence of e²·F_thr ≈ 7.4·F_thr [10,57,58]. The lower value found in our work is closer to the value of e·F_thr ≈ 2.7·F_thr, which is expected for thin film processing based on a homogenous energy deposition within a certain film thickness [10,57,78,79]. For single-pulse processing, we can conclude that absorption and thermal diffusion in combination with the surface displacement, lead to a nearly homogenously heated material, similar to thin film ablation. Heat accumulation and incubation effects in multi-pulse processing then lead to heating gradient within the depth of the material, which results in the e² - factor.

In a next step, we compare the single-pulse ESAV maxima with multi-pulse experiments from literature. The values in Table S1 in Supplement 1 highlight that multi-pulse processing is a factor of 1.9 (Al), 2.8 (AISI304) and 5.6 (Cu) more efficient than single-pulse processing. The strong efficiency increase in Cu can be assigned to the drastic roughening of the Cu surface (s. Figure 3(c)) upon laser ablation, induced by the strong vapour contribution. We suppose that a successive irradiation with multiple pulses leads to an increase in surface roughness [80], absorption [80] and surface defects [12]. Therefore, it can lead to a significant higher ESAV values of about 3.5 µm³/µJ [81] and 7.7 µm³/µJ [82], respectively, compared to the value of about 1 µm³/µJ in this work for single-pulses.

When increasing the pulse duration from 525 fs to 20 ps, the ESAV maximum at optimum fluence drops to about 67% (Al), 50% (AISI304) and 30% (Cu). The ESAV in multi-pulse laser processing demonstrate a stronger drop to a level of 44% for Al and about 30% for AISI304 and Cu [59]. The higher efficiency, but stronger efficiency drop in multi-pulse processing can be ascribed to heat accumulation and incubation effects [7,8,14].

Absorbed energy per volume ablated (EVA): To find the physical reasons for the efficiency decrease with increasing pulse duration, we investigate the absorbed EVA (Fig. 7, squares data points, and Sec. 3.6) by taking the measured absorbed fluences (Fig. 2) into account.

A general observation is that the absorbed EVA is of the same order of magnitude as the total evaporation energy density (s. Figure 7 and Table 2). At 525 fs pulse duration, the EVA of Al is located close to the total energy density for evaporation. The EVA for AISI304 and Cu are 2.6 and 2.8-times higher than the corresponding evaporation energy, respectively.

Since AISI304 fulfils the stress confinement ideally and exhibits the lowest thermal diffusion, laser ablation of AISI304 should be more efficient, compared to Al and Cu. However, this trend is not reflected in the measured EVA. Therefore, we consider the tensile and spall strength, which are mechanical properties that express irreversible material fracture (Table 2). When considering that Al exhibits the lowest tensile strength of 17 GPa, and a spall strength of 2 GPa, it becomes apparent, why its material removal is energetically most efficient. AISI304 reveals the highest values of tensile strength (35 GPa) and spall strength (5 GPa), and also requires approximately three times more energy for material removal than total energy for evaporation. With a tensile strength of 29 GPa and a spall strength of 3.6 GPa and, Cu lies in between Al and AISI304. This in turn is reflected in the ablation energetics of Cu, where its EVA is located a factor of 2.8 above evaporation.

The higher factor compared with AISI304 may be caused by Cu’s higher thermal conductivity and thus higher dissipation. The laser ablation energetics of the different metals at a pulse duration of 525 fs highlights once again that mechanical processes play an important role in ultrashort laser material removal.

As a final discussion, we focus on the pulse duration dependency of the EVA. The absorbed EVA stays constant for all metals up to pulse durations comparable with the minimum mechanical expansion times (s. Figure 7 and Table 1). From here on up to a pulse duration of 20 ps the EVA rises by a factor of 2.0 for AISI304, 2.2 for Al and 2.5 for Cu.

Table 2. Comparison of the energy specific ablation volume (ESAV)_max with literature values, the energy per volume with total evaporation energies and mechanical spall strength in solid and liquid phase.

View Table | View all tables in this article

As pointed out in sections 4.1 and 4.2, the photomechanical driven spallation process plays a dominant role in single-pulse material removal. When the pulse duration exceeds the mechanical expansion time, the pressure build-up during pulse irradiation is reduced and the degree of inertial stress confinement is attenuated [25]. For pulse durations longer than the mechanical expansion time, more energy is needed for material removal and the mainly photomechanical laser ablation is accompanied by photothermal phase explosion (Fig. 7). The attenuation of the stress confinement and the change from a photomechanical to a photothermal process with increasing pulse duration is also reflected in the increasing ablation thresholds (Fig. 2 and the decreasing effective penetration depths (Fig. 4).

In our previous study of double pulse laser ablation we observed the same ablation efficiency dependency: It turned out, that efficiency maintains its optimum when the inter-pulse delay time was kept within the mechanical expansion time of 3 to 5 ps [41]. As a matter of fact, the change of inter-pulse delay time and pulse duration can be regarded as a tuning of the energy deposition time, leading to the same efficiency trend in the first 3 to 5 ps. In double-pulse experiments the ablation efficiency of Cu also indicates the strongest inter-pulse delay dependency [41].

It is still an open question why Cu displays a higher loss of efficiency than AISI304 and Al, when increasing the pulse duration (as can be seen in Ref. [41] also inter-pulse delay). The EVA for Cu increases a factor of 2.5, despite the fact that Cu indicates a longer electron-phonon interaction time of about 10 ps. The lattice heating time τ_heat is controlled by either the pulse duration τ_p or the electron-phonon interaction time τ_ep, whichever is longer. Therefore, we expect a lower pulse duration dependency of the EVA in Cu, but the opposite was observed. Although Cu highlights a pronounced photothermal ablation with a phase explosion and accompanied vapour-liquid production. Obviously, the reduction of the photomechanical contribution to material removal plays a dominant role. As a result, considerably more energy is consumed for the conversion of the absorbed energy into thermal energy than into mechanical energy, leading to a higher efficiency loss for Cu comparted to AISIS304 and Al.

Irradiated and absorbed energies: At the end of this study it is interesting to compare the irradiated with absorbed energy densities in the material. We have very carefully examined ultrashort single-pulse laser ablation volumes (Fig. 6) and measured the absorption at the irradiated fluences (Fig. 2). At a pulse duration of 525 fs we determined the irradiated energy densities to about 500, 330, 1000 J/mm³ for AISI304, Al and Cu, respectively (Fig. 6, dashed horizontal lines, Table 2). The absorbed energy density amounts to 176, 35 and 152 J/mm³ (Fig. 7) and obviously is significantly lower than the irradiated energy density, but still lies well above evaporation and melting energetics in the order of 50 J/mm³ and 5 J/mm³, respectively (Supplement 1, Table S2). Thus, we can conclude that single-pulse laser ablation even at optimum conditions of pulse duration and fluence is a very dissipative method of subtractive material processing. The vast majority of the energy is simply reflected, even above threshold (Fig. 2), and the absorbed energy still matches or exceeds the evaporation energetics. Increasing pulse duration to 20 ps further reduces the efficiency by a factor of 2 to 3. The process, however, highlights an excellent sub-micron precision at femtosecond laser pulse processing [86].

When considering the more industrial relevant multi-pulse laser ablation with MHz bursts of ultrashort pulses, the irradiated energy density at optimum conditions of pulse duration and fluence reduces to a value of about 170 J/mm³ (Table 2) [11]. Reflectivity value measurements for multiple pulses (N≤10) at fluences close to the optimum range between 50% and 70% [37,87]. Thus, the minimum absorbed energy density has to lie between 50 to 85 J/mm³, which is also located near the evaporation energy density, whereby the precision of multi-pulse processing lies in the order of one micrometre [3,86,88].

Next, we can compare the energetics of ns- or GHz-burst processing [89–91] which is energetically located about one order of magnitude lower than multi-pulse laser processing [89]. This corresponds to an irradiated energy density of about 10-20 J/mm³, which is significantly below evaporation, but above melting energy density. There are no reliable studies on the absorbed energy in this case, so we estimate the absorbed energy with the 30 to 50% from the MHz multi-pulse case. Thus, energetics here would imply a more efficient ablation from a liquid state. Note that both the threshold and the incubation coefficient play an important factor for efficient processing with GHz-burst, which also depend on the number of sub-pulses in the burst, as reported for stainless steel in Ref. [92]. Unfortunately, the trade-off for a lower energy consumption is a reduced few micrometre precision, which is comparable to ns-laser processing [93].

Finally, the specific energy for a widely used mechanical machining process, such as milling or drilling of AISI304 [94,95] were determined to a value of 1 to 5 J/mm³. This value is even lower than the total melting energy density and sets a minimum benchmark with respect to the discussed laser ablation methods.

We can therefore conclude that laser machining is in all considered cases consuming more energy per removed volume than mechanical machining. The methods display a trade-off between energy consumption and machining precision. Mechanical machining resembles below melting energetics, laser methods range from melting to multiples of evaporation energetics.

5. Summary and conclusion

In summary, we present an in-depth analysis of single-pulse laser ablation for aluminium (Al), copper (Cu) and stainless steel (AISI304). We used an identical set-up for the different samples and only changed the applied pulse duration in the range of 525 fs to 20 ps over a wide fluence range. We measured ablation thresholds, depths and volumes, which fit into the state of the art. The decrease of effective ablation depth with pulse duration can be explained by interaction of the expanded surface during irradiation with the laser pulse and underpins once again the thesis of a few ps fast mechanical lattice expansion.

In addition, we determined the fluence and pulse duration dependent absorption of the incident laser pulse, which generally highlights a significantly increased absorption above ablation threshold. The morphological changes evaluated by SEM indicate stronger photothermal effects from AISI304 to Al to Cu and with rising pulse duration.

We study the energetics by calculating the ESAV and EVA. The materials indicate the maximum ESAV at an optimum fluence ranging between 3 and 4·F_thr, which differs significantly from the e² factor in multi-pulse studies. The lower factor in this single-pulse study points to a more homogenous energy deposition. The ESAV drops to 67%, 50% and 30% for Al, AISI304 and Cu, respectively, when the pulse duration is increased from 525 fs to 20 ps. We could explain the drop of ESAV for single-pulses, which has been previously known for multi-pulses. The absorbed energy per volume ablated (EVA) is energetically 2 to 2.5 above evaporation energetics, which is about two or three times higher than for multi-pulses. Single-pulse ablation is dissipative and its relatively high EVA level is reduced significantly by incubation and heat accumulation in a multi-pulse regime.

In our study, we test and confirm the hypothesis of stress confinement by increasing pulse duration and the electron-phonon interaction time from AISI304 to Al to Cu. We can confirm a predominantly photomechanical driven removal process under fulfilled stress confinement, which leads to high efficiency. For an attenuated stress confinement, we expect the simultaneous occurrence of phase explosion producing a less efficient and precise ablation. The highest energetic efficiency is confirmed for pulse durations below the mechanical expansion time of 3-5 ps for all materials.

Compared with mechanical machining, laser ablation is a relatively dissipative subtractive processing method. Our study highlights once again, that for highest efficiency it is important to couple in the energy before lattice expansion starts.