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Indium tin oxide ultrafast laser lift-off ablation mechanisms and damage minimization

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Abstract

We draw comparisons between the ablation and damage mechanisms that occur for both film and substrate irradiation using atomic force microscopy, scanning electron microscopy, and pump-probe reflectometry. For substrate irradiation, energy absorbed at the film-substrate interface creates a confined energy situation, resulting in a photomechanical lift-off. A partial ablation at the edges of the ablated zone formed the burr and was reduced in height by minimizing the area subject to the partial ablation threshold fluence. Substrate damage is understood to arise from free electron diffusion from indium tin oxide and subsequent laser heating. We establish a process window for substrate irradiation in a single-pulse ablation regime between approximately two to three times the ablation threshold of 0.18 J/cm2, validating the process window seen in literature and provide a crucial understanding for the ablation mechanisms of transparent conductive films.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Indium tin oxide (ITO) is a transparent conductive oxide with widespread use in optoelectronic devices such as displays, touchscreens, and solar cells as a frontside electrode. Pulsed laser scribing of the ITO layer is a commonly used technique that provides high throughput and selectively etches ITO as the film is more absorptive than the glass substrates they are typically deposited on. The thermal damage produced by laser scribing, such as burr formation or cracking of the film and substrate, is unacceptable for certain applications. Especially problematic is the burr produced around the scribed lines which can be several times thicker than the film itself and may result in short-circuits through subsequently deposited layers [1,2].

Burr formation has been hypothesized to arise from material transport when a surface tension gradient exists due to inhomogeneous and excessive heating of the irradiated spot [3,4]. Following the widespread availability of ultrafast lasers, literature focused on the benefit of the minimized heat affected zone that came with ultrafast laser ablation as most material is removed before it can conduct heat or solidify [5]. It was observed that while the burr was dramatically reduced to tens of nanometers for ultrafast lasers compared to Q-switched lasers, it still remained [6,7]. Most commonly, the ablating pulse is incident from air onto the film, which we refer to as film irradiation, see Fig. 1(a). Various process parameters for ultrafast processing are seen throughout literature, and optimal parameters are commonly found near peak fluences of 1 J/cm2 and pulse overlaps from 50% to 90% [8]. Notably, it was seen that the entire film could not be reliably removed with a single pulse for film irradiation and that the line scribing process benefits from using a high pulse overlap, both in terms of damage reduction and in terms of process efficiency. In a previous work, it was observed that at the optimal processing conditions, ITO is ablated with multiple photomechanical spallation events in addition to a photothermal phase explosion, but only ablates half of the film in depth [8].

 figure: Fig. 1.

Fig. 1. Sample configuration for film irradiation (a) and substrate irradiation (b) schemes in the pump-probe reflectometry setup.

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A handful of publications also investigate the process parameters for an ablating pulse which is focused through a transparent substrate onto the backside of the ITO film, which we will refer to as substrate irradiation, see Fig. 1(b). We have previously studied Mo thin-film ablation for film and substrate irradiation. Here, we saw direct laser ablation for film irradiation and lift-off initiated by a picosecond heating, expansion, and melting at Mo-glass interface for substrate irradiation. Lift-off was observed as the bulging and separation of an intact Mo disk [911]. As a result, significantly less debris and no burr was produced as well being nearly 9x more efficient when compared to film irradiation. Laser lift-off can readily remove entire films with one pulse, where the absorbed energy density necessary for ablation is typically well below 100 J/mm3, the energy density required to vaporize most metals [11]. This is because absorption takes place at the interface between the film and substrate, therefore generating higher pressures than what would normally be attained by heating a free surface in air. The result is a confined energy situation which leads to a photomechanical removal process [1214]. Complete ablation with a single pulse also allows for higher throughput as the scan speed may be increased [1517]. A process window for line scribing is found in the literature for substrate irradiation of ITO on glass substrates ranging from 0.2 J/cm2 to 0.7 J/cm2 for ITO films ranging in thickness from 150 nm to 600 nm and pulse durations from 300 fs to 15 ps. [7,18,19]. The ablation thresholds range from 0.2 J/cm2 to 0.6 J/cm2 and the pulses per position used are comparable to that of film irradiation.

Liu et al. provide an interesting theory on a method on crack and burr reduction outside of the ablated spot seen for substrate irradiation [18]. For laser powers well above the ablation threshold, a reduction of cracking is seen at the edge of the ablated spot. Here, it is hypothesized that the regions at the edge of the ablated spot are subject to partial ablation, which results in the edge of ablated spot fracturing upwards. From this, it can be concluded that there exist separate thresholds for partial and complete film ablation. Cracking may be reduced by optimizing the Gaussian beam parameters such that the area of the film exposed to the fluences between these two thresholds is minimized. A simple method to test this theory is to assume a minimum burr height when the steepest portion of the Gaussian fluence distribution is set to the ablation threshold ${F_{\textrm{thr}}}$. The steepest portion of the Gaussian fluence distribution is found by setting the second derivative with respect to the radius r to zero, given by a Gaussian fluence distribution $F(r )= {F_{0{\; }}} \cdot \textrm{exp}({ - 2{r^2}/w_0^2} ),$ where ${F_{0{\; }}}$is the peak fluence and ${w_0}$ the beam waist radius. This gives a maximum slope at $r = {w_0}/2$ and the necessary peak fluence is therefore ${F_0} = {F_{\textrm{thr}}}\sqrt e $.

Further relevant for substrate irradiation, is that when one works with ultrafast pulses capable of ablation, it is crucial to be aware of the non-linear interaction of the light with the medium through which it is propagating. E.g. Kerr lensing is capable of modifying the intensity distribution of the ablating pulse [20]. This may lead to discrepancies between measured beam waist radii focused in air and the actual intensity distribution following propagation through a non-linear medium. Non-linear absorption in the glass substrate can cause damage in the substrate, leading to longevity problems for devices that undergo mechanical stress [21] or ion diffusion when barrier layers are destroyed [2224]. As non-linear absorption is dependent on the pulse intensity, it is preferable to minimize the intensity while maintaining optimal efficiency while removing the entire film.

It has been demonstrated that irradiation of metallic targets interfacing a dielectric medium can seed optical breakdown by thermionic electron emission which is not otherwise seen for irradiation in air [2527]. Seeing as how the work function of ITO [2830] is comparable to that of glass [31,32] at 4 eV to 5 eV, diffusion of excited free electrons from ITO into glass is seen as a plausible scenario.

We have previously examined the mechanisms of ultrafast laser ablation using time-resolved pump-probe microscopy for film irradiation [8]. In the current publication, we seek to highlight the difference in ablation mechanisms between irradiation incident from the substrate and focused onto the ITO film, referred to as substrate irradiation, and the previously examined film irradiation. It is of interest to investigate whether substrate irradiation can result in laser lift-off, as observed in Mo thin-film systems, and can replicate the efficiency improvement and damage reduction for transparent conductive oxide thin-film systems. To date, we are not aware of any studies that examine the mechanisms of ultrafast laser ablation of ITO using substrate irradiation.

Is ablation photomechanically dominated near the ablation threshold which transitions to photothermal for fluences above the ablation threshold, as is seen for film irradiation in [8]? What is the justification of the parameters and the process window used in previous substrate irradiation ITO publications? Is a minimum of the burr height found where the threshold fluence is set to the steepest portion of the Gaussian fluence distribution? It is crucial to gain an understanding of the damage mechanisms such as burr formation, film cracking, and substrate damage, in order to control the process.

To answer these questions, we begin by characterizing the damage and morphology seen in the ablated spot ex-situ in the final state using atomic force microscopy (AFM) and scanning electron microscopy (SEM). Derived quantities from the final state craters are different process thresholds, burr heights, crater depths and volume, as well as ablation efficiency in dependency of the absorbed fluence. Using this information, we will establish the process window. After the process window is understood, we will use pump-probe microscopy to examine time-resolved observables, such as the transient reflectivity in dependency of distance from the spot center, which indicates the difference in ablation mechanisms throughout the process window. Single pulse experiments are performed to gain a basic understanding of the processes that occur during ablation, avoiding the additional parameters brought about by multi-pulse processing.

2. Materials and methods

A Nd:glass femtosecond laser (femtoREGEN, Spectra-Physics, Inc.) with a pulse duration of (700 ± 100) fs (pulseCheck, APE GmbH), and a central wavelength at (1056 ± 0.5) nm with a spectral bandwidth of (5 ± 0.5) nm (BLUE-Wave, StellarNet Inc.) was utilized for the experiments. The pulse energy measured at the laser head was approximately 50 µJ and was varied using attenuators comprised of a half-wave plates and polarizing beamsplitters. The investigated sample consisted of a 105 nm ITO layer, deposited on a 20 nm – 25 nm SiO2 barrier layer on a 1.1 mm float glass substrate, and has a specified sheet resistance below 20 Ω/□ (CEC020S, Präzisions Glas & Optik GmbH, Iserlohn, Germany), depicted in Fig. 1. The beam waist radius of the ablating single pulse was measured at (15 ± 1) µm (MicroSpotMonitor, PRIMES GmbH) following a plano-convex focusing lens with a focal length of 100 mm. The angle of incidence was 38.7°, which following refraction at the glass substrate becomes 24.2°. The camera pco.edge 4.2 USB (Excelitas PCO) was used in the pump-probe experiments. The probe pulse was a frequency doubled signal of the fundamental laser wavelength. The pulse duration at 1056 nm at the laser head output is 700 fs, and we expect the probe pulse duration to be reduced by a factor $\frac{1}{{\sqrt 2 }}$ following second-harmonic generation, giving an approximated probe pulse duration at 528 nm of approximately 500 fs.

Pulse-integrated photodiode measurements determine the degree of the absolute reflectance and transmittance of the ablating single pulse. This is performed by imaging the reflected and transmitted ablating pulse onto a photodiode (WL-IPD4A, Wieserlabs GmbH) with neutral density filters and comparing this to a reference with no sample. As a result of these measurements, we find the absorbed pulse energy vs. the applied peak fluence. The pulse-integrated photodiode measurement series consisted of a logarithmically spaced fluence distribution, ranging from the noise level of the photodiode setup at a peak fluence of 0.01 J/cm2, to the maximum peak fluence of the setup at 5 J/cm2. Further information about the pulse-integrated photodiode setup and its results are found in Supplement 1, section S1.

To determine the area of the ablated spots for the ablation threshold determination, a brightfield microscope (Leitz ErgoPlan) with a 50x objective was used. The ablation threshold as per Liu et al. [33] was determined from the measured area of the ablated spots from the pulse-integrated photodiode measurement series. The effective squared ablation diameter $D_{\textrm{eff}}^2$ was calculated using the area of the elliptical ablated spot with the relation $D_{\textrm{eff}}^2 = \frac{{\pi A}}{4} = \frac{{2w_0^2}}{{\textrm{cos}(\theta )}}\ln \left( {\frac{{{F_0}}}{{{F_{\textrm{thr}}}}}} \right)$, where A is the measured area, and θ the angle of incidence.

AFM (JPK Instruments, NanoWizard I) with the tapping mode was using to determine the topography of the ablated spot with a height resolution of several nm, laterally limited by the probe tip (Olympus, OMCL-AC160TS-R3), with a nominal tip radius of 7 nm. This methods has proven to be more accurate than the white-light interferometer we used in our previous publication [8], which was subject to a systematic error in the measured height of few tens of nm due to the influence of the thin-film system on the height evaluation [34]. AFM measurements were performed on the ablated spots following the pulse-integrated photodiode measurements to determine the average burr height, maximum crater depth, and volume. For the burr height, we average the maximum values recorded at each row, the AFM fast axis, where the burr is present, excluding particles that do not contribute to the burr. For the crater depth, the same technique is applied for the average minima of the inner 1/3 of the ablated spot. The complete crater volume is measured to determine the ablation efficiency when compared to the absorbed pulse energy. Additionally, 1D AFM profiles were taken along the minor axis of the ablated spots from the pump-probe measurement series.

SEM (LRYA3, TESCAN) was used to investigate the topography of the fine-structured surface of the ablated PPM with a secondary electron (SE) detector. The backscatter electron (BSE) detector provided contrast between the atomic number for the elemental compositions visible on the sample. Furthermore, the ratio between tin and indium could not be quantified as the observable characteristic X-ray lines have a spectral resolution of 125 eV, which resulted in overlapping tin and indium L-lines in the recorded spectra. The accelerating voltage had been set to 7 kV. To avoid charge build-up in the non-conductive ablated spots, a thin platinum layer with a thickness of 1.6 nm was deposited onto the sample surface following the AFM and pump-probe measurements, but prior to SEM imaging.

A conceptual visual representation of the pump-probe reflectometry setup is given in Fig. 1, where a beamsplitter is used for directing the reflected signal onto the camera. For film irradiation during pump-probe measurements, a layer of matte adhesive cellophane tape is applied to the glass-air interface to suppress reflections of the probe at this surface, as seen in Fig. 1(a). These reflections otherwise contribute to the measured reflectivity with a delay of about 12 ps, interfering with interpretations of the change in reflectivity of the ITO itself as mentioned in [8]. The time delay of zero in the pump-probe measurements was calibrated using the ultrafast Kerr effect in ITO with a peak intensity of approximately 70 GW/cm2 or one fourth of the ablation threshold. For a more detailed description of the PPM setup, please see [8,9].

Pump-probe measurements were carried out for peak fluences that were equal in terms of absorption for film irradiation and substrate irradiation, which approximately equal 2 and 4 times the threshold fluences. To provide quantitative comparisons between the reflectivities imaged with the PPM for film and substrate side configurations, it is necessary to multiply the recorded relative reflectivity values with the overall reflectance of the samples, giving the absolute change in reflectance. This is due to the fact that the sample has a different overall reflectance depending on whether or not the cellophane adhesive tape is present, corresponding to 13% or 10%, respectively.

Bulging heights for observed Newton’s rings may be calculated through the relation $h = m\lambda /2n$, where λ is the wavelength, n the refractive index of ITO at λ, assumed constant, and the number of observed intensity maximum gives the order m [8]. The order m is a discrete number which is valid at the intensity maxima which corresponds to constructive interference. Therefore, heights were calculated at the discrete intervals at the reflectivity maxima found during the bulging. If the maxima were not visible due to scattering or absorption of the probe, the closest point along the minor axis to the center where the oscillations were visible was used to determine the height. A linear fit was applied to the heights versus the delay times to determine the bulging velocity.

3. Results

The pulse-integrated photodiode measurements, which were performed to determine the degree of absorption, may be found in Supplement 1, section S1.

3.1 Final state observables

The effective squared ablation diameter $D_{\textrm{eff}}^2$ at the air interface was examined with a brightfield microscope and plotted in Fig. 2(a). AFM measurements above the threshold fluence to determine the ablated spot morphology, as discussed in the materials and methods, are plotted in Figs. 2(b)-(d). For images of typical ablated spots, please see Fig. 3.

 figure: Fig. 2.

Fig. 2. Final state observables for film (blue squares) and substrate (orange circles) irradiation. (a) Squared effective ablation diameter $D_{\textrm{eff}}^2$ vs. irradiated peak fluence on a semilogarithmic axis with its regression lines. ${F_{\textrm{thr}}}$ and ${F_{\textrm{NL}}}$ indicate the ablation thresholds and the threshold for non-linear self-focusing, respectively. (b) Average burr height of each ablated spot, where the shaded region marks the standard deviation. ${F_{Burr}}$ expresses the threshold of burr height minimization. (c) The average maximum ablated depth, where the shaded blue and orange regions mark the standard deviation. (d) Volume of removed material per absorbed pulse energy are shown on the left axis and values for the absorbed pulse energy per volume of removed material are shown on the right axis. The hashed regions indicate the process windows for substrate and film irradiation from left to right, respectively.

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The parameters of the $D_{\textrm{eff}}^2$ fits in Fig. 2(a), which give the calculated ablation thresholds ${F_{\textrm{thr}}}$ and effective beam radii ${w_{\textrm{eff}}}$, are found in Table 1. The regression lines are plotted to indicate the x-intercept, which correlate to the calculated ablation thresholds of 0.21(5) J/cm2 and 0.18(5) J/cm2 for film and substrate illumination, respectively. At ${F_{\textrm{NL}}} = \; $0.6 J/cm2 the approximated threshold of non-linear self-focusing in glass from Fig. 2(a) (orange dots) is indicated by a reduced slope of the $D_{\textrm{eff}}^2$ plot corresponding to a distinct reduction of the effective beam waist radius ${w_{\textrm{eff}}}$ for substrate irradiation. Here it is seen that although substrate irradiation has an ablation threshold 0.03 J/cm2 lower than film irradiation, the measured $D_{\textrm{eff}}^2$ values are comparable at the ablation threshold and the substrate irradiation $D_{\textrm{eff}}^2\; $values become lower than those for film irradiation for increasing peak fluences approaching ${F_{\textrm{NL}}}$. Here it can be understood that self-focusing has an impact on ablation threshold fit, as seen by the deviation from the orange regression line in Fig. 2(a), which may result in a slight underestimation of the ablation threshold for substrate irradiation.

Tables Icon

Table 1. ${ D}_{{\textrm eff}}^2$ regression results and film removal thresholds

Burr heights determined from the AFM measurements are displayed in Fig. 2(b). A distinct reduction of the burr height for substrate irradiation is observed above peak fluences of ${F_0} = $ 0.4 J/cm2. This threshold is labeled as ${F_{\textrm{Burr}}}$ and denotes a reduction of the burr height below 250 nm. This peak fluence lies slightly above the predicted value of ${F_0} = $ 0.30 J/cm2 using the relation ${F_0} = {F_{thr}}\sqrt e $ defined in the introduction, where the highest slope of the irradiating Gaussian intensity is expected [18]. The burr height for substrate irradiation continues to reduce until a minimum is achieved at ${F_0} = $ 0.65 J/cm2, which roughly corresponds to ${F_{\textrm{NL}}}$, where self-focusing is observed in the $D_{\textrm{eff}}^2$ plot in Fig. 2(a). Above ${F_0} = $ 0.65 J/cm2, the burr height for higher peak fluences increases by a few tens of nanometers. The burr height for film irradiation is seen to remain constant at approximately 100 nm for all peak fluences.

The crater depths derived from AFM measurements are shown in Fig. 2(c). For substrate irradiation, the average of the maximum crater depth across all rows demonstrates that a penetration of the ITO film occurs at ${F_0} = $ 0.4 J/cm2 and above, where also the SiO2 layer is penetrated above ${F_0} = $ 0.6 J/cm2. For film irradiation, the penetration of the ITO film occurs at ${F_0} = $ 1.6 J/cm2. The process window in for substrate irradiation in Tab. 1 is determined in the region where the entire film is ablated (${F_0} = $ 0.4 J/cm2), yet the SiO2 layer is not penetrated (${F_0} = $ 0.6 J/cm2).

The ablation efficiency is shown in Fig. 2(d). We see that substrate irradiation within the process window remains more efficient than film irradiation. The ablation efficiency, given here by the volume removed per absorbed pulse energy, is seen to have a maximum near 40 µm3/µJ for substrate irradiation near ${F_0} = \; $0.45 J/cm2. The absorbed pulse energy was determined from the pulse integrated measurements in Supplement 1. Similar to other works with a homogenously heated material, we see that the ablation efficiency for substrate irradiation is found at approximately e times ${F_{thr}}\; $[35]. For film irradiation, utilizing multiple overlapping pulses to scribe galvanic isolating lines is preferential to avoid damage of the SiO2 layer entirely [8]. Therefore, the process window for film irradiation in Tab. 1 is suggested at the onset of maximum efficiency near 20 µm3/µJ from ${F_0} = $ 0.5 J/cm2 up to 1.3 J/cm2, before the onset of SiO2 damage. For both irradiation configurations, the absorbed energy density is seen to remain significantly below 100 J/mm3 within the process windows.

Now that the process window and the absorbed pulse energy have been determined, we move onto identifying the exact ablation mechanisms within the process window, comparing sets of identical absorbed energies near both ends of the substrate irradiation process window. The ablation mechanisms was examined in [8] for film irradiation, and we will now compare the ablation mechanisms for film and substrate irradiation corresponding to at twice and four times of the threshold fluence, by means of secondary electron (SE)-SEM and PPM. Figure 3 displays a side-by-side SE-SEM comparison of ablated spots for film and substrate irradiation. SE-SEM imaging of the ablated spots without the 1.6 nm Pt layer revealed that peak fluences above ${F_0} = $ 0.4 J/cm2 underwent charge buildup and were no longer considered conductive. Note that the shown irradiated fluences and effective beam waist radii differ when comparing film irradiation and substrate irradiation, which accounts for the mismatch seen in the ablated area as verified by Fig. 2(a).

 figure: Fig. 3.

Fig. 3. Secondary electron SEM images with 1D AFM depth profiles taken along the minor axis of the ablated spots are shown above the overview images (b) and (k) for film irradiation by (a) and (j), and below the overview images (c) and (l) for substrate irradiation by (d) and (m), respectively. Close-ups of sections indicated by the labeled dotted boxes in the overview images are found in (e)-(h) and (n)-(q). (i) and (r) refers images taken with a tilt stage with an angle of 55°, viewing outwards from the center of the spot. (i) and (r) are imaged on the opposite side of the ablated spot from the location of (h) and (q), and therefore not visible in the overview images (b), (c), (k) and (l). Please note the differing scale bars for each image.

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3.1.1 Morphology at twice the ablation threshold

The AFM 1D depth profiles for film irradiation are displayed in Fig. 3(a) for film irradiation and Fig. 3(j) for substrate irradiation. The burr for film irradiation seen in Fig. 3(e) is comprised of solidified droplets, where a typical height profile for a droplet is visible on the right side of the profile in Fig. 3(a). Cracking was prevalent approximately 750 nm outwards of the burr is observed in Fig. 3(e), which extends across the entire ablated spot. Cracks observed in the center of the ablated spot in Fig. 3(f) produce grain islands similar in size to those seen outside of the droplet burr. For substrate irradiation droplets are observed throughout the ablated spot, see Fig. 3(g). No cracking is observed inside of the ablated spot. For Fig. 3(h), the burr for substrate irradiation is comprised of a continuous strand of material where liquid material has been ejected, characterized by the solidified droplets, approximately 200 nm in width, drawn outwards. A representative height profile of a typical burr is seen on the left side of Fig. 3(d), with a width of about 0.5 µm. Cracking that extends approximately 1.5 µm outwards of the burr is observed. Crevices demonstrate the mechanical dislocation of the burr from the rest of the intact film. Figure 3(i) displays SE-SEM images with a tilt stage at a 55° angle of incidence which reveals that a void is found below the burr. Stalagmite-like structures are observed within approximately 1 µm inwards of the burr.

3.1.2 Morphology at four times the ablation threshold

Similar findings to Fig. 3(e) are found at the edge of the ablated spot at circa four times the ablation threshold in Fig. 3(n). Cracking is seen in Fig. 3(o) which produce islands similar to those seen in Fig. 3(f). Notably, an elliptical crevice produced by the cracking is found at the transition from decreasing to constant depth in the 1D AFM depth profile as one moves inwards. Similar to Fig. 3(a) and 3(d), typical height profiles of the burr may be seen at the either side of the height profiles. In Fig. 3(p), droplets are found in the inner 5 µm of the ablated spot. These droplets, concentrated in the center, are seen to be about tens of nm in height, compared to the larger droplets otherwise seen that are typically 100 nm in height. By imaging the backscattered electrons, shown in the Supplement 1, it was observed that the atomic number of the droplets concentrated in the center is lower than those typically seen, which suggests that these are primarily comprised of Si produced by glass ablation whereas the other droplets are comprised primarily of In or Sn. As the electron beam is approximately 1 µm in diameter, an analysis per energy dispersive X-ray spectroscopy of the constitutes of the observed droplets, typically limited to 100 nm in diameter was not possible.

3.2 Pump-probe reflectometry

Stop-motion pump-probe reflectometry measurements at selected delay times may be observed in Fig. 4. Videos of the pump-probe images may be found in the Visualization 1, Visualization 2, Visualization 3 and Visualization 4. The numerated effects from 1 to 6 observed for film irradiation which have been discussed in detail in [8] are summarized below and their equivalents are labeled for substrate irradiation, which additionally displays an effect 7. A description of the observed effects 1–7 is given below.

 figure: Fig. 4.

Fig. 4. Stop motion images showing the relative reflectivity at different delay times recorded with the pump-probe reflectometry setup. The color bar on the left shows the colors which correspond to a given relative reflectivity value. Delay times are found below the images. The same AFM 1D depth profiles as displayed in Fig. 3 are depicted on the right. Labeled numerated effects are marked with dotted lines in the first row of images and for effect 6 in the second row at 1500 ps. A detailed description of effects 1 to 7 are found in the main text.

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Effect 1: a) Increase in reflectivity due to free electron generation for film irradiation during pump irradiation. b) Quenched increase in reflectivity due to free electron generation for substrate irradiation compared to that of film irradiation during pump irradiation. Effect 2: a) Drop in reflectivity due to the formation of a liquid-gas mixture that scatters and absorbs the probe signal for film irradiation, visible after about 10 ps after electron-phonon coupling has taken place. b) Prolonged drop in reflectivity due to absorptive liquid-gas mixture for substrate irradiation. Effect 3: Newton’s rings inside the spot due to a spherical bulging film, growing in height and consequently an increase in the number of rings as time progresses. This effect is visible after a few hundred ps. Effect 4: Diffraction rings appear outside the spot due to the presence of a sharp edge and occurs simultaneously with film bulging. This occurs due to Fraunhofer diffraction by imaging with an objective with a limited acceptance angle or numerical aperture. A detailed discussion of the diffraction rings with supporting simulations are given the in the Supplement 1. Effect 5: The probe scatters on particles as the film disintegrates after about 1 ns. Effect 6: A second set of Newton’s rings, observable from a delay time of about 1 ns. Effect 7: A change of the refractive index as the beam propagates through glass, which is incident from the bottom of the image due non-normal angle of incidence. A positive change in reflectivity with a maximum in relative reflectance of about 0.1 at -600 fs, and a temporal FWHW of about 900 fs is visible at in the center of the dotted box marked by effect 7, about 15 µm below the center of the irradiated spot. As the increase in relative reflectivity at a delay of 0 ps is only about 0.05, this reversible effect is visible in the images as a slight whitening of the area inside of the dotted box near a delay time of zero.

The change in the angle of incidence due to refraction is evidenced through the reduction of the ellipticity of the irradiated spots when comparing film irradiation to substrate irradiation. Further notable differences between both irradiation schemes are seen in the amplitudes of effect 1, the contrast difference of effect 3, as well as the contrast and spacing of effect 4. Effect 7 can be understood as a change in the refractive index of the glass substrate due to the Kerr effect and is consistent with self-focusing seen in Fig. 2(a) ($D_{\textrm{eff}}^2$).

Figure 5(a) shows a contour plot of the relative reflectivity change, given by the color, across the minor axis of the irradiated elliptical spot, the x-axis, to at given delay times along the y-axis. This is useful for demonstrating the magnitude of the changes in relative reflectivity in dependence of beam radius given a Gaussian spatial beam profile. In other words, the localized fluence has a localized impact on an effect’s characteristics throughout time. Figure 5(b) shows the change of the absolute reflectivity at the center of the irradiated spot for an evaluation radius of 2 µm. This allows for a quantitative comparison of the temporal progression of the relative reflectivity changes observed in the contour plot. To compare between film and substrate irradiation, it is necessary to show only the change in absolute reflectivity, as the reflection from the glass-air interface under film irradiation is suppressed with matte cellophane adhesive tape, reducing the overall reflectivity from 13% to 10% for the probe wavelength.

 figure: Fig. 5.

Fig. 5. (a) Contour plots of the relative reflectivity change for four different peak fluences with the observed effects and the same numbering scheme as Fig. 4. The effects are shown in dotted black boxes. (b) The absolute change in reflectivity for 12 µm2 in the center of the irradiated spot and the shaded regions show the standard deviation. The absolute change in reflectivity is shown here instead of the relative change in reflectivity.

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Effect 1, increase in reflectivity, in Fig. 5(a) has an amplitude and decay rate that is dependent on the fluence, where the amplitude is higher and the decay time lower for a higher irradiated fluence. Effect 2, drop in reflectivity, has a longer lifetime and onset for a higher irradiated peak fluence. For effect 3, the contrast of the Newton’s rings is highest for fluences that are near the ablation threshold (e.g. at the edge of the ablated spot), and that a higher degree of absorption and scattering is present for an increase in fluence. The diffraction rings, effect 4, are seen to persist approximately 1 ns longer for substrate irradiation when compared to film irradiation.

In Table 2, the absolute and minimum reflectance values and delay times are displayed along with the exponential rise and decay times. The maximum values are approximately 3 times larger for film irradiation than for substrate irradiation. The rise time refers to the time between 10% and 90% of the maximum ΔR on the rising flank. The exponential decay time refers to the time for a decay of 63% from the absolute maximum ΔR value to the minimum ΔR values given in Table 2. Notably, we see that exponential decay and absolute minimum values between the two irradiation schemes are similar, yet that the time until a minimum value is two to four times longer. We see no impression of a non-linear effect from the rise and decay times but would expect transition times significantly faster than the cross-correlation time of the pump and probe signals for stronger irradiation that would result in an optical breakdown, as is the case for gold in water [25].

Tables Icon

Table 2. ΔR Maxima, Minima, and Exponential Decay Values

In Table 3, the bulging speed calculated from the calculated height of the film at various delay times, as described in the Materials and Methods, is given. Here it is seen that the film irradiation velocities are 2 to 3 times those of the substrate irradiation velocities. The second bulging velocity is noticeably lower at 88 m/s. We may further compare the kinetic energy at twice the ablation threshold of the two irradiation configurations as these peak fluences display less of a photothermal influence when compared to four times the ablation threshold. We may then use the relation ${E_\textrm{k}} = \frac{1}{2}mv^2$, where ${E_\textrm{k}}$ is the kinetic energy, m the mass, and v the velocity. As volume is proportional to mass, we use interpolated of the measured volume used in Fig. 2(d) to approximate the photomechanically ejected volume for the pump-probe measurement series at twice the ablation threshold to find the ratio of the kinetic energy of the ejected film for both irradiation configurations. As a result, we find that the ratio of the kinetic energy of the ejected volume for film irradiation vs. substrate irradiation with this approximation is 6.6.

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Table 3. Bulging Velocities

To summarize the notable findings, interconnected bridges and a void beneath the burr is, as well as notably thicker cracks outside of the ablated spot is observed for substrate irradiation. Burr heights remained constant near 100 nm in height for film irradiation whereas burr heights range from 200 nm to 400 nm for substrate irradiation depending on the applied peak fluence. Self-focusing is observed for peak fluences above 0.6 J/cm2 for substrate irradiation. A process window of 0.5 J/cm2 to 1.3 J/cm2 for film irradiation and 0.4 J/cm2 to 0.6 J/cm2 for substrate irradiation is determined. Substrate irradiation shows a quenched increase in reflectivity during pump irradiation, as well as a longer delay time required to attain the absolute minimum for reflectivity. Substrate irradiation exhibits decreased contrast in Newton’s rings and increased contrast and duration of diffraction rings. The kinetic energy of the spalled layer for film irradiation is approximately 6.6 times larger than layer ejected by lift-off for substrate irradiation for an equal amount of absorbed energy at two times the ablation threshold.

4. Discussion

4.1 Ablation mechanisms

We examine the ablation mechanisms in terms of a thermodynamic relaxation following laser heating of ITO, categorizing photomechanical and photothermal processes. For film irradiation, the energy is primarily absorbed at the ITO-air interface and results in a spallation or phase explosion when stress confinement conditions are relevant [8]. Recent simulations have confirmed the photomechanical nature of the ablation process [36]. For substrate irradiation, the energy is primarily absorbed at the ITO-glass interface, which creates confined energy situation that drives a photomechanical lift-off.

The ablation mechanisms for substrate irradiation are seen to be photomechanical near the ablation threshold, visible in Figs. 4 and 5 by film bulging, effect 3, and flat depth profiles [37]. The ablation mechanism transitions towards photothermal at higher fluences due to the increase in absorption and scattering seen in Fig. 5(a), effects (2a) and (2b), as well as a partial rounding of the depth profiles [37]. A decrease of the absolute minimum is seen in Table 2 for an increase in the peak fluence for both irradiation configurations. This decrease indicates a stronger contribution of scattering and absorption from a liquid-gas mixture, whose droplet density is increased by a stronger photothermal contribution. The additional time for absolute minimum decay in Table 2, 100 ps – 200 ps for substrate irradiation compared to ca. 50 ps for film irradiation, may be understood through the higher pressures present in substrate irradiation as no free surface is present. Since higher pressures are present, the complete decay into the gas phase and its expansion therefore takes longer [10].

The contrast of the Newton’s rings, Figs. 4 and 5(a), effect 3, for substrate irradiation is notably lower in the center of the irradiated spot compared to film irradiation, especially for higher peak fluences. In the case of film irradiation, it is not necessary for the probe signal to travel through the liquid-gas mixture separates the spalled layer from the rest of the film to give contrast to the Newton’s rings. The contrast of the Newton’s rings may be understood as a partial reflection from the top and the bottom of the bulged surface. In the case of substrate irradiation, the probe makes a round trip through the liquid-gas mixture before the signal from the two partial reflections of the bulged surface can be detected.

The diffraction rings, effect 4, for substrate irradiation is approximately 4 times larger and persist about 3 times longer than for film irradiation. This is consistent with the observed bulging velocities in Table 3, which were approximately 3 times slow for substrate irradiation. Here it may be concluded that ejected film for substrate irradiation undergoes disintegration at a later time than for film irradiation. The sharp edge exists due to bulging, which is consequent of void formation and gas expansion below the film, exemplified by Fig. 3(i) and (r). The contrast of the rings is discussed in detail in the Supplement 1.

Through the measured energy densities necessary for ablation, shown by Fig. 2(d), we see that the process remains primarily photomechanical as the absorbed energy densities required for photothermal ablation remain well below 100 J/mm3, as discussed in the introduction. The maximum ablation efficiency of substrate irradiation, 40 µm3/µJ, is seen to be approximately double that of film irradiation at 20 µm3/µJ. When comparing kinetic energies from the bulging velocities in Table 3, we see that considerably more energy goes into accelerating the ejected film for film irradiation compared to substrate irradiation. This factors into the ablation efficiency as more energy is used to accelerate the film than is necessary for its removal. It is also worth revisiting that the ablation thresholds for both film and substrate irradiation are found at a peak fluence of about 0.2 J/cm2, Fig. 2(a) and Table 1. It has also been observed for Mo on glass for film thicknesses comparable to the optical penetration depth that the ablation thresholds for both film and substrate irradiation are comparable, where the ablation mechanism is driven by melt dynamics [10,38]. Recent simulation results have shown that the transient optical penetration depth of the ITO film is approximately that of the film thickness during pump irradiation [39].

Figure 6 shows a schematic depiction of the ablation mechanisms for film irradiation above the second bulging threshold and substrate irradiation above the SiO2 damage threshold, adapted from [8]. During the presence of the pump pulse, free electrons are generated and excited in the ITO which diffuse into the glass, effect 1. These electrons are subsequently excited by the laser pulse and excite further bound electrons in the glass. Once the critical free electron density is surpassed, depicted by the red dotted line, glass ablation occurs [40]. The ablation of glass is discussed in further detail in section 4.2. After several picoseconds, considerable lattice heating has occurred through electron-phonon coupling. ITO or SiO2 undergoes a phase change to the liquid and gas state following heating of the material. The reflectivity of the irradiated spot drops due to a scattering liquid-gas mixture, effect 2. For hundreds of picoseconds, the film begins to bulge upwards, effect 3, due to gas expansion at the ITO-glass interface. Light reflected at the sharp boundary of the bulged film is not able to be collected by the objective due to the limited range of accepted angles and results in the diffraction rings seen, effect 4. For thousands of picoseconds, the bulged film separates from the film and begins to disintegrate, effect 5. The liquid at the edge of the ablated spot is ejected outwards, as seen in Fig. 3, and arrows indicate where pressure is applied for substrate irradiation. Interconnected molten bridges cool and solidify under the burr. The formation of the burr is discussed in further detail in section 4.2.

 figure: Fig. 6.

Fig. 6. Ablation mechanisms for film and substrate irradiation with delay time ranges indicated in each panel. The green arrow represents the probe signal, which is reflected or absorbed at various locations throughout the sample. The numeration is analogous to those given in Figs. 4 and 5. The white region in the represents free electron excitation, effect 1. The red dotted line refers to a free electron density that overcomes a critical density that results in SiO2 ablation. The orange regions refer to material in the liquid phase. The darkened regions refer to a liquid-gas mixture that scatters and absorbs the probe signal, effect 2. For effect 5, cracking and disintegration occur in ITO and the black arrows in the cavity refer to force exerted due to pressure.

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When comparing the process mechanisms for substrate irradiation to film irradiation, Fig. 6, three notable differences are seen. The first is the non-linear interaction of the light with electrons in the glass, effect 7. The second is that we do not observe a second bulging event, effect 6, for substrate irradiation. The third is the upwards dislocation of a solid rim of material seen for substrate irradiation in Fig. 3, resulting from a partial ablation below the film surface.

4.2 Damage mechanisms

It is crucial to understand the underlying mechanisms behind ablation to minimize the damage while scribing ITO. The two types of damage that are of utmost concern for substrate irradiation is the burr formation as well as damage of the SiO2 barrier layer or glass substrate, seen in Fig. 2(b) and (c). The former may hamper device efficiency as the burr may form a partial short-circuit through subsequently deposited active layers in optoelectronic devices, creating a shunt as mentioned in the introduction. This effect is relevant if the thickness of the active layer is sufficiently thin such that it is in the same order of magnitude as the burr. The latter poses a longevity issue as damage to the substrate may lead to cracking of the substrate [21] or alkali ion diffusion from the float glass substrate into the ITO, which forms non-conductive phases within the ITO, increasing the resistivity [22]. Cracking of the ITO layer itself following ablation was observed in Fig. 3 for both irradiation configurations and is unfortunately seen to be unavoidable with laser processing.

The quenched free electron generation, effect 1b, can be attributed to the loss of free electrons in ITO due to diffusion that would otherwise be contained for an ITO-air interface [25]. As mentioned in the introduction, the work functions of ITO and glass are comparable at 4 eV to 5 eV. The suspected driving factor for the loss of reflectivity is additional free electron generation that occurs within the volume of the glass substrate during pump irradiation. As free electrons are generated and diffuse throughout the volume of the substrate, absorption throughout the growing interaction volume sharply increases. This has been confirmed in the case of bulk glass processing where the electron plasma is seen to “grow” towards the incoming laser pulse [41]. The mechanism of the SiO2 and glass damage are therefore understood to come from direct laser heating of excited free electrons in ITO that diffuse across the potential energy barrier between ITO and SiO2 due to the similar work function [25].

The burr is formed during the bulging of the surface for both irradiation configurations, which ranges from delay times between hundreds and thousands of picoseconds where effect 3, Newton’s rings, and effect 4, the diffraction rings, are most visible. Incomplete void nucleation during ablation at lower fluences, particularly near the edge of the ablated spot, results in the stalagmite-like structures seen in Fig. 3(i) and (r), otherwise known as interconnected liquid bridges [42,43]. Following the separation of the bulged film, the droplets solidify into the elongated droplets near the ablated spot edges seen in Fig. 3(i) and (r). In the case of a partial ablation where the film above the void formation is not ejected, the solidified bridges are observed in the final state in Fig. 3(i). Additionally, for substrate irradiation, liquid material is seen to have been ejected outwards upon separation of the ejected film, as evidenced by Fig. 3(h) and (q). Similar to [44], it is understood that the straining and subsequent separation of the liquid sidewall of the bulging film is ejected outwards by the high vapor pressures generated during laser lift-off. Cracking outside of the spot, Fig. 3(h) and (q) occurs due to void formation below the surface, where the pressure from ablation applies torque on the edge of the stationary solid film, which readily undergoes mechanical failure as solid ITO is known to be a brittle material [45,46].

4.3 Process window

The process window for substrate irradiation, whose process window ranges from peak fluences of 0.4 J/cm2 to 0.6 J/cm2, is notably narrower than for film irradiation, 0.5 J/cm2 to 1.3 J/cm2. Our fluence process window with a pulse duration of 700 fs, is similar to that seen in literature for substrate irradiation of ${F_0} = $ 0.2 J/cm2 to 0.7 J/cm2, where the deviation may be understood through the influence of pulse durations used in the literature, ranging from 300 fs to 15 ps. Literature on ITO scribing does not provide a strong consensus on the optimal pulses per position for both film and substrate irradiation, but typically utilizes 2 pulses per position or 50% overlap and upwards. For film irradiation, a pulse overlap of at least 50% or 2 pulses per position is beneficial for efficient galvanic isolation, removing the film with multiple pulses, as the ablated film depth is not constant throughout the ablated spot within the process window, as discussed in [8].

The proposed solutions to minimize burr heights and substrate damage determined our process window for substrate irradiation. It is seen that a peak fluence of at least 0.45 J/cm2 is needed to reduce the burr height for substrate irradiation to 200 nm, seen in Fig. 2(b), which is hypothesized to be reduced by minimize the amount of area affected by partial ablation ITO. This is done by setting the steepest part of the Gaussian intensity distribution at ${F_{\textrm{thr}}}$. The observed minimum at ${F_0} = \; $0.65 J/cm2 is higher than that calculated at ${F_0} = \; $0.3 J/cm2. What is observed, is that following the initial decrease with increasing peak fluences, the burr height remains somewhat constant at 200 nm for a further increase in peak fluence past 0.45 J/cm2. Here, it is understood that self-focusing maintains the burr height by reducing the beam waist radius, thus giving a steeper Gaussian fluence distribution.

To minimize SiO2 and substrate damage, it is crucial to work below the penetration threshold of the SiO2 near ${F_0} = $ 0.6 J/cm2, seen in Fig. 2(c). At ${F_0} = $ 0.69 J/cm2 for substrate irradiation, all ITO near the substrate is ablated and SiO2 is partially ablated, leaving behind silicon (oxide) droplets, as seen in Fig. 3(p) and Supplement 1. Yet, peak fluences below 0.4 J/cm2 suffer from burr heights above 200 nm and an incomplete removal of the ITO layer. Furthermore, we see charge buildup in the SEM for peak fluences above 0.4 J/cm2 when no Pt layer is sputtered. Based on this information, we can assume galvanic isolation for peak fluences above 0.4 J/cm2.

From our single pulse experiments, it appears favorable to use a low pulse overlap for substrate irradiation, around 30% or ca. 1.5 pulses per position, removing the entire film efficiently with one pulse. Liu et al. have demonstrated that using a 100 pulses per position results in fewer cracks observed near the edge of the ablated line compared to 10 pulses per position [18]. This demonstrates that the use of multiple pulses may be beneficial for complete removal of the material found in the partial ablation regions seen for substrate irradiation.

Depending on the application, it may be favorable to use film irradiation or substrate irradiation for the galvanic isolation of ITO. Substrate irradiation is favorable when the substrate is transparent, does not contain ions that will diffuse into ITO and reduce conductivity, the substrate is not subjected to routine mechanical stress, and when burrs of 200 nm will not create problematic short-circuits in subsequently deposited thin films. As the process window is relatively narrow, 0.4 J/cm2 – 0.6 J/cm2, the manufacturing tolerances for the beam parameters are relatively small. This entails an accurate determination of the beam waist radius and pulse energy, as well as maintaining these values throughout production.

5. Conclusion

In this work, we have made the first comprehensive study of the ultrafast ablation mechanisms for substrate irradiation of ITO where time-resolved pump-probe measurements combined with morphology analysis give a key insight into damage formation. A laser lift-off process is observed above the ablation threshold where, similar to film irradiation, a transition from a photomechanical dominated process at the threshold is seen to give way to a more photothermal process at higher fluences. The process window for substrate irradiation is established between peak fluences of 0.4 J/cm2 and 0.6 J/cm2 where charge build-up is observed in SEM, suggesting that galvanic isolation is achieved, the burr heights are minimized, the ablation efficiency is maintained, and the SiO2 barrier layer damage is minimized. Whereas, pulse overlap of at least 50% is necessary for efficient galvanic isolation for film irradiation, it is seen that the entire film can be reliably removed with one pulse using substrate irradiation.

SiO2 damage is seen to originate from direct laser absorption within the SiO2 when free electrons diffuse from the ITO into the SiO2 and undergo further electron heating and free electron ionization. This effect is minimized by utilizing peak fluences below 0.6 J/cm2. The burr formation mechanism is now understood as a combination of a fracturing of the edge of the ablated spot and the ejection of liquid material, as depicted by Fig. 6. Burr heights are reduced as per the findings of [18] when the area of the film subjected to a partial ablation at the ITO-glass interface is minimized. The optimized burr height is approximately twice as large at 200 nm for substrate irradiation when compared to film irradiation which has typical burr heights at 100 nm.

Our suggested process window allows for a larger industrial throughput as it is optimized for a low pulse overlap, maintains efficiency, and minimizes damage. With the information presented in this manuscript, we extend the knowledge of the ablation mechanisms of ITO and the origins of damage during laser processing. This allows for robust process optimization as a dependency between the underlying physics and laser parameters is provided.

Funding

Deutsche Forschungsgemeinschaft (423531130).

Disclosures

The authors declare no conflicts of interest.

Data availability

The raw data underlying the results presented in this paper are not publicly available at this time. Specific datasets of interest may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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Supplementary Material (5)

NameDescription
Supplement 1       Supplement
Visualization 1       Pump-probe reflectometry video for film irradiation at a peak fluence of 0.43 J/cm².
Visualization 2       Pump-probe reflectometry video for substrate irradiation at a peak fluence of 0.38 J/cm².
Visualization 3       Pump-probe reflectometry video for film irradiation at a peak fluence of 0.86 J/cm².
Visualization 4       Pump-probe reflectometry video for substrate irradiation at a peak fluence of 0.69 J/cm².

Data availability

The raw data underlying the results presented in this paper are not publicly available at this time. Specific datasets of interest may be obtained from the authors upon reasonable request.

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Figures (6)

Fig. 1.
Fig. 1. Sample configuration for film irradiation (a) and substrate irradiation (b) schemes in the pump-probe reflectometry setup.
Fig. 2.
Fig. 2. Final state observables for film (blue squares) and substrate (orange circles) irradiation. (a) Squared effective ablation diameter $D_{\textrm{eff}}^2$ vs. irradiated peak fluence on a semilogarithmic axis with its regression lines. ${F_{\textrm{thr}}}$ and ${F_{\textrm{NL}}}$ indicate the ablation thresholds and the threshold for non-linear self-focusing, respectively. (b) Average burr height of each ablated spot, where the shaded region marks the standard deviation. ${F_{Burr}}$ expresses the threshold of burr height minimization. (c) The average maximum ablated depth, where the shaded blue and orange regions mark the standard deviation. (d) Volume of removed material per absorbed pulse energy are shown on the left axis and values for the absorbed pulse energy per volume of removed material are shown on the right axis. The hashed regions indicate the process windows for substrate and film irradiation from left to right, respectively.
Fig. 3.
Fig. 3. Secondary electron SEM images with 1D AFM depth profiles taken along the minor axis of the ablated spots are shown above the overview images (b) and (k) for film irradiation by (a) and (j), and below the overview images (c) and (l) for substrate irradiation by (d) and (m), respectively. Close-ups of sections indicated by the labeled dotted boxes in the overview images are found in (e)-(h) and (n)-(q). (i) and (r) refers images taken with a tilt stage with an angle of 55°, viewing outwards from the center of the spot. (i) and (r) are imaged on the opposite side of the ablated spot from the location of (h) and (q), and therefore not visible in the overview images (b), (c), (k) and (l). Please note the differing scale bars for each image.
Fig. 4.
Fig. 4. Stop motion images showing the relative reflectivity at different delay times recorded with the pump-probe reflectometry setup. The color bar on the left shows the colors which correspond to a given relative reflectivity value. Delay times are found below the images. The same AFM 1D depth profiles as displayed in Fig. 3 are depicted on the right. Labeled numerated effects are marked with dotted lines in the first row of images and for effect 6 in the second row at 1500 ps. A detailed description of effects 1 to 7 are found in the main text.
Fig. 5.
Fig. 5. (a) Contour plots of the relative reflectivity change for four different peak fluences with the observed effects and the same numbering scheme as Fig. 4. The effects are shown in dotted black boxes. (b) The absolute change in reflectivity for 12 µm2 in the center of the irradiated spot and the shaded regions show the standard deviation. The absolute change in reflectivity is shown here instead of the relative change in reflectivity.
Fig. 6.
Fig. 6. Ablation mechanisms for film and substrate irradiation with delay time ranges indicated in each panel. The green arrow represents the probe signal, which is reflected or absorbed at various locations throughout the sample. The numeration is analogous to those given in Figs. 4 and 5. The white region in the represents free electron excitation, effect 1. The red dotted line refers to a free electron density that overcomes a critical density that results in SiO2 ablation. The orange regions refer to material in the liquid phase. The darkened regions refer to a liquid-gas mixture that scatters and absorbs the probe signal, effect 2. For effect 5, cracking and disintegration occur in ITO and the black arrows in the cavity refer to force exerted due to pressure.

Tables (3)

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Table 1. D e f f 2 regression results and film removal thresholds

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Table 2. ΔR Maxima, Minima, and Exponential Decay Values

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Table 3. Bulging Velocities

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