Morphology of single picosecond pulse subsurface laser-induced modifications of sapphire and subsequent selective etching

The effect of 1030nm single picosecond pulsed laser-induced modification of the bulk of crystalline sapphire using a combined process of laser amorphization and selective wet chemical etching is studied. Pulse durations of more than 1 picosecond are not commonly used for this subsurface process. We examine the effect of 7 picosecond pulses on the morphology of the unetched, as well as etched, single pulse modifications, showing the variation of shape and size when varying the pulse energy and the depth of processing. In addition, a qualitative analysis of the material transformation after irradiation is provided as well as an analysis of cracking phenomena. Finally, a calculated laser intensity profile inside sapphire, using the Point Spread Function (PSF), is compared to the shape of the modifications. This comparison is employed to calculate the intensity threshold leading to amorphization, which equals 2.5⋅1014 ± 0.4⋅1014 W/cm2. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Processing of sapphire has been investigated widely by means of dry etching-i.e.plasma etching [6,[14][15][16], wet etching [5,8,17] and mechanical processing like diamond blade sawing [18].Although the capabilities of such methods have been demonstrated, these techniques are applicable to surface processing only.
As sapphire shows a large band gap, it is transparent to laser light with wavelengths ranging from about 0.3 µm to about 4 µm [19], which, in turn, allows the laser beam to be focused below the surface.
When exposed to ultra-short pulsed laser radiation, with pulse durations in the picosecond and femtosecond regime, crystalline sapphire is amorphized due to the absorbed laser energy [20].Hence, an amorphized volume enclosed in the crystalline bulk is formed.When exposed to an aqueous solution of hydrofluoric acid (HF), amorphous sapphire can be etched significantly faster than crystalline sapphire (selectivity 10 5 [20]).Hence, a two-step process, in which sapphire is first exposed to intense laser radiation and subsequently (selectively) etched in HF, allows the fabrication of subsurface structures-i.e.embedded in the bulk of sapphire substrates [11][12][13][20][21][22][23][24].This two-step fabrication method has been extensively studied using femtosecond pulsed laser sources, studying the effects of single pulse exposure [20,25,26] or showing the possibilities of this method in the field of microfluidics or 3D subtractive manufacturing in general [11,13,21].
Unfortunately, only few authors have investigated the characteristics of the method and the resulting armorphous modifications when applying picosecond laser pulses [12].Although more affected by complications due to the heat accumulation, picosecond laser sources are typically more competitive in terms of price and generally more industrially available than femtosecond laser sources.Juodkazis et al. [20,27] state that laser pulse durations above 1 ps induce extensive crack formation, which is attributed to heat accumulation due to high pulse rates.Unfortunately, the authors do not show the extent of these cracks experimentally in sapphire.When carefully tuning the laser parameters heat accumulation and crack formation might be minimized.Moreover, most authors study the laser-induced modifications realized by geometrically overlapping laser pulses, resulting in amorphous "channels" in sapphire [11][12][13]20,21].In order to exploit the two-step process with pulse durations in the picosecond regime, first the morphology and features of the single pulse laser-induced modifications need to be studied.
The phenomena responsible for the final morphology of the single picosecond laser modified sapphire can be roughly divided into three main phases: absorption of laser energy, amorphization of the crystalline sapphire, wet etching of the amorphized material.
The physical phenomena leading to the absorption of laser light and the ionization of the atoms in sapphire are complex and highly nonlinear [28].To trigger the ionization in the material, the electrons on the outer shells have to gain enough energy to pass from the valence band to the conduction band, thus surpassing the ionization energy.At intensities in the order of 10 14 W/cm 2 [29] the material can be ionized [20,22].The wavelength used for this work is 1030 nm; such focused laser pulses have insufficient photon energy to be linearly absorbed.Considering the band gap of 8.8 eV of sapphire, in fact, the wavelength for the linear photon absorption via the band gap, in bulk sapphire can be calculated using the Planck-Einstein relation in vacuum λ 0 = h × c 0 /E g = 0.141µm, where h is the Planck constant, c 0 is the speed of light in vacuum and E g is the bandgap energy of the sapphire used for the experiments.Hence, the linear absorption is not possible with IR radiation.At sufficiently high intensities, though, multiphoton absorption, free carrier absorption, tunneling ionization and avalanche ionization become dominant phenomena enhancing absorption [23,[29][30][31].These phenomena eventually cause an avalanche effect leading to the optical breakdown of the material.
The formation of amorphous sapphire is the result of the optical breakdown of the material near or close to the focus of the laser beam in the bulk of sapphire.The optical breakdown, in fact, causes a violent "microexplosion" generating lattice temperatures in the order of 10 5 K and pressures in the order of 10 12 Pa [22,32].The combined effect of ultra-fast cooling and high pressures triggers formation of amorphous sapphire.
At this stage, when the intensity is high enough, a void may appear enclosed by the amorphous region.In this phase also cracks are generated around the modified area.Figure 1(b) shows a schematic of a typical cross-section produced using the described processes, before the etching.
The phenomena associated with selective etching of amorphous sapphire were proposed by Misawa and Juodkazis [23]: due to a change of the angle in the bonds of the molecule of Al2O3, the amorphous material becomes more reactive to etchants such as hydrofluoric acid.
When processing using high numerical aperture (NA) lenses, optical aberrations "deform" the intensity profile of the laser beam in the bulk [33], which are expected to affect the morphology of the modification, see Fig. 1(a).In this work a detailed parameter study is presented in order to establish a relation between the laser parameters (pulse energy, focus depth) and the morphology (shape, length, width) and material transformations of the single-pulse modifications in the picosecond regime.This involves a detailed analysis of the cross-sections of modifications induced by single picosecond laser pulses (at a wavelength of 1030 nm) at various pulse energies and various locations of the focus below the surface.
A laser source with a fixed pulse duration of 7 ps was chosen for this study.This pulse duration allows to study the effects of pulses longer than 1 ps, but is still short enough to qualify as a duration in the ultrashort pulse regime.
Besides the laser-induced material changes (amorphization and crack formation), the effect of etching is studied.
A simulation tool was used to calculate the optical laser intensity profile inside the bulk of sapphire.These profiles are compared to shape and size of experimentally obtained shape and dimension of unetched modifications, from which the laser intensity threshold leading to amorphization can be derived.

Materials
Crystalline (0001-orientation along C-plane) sapphire wafers of 2" in diameter and a thickness of 430 μm, supplied by Crystec, Germany are used.Both the top and bottom surface of these substrates are polished to optical quality by the manufacturer.

Laser set-up
A Yb:YAG laser source (TruMicro5050 of Trumpf, Germany) emitting pulses of 7 ps of linearly polarized light at a central wavelength of 1030 nm is used, see 1 in Fig. 2. The power density profile of the laser beam is nearly Gaussian (M 2 <1.3).A λ/2 wave plate (2 in Fig. 2), a polarizing beam splitter (3 in Fig. 2), and a beam dump (4 in Fig. 2) are used as an attenuator, allowing to vary the pulse energy.A microscope objective (type 11101666 of Leica Microsystems, Germany), corrected for a 100 µm thick coverslip of silicon (refractive index n = 3.55) and with a numerical aperture of 0.7 is used to focus the laser beam to a diameter of 0.9 μm (calculated), see 9 in Fig. 2. The medium between the objective and the sample is air.A beam splitter (50%-50%, 5 in Fig. 2) and a tube lens (focal length 75 mm, 6 in Fig. 2) are used to image light, originating from the substrate, on a CMOS camera (DCC1545M of Thorlabs, Germany, 7 in Fig. 2).

Analysis tools
Cross-sections of laser-induced modifications in sapphire are imaged by Scanning Electron Microscopy (SEM) using a JSM-7200F SEM of JEOL (Japan).Numerous "rows" of single pulse modifications were produced at different depths below the surface (z-direction in Fig. 3(a)) of the substrate, at different pulse energies.The horizontal distance (in y-direction) between each modification in a row was set to about 10 µm.Four pulse energy levels were analyzed: 4.0 μJ, 7.5 μJ, 10.0 μJ and 18.0 μJ respectively.To prevent optical effects induced by laser processing (too) close to the edge(s) of the sapphire substrate, the laser beam was focused at least at a distance 5 mm from the edges of the sample.Moreover, in order to avoid optical "disturbances" originating from modifications produced above, the first row of pulses was produced by positioning the focus of the laser beam at a distance of 400 µm below the surface.Subsequent rows of modifications were produced at increments of 30 µm (along z direction in Fig. 3) above the first row.By doing so, modifications were produced from 400 µm to as close as 0 µm below the surface.

Methods
The polarization of the laser was set perpendicular to the scanning direction.
After irradiation, the sample was cut with a diamond scribe to allow cross-sectional analysis.After cutting, the edge of the substrate was polished, using a Struers Tegramin polishing device, to approximately the center of the single modifications in the zx-plane, see Fig. 3(b).Best polishing results were obtained by the use of silicon carbide sandpapers for the grinding and subsequent steps of finer diamond pastes (down to 1 µm).
This methodology proved to be a quite elaborated exercise, that inevitably limited the amount of data available for the analysis.
Next, the samples were cleaned in ultrasonic bath with isopropanol and the modifications were analyzed by SEM.The amorphous material in the SEM micrograph appears darker with a different texture than the surrounding crystalline material.
After that, the substrate was immersed in a 50% hydrofluoric acid aqueous solution (BASF, Germany) for about 20 minutes.Subsequently, studying the SEM micrographs allowed a comparison of the unetched and etched modifications.In this way the dimensions of the former amorphous regions were confirmed.
Presented SEM images are characteristic, since obtained data is reproducible.

Simulations
The software tool PSF Lab [34] was used to calculate the electromagnetic field induced by a laser beam focused inside sapphire, which is based on the illumination point spread function.
Input parameters to the simulation tool were the refractive index of sapphire (n = 1.75 at a wavelength of 1030 nm [35]), properties of the focusing objective (numerical aperture, the fact that it is corrected for a coverslip of 100 µm thick silicon, but which is not used in the experiments), the intensity profile of the incoming collimated beam (and the fill factor of the lens), and the distance of the objective relative to the top surface of the sapphire.The software was used to simulate the effect of the location of the focus (inside the bulk) on the intensity profile in the bulk.It should be emphasized that the simulation does not include any physical model of phenomena associated with the absorption of laser radiation.The tool calculates normalized two dimensional cross-sections of the intensity distributions of the electromagnetic field inside sapphire.These fields are rotationally symmetric around the propagation axis of the laser beam and were converted into a three-dimensional profile, using MATLAB [36].Next, the intensity profile was calculated by squaring the absolute electric field in every node in the simulation grid, so |E| 2 .Finally, the intensity profile was scaled in order to match with the laser pulse energy used in the experiments.Comparing the simulation results to the experimental morphology of the modifications, allows to conclude whether the shape and size of the modifications are mainly the result of the beam profile inside the sapphire, or by phenomena associated with the absorption of laser radiation.

Effect of pulse energy on morphology of modifications
Figure 4 shows SEM images of typical modifications, consisting of amorphized sapphire, induced by single laser pulses at four pulse energy levels: 4.0 μJ, 7.5 μJ, 10.0 μJ and 18.0 μJ respectively.These modifications are all located at the same depth below the surface of the sample-i.e. at 30 µm below the surface.Note that, to highlight the details of each modification, the SEM pictures were taken using different magnifications.From these and other, not shown SEM images, it was found, that modifications only occur if the pulse energy is above a threshold of 4 µJ, see Fig. 4(a).As can be observed from Fig. 4, all modifications are elliptically shaped, with the major axis coaxially aligned to the propagation axis of the laser beam.Bulk processing of sapphire is affected by spherical aberrations.The specimen, in this case, acts as a "non-corrected lens" in the path of the laser beam.Increasing the depth of processing causes the stretching of the focal spot (mainly in the z direction), thus, reducing the applied intensity.It can be concluded from Fig. 4 that, the length and width, and therefore the volume of the modifications, increase with the increasing pulse energy.At pulse energies of about 7.5 µJ and higher, a void is observed in the upper center of the amorphized region, see Figs.The position of the void is mainly influenced by absorption phenomena and will be discussed in section 3.4.It was found that the length-i.e.longest dimension (from top to bottom of the pictures in Fig. 4 of single modifications vary from 1.10 µm (for E p = 4 µJ) to 11.30 µm (for E p = 18 µJ).The short dimension, horizontal in the pictures, varied from 0.62 (for E p = 4 µJ) µm to 1.60 µm (for E p = 18 µJ).

The effect of focus depth on the morphology of modifications
Figure 5 shows SEM images of typical modifications, consisting of amorphized sapphire, induced below the surface, by single laser pulses at a fixed pulse energy of 10 µJ, but at four different focus depths: 10 μm, 30 μm, 100 μm and 200 μm respectively.This pulse energy proved to be sufficiently high to modify the bulk at relatively large depths, allowing to study the effect of spherical aberrations in detail.
It was found that, at processing depths of about 100 µm or more, a void no longer occurs within the amorphized region, see Figs. 5(c) and 5(d).It was found that the length-i.e.longest dimension of the modifications varied from 2.3 µm (for a depth of 10 µm) to 5.9 µm (for a depth of 200 µm).The short dimension (width) varied from 1.01 (for a depth of 10 µm) to 0.42 µm (for a depth of 200 µm).

Cracks
The presence of cracks was observed even at the lowest pulse energy of 4 µJ.Varying the depth of processing or the applied pulse energy we found to have a similar effect on the presence (and extension) of the cracks.This suggests that the phenomenon is mainly influenced by the applied intensity.At high intensity, cracks are large and propagating through the material.The most frequent type of crack is displayed in Fig. 6(a), propagating from the bottom of the modification and extending in the direction of the longest dimension of the modification (vertical in the picture).This type of cracks was found for all the energies per pulse analyzed, growing in size typically from 800 nm (4 µJ at 30 µm depth) to tens of microns for higher intensities.
In the case of a pulse energy of 18 µJ (Fig. 6(b)), cracks extended to neighboring modifications.It is assumed that, given the distribution of the modifications inside the bulk of the material, this effect is similar to what was shown by Izawa et al. in [37], where cracks propagate via other close cracks.When a low intensity is applied, and the focus is close to the surface of the substrate, the crack length is similar to the width (shortest dimension of the modification) see Fig. 6(c).
As mentioned, cracks are considered to be caused by thermal effects in particular for pulse durations longer than one ps.However, the cracks shown in Fig. 6(c), are similar to the cracks observed by Juodkazis et al. [22] for femtosecond pulsed processing, where single pulse modifications are surrounded by cracks of the size of the modifications themselves (about 0.1 μm).

Simulation and experimental validation
Figure 7 shows three examples of a comparison of the cross sectional morphology of laserinduced modifications (SEM microgaphs) with "cross-sections" of calculated 2D laser intensity profiles (contour plots), using PSF Lab, for three processing depths and two pulse energies.As can be observed from Fig. 7, the "shape" of the modifications matches well with the shapes of the calculated intensity profiles.From these comparisons, it can be found that, when averaged over 10 measurements at different depths and energies (from these and other not shown SEM micrographs), the modification intensity threshold value for sapphire equals 2.5⋅10 14 ± 0.4⋅10 14 W/cm 2 .
This value matches well with the threshold of 10 13 -10 14 W/cm 2 found in literature for femtosecond processing of sapphire [20,29].
The high standard deviation of the intensity threshold value ( ± 0.4⋅10 14 W/cm 2 ) is attributed to the fact that the determination of the dimensions of the single modifications is limited by the accuracy of the polishing process.In addition, the amount and magnitude of cracks, induced by energy laser pulses, bias the measurements.Nevertheless, the comparison (shown in Fig. 7) shows a strong correlation between the shape of the modification and the laser beam intensity profile in the sapphire, caused by spherical aberration.
The void is always found above the center of the modification (towards the impinging laser beam) and not in the center of the calculated maximum intensity.This phenomenon is attributed to the front of excited electrons, which travel in the opposite direction of the beam, spreading the excited electron density and the absorbed laser energy towards that direction [38].Using PSF lab and MATLAB, the modification intensity threshold was used to calculate the length of the laser-induced modifications as function of the pulse energy and the locations of the focus below surface, see Fig. 8.
In this figure, the central curve of each region represents the value calculated using the modification threshold of 2.5⋅10 14 W/cm 2 .The top and bottom curve of each colored area represent the standard deviation ( ± 0.4⋅10 14 W/cm 2 ) relative to the average threshold value of 2.5⋅10 14 W/cm 2 .The diamond shaped markers are data points as derived from SEM micrographs.
It can be concluded from this graph that, for low pulse energies (pink curve), the intensity is not enough to induce modifications.That is, the curve associated with the 4 µJ (in pink) is only appearing for the lowest modification threshold and only up to about 100 µm focus depth.The curves for 7.5 µJ (in blue) are also "interrupted" for the same reason.For pulse energies of 10 µJ and 18 µJ, the curves are only shown up to a focus depth of about 220 µm-i.e.deeper focus locations result in modifications which are often "disrupted" and difficult to measure.
The measured modification lengths follow the trends of the simulation curves.That is, both the measured and simulated length show a minimum length at a focus depth of about 50 µm.At this focus depth, the objective lens is designed to compensate for the aberrations (about half of the theoretical value specified for silicon).For larger focus depths, the stretching of the intensity profile (caused by the aberrations) and the related loss of intensity play opposite roles in the final dimension of the modifications.That is, stretching of the profile results in an increase of the length of the modification, but the loss of intensity decreases the length.
As can be observed from Fig. 8, the simulation values underestimate the measured length of the modifications.This can be attributed to the fact that the simulations do not take absorption phenomena and the effects of the material heating into account.In fact, nonlinear absorption phenomena could cause an increment in the size of the modification.The same phenomena can cause the void to "move" up towards the incident laser beam.Self-focusing caused by Kerr effect, however, can be excluded because the critical power threshold to trigger this effect is calculated as [25] 2 0 0 2 where λ 0 is the wavelength, n 0 the linear refractive index [1] and n 2 the nonlinear refractive index [39].P crit is at least one order of magnitude bigger than the peak power calculated for the experimental conditions.The presence of large cracks (in particular in the case of a pulse energy of 18 µJ) also biases the measurements of the modifications, thereby causing the measured length to be larger than the length derived from simulated profiles.
Similar results can be found-and conclusions can be drawn-when comparing the measured width of modifications, to the width derived from the intensity simulations.

Morphology of etched amorphous sapphire
Using the procedure discussed in section 2.4, the cross-sectioned samples were etched in order to remove amorphous sapphire.As an example, Fig. 9 shows SEM micrographs of the same modification before and after etching.It was found that the dimensions of the modifications, delimited by the border between crystalline and amorphous, before and after etching were unchanged.That is, the etching process completely removes the amorphous material.This explains why the void, surrounded by the formerly amorphous material (see Fig. 1(b)), is not observed anymore.This leaves an "empty structure".Note that the boundary between crystalline and formerly amorphous is remarkably smooth.These results are very similar to what has been reported by Juodkazis et al. [20,22] for femtosecond laser processing.In addition, also in the case of ps processing, the etching does not have any observable effect on the cracks surrounding the modification

Conclusions
In contrast to femtosecond laser sources, picosecond pulsed laser sources are generally regarded as unsuitable in a two-step method involving laser-induced amorphization bulk sapphire and subsequent chemical wet etching.To study the effect of picosecond irradiation on single pulse modifications, a study has been performed using a 7 ps infrared (1030 nm) laser, varying the energy per pulse (4 µJ to 18 µJ) and the depth of processing (from 0 µm to 400 µm).Both the shape and properties of the modifications were observed.
The shapes and dimensions of the modifications obtained are in line with results found when using femtosecond laser pulses.Like in femtosecond laser processing, we found a relation between the appearance of a void inside the amorphized region and the applied intensity.
A qualitative study on the cracking phenomena was performed, showing that, for low levels of intensity, cracks do originate from the laser-induced modification, but these cracks are limited in extension and resembled the cracks found in literature for femtosecond single pulse modifications.
The shapes of the modification were related to optical laser intensity profiles calculated using the illumination Point Spread Function (PSF).The relation allows to predict the shape of the single modifications in sapphire as function of the pulse energy and as function of the focus location (depth) below the surface of the sample.It was found that the laser intensity modification threshold above which sapphire amorphizes equals 2.5⋅10 14 ± 0.4⋅10 14 W/cm 2 .
Finally, it was found that hydrofluoric etching is affecting only the amorphous material, without causing observable changes on the crystalline sapphire.
Based on this study, we conclude that when carefully tuning processing parameters, picosecond pulsed laser sources can be applied for amorphization and selective wet chemical etching of sapphire.

Fig. 1 .
Fig. 1.(a) The sapphire specimen behaves like a non-corrected lens in the path of the focusing beam and the morphology of the modifications will change depending on the depth of focusing below the surface.(b) After the irradiation, a modified volume is created, enclosed inside the crystalline phase (light blue), which consists of amorphous material (dark blue).Depending on the experimental parameters, a void (black) may or may not occur in the amorphous region.Cracks typically originate from and surround the modified region.

Fig. 2 .
Fig. 2. Schematic of the experimental set-up used for the experiments These components allow to position the focus of the laser beam relative to the surface of the substrate.The sample is mounted on a vacuum chuck, which is positioned in the xy-plane by servo-controlled stages (UPS-150 of Physik Instrumente, Germany) with a resolution (minimum incremental motion) of 15 nm and bidirectional repeatability of ± 35 nm.The objective (9 in Fig. 2) is also positioned by a servo-controlled stage (M-511 of Physik Instrumente, Germany) with a resolution of 50 nm and bidirectional repeatability of ± 200 nm.The laser experiments are carried out in a cleanroom environment (class ISO 8, air exchange rate of 6 times per hour, temperature of 21°C, relative humidity of 40%).

Fig. 3 .
Fig. 3. Schematic process sequence: (a) first, the sample is irradiated to form a pattern (array) of single modifications in rows, repeated at different depths beneath the surface of the sapphire specimen.Here, two rows are shown.The deepest row is formed first, (b) after laser processing the substrate is polished to remove bulk material (red in the graph) in order to "expose" cross-sections of the modifications. 4(b)-4(d).

Fig. 4 .
Fig. 4. SEM micrographs of typical modifications (not etched) induced by single 7 ps laser pulses at 30 µm below the sapphire surface, applying various pulse energies (Ep).On top, for an easy comparison, the micrographs are presented using the same scale.On bottom, to highlight the details of each modification, the pictures have different magnifications (see scale bars).The debris shown in (b) is a polishing particle.The laser beam propagated from top to bottom.

Fig. 5 .
Fig. 5. SEM micrographs of typical modifications (not etched) induced by single 7 ps laser pulses at various depths (depth of processing, DP) below the surface of sapphire, at a fixed pulse energy of 10 µJ.The laser beam propagated from top to bottom.

Fig. 6 .
Fig. 6.Cracks induced by single 7 ps laser pulses at various depths (depth of processing, DP) below the surface of sapphire and various pulse energies (Ep).The laser beam propagated from top to bottom.To show the details of the modifications, they were imaged at different magnifications, see scale bars.

Fig. 7 .
Fig. 7. Three SEM micrographs of modifications obtained at different processing conditions and overlaid calculated 2D laser intensity profiles (contour plots).To highlight the details of the comparison of the experimental data and the calculated data, the images were cropped and show different magnification in vertical and horizontal directions (see scale bars).The laser beam propagated from top to bottom.

Fig. 8 .
Fig.8.The four areas (pink, blue, yellow, red, green for the overlapping area between blue and yellow) represent the length of the amorphized regions (including the confidence intervals) calculated using PSF tool varying the depth below the surface of the specimen.The plot lines are for easy visualization of the trends; the actual graphs were made by single points for each depth.The diamond shaped markers represent the measured values.

Fig. 9 .
Fig. 9. SEM micrographs of a modification produced by a 7 ps pulse at a pulse energy of 10 µJ, and a focus location at 30 µm below the sapphire surface, (a) before and (b) after etching for 20 min in stagnant 50% aqueous solution of hydrofluoric acid at room temperature.