Femtosecond-laser induced ablation of silicate glasses and the intrinsic dissociation energy

Moritz Grehn; Thomas Seuthe; Michael Höfner; Nils Griga; Christoph Theiss; Alexandre Mermillod-Blondin; Markus Eberstein; Hans Eichler; Jörn Bonse

doi:10.1364/OME.4.000689

1. Introduction

An outstanding characteristic of femtosecond (fs) laser pulse ablation is its high intensity and the absence of laser interaction with the ablation plume. The result is a minimal heat-affected zone and a precise, efficient energy deposition to the irradiated solid. Material removal (ablation) takes place when the deposited areal energy density (fluence) overcomes a material dependent threshold. At fluences close to this threshold, material can be removed over areas smaller than the diffraction limit [1]. The origin and the dynamics of the ablation have been studied extensively in the last decades, investigating the optical absorption mechanisms [2–7], the pulse duration dependence of the ablation threshold [8–13], the surface morphology upon fs-laser irradiation [14–16], and the temporal evolution of the material response/removal [17–20]. Considerable work is devoted to the permanent structural modification of the material after fs-induced modification [21–27]. For ablation of dielectrics, the generation of free carriers in the conduction band (CB) of the solid is of uppermost importance, as it is the origin of the materials response to the ultrashort laser pulse irradiation. Different approaches to model a rate of the generation of free carriers by strong electric field ionization (SFI) are based on the Keldysh theory, which derives a SFI rate W for the excitation of the dielectric involving the parameters of the band gap and the reduced effective mass of the electron-hole pair [28]. For comparatively low laser pulse intensities I, the Keldysh theory converges to a multiphoton absorption law, namely W~I^m, which scales with the number of simultaneously absorbed photons m necessary to overcome the band gap energy E_g [29,30]. For higher laser pulse intensities, the strong electric field distorts the electronic band structure of the material to that extent that tunnel ionization becomes a more appropriate (simplified) physical picture describing the carrier generation rate. Quasi free electrons in the conduction band, which are generated from these initial (nonlinear) excitation processes, are subsequently able to absorb further photons in a stepwise (linear) absorption process (free-carrier absorption). Once such electrons gained enough energy E_e > E_g, they can transfer their kinetic energy to another electron in the valence band which then gets excited to the conduction band. This process is referred to as impact ionization.

While for strong absorbing materials and pulse durations in the ns-range (or longer), thermodynamical criteria for the ablation threshold are generally accepted [31], defining a theoretical criterion for the ablation threshold is a very controversial subject in the field of femtosecond laser interaction with dielectrics. Two fundamentally different approaches are found in the literature. The first criterion considers that the ablation commences when the free-electron plasma density N_e in the CB exceeds a critical density N_c. This critical density is often defined as the density at which the density dependent electron plasma frequency ω_Pl equals the laser frequency ω_L. When the laser wavelength is centered around 800 nm, N_c should be 1.74 x10²¹ cm⁻³ in the approximation of a free electron gas [8,32].

In recent publications, a second more thermodynamical criterion is suggested, which is based on an intrinsic material property [5,33,34]. In this case, a certain material related energy density needs to be overcome to predict the materials response to the impact of the laser pulse. It is suggested by Chimier et al. [15] and others [5], that this energy density might be the one to heat and decompose the dielectric into its atomic constituents. This is reasonable, since upon femtosecond laser pulse irradiation the total absorbed fraction of the laser pulse energy will initially be stored in the electron gas, which previously formed the binding orbitals of the dielectric. The absorbed energy is transferred from the electron gas to the lattice after the laser pulse has passed the excited volume. If then the absorbed energy density exceeds the average binding energy density the glass will start to decompose. The ablation characteristics are sometimes derived from a model for the crater depth [17,32,33,35]. However, studies that reveal the intrinsic material influence on the fs-laser induced ablation are still scarce [33,36].

This paper shows the materials influence on the femtosecond laser-induced ablation by systematically investigating a series of silicate glasses of varying chemical composition with different kind and content of network modifying ions. Taking benefit of the tailored chemical glass compositions, the hypothesis is tested if the single-pulse ablation threshold can be correlated to the material specific average bond or dissociation energy density of the silicate glasses which has to be provided by the nonlinearly absorbed femtosecond laser pulses.

2. Experimental methods

Glass systems based on silica (SiO₂) with different kinds and concentrations of network modifying oxides (Li₂O, K₂O, Na₂O, MgO, CaO) and network forming oxides (B₂O₃, Al₂O₃, GeO₂) were selected. The glasses (except LNMBS, which was provided by Schott Glas AG, Germany) were prepared by mixing reagent grade raw materials of the oxides and subsequent melting in a platinum crucible for 1 hour. The glass melt was quenched between two steel plates and subsequently annealed at temperatures approx. 10 K above the glass transformation temperature (T__g). Then, the manufactured glass plates were cut into pieces of 20x20x2 mm³ and polished with water free lubricant and stored in a desiccator to avoid a possible modification of the glass surfaces. The polishing process assured an optical quality grade of the glass surfaces.

To distinguish the characteristics of each network modifier preferentially binary and ternary glasses were investigated with respect to their fluence thresholds and laser-induced surface morphologies. Characterization of thermophysical properties can be found elsewhere [21]. The stoichiometric (batch-) compositions of the different binary and ternary silicate glasses and two commercial reference glasses (fused silica and Borofloat glass) used in this study are compiled in Table 1. The compositions of the glasses show significant differences to provide direct examinations of the covalent to ionic bonding ratio (i.e. Fused silica, LiSi75, LiSi66, LiSi60, and others), ion radii (i.e. LiSi66, LiNa11Si66, LiNa22Si66, NaSi66, and others) and ion charge (i.e., LiSi60, LiMg20Si60, and others).

Table 1. Stoichiometric batch composition of the glass samples

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Ultrashort laser pulses were provided by a Titanium:sapphire fs-oscillator and subsequently amplified via chirped-pulse-amplification (Spitfire, Spectra Physics) to pulse energies up to 1 mJ at 1 kHz pulse repetition rate. Single laser pulses with the duration of 120 fs and a center wavelength of 800 nm were selected by electronically gating the synchronization and delay generator unit of the regenerative amplifier. The laser pulse energy was coarsely adjusted to the appropriate regime using a semi-reflective dielectric mirror. Fine control of the laser pulse energy was obtained by a half-wave plate and a Glan–Taylor linear polarizer. The pulse energy was monitored in situ via the peak voltage of a photodiode, which was calibrated against a pyroelectric energy detector (Polytec RJ750). The glass samples were placed on a motorized translation xyz-stage (MICOS PLS 85) in the focal plane of a plano-convex lens with 80 mm focal length. The spot radius (1/e² decay of maximum intensity) of the Gaussian beam was determined with the method proposed by Liu [37] as w₀ = (16.2 ± 0.3) µm. All single-pulse irradiations were performed in air. The irradiation spots were separated by a distance of 100 µm in order to avoid incubation effects and material redeposition (debris). The inspection of the irradiated samples has been performed by brightfield optical microscopy (OM) and by scanning force microscopy (SFM) in contact mode.

3. Results and discussion

3.1 Ablation threshold

The diameters of the ablation spots were measured by OM. The beam waist radius w₀ is calculated by a series of ablation crater diameters generated at different laser pulse energies. Assuming a spatially Gaussian shape of the beam profile, the ablation threshold fluence $F_{th, d i a}^{}$ is obtained from the series and their associated square of crater diameters (D²) by a least-squares-fit from the relation $D ² = 2 w_{0} ² \ln (F_{0} / F_{th, d i a})$ , where $F_{0} = 2 E_{0} / (π w_{0} ²)$ describes the incident peak fluence in front of the sample [37].

Figure 1 exemplifies this evaluation procedure of the single-pulse ablation threshold fluences for commercially available Borofloat glass (Schott AG, Germany, black squares) and for the LiGe₅₀Si₂₅ glass (red triangles).

Fig. 1 Plot of the squared ablation diameter D² vs. the peak fluence F₀ for LiGe50Si25 (red triangles) and Borofloat glass (black squares). Note the semi-logarithmic data representation. The solid lines correspond to least-squares-fits with the method proposed in [37]. The arrows indicate the ablation threshold obtained from the fits. The horizontal and vertical bars correspond to the statistical errors.

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The ablation threshold value for Borofloat glass of 4.4 J/cm² obtained by extrapolation to D² → 0 is in agreement with the ablation threshold fluence value reported in [38].

All glass samples listed in Table 1 have been investigated with the above mentioned method. In order to calculate the fluence entering the sample material, the threshold fluences obtained from the crater diameters are subsequently revised by a factor for the transmission through the air-glass interface $Φ_{t h, d i a}^{} = F_{t h, d i a}^{} \cdot (1 - R)$ , where R represents the reflectivity of the glass surface at normal incidence. Experimental and numerical simulations show that R is similar to the Fresnel reflectivity for fluence values up to the ablation fluence threshold [39]. The obtained values for $F_{t h, d i a}^{}$ , $Φ_{t h, d i a}^{}$ , R and n_d of all glass samples are compiled in Table 2.

Table 2. Incident ablation threshold fluences F_th,dia obtained by the D²-method along with the ablation threshold fluence Φ_th,dia corrected by the reflection losses (R). All error bars are derived from the fitting procedure. The refractive indexes n_d are taken from [40]. The Fresnel reflectivity is calculated neglecting the difference in n of the two wavelengths 589 and 800 nm, which is not significantly affecting the values of R here

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3.2 Crater topography

Additionally, a second assessment of the ablation craters has been performed by means of their topography measured by SFM. For the evaluation of an ablation criterion and the modeling of the absorbed fraction of the laser pulse at the ablation threshold fluence, a nonlinear absorption model was used [41]:

\frac{d I (z)}{d z} = - α_{m} I^{m} (z) .

Here, I represents the laser beam intensity within the sample, the coordinate z denotes the position below the glass surface and α_m the linear and nonlinear absorption coefficients of the order m. For reasons of simplicity, all absorption mechanisms except the multiphoton absorption of the m-th order are neglected and I is substituted with $I = Φ / τ = F (1 - R) / τ$ where τ is the pulse duration. Considering the reflected parts of the beam according to Fresnel reflection R, Eq. (1) can then be reduced to:

\frac{d F (z)}{d z} = - \frac{α_{m}}{τ^{m - 1}} {(1 - R)}^{m - 1} F^{m} (z) .

Equation (2) can be solved analytically by separation of the variables [17]. Considering the boundary condition that ablation stops in depth at the (maximum) crater depth d_max where the local fluence falls below the ablation threshold

Φ (d_{\max}) = Φ_{th, d e p}^{} = F_{th, d e p}^{} (1 - R)

, the following expression for the material and fluence dependence of the crater depth is derived:

d_{\max} = \frac{τ^{m - 1}}{(m - 1) α_{m}^{dep} {(1 - R)}^{m - 1}} [\frac{1}{F_{th, d e p}^{m - 1}} - \frac{1}{F_{0}^{m - 1}}] .

In the following it is considered that m is of the third order since the band gap energy of the silicate glass samples is around E_g = 4.5 eV. Hence, three photons are needed to bridge the band gap energy. Least-squares-fitting Eq. (3) to the experimental SFM data of the silicate glasses allows to simultaneously obtain both the fluence threshold for the specific glass and the third order nonlinear (3-photon) absorption coefficient $α_{3}^{dep}$ as fit parameters.

As an example, in Fig. 2 the maximum ablation crater depth is plotted versus the peak laser fluence along with a least-squares-fit of Eq. (3) to a series of ablation craters of two glasses (LiGe₅₀Si₂₅ and Borofloat glass). The model of Eq. (3) is in good agreement with the experimental data. The LiGe₅₀Si₂₅ glass shows a relatively low ablation threshold fluence of F_th,dep = 2.4 J/cm² and shallow crater profiles (depths up to ~150 nm), whereas Borofloat glass has almost a doubled ablation threshold fluence with comparatively large crater depths up to 330 nm. Since the average dissociation energies of the glasses are similar (see Table 6), this supposedly corresponds to the different 3-photon absorption (3-PA) coefficient α₃ of the two glasses, i.e., 9.3 × 10⁻²³ and 1.3 × 10⁻²³ cm³/W², respectively.

Fig. 2 Maximum depth of the ablation craters d_max vs. the incident peak fluence F₀ for LiGe₅₀Si₂₅ (red circles) and Borofloat glass (black squares). The solid lines correspond to a least-squares-fit using Eq. (3).

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Analogous results are found for all other glasses. The obtained fit parameters (F_th,dia, α₃^dep) are compiled in Table 3 along with the fluence thresholds Φ_th,dia corrected by the Fresnel reflection losses R of the air glass interface and with the three photon absorption coefficients obtained from z-scan technique in the fluence regime F ~0.02 × F_th,dia [42]. The values obtained for the ablation threshold fluences from the crater depths F_th,dep agree well with the ones obtained from the ablation diameters (F_th,dia) presented in Table 2.

Table 3. Ablation threshold fluences F_th,dia and 3-PA coefficients α₃^dep of the glasses derived from fits of the crater depth vs. the applied laser fluence F₀ (Eq. (3)) and ablation threshold fluences Φ_th,dia with the considered reflection losses of the air-glass interface. Additionally, nonlinear absorption coefficients from z-scan technique are listed [42]. Error values are statistical deviations obtained from the least-squares-fitting procedure

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The threshold fluences from the 3-PA model Eq. (3) are in average about 5% lower than those evaluated with the method of Liu [37]. Such a phenomenon is also found in [33], where the ablation threshold energy from the crater depth is obtained from a linear regression of the crater depth vs. the logarithmic incident energy close to the threshold. Interestingly, the 3-PA coefficients α₃ derived from the crater depths using Eq. (3) are very similar to the ones found by z-scan technique at a much lower fluence regime F₀ ~0.02 × F_th,dia [42]. From that one might conclude, that the impact ionization plays only a minor role for the given conditions. Simulations by Rethfeld [43] describe the multiphoton absorption as the dominant absorption process in this intensity (I = 10¹³ W) and pulse length (τ = 120fs) regime for a dielectric with a bandgap of 9 eV and a laser photon energy of 2.5 eV.

Moreover, the crater topography can be predicted from the 3-PA model, when substituting a spatial Gaussian fluence profile to the fluence variable in Eq. (3). One then obtains for the radial dependence of the crater depth:

d (r) = \frac{τ ²}{2 α_{3} (1 - R) ²} [\frac{1}{F_{t h} ²} - \frac{\exp {4 r ² / w_{0} ²}}{F_{0} ²}],

where r is distance from the center of the ablation crater.

Figure 3 shows the surface topographies of a selection of six ablation craters obtained from the same SFM measurements previously shown in Fig. 2. Horizontal cross sections through the center of the craters are shown on the right hand side of Fig. 3. For each material, all cross sections have been least-squares-fitted with the same 3-PA coefficient (listed in Table 3) by using Eq. (4).

Fig. 3 SFM surface topography of a selection of laser-induced ablation craters on Borofloat (upper row) and LiGe₅₀Si₂₅ (lower row) glasses. The corresponding horizontal cross-sectional profiles (open symbols) along with the plots of Eq. (4) (solid lines) are shown on the right hand side.

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From crater profiles shown in Fig. 3 it is evident that the fits based on Eq. (4) using the parameters of Table 3 are in excellent agreement with the experimentally obtained crater topographies. Hence, the 3-PA model is a sufficient model to estimate the absorbed optical energy densities.

Similar analyses can be obtained for materials with larger optical band gap energies, such as fused silica (E_g = 7.2 eV) and sapphire (E_g = 9.9 eV). Taking the crater depth measurements for both materials from Ref. [17]. allows an additional test of the model (Eq. (3)) for higher orders (m) of multiphoton absorption. The results are listed in Table 4, and show a good agreement with the model (as previously underlined in [17]).

Table 4. Ablation threshold fluences $F_{th, d e p}^{}$ and multiphoton absorption (m-PA) coefficients $α_{m}^{d e p}$ of fused silica and sapphire derived from fits of the crater depth vs. the incident laser fluence F₀ (taken from Ref [17].) and the ablation threshold fluences $Φ_{th, d e p}^{}$ with the considered reflection losses of the air-glass interface. Additionally, the band gap energies and the refractive indices are listed

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3.3 Material specific ablation criterion: dissociation energy

To relate the ablation threshold fluence to an intrinsic material property it was suggested to associate the absorbed fraction of the pulse to the minimum energy density which needs to be overcome to heat and completely decompose the material into its atomic constituents [8,15]. This energy density can be calculated for each of the silicate glasses and sapphire with a method described by Sun and Huggins [44,45]. These authors state that the dissociation energy from the oxide (bulk glass) into gaseous atoms is a constant characteristic of the element (Me) behaving approximately additive. The dissociation energy of the oxides is taken from [44,45] and converted to SI units as listed in Table 5.

Table 5. Molar mass and dissociation energy of the glass oxides

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To calculate the average dissociation energy ε_b of the chemical bonds in multicomponent glasses, the dissociation energies $ε_{i}^{_{M e O}}$ of the i-th oxide MeO in bulk glass are weighted with their corresponding molar fraction using:

ε_{b} = \sum_{i} m o l %_{i} \cdot ε_{i}^{_{M e O}}

The average dissociation energy per volume

E_{d i s s}^{c a l c}

in [

\frac{k J}{c m ³}

] is then calculated by:

E_{d i s s}^{c a l c} = \frac{ε_{b} ρ}{\sum_{i} m o l %_{i} \cdot M_{i}} = \frac{ε_{b} ρ}{M}

where M_i is the molar mass of the i-th oxide MeO, and ρ and M are the mass density and molar mass of the multicomponent glass.

Values of the mass densities ρ were obtained from a measurement based on Archimedes principle and are listed in Table 6.Some glass densities are taken from the Glass Property Information System [40]. Additionally, the available band gap energies E_g are compiled.

Table 6. Density, molar mass, dissociation energy, and band gap energy of the investigated glasses

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The dissociation energies ( $E_{d i s s}^{c a l c}$ ) of the glasses obtained from Eqs. (5) and (6) are also listed in Table 6. For fused silica, values between 54 and 64 kJ/cm³ are reported in the literature [5,33], which agree with our calculated value of 65 kJ/cm³.

A first assessment of the influence of the materials resistance to femtosecond laser irradiation is obvious when plotting the ablation threshold fluence Φ_th,dia versus the calculated dissociation energies $E_{d i s s}^{c a l c}$ , as shown in Fig. 4. A fair linear correlation can be seen in that figure which supports the hypothesis of a relation between the threshold fluence and the dissociation energy.

Fig. 4 Ablation threshold fluence $Φ_{th, d i a}^{}$ vs. the calculated dissociation energy $E_{d i s s}^{c a l c}$ for the investigated silicate glasses (black squares), Fused silica (green triangle) [17] and sapphire (blue rhomb) [17]. Additionally, values for tellurite and bismuthate glasses (red circles) from [33] are presented.

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The absorbed fraction of the laser pulse in terms of energy density can be calculated by Eq. (2) for a given depth of d below the surface. At the ablation threshold fluence, the energy density absorbed at the surface is given by:

E_{t h}^{m - P A} = {- \frac{d Φ_{d e p}^{}}{d z_{}} |}_{z \to 0} = \frac{α_{m}^{}}{τ^{m - 1}} {[Φ_{th, d e p}^{}]}^{m}

where

α_{3}

and Φ_th,dep are obtained from the least-squares-fit of the maximum crater depths to Eq. (3), as listed in Table 3.

To further support the statement that the material intrinsic property of the glass dissociation energy is a suitable parameter to predict the ablation characteristics, the absorbed energy densities $E_{t h}^{m - P A}$ obtained from Eq. (7) can be compared to the calculation of the dissociation energy densities $E_{d i s s}^{c a l c}$ for the glasses on the basis of the Eq. (6). Both of the parameters are plotted against each other in Fig. 5.

Fig. 5 Absorbed energy density at the ablation threshold vs. the calculated dissociation energy density for the investigated silicate glasses (black squares), Fused silica (green triangle) and Sapphire (blue rhomb). The solid (red) line represents the identity of both entities.

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The results shown in Fig. 5 revealed that the absorbed energy density is in good agreement with the energy density needed to dissociate the specific material (the equality of both entities is represented by the straight red line in that graph). It is concluded that the femtosecond laser ablation threshold of the different silicate glasses is determined by (1) a material specific energy barrier to decompose the material into its atomic constituents and (2) the energy deposition into the glass modeled with a nonlinear absorption law. This model can be used as a powerful tool to either predict the ablation craters topography or to determine average dissociation energy.

5. Conclusion

In this work a thermodynamically motivated model for the femtosecond laser ablation threshold is developed and tested for silicate glasses of different compositions and sapphire. The model allows to derive a specific energy density which is absorbed at the ablation threshold fluence of the irradiated material. This energy density quantitatively agrees with the value derived on basis of a work from Sun and Huggins [44,45] which provides the compositional dependent energy density to decompose the dielectric material determined primarily by kind and amount of the glass oxides in the composition. It is therefore reasonable that the femtosecond laser ablation fluence threshold of (multicomponent) glasses is determined by two intrinsic properties of the material, i.e., (1) the energy density needed to dissociate the oxidic composition of the glass to its atomic (gaseous) constituents, and (2) the intrinsic property of the material to absorb ultrashort laser pulse radiation in a nonlinear (multiphoton) absorption process.

Acknowledgments

The authors would like to thank R. Johne-Michaelis from IKTS for the mass density measurements. The authors acknowledge the funding of the German Science Foundation DFG (grants no. EB 248/4–2; EI 110/30–2; RO 2074/8–2).

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Silicate glass	Ablation threshold (incident) fluence $F_{t h, d i a}^{}$		Refractive index (Fresnel reflectivity) $n_{d}$ (R)	Ablation threshold (transmitted) fluence $Φ_{th, d i a}^{}$
	[J/cm²]			[J/cm²]
Borofloat		4.4 ± 0.1	1.47 (0.036)	4.2 ± 0.1
LiSi75		4.3 ± 0.1	1.52 (0.042)	4.1 ± 0.1
LiSi66		4.4 ± 0.1	1.54 (0.045)	4.2 ± 0.1
LiSi60		4.0 ± 0.1	1.55 (0.046)	3.8 ± 0.1
LiNa11Si66		4.0 ± 0.1	1.53 (0.044)	3.8 ± 0.1
LiNa22Si66		3.6 ± 0.1	1.52 (0.042)	3.4 ± 0.1
NaSi66		3.4 ± 0.1	1.51 (0.041)	3.2 ± 0.1
LiMg20Si60		3.8 ± 0.1	1.54 (0.045)	3.6 ± 0.1
LiCa20Si60		4.4 ± 0.1	1.57 (0.049)	4.2 ± 0.1
KMg20Si60		3.6 ± 0.1	1.52 (0.042)	3.4 ± 0.1
LNMBS		3.9 ± 0.2	1.53 (0.044)	3.8 ± 0.2
LiGe50Si25		2.6 ± 0.1	1.62 (0.056)	2.5 ± 0.1

Silicate glass	Ablation threshold (incident) fluence from crater depth F_th,dep	Ablation threshold (transmitted) fluence from crater depth Φ_th,dep	3-PA coefficient from crater depth $α_{3}^{dep}$	3-PA coefficient from z-scan [42] $α_{3}^{z - s c a n}$
	[J/cm²]	[J/cm²]	[ × 10⁻²³ cm³/W²]	[ × 10⁻²³ cm³/W²]
Borofloat	4.3 ± 0.1	4.1 ± 0.1	1.3 ± 0.1
LiSi75	3.7 ± 0.1	3.5 ± 0.1	2.4 ± 0.1	2.1
LiSi66	3.9 ± 0.1	3.7 ± 0.1	2.1 ± 0.1	3.3
LiSi60	3.8 ± 0.1	3.6 ± 0.1	2.2 ± 0.1
LiNa11Si66	4.0 ± 0.1	3.8 ± 0.1	1.6 ± 0.1
LiNa22Si66	3.5 ± 0.1	3.4 ± 0.1	2.2 ± 0.1	1.9
NaSi66	3.4 ± 0.2	3.3 ± 0.2	2.3 ± 0.2	2.3
LiMg20Si60	3.6 ± 0.1	3.4 ± 0.1	2.8 ± 0.1	1.7
LiCa20Si60	4.1 ± 0.1	3.9 ± 0.1	1.9 ± 0.1
KMg20Si60	3.6 ± 0.1	3.5 ± 0.1	1.8 ± 0.1	2.0
LNMBS	3.7 ± 0.2	3.5 ± 0.2	2.4 ± 0.1
LiGe50Si25	2.4 ± 0.1	2.2 ± 0.1	9.3 ± 0.1

Sample and order (m) of multiphoton absorption	Ablation threshold fluence F_th,dep; (Φ_th,dep)	m-PA coefficient from crater depth $α_{m}^{dep}$	Band gap [17] E_g	Refractive index n
Fused silica (m = 5)	5.4; (5.2) J/cm²	α₅ = 4 × 10⁻⁵¹ cm⁷/W⁴	7.2 eV	1.45
Sappire (m = 7)	7.0; (6.5) J/cm²	α₇ = 4 × 10⁻⁷⁹ cm¹¹/W⁶	9.9 eV	~1.76

Glass oxide	SiO₂	Li₂O	Na₂O	K₂O	CaO		MgO	Al₂O₃	B₂O₃	GeO₂
Molar mass $M_{i}$ [g/mol]	60.1	29.9	62.0	94.2	56.1		40.3	102	69.6	104.6
Dissociation energy $ε_{i}^{_{M e O}}$ [kJ/mol]	1774	1205	1004	962		1075	929	1989	2234	1803

Silicate glass	Mass density (measured) $ρ^{m e a s .}$		Mass density (calculated) $ρ^{Sci}$	Molar mass $M$	Dissociation energy from Eqs. (5) and (6) $E_{d i s s}^{c a l c}$	Band gap energy $E_{g}$
	[g/cm³] (at 20°C)			[g/mol]	[kJ/cm³]	[eV]
Borofloat		-	2.2^A	62.9	63	4.7
LiSi75		2.30	2.31	52.5	72	4.7
LiSi66		2.44	2.35	49.8	75	4.5
LiSi60		2.36	2.36	48.0	76	4.9
LiNa11Si66		2.42	2.40	53.4	70	4.1
LiNa22Si66		2.47	2.45	56.9	66	4.1
NaSi66		2.45	2.50	60.7	62	-
LiMg20Si60		2.47	2.46	50.1	73	4.4
LiCa20Si60		2.59	2.58	53.2	74	4.3
KMg20Si60		2.47	2.53	63.0	58	4.5
LNMBS		2.50	2.49	54.9	70	-
LiGe50Si25		-	3.33	74.8	73	4.4
Fused silica		-	2.20	60.1	65	7.2 [17]
Sapphire		-	3.98 [17]	102.0	78	9.9 [17]

Femtosecond-laser induced ablation of silicate glasses and the intrinsic dissociation energy

Abstract

1. Introduction

2. Experimental methods

3. Results and discussion

3.1 Ablation threshold

3.2 Crater topography

3.3 Material specific ablation criterion: dissociation energy

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (5)

Tables (6)

Equations (7)

Optical Materials Express

Silicate glass	SiO₂		Li₂O	Na₂O	K₂O	CaO	MgO	Al₂O₃	B₂O₃	GeO₂
	[mol%]
Fused silica		100	-	-	-	-	-	-	-	-
Borofloat		81	-	4		-	-	2	13	-
LiSi75		75	25	-	-	-	-	-	-	-
LiSi66		66	34	-	-	-	-	-	-	-
LiSi60		60	40	-	-	-	-	-	-	-
LiNa11Si66		66	22	12	-	-	-	-	-	-
LiNa22Si66		66	12	22	-	-	-	-	-	-
NaSi66		66	-	33	-	-	-	-	-	-
LiMg20Si60		60	20	-	-	-	20	-	-	-
LiCa20Si60		60	20	-	-	20	-	-	-	-
KMg20Si60		60	-	-	20	-	20	-	-	-
LNMBS		60	11	12	-	-	12	-	5	-
LiGe50Si25		25	25	-	-	-	-	-	-	50