Thermal model for nanosecond laser ablation of alumina

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CERAMICS INTERNATIONAL

Ceramics International 41 (2015) 6596–6603 www.elsevier.com/locate/ceramint

Thermal model for nanosecond laser ablation of alumina Sucharita Sinhan Laser and Plasma Technology Division, Bhabha Atomic Research Centre, Trombay, Mumbai-400085, India Received 27 November 2014; received in revised form 21 January 2015; accepted 21 January 2015 Available online 28 January 2015

Abstract A thermal model based on heat-conduction equation and Hertz–Knudsen equation for vaporization has been employed to simulate nanosecond pulsed laser based ablation of alumina. Heat transfer in the laser irradiated target with allowance for phase transitions, provides estimates for temperature distribution within the target and material ejection rate via ablation. Good agreement between calculated and experimentally measured data on mass ablation rate per pulse and its dependence on incident laser fluence from 5 to 22 J/cm2, validated our theoretical model. Observed deviation between calculated and experimentally measured ablation rates at high average laser fluence levels was explained by ablation induced progressive degradation of target surface. Absence of abrupt increase in ablation rate with increased laser fluence suggested material ejection largely via normal boiling rather than explosive boiling mechanism. Calculated maximum surface temperature of the target was found to lie well below empirically estimated thermodynamic critical temperature for alumina, corroborating our observations on absence of onset of explosive boiling in alumina target on laser irradiation. Our simulation study enables proper selection of laser fluence, successfully minimizing laser induced target damage, as well as, degradation of micro-structural and mechanical properties of alumina films deposited via pulsed laser ablation. & 2015 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Keywords: B. Surfaces; D. Al2O3; E. Refractories

1. Introduction Pulsed laser ablation (PLA) forms the basis for an extensive range of applications such as, Pulsed Laser Deposition (PLD) for thin films and coatings [1], surface engineering of solids for device applications [2], vapor generation for analytical characterization of materials [3], and material processing and nanostructuring [4,5]. The underlying mechanism of material removal on laser irradiation depends on the type of material being processed, processing laser parameters, as well as, the prevailing ambient conditions. Laser pulse duration critically determines the physical process of coupling and dissipation of laser energy into the target material [6]. Material ablation with nanosecond pulsed laser is largely thermal in nature. Laser energy absorbed in the medium gets transferred to the lattice through electron–phonon coupling leading to heating and phase transitions at characteristic n Corresponding author. Tel.: þ 91 22 25595352; fax: þ 91 22 25505151/ 9122 25519613. E-mail address: [email protected]

http://dx.doi.org/10.1016/j.ceramint.2015.01.106 0272-8842/& 2015 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

temperatures, culminating in evaporation of the target material. The complex mechanism of laser ablation could lead to material removal, either in the form of fine vapor, liquid droplets, solid flakes or uneven and large fragments. Reliable prediction of laser ablation rates and associated features has often been facilitated through theoretical simulation of pulsed laser ablation that closely describes the complex mass removal mechanisms [7–9]. Alumina or Aluminum oxide (Al2O3) is a refractory material widely used as, optical thin films and protective coatings [10], as a bio-ceramic material on account of its superior bio-compatibility [11], as a tribological coating [12], and in thermal barrier coatings [13]. It is an inert ceramic having a high degree of chemical compatibility with most reactive reagents, excellent wear resistance and hardness and can also be polished to a high degree of surface finish. High hardness and wear resistance endow alumina with excellent tribological qualities making it one of the most commonly used materials for hard coatings [14]. For high temperature applications the hard and thermally stable α-phase of alumina is preferred [15]. Alumina coatings deposited through Chemical Vapor Deposition [16], Metal organic chemical vapor

S. Sinha / Ceramics International 41 (2015) 6596–6603

deposition [17], Pulsed Laser Deposition [18], Magnetron sputtering [19], and Plasma spray deposition [20] techniques, have all been reported. Of the techniques employed for deposition of alumina thin films the pulsed laser based process has been particularly promising. PLD has been successfully demonstrated for deposition of multi-component, as well as, single component films of ceramics, semiconductors, metals, dielectrics and insulators. PLD has been used to generate a wide range of coating morphologies ranging from amorphous to crystalline, smooth, dense and optically homogeneous to rough and porous [1]. PLD technique not only allows decoupling of vacuum hardware and the energy source responsible for material evaporation, but also provides desired control of properties of deposited films through appropriate choice of laser parameters. That heating of the substrate is not always necessary with PLD technique is an attractive associated advantage since heating has often been observed to result in substrate degradation. Most ceramics are poor absorbers of heat and much less reflective than metals. Hence laser beams tend to penetrate effectively and deposit energy to larger depths within ceramics than metals. Amount of laser energy deposited into the target critically determines ablation parameters including ablation yield. Laser ablation based optimized processing of ceramics involves critical choice of processing laser parameters and aims at successfully avoiding generation of cracks due to thermally induced stresses within the target, explosive boiling and ejection of fragments and large droplets from the target. All these phenomena are not only detrimental for controlled and high precision micromachining of ceramic targets, but also compromise the quality of ceramic thin films and coatings deposited using a PLD approach. An understanding of the mechanism and dynamics of materialremoval process following a theoretical model based approach serves not only to accurately estimate material ablation rates but also facilitates selection of laser parameters for optimization of the application technique. At high laser fluence levels, a complex coupled process involving vaporization, ionization, gas dynamics including vapor and plasma expansion with possible shock wave generation, have been proposed [21,22]. However, for laser fluence levels maintained close to ablation threshold, simpler simulation models describing laser ablation beginning with laser induced heating and evaporation of target in the presence of heat transfer within the target, and gas dynamics to describe the generated vapor, have been reported [3]. In this paper, we have employed a thermal model for nanosecond pulsed laser ablation based on a heat conduction approach within the target and phase transition resulting in normal boiling and vaporization. Although, plasma formation and laser plasma interaction have not been considered explicitly in our model, screening effect of the plasma has been broadly incorporated through scattering and absorption losses experienced by the process laser beam as it propagates through the ablation plume. Heat transfer within the target with allowance for phase transitions provides temperature distribution generated in the target when irradiated with a nanosecond laser pulse. Velocity of the ablating vapor and ablation rate have been estimated

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following a Hertz–Knudsen approach avoiding description of vapor plume involving gas dynamic equations [9]. This simulation study of laser ablation of alumina enables processing conditions to be related to target ablation rate. In addition, our theoretical simulation facilitates proper selection of laser fluence thereby successfully avoiding onset of explosive boiling in laser irradiated alumina target hence minimizing laser induced target damage, as well as, degradation of micro-structural and mechanical properties of deposited PLD alumina films. 2. Numerical simulation 2.1. Model Laser energy is coupled into the target material via electronic excitation. Equilibrium between electrons and lattice vibrations occurs via electron–phonon interaction, typical relaxation times ranging up to 100 ps [23]. Hence, when simulating laser matter interactions in nanosecond time domain one can safely assume laser energy to have been coupled as thermal energy into the target. On irradiation with a laser pulse energy is partly reflected at the target surface and the rest is absorbed within a short penetration depth characterized by the absorption coefficient of the target material. The absorbed energy is distributed within the target largely via conduction. If the laser energy coupled into the target is sufficient for melting and vaporization, material ablation occurs. Physical processes that occur during laser ablation include energy deposition into the material followed by heat transfer within the target, radiative and convective boundary conditions, thermo-dynamics of phase-changes, a moving melt and solid interface, fluid flow and evaporation via normal boiling, as well as, explosive boiling should the target temperature approach the critical temperature of the target material. Hence, an exact theoretical model becomes extremely cumbersome and complex. However, based on the specific nature of dynamics being explored several associated processes and mechanisms often become small enough to be safely neglected. This allows considerable simplification of the numerical approach. A simplified thermal model of laser induced heating and material removal validated against experimental data on nanosecond laser heating and vaporization of ceramics [24] has been utilized to describe laser ablation of alumina. Broadly the following assumptions have been made: 1. Heat radiated from laser irradiated target surface estimated by σT4 (where T is the temperature of the hot target surface and σ is the Stefan–Boltzmann constant) has been observed to be  2  103 W/cm2 for maximum surface temperatures as high as 4300 K typically reached in case of PLA of alumina. This is negligible in comparison to typical average laser intensity of 1011 W/cm2 deposited by incident laser beam. Hence, radiative heat loss from the target has been neglected. 2. For transient laser irradiation involving a single laser pulse and in absence of cumulative effects arising from successive laser pulses, heat transport via convection has been neglected [25].

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3. Thermal diffusion length in alumina lTH  2(DτL)1/2 where D is heat diffusivity and τL ¼ laser pulse duration, is  1 mm. Typical optical penetration depth of the process laser in the alumina target is  33 mm. If both these characteristic lengths are much smaller than the typical laser beam spot size on the target, heat flow in the lateral direction, i.e. transverse plane, may safely be ignored. 4. Nonlinearities in material parameters, such as absorption coefficient have been neglected. 5. Temperature dependence of optical and thermo-physical properties of alumina have been included only in the temperature range for which data were available in literature [26,27,31] 6. Ablation and removal of successive surface layers from the target may modify target reflectivity and hence scattering loss of laser beam at the target surface. However, in the absence of accurate estimates for varying surface reflectivity of the alumina target when laser irradiated, a constant value for reflectivity has been assumed for our model calculations. 7. For moderate laser fluence levels maintained close to ablation threshold of the target being laser treated, material removal occurs largely on account of normal boiling rather than explosive boiling. Hence, phase transition involving normal boiling has been assumed. 8. At high laser fluence levels ionization of generated vapor and of background gas could often become significant enough leading to formation of a plasma plume. However, ionization of the ejected vapor plume has been neglected in our model although, effect of plasma plume in attenuating the incident process laser beam has been included.

Our model description of laser-solid interaction involves the solution of heat-conduction equation and consequent material removal from the target through vaporization. Large enough total numerical domains have been chosen such that no heat and mass transfer occurs at the domain boundaries. The laser irradiated region receives energy which finally appears as heat flux in the material. Mass transfer occurs from the target into the ambient through laser ablation purely via material vaporization. Finite difference scheme based on a non-uniform grid in space has been utilized with finer grids in the depth dimension and coarser in the radial direction, within the laser irradiated volume of the target. When a particular region reaches evaporation temperature and the energy deposited by the irradiating laser beam exceeds the latent heat of vaporization, this segment layer evaporates with associated material ablation. Heat transfer via convective and radiative routes being negligible, the temperature distribution induced by absorption of laser radiation in the target is determined by the heat conduction equation: ρðT ÞC p ðT ÞδT ðx; z; t Þ=δt ¼ ∇½κ ðT Þ∇T ðx; z; t Þ þ Qðx; z; t Þ

ð1Þ

where x denotes space coordinate in the transverse plane and z denotes depth in the direction normal to the target surface. ρ, Cp and κ are mass density, specific heat at constant pressure, and thermal conductivity of the laser irradiated material. The

two terms on the right hand side of above equation represent heat conduction and energy input, respectively. Source term denoted by Q(x, z, t) representing the laser energy absorbed by the target sample is expressed as: Qðx; z; t Þ ¼ I S ðx; t Þð1 RÞα expð αzÞ

ð2Þ

where R and α are the reflectivity of the target surface and the absorption coefficient of the target and IS(x, t) is the laser irradiance at the sample surface determined by the temporal and spatial distribution of the incident laser pulse. Laser irradiance reaching the target surface propagating through the ablation plume is given by [9] I S ðx; t Þ ¼ I 0 ðx; t Þexp½  Λðx; t Þ

ð3Þ

where Λ is the optical thickness of the ablation plume, and is given by Λ(x,t)¼ ah(x,t) þ bEa(x,t). In this expression, two time independent coefficients are denoted by a and b, h(x,t) is the ablation depth and Ea(x,t) is the density of laser energy absorbed by the ablation plume. Coefficients, a and b are treated as free parameters in the model and these are determined by fitting experimental and calculated data on mass removal through laser ablation of alumina. The heat conduction equation is solved as a function of time and space during and after the laser pulse by an explicit finite difference method. When temperature reached on the material surface becomes high enough significant material removal through vaporization occurs. The vapor pressure (pvap) of the ablated vapor is calculated from the surface temperature, by integrating the Clausius–Clapeyron equation [25],   ΔH lv ðT s –T b Þ pvap ½T s  ¼ p0 exp ð4Þ RT s T b where Ts and Tb are the surface temperature and the normal boiling point at pressure p0 ¼ 1 atm, ΔHlv is the latent heat of vaporization, and R is the gas constant. For a given vapor pressure, the vapor density at the surface (ρvap,s) is obtained using the ideal gas law: pvap ð5Þ ρvap;s ¼ KBT S where KB is the Boltzmann constant. Assuming for simplification that the vapor atoms leaving the target surface follow a one-dimensional Maxwellian velocity distribution, the flow velocity of vapor atoms (vvap,s) can be approximated by the average of the normal velocity component at temperature TS [26],  
2 K B T S 1=2 vvap;s ¼ ð6Þ πm where m denotes the mass of an alumina molecule. Hence, flow of material vaporized from the surface leading to target ablation is estimated following the Hertz–Knudsen equation [9]. Thermophysical and optical parameters used for the simulation, as well as, adjustable coefficients, a and b have been summarized in Table 1. Pulsed laser ablation of alumina target samples was carried out using a Q-switched Nd:YAG laser delivering 5 ns (full width at half maximum, FWHM) pulses at 10 Hz repetition rate,

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and at a second harmonic wavelength of 532 nm. Details of experimental setup and our data on laser ablation of alumina have been reported earlier [27]. Average mass removal rate (ng/pulse) as a function of incident laser fluence was investigated for ablation geometries: (a) laser beam incident at 451 with respect to scanned target surface, and (b) laser beam at normal incidence on scanned target surface. Space averaged laser fluence was varied ranging from  5 J/cm2 to  22 J/cm2. Average mass removal per pulse for each laser fluence value was obtained by weighing the target before and after irradiation, averaged over a total of 18,000 laser pulses.

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cell in the target evolves with laser irradiation, if at the end of a particular time step, the temperature of a mesh element exceeds the melting temperature of alumina, melting is assumed to have occurred and latent heat of fusion or heat of melting (ΔHsl) is accounted for in the following calculation time steps. Similarly, when the temperature of the surface elements is comparable to the boiling temperature of the target material, substantial ablation is assumed to occur. When this happens an ablation depth h(x,t) is estimated and compared with the element thickness, Δz. If h4Δz, the element is assumed to have vaporized and the surface temperature of the remaining target gets appropriately modified taking into account the latent heat of vaporization.

2.2. Finite difference method To simulate ablation of alumina the heat conduction Eq. (1) was solved as a function of time during and after the laser pulse employing an explicit finite difference technique. The target sample is represented by a mesh of finite elements that are modified appropriately as a function of time to account for simulation of material removal. Time dependent evolution of temperature T characterizing each of the mesh cells is obtained by solving the above set of equations. Initially the target is at a uniform temperature of 300 K. As the temperature of each mesh

2.3. Laser and alumina target parameters for model calculations Thermo-physical and optical properties of alumina target and typical process laser parameters used as inputs in the model calculations are listed in Tables 1 and 2. Data on temperature dependent physical parameters for alumina wherever available in literature have been incorporated in our calculations. Reflectivity (R) of alumina target for incident laser radiation at a wavelength of 532 nm was estimated from

Table 1 Parameters for Al2O3—input data used for our model. Parameters

Values for ThO2

Refs.

Thermal conductivity, κ (W/cm/K)

0.3696 at 300 K 0.2093 at 500 K 0.0795 at 1000 K 0.05965 at 1400 K 0.0586 at 1500 K 0.0586 at 1600 K 0.785 at 300 K 1.0467 at 500 K 1.235 at 1000 K 1.2975 at 1400 K 1.308375 at 1500 K 1.308375 at 1600 K 3.97 300 0.08 2327 3700 (0.62 to 1.36)  103 4.76  103 (i) a=1000 (ii) b=0.69

[31]

Specific heat Cp (J/g/K)

Mass density ρ (g/cm3) Absorption coefficient α (cm  1) Reflectivity used in model R Melting point Tm (K) Boiling point Tb (K) Heat of fusion ΔHsl (J/g) Heat of vaporization ΔHlv (J/g) Laser attenuation parameters in ablation plume, (i) a (cm  1) and (ii) b (cm2/J)

[31]

[32] [10,32] [28,29] [33] [32,34] [33] [32,34]

Table 2 Laser parameters—input data for our model. Nd:YAG laser parameters

Value

Wavelength λ(nm) Pulse temporal profile, and pulse duration-full width at half maximum FWHM (ns) Pulse peak t0 (ns) Spatial profile—FWHM (micron)

532 Gaussian, FWHM=5 20 Gaussian, FWHM=420

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the real and imaginary parts n and k of the refractive index [28,29] using relation R={(n 1)2 þ k2}/{(n þ 1)2 þ k2}. A value of 0.08 for R was used for our simulation. Simulation has been carried out over a total target volume extending to 80 μm in depth and 800 μm in radial dimension with respect to the axis of the propagating laser beam. Mesh size of 4 nm in the depth dimension has been used corresponding to a time step of 1 ps to satisfy the stability condition associated with explicit finite difference technique employed in this simulation. Although, heat conduction in the lateral direction has been assumed to be negligible, a temperature distribution across the transverse plane of the target is expected as the irradiating laser beam is Gaussian in profile. This transverse spatial effect has been included in our simulation by dividing the transverse plane into several concentric rings with each annular region having an appropriate source term IS(x,t) as determined by the spatial distribution across the laser irradiated spot. Mesh dimension in the transverse direction was varied between 10 μm and 50 μm to account for the Gaussian nature of spatial distribution present in the incident laser beam. Use of finer mesh in the region close to the axis of the irradiating laser beam for the simulation allows a more precise estimation of the material ablation rate. 3. Results and discussions Experimental and calculated data on ablation rate per pulse as a function of incident laser fluence is shown in Fig. 1. Good agreement obtained between calculated (solid and dotted lines) and experimental data (open circles and solid triangles) validates our model when predicting the time and space integrated mass removal rate as a function of average incident laser fluence. Our thermal model follows a single pulse irradiation approach although experimental measurements made were for mass removal averaged over a total of 18,000 laser pulses. In our model approach accumulation and (a)

Removal rate ng/pulse

800

600

(b) 400

200

0 0

8

16

24

Incident laser fluence J/cm 2

Fig. 1. Mass removal rate per pulse as a function of incident laser fluence for scanned target and ablation geometries: (a) laser beam incident at 451 with respect to target surface, (b) normal incidence of laser beam on target surface. Solid and dotted lines are calculated trends while open circles and solid triangles are experimental results [27].

incubation effects arising from successive laser pulses have been neglected since a low repetition rate (10 Hz) nanosecond laser has been employed. However, with increased ablation and material removal from surface layers the target surface is expected to degrade, modifying orientation of target, surface reflectivity and scattering, experienced by the incident laser beam at the target surface. Our simulation assumes a constant surface reflectivity for the target in the absence of accurate estimates for varying surface reflectivity as the process of laser ablation evolves. Scanning of the target ensures, to some extent, that a new region of the target surface (that has less likely to have been modified by a previous laser pulse) is exposed to each laser pulse. The two adjustable parameters, a and b characterizing attenuation of laser beam by the generated ablation plume, have been obtained by fitting experimental and calculated data on mass removal. For low plume density generated at low irradiating laser flux when attenuation of laser by ablation plume is low, experimentally observed and theoretically calculated ablation rates were matched by selection of only one coefficient, a. Having determined a, coefficient b is obtained by matching experimentally observed and calculated ablation rates in the higher fluence range [9]. Both, calculated data and trend matched well with our experimental observations (Fig. 1). No sudden increase in ablation rate was observed for laser fluence when increased up to 22 J/cm2 indicating material removal to have occurred predominantly through normal vaporization rather than explosive boiling. Restricting material ablation to occur via normal evaporation rather than phase explosion avoids ejection of large size particulates and fragments that degrade the homogeneity and quality of the deposited PLD film. Our calculations therefore, confirm our experimental observations on good quality homogeneous PLD alumina films being deposited employing laser fluence typically in the region of  11 J/cm2, successfully avoiding onset of explosive boiling at the target irradiated surface [27]. Ablation depth on target surface per laser pulse and its dependence on the incident laser fluence, were both calculated employing the model. Solid line in Fig. 2 depicts the calculated trend. In the relatively low fluence region (less than  5 J/ cm2), ablation depth per pulse increased rapidly with increasing laser fluence. However, this increasing trend slowed down and plateaued as the laser fluence was increased to 20 J/cm2 and beyond. In Fig. 2 is also shown experimentally observed average ablation depth per pulse as has been reported for a total of 600 laser pulses [27]. These experimental measurements were for the specific configuration of target surface held static and normal with respect to the incident laser beam. As is evident from Fig. 2, calculated ablation depth per pulse based on our thermal model is much higher than corresponding experimentally estimated value when averaged over a total of 600 laser pulses. However, good agreement between experimentally observed and calculated trends with increasing laser fluence was seen up to fluence levels of 15 J/cm2. Cumulative effect of irradiation with 600 laser pulses is expected to progressively degrade the target surface, more so, if the target is held static and not scanned with respect to the incident laser beam. However, for our simulation runs surface

S. Sinha / Ceramics International 41 (2015) 6596–6603 Laser pulse delivered on target Normal Incidence

100 10

50

0

0 0

10

1.0

Pulse Intensity (rel. units)

150

Ablation depth (micron) with 600 laser pulses

Ablation depth (micron) per pulse

200

20

6601

a

c 0.5

b

d e f 0.0

20 0

Incident laser fluence (J/cm )

30

40

50

Fig. 3. (a) Temporal profile of incident laser pulse employed for laser ablation of alumina. Curves (b)–(f) depict calculated temporal profiles of laser pulse reaching target after penetrating ablation plume for laser fluence levels of 1, 2.5, 5.45, 14.5 and 22 J/cm2, respectively.

5000

0

degradation and modification of target surface reflectivity during, as well as, after each laser pulse has been neglected. Effect of target surface modification caused by each laser pulse is expected to become more prominent when multiple laser pulses irradiate the same physical spot on the target. Theoretical estimates for ablation depth per pulse assuming a single laser pulse approach thus far exceeds the experimentally measured ablation depth per pulse when averaged over 600 laser pulses as experimental observations include all cumulative effects including degradation of target surface that essentially reduces the extent of laser energy coupled into the target. Uneven surface and deep crater formation, predominant at high laser fluence, results in enhanced loss of laser energy through multiple scattering on crater walls. Strong ablation and removal of surface layer at high laser fluence causes increased surface roughness also modifying the effective orientation of the target surface and hence lowering the effective laser fluence incident on the target surface. Therefore, all these surface modifications reduce the extent of laser energy that is deposited into the target hence restricting the effective material ablation rate. Observed deviation of calculated and experimentally measured dependence of ablation depth per pulse on incident laser fluence particularly for laser fluence levels exceeding 15 J/cm2 is also largely on account of induced progressive degradation of target surface when laser irradiated. The incident laser pulse delivered at the target surface gets substantially modified as it propagates through the ablation plume. Our calculations were performed for a laser pulse having a Gaussian distribution in time as depicted by profile (a) in Fig. 3. The remaining profiles in Fig. 3, (b) to (f) depict the temporal profile of the laser pulse arriving at the target surface after having propagated through the vapor plume. Ablation plume generated from the target by the leading edge of the incident laser pulse attenuates the trailing edge of the laser pulse. Evolution of the ablation plume determines the extent of attenuation of the trailing edge of the process laser pulse and this far exceeds that experienced by the leading edge of the incident laser pulse. At increased laser fluence target

20

time ns

Maximum surface temperature K

Fig. 2. Dependence of ablation depth on incident laser fluence for normal incidence of laser beam on stationary target surface. Solid line depicts calculated trend and open circles are experimental data [27].

10

4000

3000

2000

1000

0 0

10

20

30

Laser fluence (J/cm2)

Fig. 4. Calculated maximum surface temperature of alumina target as a function of laser fluence.

ablation and hence density of the plume being higher, fraction of original laser intensity absorbed by the plume becomes significant as depicted by laser profile (f) in Fig. 3. On laser irradiation, maximum temperature reached by the target surface increases rapidly as a function of incident laser fluence in the low-fluence regime followed by a slower rate of increase for high fluence values as shown in Fig. 4. The maximum temperature that the target surface can attain is determined by its boiling temperature when material removal occurs through normal evaporation. However, explosive boiling or phase explosion sets in should the temperature approach the thermodynamic critical temperature. That material removal in case of PLA of alumina occurs largely through normal vaporization with no phase explosion being initiated even at laser fluence as high as 22 J/cm2 was confirmed by checking whether laser irradiated alumina target approached thermodynamic critical point or critical temperature TC. Following

S. Sinha / Ceramics International 41 (2015) 6596–6603 radial distance from spot center (µm) 0

50

100

150

200

250

300

350

400

450

500

450

500

3000K

20000

depth in nanometer

2000K

40000

60000

1000K

80000

20ns 500K

radial distance from spot center (µm) 0

50

100

150

200

250

300

350

400

3000K

20000

depth in nanometer

our theoretical model approach, possibility of occurrence of explosive boiling could be predicted if maximum surface temperature of laser irradiated alumina target were to rise to  0.9 TC [9]. Critical temperature for alumina estimated employing empirical equations ranged between 7000 K and 8500 K [9]. Maximum target surface temperature calculated following our simulation model (Fig. 4) confirms that this remains well below TC even when average laser fluence is raised to 30 J/ cm2. The maximum temperature attained by alumina target surface as calculated by our model lies in the region of 4000 K to 4500 K for an average laser fluence of 30 J/cm2 corresponding to a peak incident intensity of  1010 W/cm2. Hence, our calculations confirm that material removal from alumina target would indeed occur through normal boiling rather than explosive boiling under typical conditions reported for PLD of alumina [27]. Our experimental observations on laser ablation at a typical laser fluence of 11 J/cm2 showed presence of no droplets or large fragments (signatures associated with onset of explosive boiling), in the ejected ablation plume [27]. Our theoretical simulation thus establishes that phase explosion could not have occurred during typical PLD runs of alumina as was also concluded from our experimental observations where neither, target damage through crater formation in localized laser irradiated zones, or presence of large fragments in the PLD deposited alumina thin film coatings were reported [27]. As the laser irradiated alumina target heats up resultant temperature distribution within the target has been calculated as a function of time during and after incidence of the laser pulse. Two typical scenarios showing isotherms calculated at 20 ns and 25 ns are depicted in Fig. 5a and b. Highest temperature is reached close to target surface and as time evolves the region with elevated temperature expands both axially and laterally due to thermal conduction. Thermal conductivity and specific heat being higher for alumina in comparison to ceramics Thoria and Yttria [24,30], temperature reached in alumina is the lowest under identical conditions of laser irradiation. Also, penetration depth of process laser at a wavelength of 532 nm in case of alumina being  50 times higher than in Thoria and  4 times higher than in Yttria, the laser beam penetrates deeper into the target in case of alumina resulting in a larger heat affected volume, hence limiting the effective temperature reached within the hot zone in case of alumina target. Both these causes restrict the possibility of material ejection via explosive boiling in case of alumina when compared to either Thoria or Yttria. In order to estimate the maximum depth within the alumina target that melts on laser irradiation, time evolution of the solid liquid interface was also calculated. Our model shows that although the surface temperature of the target drops once the laser pulse has ended; the target continues to remain in molten phase for a significantly long duration of time even after culmination of the laser pulse as seen in Fig. 6. As shown in Fig. 6, on irradiation with the laser pulse the target melts rapidly up to a depth of  20 mm. Thereafter, rate of heat dissipation from the laser irradiated zone determines how rapidly resolidification of the molten phase occurs once laser irradiation

2000K

40000

60000

1000K

80000

25ns 500K

Fig. 5. Calculated temperature distribution within alumina target at varying depths at two typical time instants: (a) 20 ns and (b) 25 ns for average laser fluence of 22 J/cm2.

30000

(a)

melt depth in nm

6602

(b)

20000

10000

0 0

100

200

300

400

500

Time nanosec

Fig. 6. Calculated time evolution of melt-depth in alumina target irradiated at typical average laser fluence of (a) 22 J/cm2 (b) 14.5 J/cm2, respectively.

has ended. Heat dissipation from hot zone via conduction is characterized by time τT  z20/4D, where z0 is the typical thickness of the heated layer and D is the thermal diffusivity of the target material. Estimated typical heat dissipation time subsequent to

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nanosecond laser irradiation of alumina for a heat affected depth of  80 mm corresponds to  990 ms. Hence re-solidification of molten pool in case of alumina target occurs gradually once laser irradiation has ceased. 4. Conclusion Theoretical simulation of pulsed laser ablation of alumina based on a two-dimensional thermal model was carried out employing an explicit finite difference method. Good agreement between calculated and experimental data validated our model while predicting time and space integrated mass ablation rate as a function of average incident laser fluence. Observed deviation between calculated and experimentally measured dependence of ablation rate per pulse on incident laser fluence for high laser fluence occurred largely on account of ablation induced progressive degradation of target surface. Comparison of calculated maximum target temperature and thermodynamic critical temperature TC for alumina confirmed that material removal in case of PLA of alumina occurs largely through normal vaporization, with no phase explosion being initiated even at laser fluence as high as 30 J/cm2. This simulation study enabled PLD processing conditions to be related to target ablation rate thereby allowing proper selection of laser fluence, successfully avoiding onset of explosive boiling in laser irradiated alumina. Restricting material ejection from alumina target through normal vaporization minimizes laser induced target damage and degradation of micro-structural and mechanical properties of deposited PLD alumina films. References [1] D.B Chrisey, G.K Hubler (Eds.), Pulsed Laser Deposition of Thin Films, Wiley Interscience, New York, 1994. [2] V. Zorba, N. Boukos, I. Zergioti, C. Fotakis, Ultraviolet femtosecond, picosecond, and nanosecond laser microstructuring of silicon: structural and optical properties, Appl. Opt. 47 (2008) 1846–1850. [3] A. Bogaerts, Z. Chen, R. Gijbels, A. Vertes, Laser ablation for analytical sampling: what can we learn from modeling?, Spectrochim. Acta Part B 58 (2003) 1867–1893. [4] D. Sola, J.I. Pena, Study of the wavelength dependence in laser ablation of advanced ceramics and glass–ceramic materials in the nanosecond range, Materials 6 (2013) 5302–5313. [5] I.N Zavestovskaya, Laser nanostructuring of materials surfaces, Quantum Electron. 40 (2010) 942–954. [6] E.G Gamaly, N.R Madsen, M. Duering, A.V Rode, V.Z Kolev, B. L. Davies, Ablation of metals with picoseconds laser pulses: evidence of long-lived nonequilibrium conditions at the surface, Phys. Rev. B 71 (174405) (2005) 1–12. [7] J. Steinbeck, G. Braunstein, M.S Dresselhaus, T. Venkatesan, D.C Jacobson, A model for pulsed laser melting of graphite, J. Appl. Phys. 58 (1985) 4374–4381. [8] B. Wu, Y.C Shin, Modeling of nanosecond laser ablation with vapor phase formation, J. Appl. Phys. 99 (084310) (2006) 1–8. [9] N.M Bulgakova, A.V Bulgakov, Pulsed laser ablation of solids: transition from normal vaporization to phase explosion, Appl. Phys. A 73 (2001) 199–208. [10] J. Houska, J. Blazek, J. Rezek, S. Proksova, Overview of optical properties of Al2O3 films prepared by various techniques, Thin Solid Films 520 (2012) 5405–5408. [11] A. Chiba, S. Kimura, K. Raghukandan, Y. Morizono, Effect of alumina on hydroxyapatite biocomposites fabricated by underwater-shock compaction, Mater. Sci. Eng. A 350 (2003) 179–183.

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