Keywords

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

1 Introduction

The interaction between laser radiation and solids has been investigated extensively for a large variety of materials, for different pulse duration and spectral domains. The spatio-temporal distribution of the laser-induced temperature profile plays a significant role in the initial stage of material ablation, although afterwards thermally induced stress, plasma and shockwave will be possibly involved [1, 2]. Footnote 1 The laser energy deposition into the material starts from the photon-electron interaction and the electron temperature \(T_e\) increases. The following lattice temperature \(T_l\) rise is due to the elevation of the kinetic energy of the lattice through electron-lattice energy exchange [3, 4]. Usually the removal process (ablation) takes place as the material melts or evaporates.

The ablation geometry is highly dependent on the temperature distribution governed by the laser absorption profile and the heat diffusion length. The latter determines the heat affected zone (HAZ) surrounding the ablation spot. The HAZ is found to be strongly dependent on the applied laser pulse duration \(\tau \). A shorter pulse provides smaller heat affected zones and higher ablation accuracy. In the selective laser ablation of thin films [5], besides the lateral resolution, the precise in-depth profile is also critical. In order to avoid damage of the substrate, the ablation crater has to be restricted to the thin film thickness \(b\). In this case, both optical penetration depth \(l_{ opt}\) and heat diffusion length \(l_{ th}\) have to be taken into consideration, because both affect the temperature distribution during the pulse irradiation. The depth to which the heat penetrates into the ablated material during a laser pulse is the effective thermal penetration depth \(l_{ eff}\).

In [6], the authors treated the effective thermal penetration depth by adding the optical penetration depth and thermal diffusion length. In [7, 8] the authors pointed out that for the effective optical penetration depth, both the optical penetration depth and the electron heat penetration depth have to be taken into consideration for ultrashort pulse laser ablation of metals. The effective thermal penetration depth is a superposition of \(l_{ th}\) and \(l_{ opt}\), although it is difficult to give an explicit math expression from theoretical derivation. For strongly absorbing materials like metals where \(l_{ th}\gg l_{ opt}\) is fulfilled, it is justified to treat the laser source as a surface heat source. Hence the thermal penetration depth is mainly determined by the heat diffusion length, which is proportional to the square root of the product of the thermal diffusivity \(\alpha \) and the applied pulse length for nanosecond pulses [9]:

$$\begin{aligned} l_{ eff}\simeq l_{ th}=\sqrt{2\alpha \tau } \end{aligned}$$
(9.1)

In the ultrashort pulse regime, the situation is more complex because hot electron scattering plays a dominate role in the transportation of heat and phonon-phonon coupling could be neglected. In this case the thermal penetration depth is mainly caused by the electrons. In case when surface lattice melting occurs, it can be calculated for metals by using the TTM model [10]:

$$\begin{aligned} l_{ eff}\simeq \left( \frac{128}{\pi }\right) ^{1/8}\left( \frac{k^2C_l}{C_0T_mg^2}\right) ^{1/4} \end{aligned}$$
(9.2)

Here \(C_0=C_e/T_e\) with \(C_e\) and \(C_l\)—the electron and lattice heat capacities, \(k\)—the thermal conductivity and \(g\)—the electron-phonon coupling constant.

However, for wide-bandgap semitransparent materials, which exhibit a large optical penetration depth, \(l_{ opt}\gg l_{ th}\) is valid. Here the absorption of the laser energy has to be treated as a volume heat source, and the effective thermal penetration depends on both the optical penetration and the thermal diffusion. In this case it is difficult to give an explicit math expression from theoretical derivation.

Fig. 9.1
figure 1

Schematically illustration of ablation threshold fluence for metals and semiconductors in different pulse duration regime. For short pulse ablation, the \(\tau ^{1/2}\) scaling rule is valid

Full size image

The relation of the thermal penetration depth and the pulse length can be determined by the damage threshold fluence \(q_*\) versus pulse length experiments. For short pulse \(q_*\propto \tau ^{1/2}\) for both metals and semiconductors. In ultrashort pulse regime, the ablation threshold keeps almost constant for metals, but a nonlinear feature is observed for semiconductors, schematically shown in Fig. 9.1 [11]. A characteristic time \(\tau _c\) can be defined, which distinguishes the different dependence of the ablation threshold fluence on the pulse length and separates the short and ultrashort pulse regimes, as defined by the equation [10]:

$$\begin{aligned} \tau _{c}=\left( \frac{8}{\pi }\right) ^{1/4}\left( \frac{C_l^3}{C_0T_mg^2}\right) ^{1/2}. \end{aligned}$$
(9.3)

In bulk material ablation, the laser generated heat freely conducts in spatial dimensions in the target solid. The heat diffusion length is mainly determined by a critical temporal variable, such as the pulse width. However, when film-substrate system is concerned, the heat diffusion is affected by the film thickness also. The film thickness could affect the temperature distribution for certain pulse-width range. If the film thickness is smaller to the effective thermal penetration depth \(l_{ eff}\), the influence from the substrate has to be considered.

2 Thermal Penetration Depth in Laser Ablation of Films

The influence of film thickness on the ablation of metal films has been studied for different pulse length regimes [5, 12–15]. By nanosecond laser ablation of thin absorbing films the material is partly removed by two mechanisms: evaporation and melt flow out of the crater. The flow in this case is induced by reactive pressure of the evaporating material [16, 17]. The spots size by single picosecond laser pulse ablation of tungsten film on silicon substrate as the function of applied pulse energy for different film thicknesses are illustrated in Fig. 9.2a. A well-defined linear dependence in semi-log plot can be observed with almost a constant slope for all cases. The intersection of the interpolation of these lines with the energy-axis define the ablation thresholds. Figure 9.2b shows the dependence of ablation threshold on film thickness. The dependence trend of the ablation threshold fluence \(q_*\) on the film thickness \(b\) can be divided into two regimes. For films below a thickness of about 95 nm, the thresholds increase with the thickness. For thicker films, \(b \gtrsim 95\,\)nm, the ablation threshold keeps constant equal to the bulk ablation threshold value. The effective thermal penetration length can be determined as \(l_{ eff}\approx 95\,\)nm, which separates the film and bulk ablation features for tungsten.

Fig. 9.2
figure 2

a Dependence of the ablation spots size on the pulse energy; b dependence of ablation threshold fluence on the film thickness. Measured for tungsten film ablated by 10 ps laser pulse at 1,064 nm

Full size image

In most studies which deal with metal films, the influence of film thickness on the damage threshold exhibits two distinguished regimes. However, by taking very thin film into investigation, a third regime can be observed. In [18] femtosecond laser ablation of very thin gold films was investigated. If the film thickness is in the range of optical penetration depth, the ablation threshold fluence is found to decrease with the film thickness.

In summary, the threshold as a function of film thickness can divide into three regimes for metals. It decreases with the film thickness if \(b\lesssim l_{ opt}\). When the film thickness exceeds the optical penetration depth it starts increasing with the thickness and finally saturates at a constant value of the ablation threshold of the bulk material for \(b\gtrsim l_{ eff}\), see Fig.  9.2b.Footnote 2 Although the laser pulse parameters such as the pulse length or laser wavelength will affect the ablation threshold value, it always reveals these three distinguished regimes for metal films, where the condition \(l_{ th} \gg l_{ opt}\) is fulfilled.

Fig. 9.3
figure 3

a Ablation spots size increases as the rising of pulse energy for ITO films ablated by 10 ps pulses at 1,064 nm; b dependence of threshold fluence on the film thickness for ITO ablated by 10 ps pulses at 1,064 nm and 150 fs pulses at 800 nm

Full size image

The ablation of transparent ITO films on glass substrate for different film thicknesses are investigated as well. Figure 9.3a shows the linear dependence of the ablation spots size on the applied single pulse energy in semi-log plot. More energy is required for thinner films ablation to obtain the same ablation spot size compared to thicker ones. Figure 9.3b illustrates how the ablation threshold fluence depends on the film thickness for femtosecond and picosecond laser ablation. The dependence of the ablation threshold fluence \(q_*\) on the film thickness \(b\) for ITO film demonstrates two regimes, in contrast to metals where three regimes can be distinguished. For thinner film, the ablation threshold fluence decreases as the film thickness increase, similar to the case of metals, which thickness is in the range of optical penetration depth [18]. The decreasing trend alters when the film thickness exceeds a certain value, where the effective thermal penetration depth of ITO is defined. Afterwards it tends to a constant value, which is equal to the ablation threshold of the bulk material. The same trend can be found for the low absorption polymer films [19]. The optical penetration depth of ITO is \(\sim \)2 \(\upmu \)m at 1,064 nm by taking linear absorption part (\(\delta =l_{ opt}^{-1}=5.3\times 10^5\) cm\(^{-1}\)) into account. Whereas the thermal diffusion length is \(\sim \)15 nm be calculated by \(\sqrt{2\alpha \tau }\) for 10 ps pulse length irradiation. The difference from metals is due to the fact that \(l_{ opt} \gg l_{ th}\) for such low absorption ITO films.

In order to describe the dependence of the film thickness on the threshold fluence we assume a purely thermal origin of the observed ablation effects. Regarding the film temperature \(T\) reaching its melting point \(T_m\) as the criterion for ablation. Neglecting the lateral heat diffusion and only considering the depth profile due to the large beam size, the temperature increase in the heated volume due to the absorption of laser energy can be expressed as

$$\begin{aligned} \varDelta T_m=\varDelta Q/C, \end{aligned}$$
(9.4)

where \(\varDelta Q\) is the total absorbed energy and \(C\) is the heat capacity at constant pressure. A uniform model for threshold fluence of melting can be obtained based on (9.4) written in the form [13]:

$$\begin{aligned} q_*\simeq \frac{\varDelta T_m}{(1-e^{-\delta b})(1-R)}\left[ \rho _fc_f-\left( \frac{l_{ th,s}}{l_{ th,f}}\right) \rho _s cs\right] L_f+\frac{\varDelta T_m}{(1-e^{-\delta b})(1-R)}l_{ th,s}\rho _sc_s. \end{aligned}$$
(9.5)

Here \(\varDelta T_m\) is the temperature increase needed for melting, which is a constant for specific material. \(\rho \), \(c\) are the mass density and specific heat, where the subscript \(f\) and \(s\) denote the film and substrate quantities, respectively. \(L_f\) is the minimum dimension of the heated volume, which can be the film thickness, the optical penetration depth or the effective thermal penetration length. From this equation the different regimes of ablation threshold variation trends for metal and transparent ITO films can be identified.

For metal films, \(l_{ opt}\ll l_{ th}\), the ablation threshold dependence on film thickness can be characterized in three regimes:

  • In the first regime I, \(b \ll l_{ opt}\ll l_{ eff}\) and \(L_f=b\) are fulfilled. For small \(b\) in the (9.5), the limit in the first item on the right hand is found to be constant: \( \lim \limits _{b\rightarrow 0}\frac{b}{1-e^{-\delta b}}=\frac{1}{\delta }\). However, for the second item which defines the influence of the substrate, the limit goes to infinity due to \((1-e^{-\delta b})\sim 0\) when \(b\rightarrow 0\). This implies that as film becomes thinner, the substrate influence increases and more pulse energy is required to promote the film to its melting temperature, \(q_*\sim 1/b\) is found.

  • In the second regime II, \(l_{ opt}\ll b \ll l_{ eff}\) and \(L_f=b\) are fulfilled. In this case the pulse energy is regarded to be totally absorbed, where the item \((1-e^{-\delta b})\sim 1\). The influence from the substrate is limited and one can find that \(q_*\sim b\).

  • In the third regime III, \(l_{ opt}\ll l_{ eff}\ll b\) and \(L_f = l_{ eff}\) are fulfilled. The laser energy is regarded to be totally absorbed and the heat volume is limited by \(l_{ eff}\). The influence from the substrate is neglected. Hence the ablation threshold \(q_*\) is no longer dependent on the film thickness, behaves as ablation of bulk material.

For transparent ITO films, \(l_{ opt}\gg l_{ th}\), the ablation threshold dependence on film thickness can be characterized in two regimes:

  • In the regime I, \(b \ll l_{ eff} \ll l _{ opt}\) and \( L_f=b \) are fulfilled. Similar to the case of metal films in the regime I, the substrate influence plays a dominate role on ablation threshold fluence. \(q_*\) decreases as the rising of film thickness.

  • In the regime II, \(l_{ eff} \ll b\ll l_{ opt} \) and \( L_f= l_{ eff}\) are fulfilled. Because of the large optical penetration depth \(l_{ opt}\), the changing of the film thickness \(b\) in this regime only leads to a very small variation of \((1-e^{-\delta b})\) item, which can be regarded approximately as a constant. On the other hand, the heat volume is controlled by \(l_{ eff}\) which is independent on the film thickness \(b\). Therefore \(q_*\) keeps approximately as a constant.

Fig. 9.4
figure 4

Simulation result of threshold fluences dependence on the thickness of metal and transparent ITO films

Full size image

These regimes are simulated according to the (9.5) in the Fig. 9.4 for metals and ITO.

3 Front- and Rear-Side Laser Ablation of Films

For selective laser ablation of thin films, weak absorption of the substrate and high absorption of the film are needed. Some experiments [20, 21] advise that rear-side ablation can achieve better ablation quality. Here we investigate the thermal penetration depth influence on the ablation of ITO films by front- and rear-side irradiation.

Fig. 9.5
figure 5

Numerical simulation results of temperature distribution induced by laser irradiation from a front-side, and b rear-side. The location marked by “x” denotes the maximum temperature point

Full size image

Previous works already demonstrated that the different ablation geometry could happen for laser ablation of metals by front- and rear-side irradiation, when the film thickness exceeds the thermal penetration depth [22, 23]. The film thickness is crucial in determining the amount of energy guided to the substrate: If it is smaller than the thermal penetration length, the temperature field can be regarded to be the same for both irradiation directions. On the other hand, if the film thickness is larger than the thermal penetration length, the influence of the substrate can be neglected for front-side ablation. Hence the temperature distribution induced by laser irradiation from the front- or rear-side ablation could make a strong difference and alter the surface ablation morphology. Figure 9.5 demonstrates the numerical simulation of the temperature distribution for the film thickness larger than the thermal penetration depth. One can detect a significant difference of the temperature distribution for front- and rear-side irradiation.

Fig. 9.6
figure 6

Laser ablation geometry of ITO films from front- and rear-side single pulse irradiation by 300 ms pulse with \(\lambda =\) 1,064 nm, 10 ps pulse with \(\lambda =\) 1,064 nm and 150 fs pulse with \(\lambda =800\) nm

Full size image

The SEM images in Fig. 9.6 are the single-pulse ablation results of transparent ITO films of 100 nm thickness on glass substrates, which are irradiated by 300 ms (\(\lambda =\) 1,064 nm), 10 ps (\(\lambda =\) 1,064 nm) and 150 fs (\(\lambda =800\) nm) laser pulses from front- and rear-side. The laser fluence is the same for front- and rear-side ablation. For the 300 ms pulse ablation, the film is seriously cracked for both thicknesses due to the large laser induced thermal stress. The ablation spot geometries do not show so much difference due to the large thermal penetration depth at this pulse duration. For 10 ps and 150 fs pulses ablation, the films are likely to be removed by thermal melting and vaporization without film cracking. For the thickness of 100 nm films, much cleaner and clearer ablation spots can be obtained by rear-side ablation. The images reveal that the ablation quality is different for those film thicknesses exceeding the thermal penetration depth, see Fig.  9.6 for \(\tau =10\) ps and \(\tau =150\) fs pulse ablation of 100 nm ITO films. However, no apparent difference in the ablation geometry for the front- and the rear-side ablation can be found for a thinner film with \(b=50\) nm.

Fig. 9.7
figure 7

The ablation threshold fluence of ITO films alternative as the function of the film thickness for different pulse length of 300 ms (left), 10 ps pulse (left) and 150 fs (bottom). Both front- and rear-side irradiations are presented

Full size image

The corresponding thresholds for the front- and the rear-side ablation of the films of different thickness can be found in Fig. 9.7. The threshold fluences curves are different when the film thickness exceeds the thermal penetration depth. Here the rear-side ablation is slightly higher compared to the constant value for front-side ablation. In the case of long pulse irradiation, or for thin films, the ablation does not demonstrate so much difference in threshold fluence and spot morphology. Also the ablation spots show much better rim quality by the rear-side short and ultrashort pulse irradiation of the 100 nm ITO films.

Fig. 9.8
figure 8

Schematic dependence of laser ablation threshold as a function of film thickness for a metal and b ITO films for different pulse lengths. \(l_{th}\) indicates the thermal diffusion length which differentiates the film and bulk solid features for laser ablation. The results were obtained by laser front-side irradiation

Full size image

The difference between metal and ITO materials is schematically shown in Fig.  9.8, where the the film ablation and the bulk ablation features can be separated by the thermal penetration depth.

4 Incubation Effect in Laser Ablation of Films

Laser-induced damage to a material surface under multi-pulse irradiation demonstrates an interesting phenomenon: the material surface becomes damaged at pulse fluence far below the single-shot ablation threshold, so called “N-on-one” accumulation effect. The incubation phenomena have been observed in various materials processing by pulsed lasers, including polymers [24, 25], metals [26, 27], semiconductors [28] and insulators [29].

The origin of the incubation is not yet fully revealed. For example, in uv laser processing of PMMA, some authors argued that the incubation was associated with the buildup of pressure due to the formation of polymer fragmentation [30–33]. On the contrary, Küper and Stuke showed that the incubation of PMMA with 248 nm laser was attributed to the photochemical degradation and mechanical stability reduction by means of spectroscopy studies [24, 25]. Graciela and co-workers suggested that the decomposition of PMMA by uv incubation pulses was the result of photoinduced formation of defect centers, which enhanced the absorption of uv light [34]. From their calculation, the ablation threshold is associated with the pulse number by

$$\begin{aligned} q_*(1)=q_*(N)[1+kq_*(N)(N-1)], \end{aligned}$$
(9.6)

where \(q_*(1)\) and \(q_*(N)\) are the single-shot and N-shot damage thresholds, respectively. \(k\) reflects the incubation, which is the function of absorption cross section of PMMA (\(\sigma \)) and the absorption cross section of the induced defect center (\(\beta \)). Based on the (9.6) the authors successfully obtained the value of \(\sigma \) and \(\beta \).

For metals, it was reported that for multi-pulse laser induced damage by 10 ns Nd:YAG laser pulses with 1,064 nm wavelength, the accumulation process was attributed to thermal stress-strain energy storage [26]. The authors argued that multi-pulse laser ablation on a site was similar to the bulk mechanical fatigue damage. On the analogy of the fatigue failure induced by the stress for \(N\) cycles, the authors derived a cumulative equation

$$\begin{aligned} q_*(N)=q_*(1)N^{S-1}, \end{aligned}$$
(9.7)

where \(S\) is so called incubation coefficient which quantifies the degree of incubational behavior. The model gives a reasonable interpretation for the incubation behavior of metals for the reported experiments in many research works, see e.g., [15, 35]. It is also appropriate to fit the experimental data in pulsed laser ablation of some semiconductors [28]. It also appears in evaluation of the incubation effect in femto- and nanosecond laser ablation of doped PMMA conducted by Krüger et al. [36].

For dielectric or some semiconductor materials with “N-on-one” irradiation, the incubation effect can be attributed to laser induced defects. Multi-shot irradiation onto a site of dielectrics could induce the generation of point defects by multi-photon excitation, for example formation of color centers [37, 38]. The strength of such accumulation process is related to the excitation and generation of electrons initiated by combined multi-photon and avalanche ionization. The threshold fades due to the decrease of defect accumulation for increasing \(N\) until reaching a constant level. Therefore a different equation was proposed for this case [39]:

$$\begin{aligned} q_*(N)=q_*(\infty )+[q_*(1)-q_*(\infty )]e^{k(N-1)}, \end{aligned}$$
(9.8)

where \(q_*(\infty )\) gives the maximum fluence at which the material could be permanently irradiated without causing damage, \(k\) is the factor characterizing the incubation degree. In this case the ablation threshold drops dramatically at low pulse numbers and stays constant for a large number of pulses. This dependency is mainly used in laser processing of dielectric materials [40].

Equation (9.7) is only valid for a limited number of pulses since \(q_*\ne 0\) [41]; on the other hand it is also not applicable to all experiments with metals. An exception has been described by Kern et al. for femtosecond laser-induced damage of thin Au films [42]. They adopted (9.8) to fit the multi-shot damage threshold versus the pulse numbers and argued that surface modification is responsible for incubation for films significantly thinner than the characteristic penetration depth [27].

Here we investigate the incubation behavior of the wide band-gap semiconductor ITO material when exposed to picosecond laser pulses. Structuring of ITO films has a great impetus from industrial applications. Accordingly, laser patterning of ITO thin films on glass substrates has been extensively studied with various pulsed laser sources [43–51]. However, a detailed study of the incubation behavior of ITO films and its influence on laser patterning has not yet been reported. Here we will show the decline of ablation thresholds as a function of the pulse number and investigate the incubation coefficient as well as its dependence on film thickness and its influence on laser line patterning of thin ITO films.

Fig. 9.9
figure 9

Laser induced damage micro morphologies of the ITO films irradiated by different pulse numbers recorded by SEM, where a 1 pulse, b 10 pulses and c 100 pulses. The applied laser fluence was 0.83 J/cm\(^2\). The film thickness was 100 nm for all cases

Full size image

Figure 9.9 illustrates the typical surface damage morphologies of ITO films irradiated by different number of laser shots recorded by SEM. The laser fluence was set to 1.33 J/cm\(^2\), slightly above the single-shot threshold. By increasing the number of incident laser pulses the damage site area grows and the rims are getting sharper. Figure 9.10 demonstrates the surface damage morphologies induced by different laser fluences with a fixed number of laser shots (\(N= 10\)). Increasing the laser fluence will enlarge the ablation area, which is basically the same effect as to increasing the number of laser pulses.

Fig. 9.10
figure 10

Laser induced damage micro morphologies of the ITO films irradiated by different pulse energies recorded by SEM, where a 0.53 J/cm\(^2\), b 0.88 J/cm\(^2\) and c 1.33 J/cm\(^2\). The applied pulse number was 10. The film thickness was 100 nm for all cases

Full size image
Fig. 9.11
figure 11

The measured squared diameter of ablated spots plotted against the applied pulse energy, a 1 shot, b 1,000 shots

Full size image

To determine the damage thresholds of ITO films as a function of the incident pulse number as well as its dependence on film thickness, a series of experiments was performed with different laser fluence levels on samples with thicknesses of 10, 50 and 205 nm. Figure 9.11 presents the relationships of measured squared diameter plotted against the logarithm of the applied pulse energy for \(N\) = 1 and 1,000 laser pulses, respectively. From the data plots a well-defined linear dependence in semi-log plot can be observed with almost a constant slope for all cases which yields a beam radius of about 20 \(\upmu \)m. In all plots, for the same pulse energy, the ablation site is bigger for thicker films, especially for lower pulse shots. As the pulse number has been further increased up to 1,000, the ablation site area changes almost similar for the three film thicknesses. This effect can be reflected from the calculated damage thresholds. For a 1 pulse shot, the damage thresholds are 1.48, 0.89 and 0.35 J/cm\(^2\) for 10, 50 and 205 nm films, respectively. On the contrary, for 1,000 pulse shots, the threshold values become 0.36, 0.26 and 0.25 J/cm\(^2\). In this case the differences between the three thicknesses are getting much smaller in terms of ablation thresholds. This implies for a large pulse number that the damage threshold is nearly independent on the film thickness. Another result one can observe is that the thinner ITO film with lower pulse shots yields higher damage thresholds, which however, drops faster with an increasing number of laser shots. This is contrary to the metal films where the ablation thresholds decrease when the film thicknesses getting thinner if it is in the range of the thermal penetration penetration length [52].

It has to be mentioned that for multi-pulse shots, the delay between two neighboring pulses in our experiments is 5 \(\upmu \)s, which is much longer than all relaxation times of electrons and phonons, in the range below 10 ps [53].

Fig. 9.12
figure 12

a Log plot of the ablation thresholds in dependence on the number of pulses for ITO. The lines are a fit to (9.7) with only the filled data points are used in the fit. The incubation coefficient can be estimated as \(S= 0.82\). b Ablation threshold fluence of various Au layer thicknesses in dependence of pulse number per damage site. The lines are a fit to (9.8), the fit parameters for an infinite number of shots on a layer of given thickness are presented in the graph

Full size image

The threshold fluence versus the number of applied pulses is shown in Fig.  9.12a. It is obvious that the threshold fluence drops strongly when the surface is exposed more than once with otherwise identical laser parameters. Especially for thinner films, the damage threshold drops dramatically when increasing the number of pulses. For thicker films, a less pronounced drop can be observed, only apparent for a low number of laser pulses. For example, at 1 shot and 1,000 shots, for a thickness of only 10 nm the ablation threshold drops by \(75\,\%\) but only by \(30\,\%\) in the case of a 205 nm film thickness. These observations indicate that for very thin films and only a few pulses, a strong cumulative effect occurs. As also shown in Fig. 9.12a, the thresholds will drop with an increasing number of incident pulses.

However, beyond a specific number of pulses the fluence threshold stays constant. The threshold value turned to its final value with less pulses for thick films, e.g. for a thickness of 205 nm the characteristic value for laser pulses is about 10, whereas for 50 nm thick films the threshold falls within the first 100 pulses. Therefore, it is reasonable to exclude the points in Fig. 9.12a which have reached the final threshold value for high pulse numbers [41]. The relationship between threshold and pulse number can be quantitatively expressed by (9.7), as shown in Fig. 9.12a by the dotted lines. It is interesting to see that the linear fitting lines yield the same slope values of \(-0.18\), although there is a high uncertainty for the 205 nm thickness due to a lack of enough experimental data. This is justified to conclude that the incubation effect is attributed to the surface stress-strain energy storage by the linear relationship in the logarithmic plot of the damage thresholds against the incident pulses number, yielded by (9.7). The incubation coefficient can be calculated to \(S= 0.82\).

The dependency of the threshold fluences on the film thickness is different for metals and ITO: For metal films, the ablation threshold fluence is found to increase as the rising of film thickness in the range of thermal penetration depth, when same pulse number is applied. For ITO films, the inverted trends can be defined, where the ablation threshold is found to decrease as the rising of thickness. The incubation effect depends differently on the film thickness for the both types of materials.

Usually the storage of strain-stress energy induced by multipulse irradiation is regarding to the reason of the incubation effect when talking about the ablation of thick metals. Quite a few people come to this point of view where (9.7) is found to be fitted quit well with their experimental data [26, 27]. However, when the film becomes thinner, the dependency of the ablation threshold fluence on the pulse number changes. As shown in Fig. 9.12b obtained in [42], the multi-shot damage thresholds fit quit well with (9.8) instead of (9.7) when the film thickness is in the range of thermal penetration depth. From their experiment, the largest differences between single and multi shot of laser induced damage occur for the thickest layers, which gets higher cumulative effect. For thinner films that are significantly smaller than the thermal penetration depth, the strengthen of the surface modification is regarded to be responsible for incubation increases, rather than in multipulse ablation the storage of strain-stress energy as the bulk metal samples.

For wide bandgap semiconductors, the multi pulses irradiation on a bulk solid with fluence below single pulse ablation threshold is more likely to cause the defect of the material’s band structure, for example form color center [46]. This is considered to be the reason for the incubation effect here. Hence the (9.8) is more suitable to describe the incubation effect rather than the strain-stress deformation model by (9.8), which can be found in several publications [46]. However, as we found in our experiment on ablation of ITO films, the strain-stress deformation model described by (9.7) gives a better fitting to the experimental data, shown in Fig.  9.12a. Different to metal films, the largest differences between single and multi shot of laser induced damage occur for the thinner layers. It can be regarded that the behavior of the storage strain-stress energy induced by multipulse irradiation is responsible for the incubation effect for ITO film.

The discussion above was completely referred to multi-pulse shots on a single site, based on the “N-on-one” experiment. In most practical applications, however, laser patterning of lines or areas is the result of a laser pulse train with a fixed overlapped area \(R_{ ov}\) usually determined by the laser scanning speed \(v\), laser repetition rate \(f\) and the spot diameter \(D_1\). If \(0<v/f\le D_1\), the overlapped area can be expressed as \(R_{ ov}=1-v/( {fD}_1)\).

Assuming there is no incubation effect, the width of the patterning line would be always equal to the diameter of single-shot site, the line width \(L= D_N= D_1\), no matter how much overlapping rate has been used. Figure 9.13 illustrates the patterning lines with different overlapping rates at the laser fluence of 0.88  J/cm\(^2\). As one can see the line width increases with higher overlapping rate and stays no longer equal to the diameter of a single-shot site. This indicates the significant incubation effect on the width of the patterning lines.

Fig. 9.13
figure 13

Laser induced patterning line morphologies on the ITO films irradiated by different overlapping rates recorded by SEM, where a shows the results for \(R_{ ov}= 0\), b \(R_{ ov}= 30\,\%\), c \(R_{ ov}= 75\,\%\) and d \(R_{ ov}= 95\,\%\). The applied laser fluence has been 0.88 J/cm\(^2\). The film thickness was 100 nm for all cases

Full size image

For further calculations we replaced the pulse number \(N\) in “N-on-one” experiment by \(N={ fD}_1/v=(1-R_{ ov})^{-1}\), which can be considered as the effective pulse number overlapped within the single-spot site. Combining this with the (9.7), one can obtain

$$\begin{aligned} L=D_1\sqrt{1+\frac{(S-1)}{ln[q/q_*(1)]}ln(1-R_{ov})}, \end{aligned}$$
(9.9)

with \(L\) representing the ultimate line width at a given laser fluence \(q\) and \(q_*\) is the single-shot ablation threshold. It is obvious, that for an overlapping rate \(R_{ ov}= 0\), i.e. no overlapped area between two succeeding pulses, incubation effects disappear and the width of the line equals to \(D_1\). As the overlapping rate increases, the width of the patterning line increases, as well. Assuming the other extreme case \(R_{ ov}= 100\,\%\), the width theoretically approaches infinity which is equal to the “N-on-one” case with an infinitely number of pulses. However, in this situation (9.7) is not valid any longer.

In order to verify (9.9), we conducted a series of experiments with 100 nm ITO films applying different overlapping rates, as plotted in Fig. 9.14. The incubation coefficient was evaluated in Fig. 9.12, where it comes to \(S = 0.82\). The single-shot ablation threshold is 0.59 J/cm\(^2\) and the applied laser fluence \(q= 0.88\) J/cm\(^2\) induces a damage site diameter of \(D_1= 15.3\,\upmu \)m. Substituting these values for the parameters in (9.9), the result is plotted in solid line shown in Fig. 9.14.

Fig. 9.14
figure 14

Width of patterning lines versus different overlapping rate. The applied laser fluence has been 0.88 J/cm\(^2\). The solid line is fitted according to (9.9)

Full size image

The plot reveals that the (9.9) agrees quite well with the experimental data. A slight deviation appears at higher overlapping rates, which is equivalent to an extremely high number of incident pulses on one site and results from the failure of (9.7) for high values of N. Taking the course of the development into account, it is reasonable to generalize (9.9) to the laser patterning of material with an incubation behavior which can be described by (9.7), e.g. most of metals. In case where (9.8) should be used to calculate \(q_*(N)\) for multi-pulse ablation, the similar derivation course could be used to model the width of the patterning line, e.g. for most of dielectrics.

5 Conclusion

The thermal penetration depth for both metals and transparent ITO films are discussed. For metals, the thermal penetration depth can be analytically calculated by treating the laser as surface heat source. Due to the complicated nonlinear absorption of laser pulses for transparent semiconductors, a theoretical prediction of thermal penetration depth is difficult. By experimentally measuring the relation of the ablation threshold fluence dependent on the film thickness, the effective thermal penetration depth for both metal and ITO films can be obtained. When the film thickness is in the range of thermal penetration depth, the influence from the substrate can not be neglected and the ablation features are heavily dependent on the film thickness, demonstrating a different behaviors to the ablation of bulk material, such as the ablation threshold fluence for front- and rear-side ablation, for multi-pulse ablation.