Laser Ablation

4.06

Laser Ablation

D Zhang, Huazhong University of Science and Technology, Wuhan, China L Guan, Hebei University, Baoding, China Ó 2014 Elsevier Ltd. All rights reserved.

4.06.1 4.06.1.1 4.06.1.2 4.06.1.3 4.06.1.4 4.06.2 4.06.2.1 4.06.2.2 4.06.2.3 4.06.2.3.1 4.06.2.3.2 4.06.2.3.3 4.06.2.4 4.06.3 4.06.3.1 4.06.3.2 4.06.3.3 4.06.4 4.06.4.1 4.06.4.2 4.06.4.3 4.06.5 4.06.5.1 4.06.5.2 4.06.5.3 4.06.5.4 4.06.5.5 References

Laser Ablation Technology: Introduction and Physical Fundamentals Laser Ablation History of Laser Ablation Technology Long-Pulsed Laser Ablation Femtosecond Laser Ablation Applications of Laser Ablation in Material Processing I Laser Drilling and Cutting Laser Welding and Laser Modification of Physical Properties of Functional Materials Laser Surface Modification Surface Hardening Laser Cladding Alloying Femtosecond Laser-Induced Surface Periodic Structure and Nanogratings Applications of Laser Ablation in Material Processing II Microimage of Femtosecond Laser Interaction with Transparent Material Applications of Femtosecond Laser Ablation of Transparent Materials Applications of Femtosecond Pulsed Laser in Nanoparticle Formation Pulsed Laser Ablation and Pulsed Laser Deposition Technology Physical Picture of Pulsed Laser Deposition Introduction to Plasma Expansion in Pulsed Laser Deposition Introduction to Film Growth in Pulsed Laser Deposition Thermodynamics of Laser Ablation Theoretical Framework of the Thermodynamics of Long-Pulsed Laser Ablation – The Basic Equation and Plasma Shielding Effect Theoretical Framework of the Thermodynamics of Long-Pulsed Laser Ablation – Dynamic Physical Parameters and the Vaporization Effect Main Theoretical Results of the Thermodynamics of Long-Pulsed Laser Ablation Femtosecond Laser Ablation Models: Classic and Improved Two-Temperature Equations Femtosecond Laser Ablation Models: Unified Two-Temperature Equations and Density of State Effect

4.06.1

Laser Ablation Technology: Introduction and Physical Fundamentals

4.06.1.1

Laser Ablation

125 125 126 128 130 130 130 133 133 134 134 134 135 137 137 139 139 143 143 144 146 147 148 150 152 156 160 165

Laser ablation is the thermal or nonthermal process of removing atoms from a solid by irradiating it with an intense continuous wave (CW) or pulsed laser beam. As one of the most important techniques for material processing, laser ablation can be used for drilling extremely small, deep holes through very hard materials such as metals or diamonds, producing thin films or nanoparticles, preparing material surface in a micro- and nano-controlled fashion, and so on. The CW laser beam refers to a continuous output once the laser system is powered on, while the pulsed laser refers to a short time (e.g., milliseconds to femtoseconds) output, as illustrated in Figure 1. The peak output power of a pulsed laser beam is much higher than that of a CW laser beam, giving the same average output power. When a solid surface is irradiated by a CW laser beam or long-pulsed (e.g., nanoseconds pulsed) laser beam, the material is heated by the absorbed laser energy. The thermal motion of some particles is accelerated. Once the absorbed energy exceeds the sublimation energy, these particles evaporate or sublimate and become vaporized particles; that is, part of the target is ablated. The laser ablation rate N_ is defined as the vaporized particles per unit area per second: _ ¼ rd=sm N

[1]

where s is the duration time of the laser pulse, r is the density of the target, d is the thickness of the ablated material, and m is the average mass of ablated atoms. However, for a short-pulsed laser (e.g., femtosecond laser), the laser-material interaction time is very short. Thus, the heat energy has no time to diffuse in lattice. The irradiated zone of the material quickly reaches vaporization temperature and the ablated

Comprehensive Materials Processing, Volume 4

http://dx.doi.org/10.1016/B978-0-08-096532-1.00406-4

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Laser Ablation

Average output power & Peak output power

Output power

Output power

Peak output power

Time (a)

Continuous wave (CW) laser beam

Average output power

Time (b)

Pulsed laser beam

Figure 1

Illustration of the peak output power and the average output power of a CW laser beam and pulsed laser beam.

Figure 2

The characteristics of different laser ablation processes. Reproduced from Yang, J. J. Laser Optoelect. Prog. 2004, 41, 44 (in Chinese).

particles evaporate from the surface. The duration time of the pulse is much less than the time taken by excited molecules, atoms, and electrons to release heat energy by moving or rotating motion (i.e., electron–phonon relaxation time), which is too short for linear absorption processes such as the single-photon process, electron–phonon interaction process, and thermal diffusion process to happen. Consequently, nonlinear absorption of laser energy (e.g., multiple-photon process) does occur during short-pulsed laser ablation. The short-pulse laser process is a nonthermal melting process. The characteristics of different laser ablation processes are shown in Figure 2 (1).

4.06.1.2

History of Laser Ablation Technology

The thermal effect of laser ablation is utilized in thin-film preparation, laser welding, laser surface treatment and modification, laser cladding, drilling, cutting, and so on. In 1960, the first working laser, a ruby laser, was realized by Theodore Maiman at Hughes Research Laboratories (2). In 1965, it was discovered that a laser could be used for diamond drilling using laser ablation mechanisms (3). In 1967, British scientists started research on cutting titanium metal with a laser-assisted oxygen jet, which was later widely used in aerospace projects. Due to its longer wavelength, CO2 laser was only used for nonmetal cutting (3). In the 1960s and 1970s, laser equipment consisted mainly of CW or long-pulsed lasers such as CO2 and Nd:YAG, which are typical high-power laser systems. Figure 3 presents the main process of laser evaporation by thermal effect. Once the incident laser energy density exceeds the threshold, the thermal effect leads to evaporation. In the middle 1960s, it was found that in the process of laser beam irradiation, electrons, ions, and neutral atoms removed from the solid surface form a glowing plasma near the surface with the temperature of 103–104 K. Then the ablated material is condensed on the substrate, and the film is finally obtained. This is the initial principle of laser deposition (4,5). In 1965, Smith and Turner deposited optical thin films by a ruby laser for the first time (6). This is one of the earliest pulsed laser deposition (PLD) techniques for thin-film preparation. Limited to low laser energy density at this stage, the high quality of the deposited films was not achieved. The long wavelength of the laser beam led to a deep melted liquid layer, where sputtering easily occurred. The sputtering produces many droplets in the deposition process and strongly affects the quality of films. In the 1980s to 1990s, with the development of lasers with high-energy density and short wavelength, the sputtering effect was gradually reduced in film deposition. The PLD technique became one of the most successful film fabrication techniques (7,8). PLD is a physical vapor deposition technique. Figure 4 gives a typical setup of PLD equipment. Under laser irradiation, the target is

Laser Ablation

Figure 3

The process of laser ablation by thermal effect.

Figure 4

A typical experimental setup of pulsed laser deposition technique.

127

ablated and vaporized to form plasma. The plasma plume expands in vacuum or a background gas, and finally arrives at a substrate surface to deposit a film. In the 1970s, since lasers with sufficient power and energy density to melt metals were realized, laser welding technology was developed (9). The Avco Everett Research Laboratory brought the world a laser surface modification machine for heat treatment of metals in 1973 (10). The laser beams produced in this era had a relatively long wavelength and duration time. The interaction between the laser and the target is mainly the linear absorption of energy via electron photon resonance, resulting in melting, vaporization, and removal of material. Therefore, the ablation essentially depends on the optical and thermal properties of the material. A heat effect zone is unavoidable around the processing zone, which causes heat stress and other defects. In the 1980s and 1990s, various laser techniques were developed for many applications. As an example, laser cladding and PLD technology were fully developed and made breakthrough progress in this period. As laser power density is enhanced and pulse duration is shortened, a nonthermal effect was observed in laser ablation for material processing. In the 1980s, ultraviolet excimer lasers with nanosecond or picosecond pulse width could accomplish many precise processing tasks, such as drilling, etching, and surface heat treatment, on nonmetallic materials such as polymers and ceramics (11,12). Each photon of an excimer laser has a large energy, which is enough to break the bonds of molecules or atoms to generate plasma near the target surface. This is actually a photochemistry reaction rather than a thermal melting process, as shown in Figure 5. Due to its short wavelength, the laser beam can easily focus on a tiny area, which greatly improves the processing precision. In 1976, the dye laser for the first time was mode locked to produce pulses with durations as short as 0.3 ps (13). In 1981, Fork et al. reported a colliding pulse mode-locking technique to produce a continuous and stable train of pulses shorter than 0.1 ps (14). Asaki et al. utilized a self mode-locked technique to obtain an 11 fs pulse laser in 1993 (15). In 2000, the emergence of photonic crystal fibers indicated a new stage of femtosecond laser development. The femtosecond laser has two prominent characteristics: (1) the pulse width can be as short as a few femtoseconds, which is 10 trillion times smaller than the resolution limit of the human eye, and (2) the transient power is extremely high (16). 200 TW peak power has been achieved experimentally by chirped pulse amplification (17). The focused peak intensity of a femtosecond laser can run up to 1021 W cm2, or even higher (16,18). The emergence of femtosecond laser technology further expanded the application field of nonthermal laser ablation. As a nonthermal and ‘cold’ treatment technique, the femtosecond laser started a new era of laser material processing, showing many advantages such as superprecision, high spatial resolution, versatility, and universality.

128

Figure 5

Laser Ablation

The process of laser ablation by photochemistry effect.

Femtosecond laser technique is an effective way of fabricating nanoparticles and large-area regular nanogratings (19,20). Femtosecond laser-induced periodic surface structures (LIPSSs) have potential applications in the photoelectronics, thermal radiation source, and bio-optic devices fields (21). For example, the so-called black metal prepared by the femtosecond laser ablation technique can absorb light of any wavelength.

4.06.1.3

Long-Pulsed Laser Ablation

When a laser irradiates the target surface, several physical processes including reflection, dispersion, absorption, and transmission are involved, as shown in Figure 6. P0, Pb, PR, and Pz are the whole incident energy, the absorbed energy, the reflected energy, and the transmitted energy, respectively. When laser energy absorbed by the target reaches a specific value (ablation threshold), the ablation phenomenon emerges. Lasers with long wavelength are not suitable for metal ablation, as most of the laser energy will be reflected by the metal surface. UV short-pulsed lasers with short wavelength, such as frequency multiplied Nd:YAG laser or excimer laser, are good candidates for metal ablation. The infrared laser with long wavelength can be effective when ablating some special materials (22). According to the energy conservation rule, the energy components in Figure 6 can be related as: P0 ¼ PR þ Pb þ Pz

[2]

PR Pb Pz þ þ ¼1 P0 P0 P0

[3]

or

R ¼ PR/P0, b ¼ Pb/P0, and z ¼ Pz/P0 are reflectivity, absorbance, and transmittance, respectively. Hence, eqn [3] can be rewritten as R þ b þ z ¼ 1. Laser ablation is a special interaction between laser radiation and matter, which depends not only on the laser parameters (e.g., the output power, the wavelength, and the radius of irradiation spot) but also on the physical properties of the material (e.g., optical parameters, such as reflectivity, absorbance, and transmittance, and the thermal properties, such as thermal conductivity and specific heat capacity). With a low power density laser, the target under irradiation will heat up. When the power density exceeds the ablation threshold energy, at which evaporation starts at the target surface, the target is ablated. Here is a detailed physical image of long-pulsed laser ablation (LPLA). When pulsed laser irradiates a solid target, most of the laser energy is accumulated on the surface of the nontransparent target. Part of the laser power is absorbed by this thin layer under the irradiated surface, which results in a continuous increase of the surface temperature. Simultaneously, part of the energy is transported into the inner layer. Thus the thickness of the heated region increases. As the thickness increases, the temperature

Figure 6

During laser irradiation of the target surface, several physical processes, including reflection, absorption, and transmission, occur.

Laser Ablation

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gradient gets smaller and smaller, leading to a gradually decreased heat conduction rate until zero. That is, the laser heat energy can only penetrate a thin layer of target. The thickness of this thin layer is defined as the thermal penetration depth. If the laser energy density is high enough, the excited electrons transfer energy to the lattice by collisions and the target heats up. Thus, the thermal motion of some of the atoms in the lattice is accelerated. These high-energy atoms can overcome the attraction of their neighbors. Then, corresponding physical phenomena such as melting, vaporization, and boiling occur. Finally, a complicated layer structure emerges near the target surface, which indicates the beginning of ablation. The vapor above the surface (including atoms, molecules, some clusters, micrometer-size droplets, and solid particles) continuously absorbs laser irradiation, until it is almost ionized. Thus, the ablated material in plasma state ejects from target. Subsequently, a plume is produced near the surface. The temperature of the surface is dominated by the vaporization mechanism. The particle density of the plasma plume near the target surface, called the corona region, is very high. The corona region absorbs about 98% of the laser energy through the inverse bremsstrahlung (IB) absorption effect and photoionization (PI) effect, thus shielding the target surface from laser irradiation. The heat conduction region is the region outside the corona region where the particle density of the plasma is relatively low. The laser energy is not effectively absorbed in this region. Intense energy transport phenomena occur near the target surface, that is, the thermal penetration layer, which is mainly solid-phase, together with liquidphase and gas-phase materials. This layered structure due to pulsed laser irradiation will extend deep into the target with time. The actual physical process of the interaction between the laser and the target is much more complicated than the physical processes mentioned above. There are complex physical processes such as electron excitation effects (such as, induced electron–hole pairs), photoelectronic effects, atom or cluster emission, and so on (23,24). When laser power density increases to 1010 W cm2, the energy of the atoms in the melted target surface is dramatically increased, which usually leads to the boiling phenomenon. Due to the absence of a vaporization nucleus coupled with the extremely rapid melting process, the temperature of the melting layer rises suddenly. The target does not boil, although the temperature exceeds the boiling point. This is the so-called superheating phenomenon. The superheated melt is in a metastable state. Any small disturbance, such as density perturbation or impurity defect formation, can cause an explosive boiling. This abnormal boiling phenomenon is called a phase explosion, which is an important topic in pulsed laser ablation (PLA) research (25–30). The ablation evaporation is intrinsically different from normal evaporation, since a Knudsen layer is generated in the corona region during laser ablation (31,32). If the particle density of the vapor is low and the collision between the particles is negligible, only a normal evaporation phenomenon occurs. However, if the laser power density increases to 109 W cm2 (a typical parameter for ablation), the density of the vapor particles can reach 1016–1027 cm3. In this case, frequent collisions between the ablated particles result in the highly preferential distribution of the particles along the perpendicular direction of target surface. The collisions take place within a few mean free paths away from the surface, which is defined as the Knudsen layer. The velocities of various particles tend to be the same in this layer, as the particles frequently collide with each other due to the high density. In fact, this is why the PLD technique can achieve the stoichiometric deposition of films. The presence of the Knudsen layer makes it possible for approximately the same flight time of different particles in the atmosphere. The related physical process is illustrated in Figure 2(a). The physical process of LPLA can be briefly described as followed. When the high-power pulsed laser irradiates the target, the laser energy is absorbed by the target surface. The surface is then melted and vaporized, which forms a high-temperature, highpressure plasma. Therefore, the target under interaction with a pulsed laser can be roughly divided into three separate parts: the high-temperature and high-pressure plasma, the liquid-phase region, and the solid-phase region, as illustrated in Figure 7. For various materials, irreversible ablation requires that the laser energy density reaches or exceeds the ablation threshold. For the interaction between the long-pulsed laser and the material, avalanche ionization brings about a final ablation, which is mainly determined by doped impurities and various defects. Therefore, the ablation threshold for LPLA is different for different materials.

Figure 7 Illustration of the regions in a laser-irradiated solid. (a) Unaffected region, (b) laser ablating region, (c) high-temperature and high-density plasma, and (d) the transparent region for laser.

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4.06.1.4

Laser Ablation

Femtosecond Laser Ablation

The physical image of femtosecond laser ablation is quite different from nanosecond laser ablation. When the pulse duration time is in the order of a femtosecond, the impact of the relaxation time of electron–phonon interaction, which is in the order of picosecond, should be considered. When the femtosecond laser focuses on the surface of a bulk, the photon energy is first absorbed by electrons, leading to an accelerated thermal motion of the electrons and a dramatic temperature increase of the electron subsystem. However, during the short pulse, the electrons have no time to transfer the obtained energy to the lattice (or the ions). At this time, the temperature of the electron gas is very high, while the lattice subsystem’s temperature keeps relatively low. Thus, a ‘cold’ ablation process occurs. Usually, the thermal equilibrium time of the metal is roughly a few femtoseconds, compared to the order of ns for semiconductors or insulators. This is in fact the relaxation time of electron–phonon interaction. The relaxation time difference is a result of the energy gap difference. The larger the energy gap, the longer it takes for the excited electron–hole pairs to reach thermal equilibrium through generation-recombination (34). In the short period of pulse, there are two temperature subsystems in the target: the electronic subsystem and the lattice subsystem. These two subsystems can be described using two electron–phonon coupling thermal conduction equations, named as the two-temperature model for femtosecond laser ablation. In contrast to LPLA, electrons produced in femtosecond laser ablation depend mainly on multiphoton ionization or tunneling ionization mechanisms (see Section 4.06.3.1). The dopants and defects in the lattice only have a very small influence on generationrecombination of electron and vacancy pairs. Therefore, the ablation thresholds for different materials are similar for femtosecond laser ablation (35). Assuming the same energy density and repetition frequency, the pulse laser with shorter pulse width and hence higher peak power easily satisfies the ablation threshold of target. Figure 2(b) demonstrates the main physical processes of femtosecond laser ablation. The features are summarized here: 1. Nonthermal processing. This reduces or even eliminates some defects (the roughness of the ablation edge and large crack formation) in the traditional long-pulsed laser material processing. 2. High-precision processing. Suppression of the heat conduction effect and the hydrodynamics effect dramatically improves the working precision of femtosecond laser ablation. 3. Accurate three-dimensional spatial processing. When a femtosecond laser with a focused intensity close to the ablation threshold irradiates transparent materials, the low-beam intensity at the positions other than the focus point cannot meet the requirement for the nonlinear absorption of multiphotons. Thus, the laser beam arrives at the focal point inside the material without any attenuation. The high energy accumulated here induces multiphoton absorption and ionization. Consequently, femtosecond laser ablation can be precisely controlled at any focused position inside a three-dimensional transparent material, leading to a highly accurate spatial selection and positioning ability. 4. Universality of femtosecond laser material processing. The extremely high peak intensity induces only multiphoton absorption. The ablation is dominated by laser intensity, suggesting an invariable ablation threshold. The multiphoton absorption and ionization threshold mainly depend on the atoms rather than on the density of the electrons in the material. Therefore, a femtosecond pulse laser can theoretically accomplish precision processing, repair, and treatment for any kind of materials.

4.06.2

Applications of Laser Ablation in Material Processing I

4.06.2.1

Laser Drilling and Cutting

The two remarkable applications of laser ablation are laser drilling and cutting. The use of lasers for drilling and cutting was first developed in the 1960s. These two techniques have the longest history and the most mature technology for laser material processing. Figure 8 represents the main steps for laser drilling. Two physical processes are involved: (1) The temperature of irradiated material exceeds the melting point, and surface vaporization occurs; (2) the internal pressure of the vapor is so great that the ablated material is sputtered. Laser drilling requires incident laser energy above the ablation threshold. Thus, high-power pulsed lasers are extensively used in industry. The pulsed laser has many advantages, such as short interaction time, small heat effect zone, and precise dimension control. The factors that affect the quality of laser drilling are the laser parameters (laser power density, irradiation spot area, incident angle, pulse width, and pulse repetition frequency), the parameters of the desired hole (diameter, shape, and depth), and the physical properties of the material (absorption coefficient, reflectivity, and thermal conductivity). To accomplish a high-quality hole, the material with low-heat conductivity (ensuring less dissipation around the drilled hole), low reflectivity, and high absorbance (ensuring much laser energy absorbed by target) is preferred. Figure 9 shows micrographs of the laser-drilled holes using a pulsed laser with the same wavelength and different pulse widths. It is obvious that as the pulse width reduces, the quality of the holes improves, while the power required decreases (36). The process of Figure 9(c) is the best. This is processed by femtosecond laser drilling, and it keeps a sharp, clean edge and a regular shape. The worst is the one drilled by nanosecond laser, as shown in Figure 9(a). Nowadays, many kinds of materials including metals, semiconductors, ceramic, and polymers dielectric materials can be drilled by laser. As mentioned earlier, metals are suitable for drilling by short-wavelength lasers, such as excimer lasers (36). For most ceramic materials with a low reflectivity for infrared lasers, CO2 laser is a good candidate for ceramic drilling (37,38). However, for

Laser Ablation

Figure 8

(a)

(b)

(c)

(d)

131

Schematic diagram of laser drilling processing: (a) unstructured, (b) Cu opened, (c) dielectric opened, and (d) hole formation.

Figure 9 Micrographs of the laser-drilled holes on steel. The wavelength is 780 nm. The pulse widths are (a) 3.3 ns, (b) 80 ps, and (c) 200 fs, respectively. Reproduced from Chichkov, B. N.; Momma, C.; Nolte, S.; Alvensleven, F. V.; Tunnermann, A. Appl. Phys. A 1996, 63, 109.

polymers, phase transitions (e.g., solid / melt / vapor) and chemical degradation often occur at high temperatures (39). Unlike most metals, the polymer materials under laser irradiation can produce a deeper thermal penetration. Lawrence et al. confirmed that for CO2 laser, the absorption length for Al2O3/SiO2-based refractory material is three orders of magnitude greater than most of metals (38,40). Generally, both polymers and ceramics have a deeper heat penetration, so the heat transport theoretical model considering a volumetric heating for drilling is more accurate than a model only considering surface heating (41–43). Laser cutting is a technology that uses a high-power laser to scan material surface, and the material is heated in an extremely short time, leading to the temperature rises up to 103 or 104 K, then the melting and vaporization phenomena occur. The ablated material is blown away by an assisted jet gas, and finally a cut edge with a high quality is left. Figure 10 is a schematic diagram of the

Figure 10

A typical experimental setup of laser cutting technique.

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Laser Ablation

Figure 11 Configuration of the laser-cutting system with the dual-laser-beam method. Reproduced from Jiao, J. K.; Wang, X. B. Opt. Laser Eng. 2009, 47, 860.

laser-cutting technique. The experimental system usually includes a laser device, a laser delivery system, an assisting gas output device, and a computer-assisted work-piece or laser movement system. Initially, laser technology was utilized to cut metals, and gradually its applications extended to the cutting of various materials such as glass and wood, as well as polymers. A typical laser beam used for cutting needs a power intensity of 1000–2000 W. In the cutting process, the quality of the cutting edge depends on some parameters at different extent, such as the output mode (pulsed or CW) of laser, power density, pulse repetition frequency, cutting speed, type and pressure of assistant gas, as well as the type and thickness of the workpieces (44). Compared to conventional methods, the laser-cutting technique relies on the thermal rather than mechanical properties of materials, avoiding mechanical damage of the workpiece. Laser cutting is noncontact, which can deliver a finer finish without cracks. Therefore, computer-assisted laser cutting is widely applied in industry to continuously and precisely accomplish any desired shape, although the machining process sensitively depends on the physical properties of materials and laser parameters. The most commonly used lasers for cutting are Nd:YAG laser and CO2 laser (45). CO2 lasers with high average power and better beam quality are suitable for cutting thick materials except for metal workpieces with high reflectivity for the longer wavelength. Nd:YAG lasers have a shorter wavelength, which is able to process highly reflective materials, such as titanium and titanium alloy (46,47). Lv. Shanjin et al. (47) investigated the influence of the laser-cutting parameters, for example, pulse energy, pulse rate, cutting speed, and the type and pressure of gas on the heat-affected zone (HAZ) and surface morphology of titanium alloy. The CO2 laser is frequently applied to cut glass. There are two main methods for glass cutting: the controlled-fracture lasercutting technique and the evaporative laser-cutting technique. The key problems in glass cutting involve how to improve the control precision, how to reduce the thermal stress generated during glass cooling, and how to avoid the fracture propagation along an unexpected path. Recently, a dual-laser-beam method was proposed to cut glass substrates in order to further improve the cutting quality. In this method, a focused laser beam was used to scribe a straight line on the substrate, and a defocused laser beam was used to irradiate on the scribing line to generate a tensile stress and separate the substrate. With this method, the fracture propagates stably, and the glass substrate can be separated along the desired path (48,49). The configuration of the laser-cutting system with the dual-laser-beam method is illustrated in Figure 11. The important procedures in laser cutting are: (1) controlling the focus position to obtain an accurate focus and small spot diameter, and (2) adjusting the nozzle parameters to ensure an appropriate direction and flux of the assisting gas. To avoid the oxidizing reaction and molten dross formed in the process, high-pressure and high-purity nitrogen or inert gases as assisting cutting gases have been used in laser cutting. Hong Lei et al. (50) used a CO2 laser with a power of 1800–4000 W to cut silicon steel sheets. In their experiments, a cyclone slag separator was used to form dross-free cutting kerfs (Figure 12).

Figure 12 Photography of the cutting kerfs: (a) by using a cyclone slag separator and (b) by traditional laser-cutting technology. Reproduced from Hong, L.; Zhang, Y.; Mi, C. L. Opt. Laser Technol. 2009, 41, 328.

Laser Ablation

4.06.2.2

133

Laser Welding and Laser Modification of Physical Properties of Functional Materials

As a high-efficiency and inexpensive technology, lasers are widely used to weld metals or alloys in industry. In 1970, the CO2 laser was first utilized to weld metal, but thermal damage was easily generated during welding due to the long wavelength of the CO2 laser and the low absorbance of the material (9). In the following years, the Nd:YAG laser with shorter pulse width and higher peak power was employed to weld metals. The metal surface can effectively absorb the laser energy to achieve a deeper heat penetration, and thus the strength of the welded joint is remarkably improved (51). It was found that the Nd:YAG laser could produce a minimal HAZ and less thermal damage. With the introduction of fibers into laser technology, a more flexible delivery system can produce a higher-efficiency and better-quality welding. When a laser beam hits a metal surface, the material at the irradiation spot is heated up to the melting and vaporization temperature, and then vaporization occurs. As a result, several unexpected blowholes may be left on the metal surface. How to obtain a desired ‘deep-weld effect’ is a key problem in laser welding technology. Because metals have a temperature-dependent absorption coefficient and a high reflectivity (40,41), laser energy cannot be effectively absorbed by the workpiece, resulting in unexpected thermal damage on the surface. Recently, CW laser matched with an appropriate pulsed laser can perform dual-beam laser welding (51) shown in Figure 13. It was found that dual-beam laser welding could markedly reduce or avoid the formation of the blowholes in the welded joints. The welding efficiency 3 can be expressed as follows: 3 ¼ ½ydWDHm =P

[4]

where P is the incident laser power, y is the speed of welding, d is the thickness of weldment, W is the laser beam width, and DHm is thermal enthalpy at the melting point. For thermal penetration welding, the welding efficiency 3 is 0.48, while for heat conduction welding, 3 is 0.37 (52). The parameters, such as pulse width, power density of laser, irradiation spot area, absorption coefficient, and the thickness of weld, substantially influence the quality of weld. Compared to the conventional arc welding technique, laser welding can lead to a deeper penetration, a smaller HAZ, and a rapid cooling rate. However, the same problem in these methods is still that the internal residual stress caused by heat penetration cannot be fully released, affecting the physical properties of the workpiece. In the 1990s, it was found that the physical properties of materials can be modified by laser irradiation. Table 1 lists the recent progress on the modification of the electrical, optical, and magnetic properties of functional materials, including semiconductors, conductors, superconductors, and magnetic materials.

4.06.2.3

Laser Surface Modification

Conventional surface modification techniques, for example, ion carburizing, boriding, and nitriding, are conditioned by the incident energy of ions. The common disadvantages of these techniques are a shallow strengthened layer, a long processing period, a high required temperature, and an easy transformation of the workpiece. Laser surface modification is noncontact processing by high-power laser beam heating the material surface, and the subsequent cooling takes place through the heat conduction of the material itself. The characteristics of laser surface modification are as follows: (1) the convenient delivery of laser energy, which easily allows selective positioning on the surface for strengthening, and (2) a concentrated laser energy acting on the material, giving

Figure 13 Schematic of the experimental setup of the dual-beam laser welding technique. Reproduced from Yan, S.; Hong, Z.; Watanabe, T.; Tang, J. G. Opt. Laser Eng. 2010, 48, 732.

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Laser Ablation

Table 1

Applications of the modification of physical properties of materials by laser irradiation

Irradiated films

Modification of properties

Wavelength (nm)

References

Al2O3 YBCO ITO n-GaAs SnO2 Mg-doped GaN Doped ferrite ZnO n-type ZnO Ta2O5 ceramic La0.67Ca0.33MnO3 ZnO

Increasing the resistivity of surface Enhancement of electrical conductivity Enlarged grain size and reduced resistivity Decrease of photoconductivity and resistivity Improved Hall mobility and refractive index Enhanced fluorescence intensity of blue light Improved magneto-optical effect Reduced UV emission intensity Improved electrical conductivity Enhanced dielectric permittivity Improved electrical and ferromagnetic properties Improved UV emission intensity

10640 248 248 694 1064 10640 632.8 248 248 10640 10640 248

(53) (54) (55) (56) (57) (58) (59) (60) (61) (62) (63) (64)

short processing time, a small HAZ, and a small deformation of the workpiece. This technique is suitable for dealing with some sheet metals but not with thicker sheets. The laser surface modification process includes surface hardening, laser cladding, and alloying.

4.06.2.3.1

Surface Hardening

Surface hardening, also known as surface heat treatment, includes transformation hardening and shock hardening. Transformation hardening is a heat-treatment process by high-power laser beam irradiation on the surface of metals and other materials. The temperature of the heated material reaches the phase transition point, but melting does not occur. After the end of the laser pulse, the metal begins to quench due to the cooling of the material itself. Compared to conventional heat treatment, the laser modification process induces an increase of 15–20% in the hardness of the material. For shock hardening, a high-strength shock wave or stress wave is generated by the pulsed laser acting on the material surface, and then a strong plastic deformation occurs on the metal surface. In the laser-impacted zone, the microstructure of the material shows a network of dislocation tangles, which is similar to the substructure produced by an explosive shock or fast plane shock, significantly improving the surface hardness, yield strength, and fatigue life of the material. In fact, transformation hardening relies on the thermal properties of materials, while shock hardening relies on the dynamics properties of materials.

4.06.2.3.2

Laser Cladding

Under laser beam irradiation, a coating material on the substrate surface will melt. Then, when the beam is removed, the molten coating material will rapidly cool (the cooling rate up to 103–108 K s1) and then be solidified and combined with the matrix material. In the cladding process, the crystal grain is refined, the composition segregation decreases, and the defect formation is reduced. A higher compressive stress exists in the solidified structure, which greatly leads to surface wear resistance and antifatigue properties. The laser cladding process is used mainly for cast iron and alloy materials. For example, Ni-based powder was selected as laser-surface-modifying material to improve the wear resistance of copper by CW CO2 laser (65).

4.06.2.3.3

Alloying

When a stoichiometric alloy coating on a metal substrate surface is irradiated by a high-energy laser beam, then a mixed melting occurs within a very short time to form a new surface alloy. Because of a fast heating, the composition, structure, and properties of the workpiece only have a slight difference in the melted and heat-affected zone, and the deformation of the workpiece also is small. Finally, the elements of the alloy coating are fully dissolved in the substrate surface layer. Hence, the modified layer has a uniform composition, low porosity, and dense structure. Experiments indicate that the energy and the moving speed of the laser beam on the workpiece surface can influence the composition of the alloy (66). An excimer laser having a high photon energy is often used for surface modification of various materials, such as pure metals or alloys, glass, ceramics, plastics, and many wide-gap materials (67,68). For many wide-gap materials, an ultraviolet laser is more suitable for surface modification than other lasers. Reference (66) reported that titanium nitride was modified by the laser beams, with an energy density of 20.0 J cm2 (TEA CO2) and 2.4 J cm2 (XeCl laser), respectively. The results show that the energy absorbed from the CO2 laser is mainly converted into thermal energy, causing melting, vaporization, and shock waves in the vapor. Energy absorbed from the XeCl laser leads primarily to a quick and intense target evaporation. Thus, XeCl laser-induced target effects are localized and confined to the target surface and its vicinity. With the use of the excimer laser treatment, the corrosion resistance of the Ti-6Al-4V alloy is significantly improved (69). Experiments show that the reflectivity of metal or metal alloy is affected by laser wavelength, leading to a different ablation threshold. Figure 14 indicates that the reflectance spectrum of the Ti-6Al-4V alloy surface and a comparative sum-up of effects produced by the three laser wavelengths 1064, 534, and 266 nm of Nd:YAG laser is given in Table 2 (70). According to the results, it can be seen that laser surface modification of metals significantly depends on laser wavelength.

Laser Ablation

135

65 60 1064 nm

Reflectance (%)

55 50 45

532 nm

40 35 266 nm 30 25 1000

800

600

400

200

Wavelength (nm) Figure 14 Reflectance spectrum of the nonirradiated Ti-6Al-4V surface, with laser wavelengths indicated. Reproduced from Milovanovic, D. S.; Radak, B. B.; Gakovic, B. M.; Batani, D.; Momcilovic, M. D.; Trtica, M. S. J. Alloy Compd. 2010, 501, 89. Table 2

A comparative sum-up of effects produced by the three laser wavelengthsa

Laser at 1064 nm Laser at 532 nm Laser at 266 nm

Reflection

Damage threshold

Periodic surface structures

57.00% 42.70% 29.00%

0.9 J cm2 0.25 J cm2 0.12 J cm2

Nanometer scale: parallel waves, tto . E , period: 800 nm after 30 pulses Nanometer scale: parallel waves, tto . E , period: 400 nm after 50 pulses Nanometer scale: parallel waves, tto E , period: 200 nm after 8 pulses

.

a

Reproduced from Milovanovic, D. S.; Radak, B. B.; Gakovic, B. M.; Batani, D.; Momcilovic, M. D.; Trtica, M. S. J. Alloy Compd. 2010, 501, 89

The integrated surface modification technology by laser combined with other modified methods is growing rapidly. Reference (71) reported that titanium alloy matrix can be treated by glow discharge plasma nitriding and laser remelting processing at the same time. Composite gradient coatings containing TiN and Ti2N were prepared, and thus the surface morphology of titanium was remarkably improved and cracks were reduced.

4.06.2.4

Femtosecond Laser-Induced Surface Periodic Structure and Nanogratings

Femtosecond LIPSSs have become a focus in this field (72–74). The ripples or nanogrooves have a period on the scale of the incident laser wavelength, and the orientation of these periodic structures is perpendicular to the polarization of the incident laser. The mechanism of LIPSSs has been extensively studied by many scientists in the past several decades, and some theoretical models have been established, such as the uneven energy distribution model (75,76), general surface scattering (GSS) model (77,78), Coulomb explosion model (79), photon resonance absorption model (80), Boson condensation model (81), and energy accumulation effect model (82).Of these models, the most famous one is the GSS model. The GSS model to explain the nature of the observed periodic structure was proposed by M. Oron and co-workers (77,78). The incident laser light is partially scattered by surface defects and produces a tangential wave propagating along the surface. The formation mechanism of LIPSSs is the interference at the air-material (or vacuum-material, etc.) interface between the incident laser light and the matter polarization associated with laser-induced surface excitation. Predictions given by the GSS model were in good agreement with experimental observations up to nanosecond pulse duration, but for the femtosecond pulse laser, a morphology emerged that was not predicted by the theory (74), implying that other processes were taking place. In 1992, M. Bonch-Bruevich et al. (83) modified the GSS model and showed that LIPSS is induced by interference between the incident femtosecond laser with the excited plasmons on the surface. In the modified model, the separation of period structure for linear polarization laser can be expressed as: d¼

l h  sin q

[5]

where h ¼ Re[3/(3 þ 1)]1/2 is the real part of the effective refractive index of the surface plasmon, and 3 is the dielectric constant of the metal.

136

Laser Ablation

In 2002, Jurgen Reif et al. (79) studied femtosecond laser ablation of wide band gap insulators and presented a Coulomb explosion model. They observed a complex structure of fine ripples at the bottom of the ablated crater, and they assumed that the ripples structures were due to self-organized structure formation during the relaxation of the highly nonequilibrium surface after explosive positive ion emission. This model explained that for dielectric material, LIPSS with a period less than laser wavelength scale was produced by multipulse ablation with pulse energy less than the threshold energy. Three-dimensional, periodic nanowriting on diamond clusters was reported (84). Periodic ripples have been observed on singlecrystal and polycrystalline diamond surfaces, shown in Figure 15. Further, it has been experimentally shown that the periodicity of these corrugated two- and three-dimensional structures is shorter than that of the laser wavelength used (248 nm for the excimer femtosecond laser and 825 nm for the Ti: sapphire femtosecond laser). In 2006, B. Tan et al. (85) found that a femtosecond LIPSS was formed on the surface-polished crystalline silicon. Unlike the patterns formed by a continuous or nanosecond pulsed laser, the spacing of the ripple formed by femtosecond pulses was not affected by the incident angle of the laser beam. Also, the pulse repetition rate had no impact on the ripple formation on crystalline silicon. The orientation of these periodic structures was perpendicular to the vector of the electric field of the laser beam. Wang and Guo et al. (86,87) investigated periodic structures on the surfaces of three different noble metals, Cu, Ag, and Au, following femtosecond laser radiation. Under identical experimental conditions, laser-induced surface patterns show a higher morphological clearness on the metal with a larger electron–phonon energy coupling coefficient. Angular dependence of the period of these structures was studied, and the results indicated that these structures were formed by the interference between the incident light and the excited surface plasmons. A. Y. Vorobyev et al. (88) performed a detailed study of the formation of LIPSSs on tungsten at near-damage threshold fluences and found a unique type of LIPSS entirely covered with nanostructures, illustrated in Figure 16. In Figure 17, periodic nanostructures were observed on the surface of ZnSe after irradiation by a femtosecond Ti: sapphire laser, which was aligned perpendicularly to the laser polarization direction (89). With the laser polarization parallel to the moving direction, long-range gratings by slowly moving the crystal were produced. Huang and Xu et al. reported that by the simple scanning technique with appropriate irradiation conditions, arbitrary size of uniform nanograting could be produced on wide band-gap materials as well as graphite (90). In 2009, Eric Mazur et al. induced periodic linear grooves with 40 nm wide, 500 nm deep, and up to 0.3 mm long synthetic single-crystal diamond with femtosecond pulses at 800 nm (20). L. Sudrie et al. (91) prepared permanent birefringent

5 μm

2 μm

Figure 15 Three-dimensional periodic ripples induced by a femtosecond laser on single-crystal and polycrystalline diamond surfaces. Reproduced from Ozkan, A. M.; Malshe, A. P.; Railkar, T. A. Appl. Phys. Lett. 1999, 75, 3716.

(b)

(a)

542 nm

2 μm

λ =800 nm

500 nm

λ =800 nm

Figure 16 Femtosecond laser-induced periodic surface structures on W surface. Reproduced from Vorobyev, A. Y.; Guo, C. J. Appl. Phys. 2008, 104, 063523.

Laser Ablation

(a)

NONE

Figure 17

(b)

SEI

10.0kV X 20.000 1μm

137

(c)

WD 8.2mm

SEM images of gratings at the angle 0 (a), 45 (b) and 90 to the moving direction of laser and its polarization direction.

(a)

d = 120 μm

(b)

d = 430 μm

Figure 18 Photographs of the titanium samples. (a) The sample with a groove period of 120 mm. (b) The sample with a groove period of 430 mm. Reproduced from Vorobyev, A. Y.; Topkov, A. N.; Gurin, O. V.; Svich, V. A.; Guo., C. L. Appl. Phys. Lett. 2009, 95, 121106.

structures with controllable microscopic dimensions inscribed in pure fused silica platelets. The birefringence properties of transmission gratings and of a quasi-uniform layer have been established. S. H. Cho et al. fabricated an internal diffraction grating with photo-induced refractive index modification in planar silica plates by a high-intensity femtosecond (150 fs) Ti: 0 sapphire laser (lp ¼ 790 nm). The low-density plasma formation causes the refractive index modification with a SiE center defect (92). Self-organized nanograting periodical structures were induced by an ultrashort intense pulsed laser, which effectively changed the absorption and reflective properties of metal surfaces. Guo et al. investigated femtosecond laser-induced grating structures with different periods on titanium surfaces (72–74,93). They found that by using a femtosecond laser structuring technique, nearperfectly reflective metals are transformed to highly absorptive over an ultrabroad electromagnetic spectrum, ranging from ultraviolet to terahertz, indicated as Figure 18. The so-called ‘black metal’ phenomenon can be applied to the metal shell surface of military weapons, allowing weapons to achieve effective stealth.

4.06.3

Applications of Laser Ablation in Material Processing II

4.06.3.1

Microimage of Femtosecond Laser Interaction with Transparent Material

From a microscopic point of view, laser–solid interaction is achieved via the electrons absorbing energy from photons and being excited from the initial equilibrium state. The absorption mechanisms include single-photon resonance transition, two-photon and higher-order multiphoton transitions, tunneling ionization, and above-barrier ionization (94). Typically, the single-photon transition mechanism plays a dominant role due to a larger cross-sectional area. The interaction between femtosecond laser pulses and transparent materials has a unique nature. The key lies in the transparent dielectric material usually having a wider band gap, which is much larger than the visible and near-infrared single-photon energy, so the linear absorption of solid from a low-intensity laser is weak. For example, a wavelength of an 800 nm fs laser, single-photon

138

Laser Ablation

energy is 1.5498 eV, far less than the band gap of some transparent materials, such as glass. It is not possible for electronic transition from the valence band to the conduction band by single-photon absorption, that is, linear absorption, and consequently color centers cannot be produced in glass. Femtosecond laser-induced color centers in glass are attributed to nonlinear effects caused by multiphoton absorption, which requires the intensity of a laser exceeding w1 GW cm2. When a high-intensity femtosecond laser interacts with transparent dielectrics, the bound electrons in solid absorb incident multiphoton energy and their kinetic energy exceeds the ionization potential energy to become free electrons by jumping from the valence band to the conduction band; this process is called multiphoton ionization, namely, multiphoton absorption, as shown in Figure 19. Multiphoton ionization is a multi-order and nonlinear process, and the reaction cross section is very small. Thus, only an intense laser with a high-photon density could give rise to such a reaction. Furthermore, if this ionization process shows avalanche characteristics, this process will be called avalanche ionization. The mechanisms of femtosecond laser interaction with transparent materials can be described by several theoretical models, such as, the micro-explosion model (95), the Coulomb explosion model (96–98), the avalanche breakdown model (99), and the threshold model (100). Early studies suggest that avalanche ionization is the main reason for ablation (101). However, femtosecond laser ablation of dielectric materials relies on multiphoton ionization or avalanche ionization, and there is some dispute about the mechanism (102,103). Most researchers believe that the multiphoton ionization process first provides seed electrons in the ablation process and subsequently leads to avalanche ionization to accelerate ablation (104). This is the physical meaning of the so-called multiphoton collision ionization. In 2001, Chris B. Schaffer of Harvard University presented that in femtosecond laser irradiation, the nonlinear ionization of transparent materials includes three processes: multiphoton absorption, tunneling effect, and avalanche ionization. The three processes can be determined by the Keldysh parameter (eqn [6]). They measured the ablation threshold of transparent materials with a 110 fs pulse laser, and the damage threshold was found to depend on the laser wavelength and band gap of the material itself: For the center wavelength of 400 nm, multiphoton ionization plays a dominant role in ablation, while for the wavelength of 800 nm, the tunneling effect does; for wide gap materials, the generation of free electrons is largely due to the role of avalanche ionization; for narrow gap materials, PI provides a large number of free electrons (105). The Keldysh parameter g is defined as (106): g¼

uð2m Eg Þ1=2 eE

[6]

where m and e are effective mass and charge of electron, respectively, u and E are angular frequency and amplitude of the incident electric field, respectively, and Eg is the band gap of solid dielectric. If the width of the band gap is narrow and the incident electric field is strong, the Keldysh parameter g w1.5 and then tunneling ionization dominates the ablation process; if g w1.5, multiphoton ionization does; if g w1.5, a mixture mechanism of tunneling ionization and multiphoton ionization. Three ionization modes of femtosecond laser ablation of transparent material are indicated in Figure 20.

Figure 19

Schematic diagram of multiphoton ionization.

Figure 20

Photon ionization mechanism with different Keldysh parameters.

Laser Ablation

4.06.3.2

139

Applications of Femtosecond Laser Ablation of Transparent Materials

A variety of nonlinear effects produced by ultrashort pulse laser interaction with transparent dielectric material led to many microstructures induced in materials, suggesting that the ultrashort laser has a broad prospect for development of high-density three-dimensional data optical storage, optical waveguides, photonic crystals, and so on. The Mazur group at Harvard University first studied the micro-explosion process and the scale of the microcavity formed in femtosecond laser interaction with transparent materials (94). Intense laser beam is focused inside the transparent material, and then ultrahigh-temperature, high-pressure plasma is produced near the focus, causing micro-explosions and microcavity in the body of the material, and the surrounding material becomes compact because of compression. The diameter of the microcavity formed in explosions is less than the optical diffraction limit (94). Through multiphoton absorption, this femtosecond laser process induced a microstructure with an ultra-diffraction limit, mainly applicable in optical storage, as shown in Figure 21. The femtosecond laser can achieve three-dimensional precise positioning in the transparent material ablation. The principle is as follows: The femtosecond laser with the intensity near-damage threshold is focused at any internal position of transparent material. Due to the low-energy beam intensity, it cannot meet the material requirements for multiphoton nonlinear absorption, so the laser beam has almost no attenuation before it reaches the focal point. Therefore, an accurate adjustment of the focal point is necessary for more energy absorption to complete multiphoton absorption and ionization, accomplish ultra-precision machining of any parts of the internal three-dimensional space of the transparent material, and induce the expected microstructure. For example, a femtosecond laser can engrave a ‘micro bull’ inside transparent materials, with approximately 7  106 pixels with a spatial resolution of about 150 nm, as shown in Figure 22 (107). Femtosecond laser-engraved ‘micro spider’ and ‘m-dragon’ models are given in Figure 23 (108,109). Figure 24 illustrates that micro-tweezers with submicron probe tips are fabricated by a two-photon microstereolithography system developed with a Ti: sapphire femtosecond laser (110). When the laser beam is focused on amorphous materials, such as quartz glass and a variety of doped glasses, the material will absorb more laser energy at the focal point, causing changes of lattice structure and the refractive index. This process is helpful for the successful preparation of three-dimensional optical waveguides (105,111,112).

4.06.3.3

Applications of Femtosecond Pulsed Laser in Nanoparticle Formation

Droplets are often generated in the laser ablation stage of the PLD technique, leading to a reduced surface smoothness of films, which is not expected in the film growth process. However, in the preparation of granular materials, especially for nanoparticles, the PLA technique has great development potential. Since the mid-1990s, nanoparticles have been successfully synthesized in a gas medium using laser ablation in the laboratory (113–119). This preparation technology has rapidly developed since the advent of the femtosecond laser (120–123). Currently, according to the type of medium, the laser methods for the laser preparation of nanoparticles can be classified into two categories: one is the synthesis of nanoparticles in the atmosphere, caused by condensation of the vapor during laser ablation of targets, and the other is the preparation of nanoparticles in a liquid medium. Many theoretical mechanisms have been discussed to make the formation of nanoparticles clear, and most of them show that the nanoparticles are formed during the plasma expansion and flight in gas or liquid medium. Of course, it is possible to synthesize particles after the plasma reaches the substrate surface, and even directly produce nanoparticles in the jet of the ablation process (117,124,125). In 2000, F. Mafuné in the Clusters Research Institute of Japan’s Toyota investigated in detail the dynamics of metal nanoparticle formation and consequently presented a theoretical model (126,127). The synthesis process of nanoparticles by the laser technique can be simply described as follows. In the atmosphere or liquid medium, the plasma generated during laser ablation continuously absorbs the laser energy and expands in the medium. Subsequently, various ions, atoms, or clusters interact with the atmospheric species in the deposition chamber, leading to the combination of the larger particles under certain technical conditions (Figure 25). The characteristic parameters of plasma such as temperature and density are dependent on the thermophysical properties of the target material and the laser parameters, such as laser fluence and ambient atmosphere (128,129). The earliest technology for nanoparticle preparation using the laser is accomplished in the gas phase. When a pulsed laser irradiates the target, a high-temperature and high-density plasma plume is formed in the target surface, and the plume rapidly

Figure 21 medium.

Diagram of femtosecond laser direct writing in transparent solid materials within the layered three-dimensional optical data storage

140

Laser Ablation

Figure 22 Application examples of femtosecond laser ablation of transparent materials. (a) A micro-gearwheel, (b) a micro-chain, (c) and (d) illustrate two different scanning modes: raster scanning and profile scanning, and (e) a microbull. Reproduced from Tanaka, T.; Sun, H. B.; Kawata, S. Appl. Phys. Lett. 2002, 80, 312.

expands due to continuous energy absorption from the laser in the gas medium. Ashfold et al. estimated that the density of neutral species nn ¼ 1018 cm3, the temperature of plasma T ¼ 4500 K, and the density of ions ni ¼ 1013 cm3; if the expansion speed of plasma is 20 km s1, there will be 1015 atoms in a 0.13 mm3 plume and the generated pressure will be several times atmospheric pressure (130).

Figure 23 A scanning electron microscopic image of a microspider-array (Reproduced from Chichkov, B. N.; Fadeeva, E.; Koch, J., et al. Proc. SPIE 2006, 6106, 610612.) and m-dragon model (b) (Reproduced from Juodkazis, S.; Nishimura, K.; Misawa, H. Chin. Opt. Lett. 2007, 5, 198.) fabricated by femtosecond laser machining of transparent materials.

Laser Ablation

141

Figure 24 SEM image of the micro tweezers, with submicron probe tips fabricated by two-photon microstereolithography. Reproduced from Maruo, S.; Ikuta, K.; Korogi, H. Appl. Phys. Lett. 2003, 82, 133.

Figure 25

Illustration of nanoparticle formation in plasma.

After a laser pulse, the plasma persistently and rapidly expands, and temperature and pressure sharply decline, resulting in collisions and aggregations between the atoms, electrons, and ions, and then new condensed matter, or a phase transition to form a new substance, is generated. The experiments show that neutral species play a leading role in the phase transition process: The condensation between the species helps to form the nuclei, and subsequently the plasma rapidly cools and the condensation occurs in a different way. If the condensed process is completed on the substrate surface, this is just the principle of PLD of thin films. If the particles of the plasma freely coalesce, nanoparticles or other shaped material will be formed, accompanied by a large number of complex physical and chemical processes. The properties of the substrate (such as surface structure and temperature) as well as the surrounding gas medium will affect the quality of the final synthesis. In 1998, Geohegan et al. (115) reported the first time-resolved measurements of photoluminescence from gas-suspended nanoparticles and utilized gated intensified CCD-array imaging of this PL to reveal dramatically different Si-nanoparticle formation and propagation dynamics in He and Ar. Ar (1.0 Torr) stops and reflects the Si plume, resulting in a stationary, uniformly distributed nanoparticle cloud. He (10 Torr) slows the silicon plume, angularly segregating most of the nanoparticles to a turbulent smoke ring that propagates at w10 m s1 through the chamber. This experiment confirmed that the nanoparticles can be condensed in the gas phase. The first essential factor is the type and pressure of the atmosphere. The background gas pressure is one of the most important parameters affecting the size of the nanoparticles (131,132). The experiments (131), in the laser ablation system filled with inert buffer gas, show that the uniform and dispersed nanoparticles can be successfully prepared. As the buffer gas pressure increases, the size of the nanoparticles is increased accordingly. Grigoriu et al. discussed the relation between the average size and the ambient pressure by an inertia fluid model (133). In 2000, Ozawa et al. synthesized nanometer-size particles of tungsten W using a Q-switch Nd:YAG laser (134). Particle size with the maximum particle generation increased from less than 10 nm to more than 80 nm, depending on the increase of the ambient pressure. In 3.8 J cm2, the number of nanoparticles generated larger than about 80 nm does not depend on the pressure. On the other hand, the number of particles less than 80 nm in size depends on the ambient pressure. The measurement results are shown in Figure 26. The type of atmosphere has a direct impact on the preparation of nanoparticles. N. Okubo et al. (135) have fabricated nanoparticles of titanium oxide by ablating a Ti target with pulsed CO2 laser in an Ar-diluted oxygen environment. In the Ar gas environment, the Ti atoms collide with gaseous atoms and create the ions and electrons, that is, a plasma plume. The formation of the plasma indicates that Ti atoms have chances to form TiO2 nanoparticles in the O2 as reactive gas. The mean size of NPs fabricated at

142

Laser Ablation

Figure 26 The comparison of size distributions with different fluences, (a) 1.9 J cm2 and (b) 3.8 J cm2. Reproduced from Ozawa, E.; Kawakami, Y.; Seto, T. Scr. Mater. 2001, 44, 2279.

the lower pressure are small (5 nm) and cohesive to each other, and the major part of the deposit is amorphous, suggesting that the oxygen supply is not high enough to grow crystalline oxide particles. On the contrary, at the higher pressure, the average size of the independent NPs significantly increases (28 nm). Under this condition, the oxygen is plentiful, and the generated nanoparticles of anatase TiO2 crystal and amorphous hybrid structure. It should be emphasized that the NPs are spherical crystals of single anatase, if sufficient environmental gas is supplied. No rutile phases were observed in any of the conditions studied (Figure 27). In a liquid medium, pulsed laser synthesis of nanoparticles is a more effective technique. The first attempt to prepare metal nanoparticles in liquid medium by laser ablation technique was made by German scientists A. Henglein and A. Fojtik. In 1993, a glass-supported gold and nickel film in the solution was irradiated by the ruby laser with 694 nm wavelength, and gold and nickel nanoparticles were prepared. The results show that the average particle size was dependent on laser intensity (136). In the same year, T. M. Cotton and his colleagues developed this technology. In their experiments, a 1064 nm Nd:YAG pulsed laser was used to synthesize different sizes and distributions of gold, silver, copper, platinum, and other metal nanoparticles, that is, nano-metal colloids, by controlling the experimental conditions in different solutions (137). In liquid medium, the better preparation efficiency of NPs is not accidental. In liquid medium, plasma was rapidly formed on the surface zone of a solid target irradiated by laser. Some researchers (138–142) show that the liquid medium has a greater influence on the evolution of the plasma than does gas. As the laser ablation proceeds, plasma continues to absorb the laser energy, and simultaneously the ablated target continues to supply new ablation products for the plume, which prompts the rapid expansion of plasma at supersonic speed, thus forming a shock wave. The shock wave generated in the plasma produces an additional pressure, leading to an increase in the temperature of the plasma. Therefore, the liquid medium limiting the shock waves elevates the temperature, pressure, and density of the plasma.

Figure 27 TEM and SAD images of nanoparticles fabricated by PLD at a total pressure of 1.5  104 Pa (a) and 6.7  104 Pa (b), where flow rates of Ar and O2 gas for both cases are 83 cm3 s1 and 8.3 cm3 s1, respectively. Reproduced from Okubo, N.; Nakazawa, T.; Katano, Y.; Yoshizawa, I. Appl. Surf. Sci. 2002, 197–198, 679.

Laser Ablation

143

Figure 28 TEM images of nanoparticles at fluence: (a) 10, (b) 20, and (c) 35 J cm2 and the particle distribution. Reproduced from Kumar, B.; Yadav, D.; Thareja, R. K. J. Appl. Phys. 2011, 110, 074903.

For example, Berthe et al. investigated the pressure (2–2.5  109 Pa) of laser-induced Al-plasma in a water-confinement regime by a XeCl excimer laser with the intensity of 1–2  109 W cm2 and the pulse width of 50 ns (139–141). Peyre et al. found that higherpressure plasma (1010 Pa) was induced by short pulse laser (3 ns) (140–142). Laser wavelength and pulse width will affect the pressure of induced plasma. In Sakka’s experiments (143,144), a 532 nm Nd:YAG pulsed laser was used to produce graphite plasma in water, and the density 1022–1023 cm3, the temperature 4000–5000 K, and the pressure 1010 Pa of C-plasma could be obtained. The presence of a high-temperature, high-pressure, and high-density plasma zone is advantageous to growing high-temperature and high-pressure nuclei, and thus the metastable phase is formed at room temperature. A variety of chemical reactions may occur during the evolution of the plasma. The last stage of the evolution of plasma in the liquid limit is cooling and condensation. Different types of nucleation have different applications in materials processing. After plasma quenching, part of the plasma is deposited on the surface of a solid target due to fluid restriction, which will lead to the coating of the target surface, applicable to the surface treatment of materials (145,146). Another part of the plasma is condensed and dispersed into the liquid medium, and small particles can generally be suspended or floating on the liquid surface. This can be used for the preparation of nanoparticles themselves. The average size and size distribution of laser-fabricated nanoparticles in liquid medium are affected by the physical properties of the target material, laser parameters (laser power density, pulse number, and pulse duration time) and liquid concentration (147). Figure 28 (148) shows the TEM image of NPs synthesized using PLA in deionized water and their particle size distribution at laser fluence of 10, 20, and 35 J cm2, respectively. NPs have a spherical shape with a narrow size distribution. The particles are mainly distributed in the range w5–35 nm with an average of 10, 13, and 15 nm at the fluence of 10, 20, and 35 J cm2, respectively. Laser ablation synthesis of nanoparticles in liquid medium technology continues to develop, succeeding in the preparation not only of elemental nanoparticles, but also the alloy nanoparticles. I. Lee et al. (149) fabricated nanometer-sized gold-silver alloy nanoparticles by ablating gold-silver alloy with an ideal ratio in solution. Nanometer-sized alloy particles have unique physical, chemical, and catalytic properties, and thus the laser ablation preparation method has a great market potential in the fields of microelectronic materials, catalysts, and biological engineering applications.

4.06.4

Pulsed Laser Ablation and Pulsed Laser Deposition Technology

4.06.4.1

Physical Picture of Pulsed Laser Deposition

The PLD technique is now widely used in film preparation, which is one of the most important applications in the field of laser ablation. In the 1970s, with the advent of the excimer laser and the popularization of the electronic Q-switched laser, the PLD technique began to attract a significant amount of attention (150). The excimer laser has a high-power density and a very short pulse

144

Laser Ablation

Absorption Thermal Conduction

Surface Melting

Vaporization Plasma Production

Plasma Shielding Inverse Bremsstrahlung Absorption

Figure 29

Illustration of the pulsed laser deposition process.

duration, which could lead to a lower ablation depth and hence the droplets caused by the melting effect are reduced greatly during the ablation process. Therefore, the excimer laser deposition technique can remarkably improve the quality of the film. In 1987, D. Dijkkamp et al. at Bell Laboratory first successfully prepared the high-temperature superconducting thin films by using the highenergy KrF excimer laser (151). Also, it was discovered that PLD can be used for fabrication of epitaxial thin films and multicomponent ceramic oxides, nitrides, metallic multilayers, as well as a variety of superlattice materials (152). Therefore, the PLD technique has undergone rapid development in the following years (153). In the late 1990s, femtosecond laser was utilized in the PLD technique, and diamond-like carbon (DLC) films were successfully prepared (154,155). The power density of the femtosecond laser is extremely high (up to 1021 W cm2) within a very short pulse duration time (1014–1015 s). The laser ablation process shows several new features, such as nonthermal effects and high-precision micro-machining to achieve clean ablation during preparation of the targets, which can greatly improve the quality of the films and promote the development of PLD technology. Research on the mechanisms of femtosecond laser ablation and deposition is increasing, and some theoretical work has been carried out. For example, the ultrashort pulse laser interaction with the target should obey the non-Fourier heat conduction rule; the high-energy photon colliding with the target will significantly affect the physical parameters of the target; the electron–electron collision effect and electronic density of states (DOSs) effect should be considered in heat transport process; and so on (33,156). The experimental setup is shown in Figure 4, and the whole preparation process includes three regimes (7) as shown in Figure 29: (1) Laser ablation and plasma formation A focused high-energy pulsed laser irradiates the target surface, and then the target absorbs the laser energy, resulting in surface temperature up to the vaporization point. Subsequently, the vapor is ionized, and local high-density plasma is formed. (2) Isothermal and adiabatic expansion of plasma Plasma generated on the target surface will continue to absorb the laser energy and gain further ionization, resulting in a rapid rise of temperature and internal pressure of the plasma. The elliptical plasma, that is, the plasma plume, normal to the target surface is formed, and the plasma plume expands and travels in vacuum or atmosphere. (3) Deposition of thin film When the expanding plasma plume arrives at the substrate surface, the gaseous species meet each other, combine, and finally aggregate together.

4.06.4.2

Introduction to Plasma Expansion in Pulsed Laser Deposition

Figure 30 indicates that under the high-energy laser irradiation, a high-temperature and high-pressure plasma is sputtered from the target surface. Figure 31 shows experimentally the plasma plume observed under conditions of different times and different oxygen pressures (157).

Laser Ablation

145

For nanosecond laser ablation, the expansion evolution of plasma plume in the space can be roughly divided into two stages: (1) isothermal plasma expansion. When t < s (pulse duration time), the temperature of the plasma tends to decrease due to expansion, but at the same time the plasma still absorbs the incident laser energy. The two opposing processes roughly cancel each other out; thus, the plasma temperature remains constant in this stage (158). (2) Adiabatic plasma expansion. After the termination of the laser pulse, the rapid expansion of the plasma gives rise to a temperature decrease. At this stage, the heat exchange of the plasma with its surroundings is negligible, so the expansion is in an adiabatic regime. Regarding the plasma as an ideal gas and using fluid mechanics, the dynamic equation of plasma expansion is established according to the overall mass and momentum conservation law (7,159,160). However, modified dynamics models have been developed based on the local mass and momentum conservation law (161–164), and the theoretical results obtained are in agreement with the experimental results. The models can naturally describe the characteristics of plasma expansion confirmed by experiments (165–168): (1) the velocity distribution of the plasma is self-similar, (2) the plasma density at the ablation surface is approximately constant, and (3) the degree of ionization has an effect on the evolution of the plasma. The laser ablation process determines that the number density distributions in radial and longitudinal directions have distinct characteristics. In the direction perpendicular to the target surface, a large-density gradient and different initial velocities of sputtered atoms lead to the maximal number density of plasma existing in the region adjacent to the target surface rather than on the surface.

z Substrate

Thin film Plasma flow

Focus lense

Target

0 Figure 30

A sketch of plasma expansion.

Figure 31 Photos of plasma plume at different oxygen pressures. Reproduced from Harilal, S. S.; Bindhu, C. V.; Tillack, M. S.; Najmabadi, F.; Gaeris, A. C. J. Appl. Phys. 2003, 93, 2380.

146

Laser Ablation

In the radial direction parallel to the target surface, the plasma expansion is mainly caused by the large density gradient, so the maximal number density locates just on the target surface. Near the surface, the number density in several mean free paths approximately retains a constant value in the whole ablation process. Studies have shown that the plasma generated by each pulse may be considered to expand independently and finally reaches the substrate surface. The state of the plasma is critical for the thin-film growth process of PLD. Based on the above mentioned, the whole plasma as a single pulse eventually arrives at the substrate. Because the plasma concentration in the spatial distribution is inhomogeneous, the incident species flux changes with time, which provides a theoretical basis for investigation of thin-film growth in PLD. The evolution of a femtosecond laser-produced plasma is a highly nonequilibrium and nonlinear process, and the physical conclusions based on nanosecond laser deposition cannot be simply applied to the femtosecond laser deposition.

4.06.4.3

Introduction to Film Growth in Pulsed Laser Deposition

After isothermal and adiabatic expansions, the plasma plume is collected on a substrate on which thin films grow. The deposition process has a direct impact on the quality of the thin films. First, the species impinge on the substrate and begin to gather together, and then the nuclei are continuously formed. In the following deposition process, a number of so-called island structures appear on the substrate. The existing islands gradually capture diffusing and later-arriving incident species so that the sizes of islands increase quickly. Finally, the coalescence of existing islands completes a layer of continuous film. The deposition conditions can be reasonably controlled to achieve a continuous and layer-by-layer growth, until the required film thickness is achieved. The film growth is a very complex process, and some factors, including the interaction between the ablated species (atoms, molecules, ions, clusters, etc.) and the substrate surface, the interaction between various species, the substrate temperature, and the incident kinetic energy of species, play an important role in the growth process. For the evolution of film growth, the formation of surface defects, adatom migration and diffusion on the substrate, thermodynamics of the adatoms gathered into a nucleus as well as the thin-film growth mode, and so on, are very important research topics. The island nucleation in the early stage is particularly important for thin-film growth. Two methods are commonly used to study the film growth process: the continuity equation theory and numerical simulation (169,170). Considering thin-film growth as a random dynamics process, the Monte-Carlo method is widely used in this field. Compared with other deposition techniques, the thin-film growth process of PLD has some distinct characteristics: (1) energetic deposition. The kinetic energy of the species generated by PLA is in the order of 100–103 eV. High-energy species reach the substrate surface and have a bombardment effect on the deposited film and substrate so that the adatoms obtain an instantaneous mobility that enhances their diffusion speed on the surface. Also, energetic particle bombardment can cause atomic bond breaking and structural reconstruction (171). The energetic species impinge from the plume to a surface and transfer their kinetic energies to surface atoms, leading to the formation of point defects such as vacancies or interstitials. This defect structure is likely to attract the following incident species to form nuclei. Consequently, the density of islands increases, and the layer-by-layer growth of thin film is accelerated. (2) Pulsed deposition. The production of PLA reaches the substrate in pulsed mode. After the termination of one pulsed laser, a large number of species almost simultaneously impinge on the substrate. Thus, a high instantaneous concentration of species increases the chance for the adatoms to meet each other and aggregate, which promotes layer-by-layer film growth. Therefore, the interval of two pulses needs to ensure that the incident species have sufficient time to find a suitable growing point. Namely, pulse repetition frequency for the PLD process is an important parameter (172,173). (3) Stoichiometric deposition. The most significant advantage of the PLD technique is to keep identical stoichiometry between the deposited film and the target (174– 176). The reason is that a large number of energetic species reach the substrate surface, freely diffuse, and condense to a film on the substrate. The principle can be found in Section 4.06.2. The quality of the films prepared by PLD is closely related to laser parameters (laser energy density, wavelength, pulse repetition frequency, and pulse width), type and pressure of atmosphere in the chamber, the geometric parameters of the experimental setup (the position of on-axis and off-axis, the distance between target and substrate), as well as substrate parameters (material type, temperature, and quality of surface). Here, the influences of laser parameters on film growth are emphasized. Laser energy density can directly affect the type and concentration of the species in the plasma plume (177,178), which can change the stoichiometric ratio of films. The higher the laser energy, the greater the bombardment intensity of plasma, the more the number of point defects on the substrate surface (179,180) and the higher the concentration of the active adatoms. Adjusting the laser energy density sometimes makes it possible to change the film growth mode (181), for example, such that vertical growth changes to two-dimensional growth (182). It must be pointed out that laser energy density should be near the ablation threshold in order to avoid the generation of droplets and improve the quality of the films (183). The experiments show (132,184) that, when the laser energy density exceeds the ablation threshold, the ablation plume with a large number of droplets or particles reaches the substrate surface, and the surface roughness of the film remarkably increases. Figure 32 (185) shows an SEM micrograph of an Mg:Nb film deposited at low-energy density of the laser beam, 8 J cm2 (Figure 32(a)), and at high-energy density, 47 J cm2 (Figure 32(b)). In Figure 32(a), the left and right sides of the micrographs show a 2500 and 5000 magnification, respectively. In Figure 32(b), the left and right sides of the micrographs show a 1000 and 4000 magnification, respectively. The most important difference between the low- and high-energy deposited samples is the size distribution of the spheres. At low-energy densities of the laser beam, these spheres have a diameter lower than 2 mm while at high-energy densities diameters larger than 10 mm can be observed.

Laser Ablation

Figure 32

147

SEM micrograph of the Mg:Nb thin-film samples deposited at different energy densities 8 J cm2 (a) and 47 J cm2 (b) of laser beam.

With an increase in the laser irradiation energy density, the grain size becomes larger (186,187). An explanation of this phenomenon could be that by increasing the energy density, both the plasma density and the plasma kinetic energy increase. When the species of the plasma arrive at the substrate surface, the kinetic energy of the deposited adatoms creates higher diffusion, which results in the coalescence of grains and particles (186). At fixed pulse intensity, pulse repetition frequency has a great influence on film growth and surface morphology (188,189). Hydroxyapatite coating on a metal substrate has been prepared by the ArF PLD technique (190). When the pulse repetition rate increases from 20 to 80 Hz, the structural order of the coatings decreases, and, eventually, at 100 Hz the coatings become amorphous. CeO2 films at pulse repetition frequency 1, 3, and 5 Hz were prepared, and it was found that with decreasing pulse frequency, the island density on the surface was significantly reduced and characteristically smoother films were achieved using a low deposition rate (191). Ag films were deposited at a pulse repetition frequency of 10–100 Hz, and the experimental results showed that the average size of the island decreased but the island density increased with the pulse frequency increase (192). In the growth process, a slower deposition rate, that is, a lower pulse frequency at fixed pulse intensity, means that the atoms on the island can much more easily reach the island edge and the nuclei will be given more time to ripen, avoiding a three-dimensional island growth (193,194). In a word, adjusting the frequency of pulse repetition has a significant influence on the preparation of films (195). Experimental and theoretical simulations show that there are several scaling laws in the thin-film growth process (196–199). Reference (196) reported that Ag thin films were deposited on an insulator substrate with substrate temperatures of 93  C and 135  C, respectively. Both experimental and theoretical results confirmed that the electrical percolation thickness of the films depended on pulse repetition frequency, with a scaling law with a single exponent of 0.31 and 0.34, as shown in Figure 33. Many theoretical models have been developed to describe the thin-film growth process, including the diffusion-limited aggregation (DLA) model (200), the improved DLA model (201,202), the Bruschi model considering substrate temperature (203), the Taylor model (204), the Kuzma model (205), and the pulsed kinetic Monte-Carlo model, considering pulse frequency and incident particle energy (170).

4.06.5

Thermodynamics of Laser Ablation

Laser ablation includes some complex physical phenomena: heat transfer process, plasma effects, various radiation effects, mechanical effects, and so on. The physical nature is determined by the thermodynamics of the pulse ablation process. Namely, the study of the laser ablation mechanism is based on thermodynamics in order to study the quantitative transfer law and the related physical effects in the laser ablation process and to analyze the relationship between various technical parameters and ablation

148

Laser Ablation

135 °C

Thickness dperc at Percolation (nm)

60 50 f -0.31

40 30 (a)

93 °C

50 40 f -0.34

30

20

(b) 2

5

10

20

50

Pulse frequency (Hz) Figure 33 Effect of pulse repetition frequency on Ag film thickness at the electrical percolation transition. The data are well fit by a power law with a single exponent of about 0.33 for (a) and (b). Reproduced from Warrender, J. M.; Aziz, M. J. Phys. Rev. B 2007, 76, 045414.

results. Investigation of the laser ablation mechanism can advance the development of laser ablation technology and improve the quality of ablated workpieces or fabricated materials (such as films and nanoparticles).

4.06.5.1 Theoretical Framework of the Thermodynamics of Long-Pulsed Laser Ablation – The Basic Equation and Plasma Shielding Effect The thermodynamics of LPLA is physically based on the local equilibrium heat transport process. In this process, the interaction of laser and target depends mainly on the electron–phonon interaction. The electron–phonon relaxation time is tens of a picosecond, that is to say, the time taken by the electrons to transfer their kinetic energy, obtained from the laser, to the lattice. For a long-pulse laser such as the nanosecond laser, the electrons have sufficient time to deliver their energy to the lattice, and then thermal equilibrium is easily established between the electrons and the lattice subsystem before the termination of the laser pulse. After the target absorbs the laser energy, the temperature of the target surface will increase up to a phase transition point. If the required heat energy for phase change is satisfied, the target will melt. The heating and melting processes of pulsed laser irradiation on material constitute a three-dimensional heat flow problem. However, even if a long-pulsed laser is utilized in the ablation process, that is, nanosecond or picosecond, the thermal diffusion distance is short, too. The dimension of the laser irradiation area (in millimeters) is usually several orders of magnitude larger than the thermal diffusion distance in the vertical direction of the target surface. Thus, if the target surface is regarded as an infinite plane, the corresponding heat conduction problem can be approximately treated as the transport of laser energy along the direction perpendicular to the target surface. This is why the laser ablation thermal conduction phenomenon is theoretically simplified into a one-dimensional heat flow model. In Figure 34, a schematic of the laser–solid interaction is given. During the time for which a long-pulsed laser irradiates a target surface, the target can be roughly divided into three separate regions and five parts (33,206): (1) Solid phase region A without

A B

C

D

E

Laser

(1)

(2)

x Figure 34

Illustration of long-pulsed laser ablation of target.

(3) 0

Laser Ablation

149

melting, but absorbing the laser energy, (2) liquid-phase region generated by the melted target (including normal liquid phase region B and superthermal liquid phase region C), and (3) high-temperature and high-pressure plasma cloud D and plume E. A basic theoretical framework of the LPLA is based on the basic heat conduction equation and the corresponding boundary and initial conditions. Only considering the coexistence of a solid and liquid phases in the ablation stage, a basic thermodynamics equation, that is, a classical Fourier conduction law, can be expressed as:
 vTi ðx; tÞ v vTi ðx; tÞ ri ðTÞcpi ðTÞ ¼ ki ðTÞ ð0 < t  s; 0 < x  dÞ [7] vt vx vx where i ¼ 1, 2 represents the solid and liquid phases, respectively, r(T) is the temperature-dependent density of target, and cp(T) is the temperature-dependent specific heat capacity under constant pressure, s is pulse width, d is the target thickness, and x refers to the vertical direction of the target. The right side of eqn [7] presents the transferred heat flow caused by the existing temperature gradient in the target, and the left side presents target temperature changes due to the heat conduction. This equation does not take into account the heat source term, that is, the laser energy radiation during the heat conduction process. During laser irradiation, the formed plasma plume can absorb 98% of the laser energy by IB and PI mechanisms, and the remainder (only 2%) can transmit to the target surface. As an approximation, the heat diffusion equation, without considering a heat source term, can be used to describe the laser–target interaction. For long-pulse ablation, thermal conductivity ki is assumed to be a constant due to the temperature only having a small effect on it. The thermal diffusion coefficient ai ¼ ki/(rcp), so eqn [7] can be changed into: v2 Ti ðx; tÞ 1 vTi ðx; tÞ ¼ vx2 ai vt

ð0 < t  s; 0 < x  dÞ

[8]

However, to adequately describe the physical nature of the laser–material interaction, the heat diffusion equation with the heat source term should be considered. Here are two evolution stages of plasma: (1) one is that at the beginning of ablation, the vapor is not significantly ionized and plasma cannot be formed, (2) the other is that plasma rapidly expands and consequently its density decreases, which makes plasma transparent to the incident laser beam. For the two stages, the pulsed laser can directly illuminate the target surface, and the laser energy absorbed by the corona zone will be transferred to the target surface by plasma radiation. In order to deeply investigate the temperature evolution of the target, the heat diffusion equation with a heat source term can be expressed as:
 vTi ðx; tÞ v vTi ðx; tÞ ri ðTÞci ðTÞ ¼ ki ðTÞ þ Sðx; tÞ ð0 < t  s; 0 < x  dÞ [9] vt vx vx where S(x,t) is the heat source term, usually regarded as the Gaussian profile (207–209), that is, S(x,t) ¼ (1  R)I0(x,t)$bebx. Here, I0(x,t) is the output power density of laser, R is the reflectance, and b is the absorption coefficient of the target. In addition to considering the source term, the shielding effect of plasma and the evaporation effect should be considered (210). The shielding effect of plasma is caused by two methods – IB radiation and PI – which absorb laser energy. High-temperature and high-pressure plasma formed on the target surface absorbs the incident laser radiation and prevents the laser energy from reaching the surface. This blocking effect is called the plasma shielding effect. For infrared laser ablation, the shielding effect is caused mainly by IB radiation. For UV laser ablation, the shielding effect of plasma is based on the PI mechanism (211). It is assumed that the plasma radiation can be regarded as blackbody radiation. Assuming that plasma is an ideal gas, the ionization process of the vapor is accomplished through IB and PI absorption mechanisms. The IB process is usually described by the inverse absorption length aIB (cm1) (212):  
 N0 þ Ne Ne ¼ sIB Ne [10] aIB z 1:25  1046 l3 Te0:5 200 where l is the laser wavelength, Te is the electron temperature, N0 and Ne are the density of the neutral atom and electron, respectively, and sIB is the cross section of IB absorption. For the excimer laser ablation of metals, such as iron, the plasma particle density is in the range of 5  1018 cm3, and the electron temperature is 3 eV (211). In eqn [10] sIB represents the total cross section of the IB process, and the contributions of both neutral and ion in IB processes are included (213,214), that is, sIB ¼ sIB,neu þ sIB,ion. The cross section of neutral sIB,neu equals approximately 2.75  1023 cm2. A laser fluence of 1–6 J cm2 is equivalent to 0.125  1019–0.75  1019 photons cm2, thus, 0.0034–0.02% photons can be absorbed by IB due to neutrals, which is too small to significantly attenuate the laser or heat plasma. In the UV laser ablation process, direct PI of excited atoms plays an important role in the shielding effect of the vapor. The cross section of PI, sPI can be expressed by (212): sPI z7:9  1018

0:5 ðEI  E Þ2:5 IH

ðhvÞ3

cm2

[11]

where IH is the ionization potential of hydrogen, EI is the ionization potential of the atom, and E* is the energy of the excited level that can be photoionized. For example, the photon energy of the 248 nm excimer laser is 5 eV, making sPI z 1.3  1017 cm2, which are several orders of magnitude higher than the IB cross section. If a laser fluence of 1–6 J cm2 is

150

Laser Ablation

equivalent to 0.125  1019–0.75  1019 photons cm2, the probability of an excited atom absorbing an UV photon equals approximately 100%; that is, the ionized condition is formed. As a consequence, the vapor ionization degree is readily enhanced, and the PI is the most important absorption mechanism in this case. During the pulse duration time, the total energy E absorbed by the target can be expressed as: Z s E¼ E0 ðtÞdt [12] 0

E0 (t)

where is the laser energy transiently absorbed by the target. For convenience, the time tth is defined as the time taken by the target to absorb laser energy to reach the ablation threshold Eth. So, when 0 < t < tth, the transient power density absorbed by the target I(t) is as follows: IðtÞ ¼ ð1  RL ÞI0 ðtÞ

ð0 < t < tth Þ

[13a]

Here RL is the target reflectivity for the laser. For tth < t < s, I(t) can be given as: IðtÞ ¼ ð1  RL ÞI0 ðtÞexp½ðaIB þ sPI nz ÞH þ ð1  RP ÞIem

ðtth < t < sÞ

[13b]

z

Here, I0(t) is the laser pulse intensity profile, n is the number density of the excited neutrals, and H is the dimension of the plasma perpendicular to target. RP is the target reflectivity for the plasma emission. Iem is the plasma-emitted intensity. The second term in the right side of eqn [13a] indicates the absorbed laser power density by the target after plasma irradiation. Equation [13] presents the heat source term in the heat conduction equation considering the shielding effect of the plasma. It is assumed that the target ablation threshold Eth is a constant. According to the Lambert–Beer law (215): EðxÞ ¼ Einc expðbxÞ

[14]

where E(x) is the energy density at target depth x and Einc is the total incident energy density. Substituting E(x) ¼ Eth and eqn [12] into eqn [14], then the maximum ablation depth x can be expressed as:
Z s  1 x ¼ ln E0 ðtÞdt=Eth [15] b 0

4.06.5.2 Theoretical Framework of the Thermodynamics of Long-Pulsed Laser Ablation – Dynamic Physical Parameters and the Vaporization Effect Normally, the thermophysical parameters of the target such as the absorbance and the absorption coefficient are all temperature dependent, which affects the heat conduction process (216,217). For simplicity, the ablation of transparent material and the plasma radiation effect are not considered in the following discussions. The absorption by the material of energy from the laser can be regarded as a ‘secondary’ energy source on the surface and a variety of physical effects occur due to this energy source (218,219). The experiments show that for ordinary metals, the resistivity of the melted metal linearly increases with temperature (220) and is two times larger than that of solid metal below the melting point. Thus, the absorption coefficient rises, and the reflectivity declines after the melting. Reference (221) shows that the absorbance of material is proportional to the resistivity. For semiconductors, the number of carriers increases with the temperature, so the lattice scattering effect is enhanced and then the mobilities of electrons and holes decrease. As a result, the resistivity of such material also increases with temperature; consequently, the absorbance also does (222). According to the time-dependent surface temperature in Refs. (216,223), the dynamic absorptivity can be written in the following explicit form: [16] b ¼ b0 þ A1 ½Ct þ ðC2 t 2 þ DtÞ1=2  where b0 is the absorbance at room temperature, and A1 is a constant varying with the material too. The value of A1 for Fe target is 0.85  105 K1 (223). Based on Maxwell’s equations and the Lambert–Beer law, the temperature-dependent absorption coefficient is given as: rffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4pk 4ps 4ps0 ¼ [17] ¼ bðTÞ ¼ 30 l0 c½1 þ aðT  T0 Þ l0 30 l0 c and the temperature-dependent absorptivity can be expressed by: rffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4py30 4pc30 ð1 þ aðT  T0 ÞÞ bðTÞ ¼ 2 ¼ s l0 s0

[18]

where s0 is the target conductance at initial temperature T0, 30 is the permittivity of vacuum 30 ¼ 8.85  1012 C2 N1 m2, c is the laser propagation velocity in vacuum, and a is the target temperature coefficient of resistance. For a general metal, a is in the range 400  105–700  105 K1 (224). The following discussion is about the effect of vaporization on laser ablation. Vaporization is the species (atoms or molecules) emitting from the surface of target, due to the phase transition from condensed matter to vaporized

Laser Ablation

151

phase. Vaporization phenomena can occur at any laser influence and pulse duration time, which does not need to satisfy the temperature threshold, but energy threshold (if E < Eth, the vaporization cannot occur). For the low-power laser ablation, the vaporization effect on laser ablation is not obvious. However, for the high-power laser, the vaporization effect is significant due to the sufficient absorption of laser energy, which should be considered in the heat diffusion equation (225):
 vTðx; tÞ vT v Tðx; tÞ rl ðTÞCl ðTÞ [19]  Cl rl yr ¼ kl ðTÞ þ Sðx; tÞ ðsm < t < s; 0 < x < sðtÞÞ vt vx vx vx where the subscript l means all parameters are under the condition of liquid state. The heat loss of the vaporized species per area is vT Cl rl yr , and the velocity of vaporization (or the velocity of surface recession) is yr, which is determined by the Hertz–Knudsen vx equation (29): p Cs [20] yr ¼ rl ð2pkB T=ml Þ1=2 where p is the gas pressure, Cs is the sticking coefficient (226), and ml is the particle average mass. Under the limit Vliq << Vgas, Vlip and Vgas are the molar volumes of liquid and gas; the relation between the equilibrium vapor pressure p and the temperature T may be computed from the Clausius–Clapeyron equation (227): 
 DHv ðTb Þm 1 1  p ¼ pb exp [21] kB Tb T where T is the temperature of the target surface, Pb is 1 atm, DHv(Tb) is the latent heat of vaporization, and Tb is the boiling temperature at 1 atm. It is assumed that for the time sv taken by the target to fulfill the requirement for the phase transition of vaporization, the ablation energy threshold is: Eth ¼ ð1  RÞI0 sv

[22]

According to the vaporization relaxation time sv (228), eqn [22] can be changed into: Eth ¼ 3½1  2expð1Þk1 cl rl ðTv =ð1  RÞÞ2 =I0

[23]

where rl is mass density of liquid material, cl is specific heat capacity per mass, and Tv is the vaporization temperature at 1 atm. Equation [23] indicates that Eth depends on target material and laser parameters. The evolution of ablation interface (229) is: xt ¼

ð1  RÞ2 I0 ðt  sv Þ ðrl cl $DT þ Lv Þ

ðsv < t < sÞ

[24]

DT is the biggest temperature difference and Lv is the latent heat of ablation. For sv < t < s, the ablation thickness, which is proportional to time, increases with the incident laser power density. The ablation surface moves forward at an even speed, which is determined by the parameters of the laser and the target (159,229,230). The maximum ablation thickness xt can be expressed as: xt ¼

ð1  RÞðE  Eth Þ r1 c1 $DT þ Lv

[25]

When pulse width is reduced on the order of a picosecond, this is roughly equal to the electro–phonon interaction relaxation time. For the nanosecond laser ablation process, the heat conduction of laser energy is a diffusion process, obeying the Fourier conduction law. In this case, pulse width is much greater than the time required for electrons to deliver energy to the lattice, which is effectively instantaneous relative to the pulse duration time. However, for picosecond laser ablation, the heat conduction is not a diffusion process but a wave-type propagation, which can be described by a hyperbolic heat process model. Different from the conventional heat transfer law, ultrashort pulse laser ablation has the characteristics of nonequilibrium heating and nonequilibrium phase transition. For example, when a pulsed laser irradiates the target with an ultrashort pulse width of 150 ps and energy density of more than 1013 W m2, a very high-temperature gradient will be produced on the target surface, and the heat penetration depth is less than several nanometers, which is equivalent to the mean free path of electrons. For uniform material, the thermal equilibrium relaxation time of the target in laser heating (electron–phonon interaction time s0) is approximately between 108 and 1014 (231–233). In other words, the heat conduction process does not obey Fourier law, but rather non-Fourier heat conduction law (231,234–236). At the end of the 1940s, Cattaneo first presented the non-Fourier heat conduction law, which is called the general Fourier law (237): q þ s0

vq ¼ kVT vt

[26]

152

Laser Ablation

It is assumed that the target is irradiated by an Nd:YAG laser with power density 109 W cm2 and a pulse width of 150 ps (238,239). The non-Fourier heat conduction considering the heat source term is: vT v2 T v2 T Sðx; tÞ þ s0 2 ¼ a 2 þ vt vt vx rc

[27]

When pulse duration time decreases on the order of a few picoseconds, the classical Fourier law will be transformed into nonFourier law as eqn [27]. In Section 4.06.5.3, for femtosecond laser ablation, two-temperature systems exist in the target, suggesting that the above-mentioned heat conduction theory is not applicable.

4.06.5.3

Main Theoretical Results of the Thermodynamics of Long-Pulsed Laser Ablation

To solve the thermodynamic equation, suitable boundary and initial conditions are necessary. Using Si as an example, the thermodynamics of LPLA is investigated. The heat conduction eqn [9] can be transformed into: v2 Ti ðx; tÞ ð1  RÞI0 ðx; tÞbebx 1 vTi ðx; tÞ þ ¼ ki vx2 ai vt

ð0 < t  s; 0 < x  dÞ

[28]

Based on the energy conservation rule and an adiabatic approximation, the boundary conditions before melting can be given as follows: vTs ðx; tÞ  ¼ ð1  RÞI0 ð0 < t < sm Þ [29a] ks x¼0 vx ks

vTs ðx; tÞ  ¼0 x¼d vx

ð0 < t < sm Þ

[29b]

where d is the heat diffusion distance, which is time-dependent d ¼ 3.37(ait)0.5 (228). After melting, there are solid and liquid phases in target; thus the boundary conditions at the solid–liquid interface can be satisfied by an energy balance equation and continuous-temperature condition:  vT1  vTs  vs  ks ¼ ð1  RÞIðtÞx¼s  Lm k1 [30] vx x¼s vx x¼s vt Tl ðx; tÞ ¼ Ts ðx; tÞ ¼ Tm

ðx ¼ sðtÞÞ

The boundary conditions at the back surface can be given by:   Ts  ¼ T0 x¼xn

During pulse duration time, the temperature at the frontier of the liquid target remains at the vaporization point Tq, so:  T1 x¼0 ¼ Tq ðsm < t  sÞ

[31]

[32]

[33]

When a pulse is finished, we assume the adiabatic hypothesis at the ablation surface, that is: k1

vT1  vx x¼0

ðs < t < s þ t0 Þ

[34]

where s þ t0 is the pulse period. Based on the above conditions, the time sm taken by the target to reach the melting point is obtained (33). sm ¼

3ðTm  T0 Þ2 Cs rs Ks 4Is2

[35]

Based on the above-mentioned heat conduction equation and the boundary and initial conditions, the space- and timedependence of target temperature before target melting is represented in Figure 35. For the melted target, the temperature and the dynamic interface position can be given analytical solutions. The evolutions of temperature in liquid and solid phases are:

Tl ðx; tÞ ¼ Tq þ

Tm  Tq 

ð1  RÞI0 ð1  ebs Þ pffiffiffiffiffiffi ð1  RÞI0 bKl erf ðx=2 al t Þ þ ð1  ebx Þ bKl erf ðlÞ

ð1  RÞI0 bs Tm  T0 þ e pffiffiffiffiffiffiffi ð1  RÞI0 bx bKs Ts ðx; tÞ ¼ T0 þ e erfcðx=2 as t Þ 
1=2 ! bKs a erfc l l as

[36]

[37]

Laser Ablation

153

Figure 35 Temperature distribution of target at different times and positions. Reproduced from Zhang, D. M.; Li, Z. H.; Zhong, Z. C.; Li, X. G.; Guan, L. Dynamic Principle of Pulsed Laser Deposition, 66; Science Press: Beijing, 2011 (in Chinese).

where al and as are the thermal diffusivity of the liquid and solid phases, respectively. l depends on the liquid–solid interface pffiffiffiffiffiffi l ¼ sðtÞ=2 al t ; here s(t) satisfies the differential equation:
exp

  2     s2 Is s Is exp $ Kl ðTm  Tq Þ  ð1  ebs Þ $ Ks ðTm  T0 Þ  ebs vs 4al t b 4as t b  

þ Lm ¼ Is $expðbsÞ  pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffi s s vt pas t $erfc pffiffiffiffiffiffiffi pal t $erf pffiffiffiffiffiffi 2 al t 2 as t

[38]

Usually, if the corresponding physical properties of the target and technique parameters are given, one can directly solve the heat conduction equation by analytical or numerical methods to obtain accurate results of target temperature at different times and positions, and the evolution of the dynamic interface. This research method for LPLA is quite universal. According to eqns [9], [13], and [19], the shielding effect of plasma, the vaporization effect, and dynamic absorptivity can be investigated for the thermodynamics of laser ablation (207,208,217). In Ref. (217), according to the Saha equation and for the example of Fe, the temperature evolution of the target is obtained from three different models: (1) neglecting the effects of vaporization and plasma shielding, (2) taking only the vaporization effect into account, and (3) considering the two effects of vaporization and plasma shielding. The results of three models are represented by curve (1), curve (2), and curve (3), respectively. The temperature dependence of the absorption coefficient and absorptivity are taken into account in all curves (Figure 36). In Figure 37, the calculated and measured ablation depths depend on the laser fluence shown, where the experimental data come from Ref. (211). Only considering the dynamic absorptivity, Lunney et al. simulated the blue dashed curve. The red dot curve is simulated to describe the thermal phenomena before and after melting (217). The satisfactory agreement between model predictions and experimental data confirms that the improved thermal model is correct and reasonable. The Saha equation is usually used to study the plasma-shielding effect in the ablation process. However, for a multielemental target, the mean ionization of crystals is difficult to define. Reference (208) presents a theoretical model to describe the high-power nanosecond LPA of multielemental oxide superconductors YBa2Cu3O7 by considering both the vaporization effect and the plasma-shielding effect. In this model, a mean ionization of crystals hU0 i is reasonably defined to analyze the plasma-shielding effect. hU0 i is the weighted mean of the first ionization energy of each atom (240): P Xi U0i hU0 i ¼ i P [39] Xi i

154

Laser Ablation

Figure 36 Comparison of the evolution of temperature at d ¼ 0.00 mm and d ¼ 0.05 mm obtained from three different models: (1) neglecting the effects of vaporization and plasma shielding, (2) taking only the vaporization effect into account, and (3) considering the two effects of vaporization and plasma shielding. Reproduced from Fang, R. R.; Zhang, D. M.; Li, Z. H.; Yang, F. X.; Li, L.; Tan, X. Y.; Sun, M. Solid State Commun. 2008, 145, 556.

Figure 37 Fluence dependence of the calculated and measured ablation depths. Reproduced from Fang, R. R.; Zhang, D. M.; Li, Z. H.; Yang, F. X.; Li, L.; Tan, X. Y.; Sun, M. Solid State Commun. 2008, 145, 556. The experimental data is from Lunney, J. G.; Jordan, R. Appl. Surf. Sci. 1998, 127–129, 941.

where the subscript i refers to the four kinds of atom in YBa 2Cu 3O 7 , U 0i is the first ionization energy of the ith type of atom, and X i is the number of the ith type atom. From eqn [39], we can obtain the mean ionization hU0 i of YBa2 Cu 3 O 7 as 10.398 eV. The ratio of IB absorption and PI absorption in the shielding effect can be estimated. If each evaporated atom in local thermal equilibrium has only one excited electron, the free electron density N e is given by the Saha equation (241): Ne2 ¼ 3  1021 ðkB TP Þ3=2 expðhU0 iÞ=kB TP

[40]

Laser Ablation

155

Figure 38 Mass removal per pulse as a function of laser fluence. Reproduced from Fang, R. R.; Zhang, D. M.; Li, Z. H.; Li, L.; Tan, X. Y.; Yang, F. X. Phys. Status Solidi A 2007, 204, 4241. The experimental data is from Bulgakova, N. M. and Bulgakov, A. V. Appl. Phys. A 2001, 73, 199.

From eqn [40], Ne ¼ 1.44  1020, at which the IB by electron–ion collisions becomes the primary mechanism of photon absorption (sIB,ion w1.25  1019 cm2). A laser fluence of 1–15 J cm2 is equivalent to 0.5  1019–8.1  1019 photons cm2; the product of the cross section and photon density clearly indicates a probability of 62.5–100% for the incoming photons to be absorbed by the IB mechanism. According to the cross section of PI in eqn [11], the photon energy of an infrared laser with wavelength of 1064 nm is 1.16 eV; thus the cross section sPI z 2.7  1022 cm2. The absorption from an infrared laser by excited atoms is 0.135–2.187%. Through the IB mechanism, 2.5–40% of the incident energy is absorbed by electron–neutral collisions, while 65–100% by electron–ion collision. Therefore, IB absorption plays a prominent role in infrared laser ablation. Figure 38 presents the numerical results of two theoretical models: considering the effects of both vaporization and plasma shielding and only taking the vaporization effect into account. We can see from Figure 38 that the two curves nearly overlap in the range of the laser fluence from 1 to 3 J cm2 and begin to separate gradually when the laser fluence is above 3 J cm2. This phenomenon can be explained by the fact that with the laser fluence increasing gradually, the plasma-shielding effect becomes more and more marked. The numerical results considering the effects of vaporization and plasma shielding produce a good agreement with the experimental data. It is clear that the modified model considering the vaporization effect and the plasma-shielding effect can describe the ablation process more accurately. Based on the non-Fourier heat conduction eqn [27], the picosecond laser ablation process was investigated using an Al target as an example. The laser power density of 1013 W m2 and pulse duration time of 150 ps were used in the calculations. Table 3 provides the parameters of the Al target. With the energy conservation law and adiabatic conditions, the boundary conditions can be depicted as: vT  ¼ bI0 ð0 < t < tm Þ vx x¼0 vT  ¼ 0 ð0 < t < tm Þ vx x¼N lim T ¼ 0

k

[41]

x/N

where tm is the time at which the target begins to melt. The initial conditions are:  T x¼0 ¼ T0 vT  ¼0 vt t¼0 Table 3

[42]

Thermal and optical properties of Al targeta

ks (J s1 cm  C)

rs (g cm3)

cs (J g1  C)

s0(s)

R

2.388

2.6991

0.86

1011

0.9

a

Reproduced from Rohsenow, W. M.; Hartnett, J. P.; Ganic, E. N. Heat Transfer Hand Book; McGraw-Hill: New York, 1985; p 236.

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Laser Ablation

700

Non-Fourier conduction model Fourier conduction model 600

Temperature/°C

500

400

300

200

100

0

0 .0

5 .0 ×1 0–12 1 .0 ×1 0–11 1 .5 ×1 0–11 2 .0 ×1 0–11 2 .5 ×1 0–11 3 .0 ×1 0–11 3 .5 ×1 0–11

Time/s Figure 39 The surface temperature evolution obtained from the Fourier and non-Fourier models. Reproduced from Zhang, D. M.; Li, L.; Li, Z. H.; Guan, L.; Tan, X. Y. Phys. B 2005, 364, 285.

where T0 is the initial temperature of the target. Under the boundary and initial conditions, the target temperature depending on depth and time was obtained (238,239).
 Z bI0 pffiffiffiffiffiffiffiffiffiffi t 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Tðx; tÞ ¼ t 02  s0 x2 =a expðt 0 =2s0 Þdt 0 a=s0 pffiffiffiffiffiffiffiffi J0 k 2s0 x s0 =a sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z t 2bI0 ba 1 þ 4ab2 s0 0 [43] þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi expðbxÞ pffiffiffiffiffiffiffiffi expððt  t Þ=2s0 Þsin h ðt  t 0 Þ 2 4s20 k 1 þ 4ab x s0 =a
 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi t 02  s0 x2 =a expðt 0 =2s0 Þdt 0  J0 2s0 where J0(t) is the zero-rank Bessel function. Under the same conditions, the dependence of Fourier temperature on depth x and time t can be expressed in the form: Z t pffiffiffiffiffiffiffiffiffi 1 pffiffiffi expðx=ð4at 0 ÞÞdt 0 Tðx; tÞ ¼ I0 a=p=k t0 0
 Z t pffiffiffiffiffiffiffiffiffi 1 x2 [44] pffiffiffi expðab2 ðt  t 0 ÞÞexp   I0 ab a=p=k dt 0 4at 0 t0 0 Z I0 a t þ expðab2 t 0 Þdt 0 k 0 The calculation results based on eqn [43] and eqn [44] are shown in Figure 39 and Figure 40, respectively. The comparison shows that the effect of non-Fourier heat conduction cannot be ignored. When t > 5  1012 s, the non-Fourier heat has an obvious effect on the temperature of the target surface; that is, the non-Fourier temperature is distinctly higher than that of the Fourier heat conduction model. There is a delay of heat conduction in the inner target, and the deeper the target is, the longer the delay time is.

4.06.5.4

Femtosecond Laser Ablation Models: Classic and Improved Two-Temperature Equations

When the pulse width exceeds 100 ps, the surface temperature of the material is determined by thermal conductivity; thus laser ablation can be regarded as an equilibrium process, obeying the Fourier conduction rule. If the laser pulse width is reduced, the nonFourier heat conduction will be applicable. However, if the pulse width is reduced on the order of a subpicosecond or femtosecond, the heat transfer process of laser ablation shows entirely different characteristics. When the laser energy is absorbed by the electrons, their kinetic energy sharply increases and then the temperature of the electron subsystem suddenly rises. In a short period of pulse, the energy cannot be transferred from the hot electrons to the target ions (delivery time roughly from subpicosecond to tens of a picosecond). After the termination of a pulse, the temperature of the ion subsystem in the target slowly rises, while the temperature of the electron subsystem declines, until the equilibrium temperature is achieved.

Laser Ablation

157

450 400

Fourier model Non-Fourier model

Temperature/°C

350 300 250 200 150 100 50 0 0.0

2.0× 10–8 4.0× 10–8 6.0× 10–8 8.0× 10–8 1.0× 10–8 1.2× 10–7 1.4× 10–7 1.6× 10–7

Position/m Figure 40 Temperature distributions for two models at t ¼ 2  10 B 2005, 364, 285.

11

s. Reproduced from Zhang, D. M.; Li, L.; Li, Z. H.; Guan, L.; Tan, X. Y. Phys.

Soviet scientists first paid attention to the special heat conduction phenomenon. In 1957, Kaganov et al. found that an energy exchange exists between electrons and lattice, and presented a theoretical model to describe the nonequilibrium heat transport process. Also, they explained the electron–phonon coupling coefficient (243). In 1974, Anisimov et al. put forward the classic two-temperature model (TTM) (244). Based on the one-dimensional nonsteadystate heat conduction equation, the two different interaction processes, that is, photon and electron, and electron and lattice were considered. The temperature evolvements of the electron and lattice subsystems can be given by two differential equations: v v Te ¼ ke 2 Te  gðTe  Tl Þ þ Sðx; tÞ vt vx v Cl Tl ¼ gðTe  Tl Þ vt

Ce

[45]

where Te and Tl are the electron and lattice temperature, respectively, Cl and Ce are the specific heat capacity of lattice and electron, respectively, and g is the electron–phonon coupling coefficient. The first equation describes the electronic temperature, and g(Te  Tl) represents the transferred energy from electrons to lattice by electron–phonon collision; the heat source term S(x,t) is the energy absorbed by electrons from the laser by photon–electron collision. The second equation indicates the temperature evolvement of the lattice subsystem, and the temperature rises due to the electron–phonon interaction g(Te  Tl). In 1984, J. G. Fujimoto et al. found that when high-intensity 75 fs optical pulses illuminate a tungsten metal surface, an anomalous heating mechanism appears and a transient nonequilibrium temperature difference occurs between the electrons and lattice. Pump–probe measurements indicated an electron–phonon energy relaxation time of several hundred femtoseconds (245). In 1987, Elsayed-Ali et al. (246) used 150–300 fs laser pulses to monitor the thermal modulation of the transmissivity of thin copper films. The experimental results show that at the beginning of the laser pulse, a larger temperature difference between the electron and lattice existed, which proved that TTM is reasonable. They also found that the process of electron–phonon energy transfer (electron–lattice coupling relaxation time) was observed to be 1–4 ps, increasing with the laser fluence. In 1987, Allen (247) presented an electron–phonon coupling coefficient equation. In 1990, Brorson et al. (248) reported the first systematic femtosecond pump–probe measurements of the electron–phonon coupling constant in some metallic films, and their experiments confirmed Allen’s theoretical predictions. In 1996, Chichkov et al. (249) studied the laser ablation of solid targets by 0.2–5000 ps Ti: sapphire laser system. They resolved the TTM equation to obtain analytical solutions. Both before and after the 1990s, with the development of the femtosecond pulsed laser, the TTM equation has been extensively investigated. In 1988, Corkum et al. (250) obtained an analytic solution of the TTM and compared the theoretical results with their experimental measurements of ultrashort laser pulse ablation of molybdenum and copper targets. Optical damage caused by laser pulses with a duration s  ns can be understood only with a TTM of metals. In 1998, A. P. Kanavin (251) studied different regimes of heat propagation in metals irradiated by subpicosecond laser pulses on the basis of TTM and obtained analytical solutions corresponding to the different temperature dependences of electron thermal conductivity. In 2002, Gamaly et al. (252) investigated the transient reflectivity of gallium films induced by 150 fs laser pulses by the pump– probe technique. The experimental results showed that the transient electron–phonon collision rate is a strong function of

158

Laser Ablation

temperature and laser intensity, which is drastically different from that observed under equilibrium conditions. In 2005, Gamaly et al. (253) carried out experiments on the ablation of metals such as Cu, Al, Fe, and Pb in both air and vacuum and revealed that the presence of air results in a significant reduction in the ablation threshold. The temperature in the skin-layer during a single-laser pulse is calculated using a two-temperature approximation while the heat conduction can be neglected. Thus, TTM equations can be transformed into: v Te ¼ gðTe  Ti Þ þ ð1  ab ÞI0 ðtÞ expðab xÞ vt v Ci Ti ¼ gðTe  Ti Þ vt Ce

[46]

Additionally, the TTM model is combined with thermoelasticity dynamics and the electron blast model to investigate the mechanisms of ultrashort pulse laser ablation. Hetnarski and Ignaczak (254,255) have summarized five nonclassical approaches that include the relaxation time effects in dynamic thermoelasticity. Chen et al. (256) extended the dual-hyperbolic two-temperature and hot-electron blast models to investigate the deformation in metal films subjected to ultrashort laser heating. The major driving force for nonthermal damage is the so-called hot-electron blast force, which is generated by nonequilibrium hot electrons. Readers can find related works on femtosecond laser ablation in a review paper in Ref. (257). Here, an improved TTM model is introduced in order to illustrate the general theoretical method of investigating femtosecond laser ablation of the target. Moreover, related theoretical work, such as a unified TTM model and electronic DOS effect, are discussed (208,217,258,259). When the electron temperature Te is higher than 4000 K, the electron–electron collision plays a very important role in the femtosecond laser ablation (260–262), causing a change in the thermophysical parameters. In this case, the TTM equation cannot reasonably describe the thermophysical mechanism. Also, it is necessary to take into account the electron–phonon and electron– electron collisions affecting the thermophysical parameters, such as electronic thermal conductivity and the optical parameters of materials. The thermophysical parameters such as specific heat capacity and thermal conductivity are temperature dependent. When 4000 K < Te < 10 000 K, the electron heat capacity is usually a linear function of the electron temperature (263), given by: ce ðTe Þ ¼ ce0 Te

[47]

where c0e is a constant. The electron thermal conductivity can be described as: kðTe ; T1 Þ ¼ ce vF2 s=3

[48]

where Tl is the lattice temperature, vF is the Fermi velocity, and s is the electron–phonon relaxation time. For good conductors, such as metals, the electron–electron collision frequency may be determined by nee ¼ ATe2 ; whereas the electron–phonon collision frequency is proportional to Tl, namely ne–ph ¼ BTl. Here A and B are constants, and both contribute to the electron collision frequency n. For 4000 K < Te < 10 000 K, a relationship between the electron–phonon coupling relaxation time s and the electron–electron and electron–phonon collision frequency for electron temperature below the Fermi temperature is given by (264): 1 ¼ n ¼ nee þ neph ¼ ATe2 þ BT1 s

[49]

Substituting eqn [49] into the expression of the electron thermal conductivity, we can obtain the following equation: kðTe ; T1 Þ ¼

vF2 c0e Te 1 BTe ¼ k0 2 3 ATe2 þ BT1 ATe þ BT1

[50]

where k0 ¼ vF2 c0e =ð3BÞ is the electron heat conductivity at room temperature (Te ¼ Tl ¼ 300 K). Now, consider the variation of the optical parameters with temperature. The experiments confirmed that the optical parameters of target directly influence the laser energy absorption, which has an important impact on femtosecond laser ablation (21). At lower electron temperatures, it is allowed to assume that the optical parameter is constant (265–269). However, when the electron temperature is rising, the optical parameters such as the absorption coefficient and the absorptivity will remarkably change with the electron temperature. According to classic Maxwell theory, the optical properties, such as the absorption coefficient and the absorptivity with electron temperature, are obtained as shown in eqn [17] and eqn [18] (270). Substituting eqns [17], [18], [47], and [48] into the classic TTM model, the following improved two-temperature model, which considers the effect of electron temperature on the heat capacity, thermal conductivity, absorption coefficient, and absorptivity of the electron (270), is obtained. c0e Te

v BTe v2 Te  gðTe  Tl Þ þ Sðx; tÞ Te ¼ k0 2 ATe þ BT1 vx2 vt c1

v T1 ¼ gðTe  Tl Þ vt

[51]

[52]

Laser Ablation

Table 4

159

The thermal and optical properties of copper

Coefficient of the electron heat capacity (Ce0 ) Lattice heat capacity (Cl) e–ph coupling coefficient (g) Electron heat conductivity at room temperature (k0) Coefficient of e–e collision frequency (A) Coefficient of e–ph collision frequency (B) Target temperature coefficient of resistance (a)

96.6 J m3 K2 3.5  106 J m3 K 1  1017 W m3 K 400 W m1 K 1.75  107 K2 S1 1.98  1011 K1 S1 4.3  103 K1

where the heat source S(x,t) is as follows:

! 4pI0 ð4ln 2Þt 2 exp  Sðx; tÞ ¼ bbIð0; tÞ expðbxÞ ¼ l0 ðsp Þ2 0:5 
 4ps0 x  exp  e0 l0 c½1 þ aðTe ðx; tÞ  T0 Þ " #   0:5 ð4ln 2Þt 2 D ¼ C exp  x  exp  1 þ aðTe ðx; tÞ  T0 Þ ðsp Þ2

[53]

where C ¼ 4pI0/l0, D ¼ 4ps0/(30l0c). The initial condition is: Te ðx; 0Þ ¼ T1 ðx; 0Þ ¼ T0

[54]

And the boundary conditions can be expressed as: ke

vTe  ¼ ð1  RÞI0 ðtÞ vx x¼0 ke

vTe  ¼0 vx d

[55]

where T0 ¼ 300 K is the initial temperature, which is uniform across the target, and d is the depth of the target. The thermal and optical properties of copper in Table 4 are adopted (246,271). Under the initial condition eqn [54] and the boundary conditions eqn [55], the improved TTM equation can be resolved and the calculation results are indicated in Figure 41. Figure 41(a) and 41(b) show the temporal evolution of the electron and lattice temperature at the surface for the copper target irradiated by a 100 fs, 800 nm pulse at 0.2, 0.3, and 0.4 J cm2, respectively. In Figure 41(a), the maximum temperature of the electron temperature at the surface is in the range 5500–8000 K for the laser fluence varying from 0.2 to 0.4 J cm2. The surface electron and lattice temperatures increase with increasing laser fluence. For a fixed laser fluence, the electron temperature rapidly increases with the ablation time, while suddenly decreasing after it reaches the maximum, as shown in Figure 41(a). The temperature of the lattice rises gradually; see Figure 41(b).

Figure 41

Temporal evolution of electron temperature (a) and lattice temperature (b) at the surface for the copper target.

160

Laser Ablation

Figure 42

Dependence of the ablation rate on the laser fluence; numerical data 1 represents the improved model.

Figure 42 shows the dependence of the ablation rate on the laser fluence. Curve 1 represents how the ablation rate depends on laser fluence based on the improved TTM model as eqns [51] and [52]. Curve 2 stands for the model without considering electron temperature-dependent heat capacity, thermal conductivity of the electron, absorption coefficient, and absorptivity. The black dot represents the experimental data (272). It can be seen that the results calculated based on the improved TTM model are in good agreement with the experimental data. In a word, the effects of physical properties on femtosecond laser ablation should be considered (246,248,272).

4.06.5.5

Femtosecond Laser Ablation Models: Unified Two-Temperature Equations and Density of State Effect

Pulsed laser ablation from nanosecond to femtosecond laser has been extensively investigated (273–275). The first stage of ablation is the absorption of the laser energy through photon–electron interactions. It takes a few femtoseconds for the electrons to reestablish the Fermi distribution. The second stage is the heat energy diffusion to the lattice through electron–phonon interactions, and the characteristic time scale of this stage is called the electron–phonon coupling time, typically on the order of tens of picoseconds (275). Experiments and theoretical research reveal that two ablation mechanisms exist in the laser ablation process: (1) equilibrium ablation (208,209,225,276–278) and (2) nonequilibrium ablation (122,279–281). We define the electron–phonon coupling time sR and the laser pulse width sL. When sR/sL >> 1, it is the nonequilibrium ablation; when sR/sL << 1, it is the equilibrium ablation; and when sR/sL w1, it can be called a mixed ablation. As for the picosecond laser ablation process, the ablation mechanism is very complex due to the coexistence of equilibrium and nonequilibrium mechanisms. The general non-Fourier law mentioned above is suitable to describe the heat conduction law of picosecond laser ablation. However, until now, no perfect heat conduction model exists that describes the thermophysical phenomenon with the laser pulse width ranging from nanoseconds to femtoseconds. A unified model would be helpful for the experimental investigations on laser ablation.

sR  Defining a factor exp  a , the following equations give a unified thermal model, which can describe the thermophysical sL phenomenon of the laser ablation process with laser pulse width ranges from nanosecond to femtosecond:
 v sR v2 ce Te ¼ ke exp  a Te  gðTe  Tl Þ þ ð1  RÞbI0 ðtÞexp ðbxÞ [56] sL vx2 vt

c1

v T1 ¼ gðTe  Tl Þ vt

[57]

Equations [56] and [57] describe the heat conduction process of electrons and lattice subsystem, respectively. In eqn [56], a is an undetermined coefficient, which varies for different materials and is obtained by fitting theoretical results to experimental data. When Te is below 3000–4000 K, the influence of the thermal excitation of electrons on the ce and ke is very small (265). Therefore, ce and ke can be regarded as constants.

Laser Ablation

161

The ratio of the electron–phonon coupling time and laser pulse width is an important criterion. As sR >> sL, that is,

sR  /0, the ablation is nonequilibrium ablation. The unified model changes into the simplified two-temperature model: exp  a sL Ce

v Te ¼ gðTe  Tl Þ þ ð1  RÞbI0 ðtÞexpðbxÞ; vt

[58]

v T ¼ gðTe  Tl Þ vt l

[59]

Cl

This is the classic TTM model. For the long pulses, when sR << sL, the ablation is a thermal equilibrium process, that is, T ¼ Te ¼ Tl, eqns [56] and [57] can be changed into one equation: Cn

v v2 T ¼ k 2 T þ ð1  RÞbI0 ðtÞexpðbxÞ; vx vt

[60]

where Cn ¼ Ce þ Cl, k, and T are the specific heat, the thermal conductivity, and the temperature of the target, respectively. Equation [60] becomes the classical equation of one-dimensional heat conduction. The first term of the right side in eqn [60] is the heat conduction term of the target.

sR  < 1, it is the mixed process, including equilibrium and nonequilibrium ablations. Therefore, the unified When 0 < exp  a sL thermal model can well describe the whole thermal conduction phenomenon, with laser pulse width ranging from the nanosecond to femtosecond time scale. For eqns [56] and [57], the initial condition is: Te ðx; 0Þ ¼ Tl ðx; 0Þ ¼ T0

[61]

and the boundary conditions can be expressed as follows: ke

vTe  ¼ ð1  RÞI0 ðtÞ; vx x¼0

[62]

vTe  ¼ 0; vx d

[63]

ke

where T0 ¼ 300 K is the initial temperature, which is uniform across the target, and d is the thermal diffusion depth. In the lowfluence ablation case, the number density of the hot electrons is considered low enough that the energy transfer occurs only within the area characterized by the skin depth d ¼ 1/ab. However, if the laser fluence is very high, the electron thermal diffusion length rffiffiffiffiffiffiffiffiffiffiffi ke should be d ¼ sR (282). Ce Under the initial condition eqn [61] and the boundary conditions eqns [62] and [63], the heat conduction eqns [56] and [57] are numerically solved by a finite difference scheme to investigate damage threshold fluences versus the pulse width. The thermal and optical properties of gold in Table 5 are adopted. Assuming that pulse width 101–103 ps, the value of a can be determined as 0.67 through fitting the experimental results with computed results. The melting point of gold is 1337.33 K (275). The computed modeling results and experimental results are shown in Figure 43. In Figure 43, for the pulse duration shorter than 2  102 ps, the threshold fluence slowly increases, and for the longer pulse duration, the threshold fluence rapidly increases with pulse duration. The results are more reasonable than those obtained by the simple one-dimensional heat conduction equation (274). The absorbance b ¼ 1  R of a pure metal consists of two parts, b ¼ b1 þ b2. b1 is the intrinsic absorbance, and b2 is the contribution due to surface roughness. For an optically smooth metal surface, the order of b2 is about 1.2% of b1, while the role of b2 is enhanced as the surface roughness increases. In fact, the damage threshold influence is an average value obtained by multipulse ablation. For low pulse duration (i.e., less than 10 ps), the modified surface is obscured and the value of b2 is very small. For pulse

Table 5

Thermal and optical properties of gold

Wavelength (l) Thermal conductivity of electron (ke) Specific heat of electron (Ce) Specific heat of lattice (Cl) Absorption coefficient (ab) Reflectance (R) e–ph coupling coefficient (g) The electron–phonon coupling time (sR)

1053 nm 318 W m1 K 67.7 J m3 K 2.30  106 J m3 K 7.88  105 m1 0.94 2.1  1016 W m3 K 6 ps

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Laser Ablation

Figure 43 Damage threshold fluences versus pulse width for the gold target irradiated by 1053 nm pulse. The experimental data is from Stuart, B. C. and Feit, M. D. J. Opt. Soc. Am. B 1996, 13, 459.

duration longer than 10 ps, the value of b2 becomes bigger (21). In our simulation, we only take into account the intrinsic absorbance b1 without considering b2. So for pulse duration longer than 10 ps, the theoretical data are a little bit higher than the experimental ones. The rapid development of the femtosecond laser has increased the demand for quantitative and predictive modeling of the fast and highly nonequilibrium processes occurring in the target material by laser excitation, especially for electron temperatures higher than 104 K. When the electron temperature is higher than 104 K, the electron DOSs and the energy band structure will change, leading to the corresponding thermophysical parameters (including electron–phonon coupling and electron heat capacity) of the target varying with temperature. The specific heat capacity of the electron is small, so its temperature can suddenly increase up to the Fermi temperature after laser irradiation. When the electron temperature reaches 104 K, the thermal excitation of the electron below the Fermi surface can significantly influence the thermophysical properties of the target (258–260,263,265). Consequently, using TTM equations to describe such a process, we must consider the temperature-dependent parameters, such as the electron–phonon coupling coefficient, the specific heat capacity of the electron, the absorption coefficient, and absorptivity. Also, investigation of the DOS effect on the physical parameters is essential to quantitatively study the ultrahigh-energy femtosecond laser ablation target (265–268). The electronic structure of the target directly determines the effect of thermal excitation of electrons on the thermal physical parameters because the different electronic structures can induce different DOS effects. For noble metals such as Au, the thermal excitation from the low-laying d band results in the positive deviation of the heat capacity from the linear dependence at sufficiently high electron temperatures. However, for transition metals, such as Ni, d band electrons through the Fermi surface lead to a high density of electrons at the Fermi surface. Therefore, the d band electrons of Ni metal with high-density electronic states can be excited to the s band, which has a low density of electronic states. This different electronic structure produces smaller thermal physical parameters than the commonly used parameters at higher temperatures. When the electron temperature is lower, the optical parameters (absorption coefficient and absorptivity) can be considered as constant (263,265,267–269). However, experiments have confirmed that both the absorption coefficient and the absorptivity are temperature dependent. If electron temperature is over 4000 K, both the thermal parameters vary with the electron temperature, while if the electron temperature exceeds 10 000 K, the temperature can much more significantly affect the parameters (283–285). In a word, since the DOSs of electrons significantly determine the thermophysical and optical parameters, an improved TTM equation describing the heat conduction process at the electron temperature 10 000 K is expected. Several theoretical studies (265–268) show that for electron temperature 10 000 K, the heat capacity of electrons as a function of temperature can be expressed as: Z N vf ð3; m; Te Þ ð3  3F Þ gð3Þde [64] Ce ðTe Þ ¼ vTe N " #  1 ð3  mÞ . þ1 where g(3) is the DOS of target, m is the chemical potential at Te, and the Fermi distribution f ð3; m; Te Þ ¼ exp kB Te Using the calculated electronic structure by Vienna Ab-initio Simulation Package (VASP) software (265–268), the DOS affecting the

Laser Ablation

163

heat capacity of electrons and the electron–phonon coupling coefficient of Ni and Au can be investigated to obtain the relationship between the parameters and electron temperature. In Figure 44, the great difference between the dashed and solid lines fully shows that when the electron temperature is high, the DOS effect must not be ignored. In Ref. (258), a simple method, that is, fitting the solid line calculated by VASP software in Figure 44, was used to obtain fitting expressions of electron heat capacity with temperature. For the Ni target,
 54:2 [65]  105 J m3 K1 ce ðTe Þ ¼ 30:72  Te 0:0745 1 þ e 0:4 and for the Au target,


ce ðTe Þ ¼

 5:05 

38:27 1þe



Te 0:8 0:38

 105 J m3 K1

[66]

Similarly, the electron–phonon coupling coefficient with temperature also can be obtained by the above-mentioned method (258). For the Ni target,
 183:6 Ge ðTe Þ ¼ 1:31 þ [67]  1017 W m3 K1 Te þ0:39 1 þ e 0:14 and for the Au target,


Ge ðTe Þ ¼

2:08 þ

2:07 Te 0:8 0:28

1þe



 1017 Wm3 K1

[68]

Substituting eqns [65]–[68] into the classic TTM model, an improved TTM model can be given as: Ce ðTe Þ ¼

v v  ke Te  GðTe ÞðTe  Tl Þ þ Sðx; tÞ vx vx Cl

v T ¼ GðTe ÞðTe  Tl Þ vt l

[69]

[70]

The initial condition is: Te ðx; 0Þ ¼ Tl ðx; 0Þ ¼ T0

[71]

and the boundary conditions can be expressed as follows: ke

vTe  ¼ ð1  RÞI0 ðtÞ vx x¼0

[72]

vTe  ¼0 vx d

[73]

ke

Figure 44 Electron temperature dependences of the electron heat capacity of Ni(a) and Au(b). Solid lines show the results of the calculations performed with DOS obtained from VASP. Dashed lines show the commonly used approximations of the thermophysical material properties.

164

Laser Ablation

Table 6

Physical parameters and optical parameters of Ni and Au

Metal

ke (W m1 K1)

Cl (J m3 K1)

a (K1)

Ni Au

91 318

4.1 2.5

4.3  103 6.5  103

Using the improved TTM model with the initial and the boundary conditions, the surface temperature evolutions of Ni and Au targets during laser ablation are investigated. Table 6 gives the physical and optical parameters of Ni and Au. And the laser parameters of pulse width 100 fs, wavelength 800 nm, and laser energy density 0.65 J cm2 are used in the calculations. Figure 45 indicates the time-dependent temperatures of the electron and the lattice of the Ni-target surface. From Figure 45, it can be seen that the electron temperature suddenly increases to 10 000 K and then slowly declines. The lattice temperature gradually increases to a final equilibrium temperature of about 2500 K. The results suggest the electron–phonon coupling coefficient of laser ablation of Ni sep z 2 ps. Figure 46(a) and 46(b) indicate that the obtained threshold fluence of Ni (a) and Au (b) in TTM simulations performed with thermophysical parameters calculated with DOS is obtained from VASP (dot lines), and the commonly used approximations (dashed dot lines) and the experimental data from (286) for the melting thresholds. The theoretical results from the new improved TTM equation and the experimental data are more consistent than the results from the traditional two-temperature equation. For

12000 11000 10000

electron temperature at 0.65J cm–2 lattice temperature at 0.65J cm–2

Temperature(K)

9000 8000 7000 6000 5000 4000 3000 2000 1000 0

1000

2000

3000

Time (fs) Figure 45

The time-dependent temperatures of the electron and the lattice of the Ni-target surface.

Figure 46 Threshold fluence of Ni(a) and Au(b) for surface melting as a function of film thickness. The dot lines are the results considering the DOS effect.

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165

Au, the theoretical values of the new improved TTM equation at film thickness larger than about 350 nm tend to a constant; the theoretical and experimental data of Ni and Au show that the melting threshold increases rapidly with the film thickness and finally tends to a constant value. The saturation threshold fluence of Ni obtained in the TTM simulations considering the DOS effect, 230 J m2, is a little higher than the experimental data 220 J m2 (286). The calculated threshold fluence with the commonly used parameters, 275 J m2, is not in good agreement with the experimental data. The saturation threshold fluence at large film thicknesses obtained in the TTM simulations performed with the commonly used parameters, 1100 J m2, is significantly lower than the experimental value, 1800 J m2 (286), whereas the value predicted in TTM simulations performed with the new thermophysical parameters, 1600 J m2, is in a better agreement with the experimental data. The comparisons confirm that the DOS effect on femtosecond laser ablation is significant. Ultrashort-pulsed laser ablation technology is developing in leaps and bounds, and the femtosecond laser ablation mechanism is becoming more complex. It is a pity that we cannot give a deeper and more comprehensive introduction to this research field in the present chapter. The interested reader can refer to the related references, such as a recent review paper in Ref. (257).

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