Fundamentals of Ultrashort Pulse Laser Interactions: Mechanisms, Material Responses, and the Genesis of LIPSS

Abstract

In recent years, ultrashort pulse laser-material processing has gained significant attention due to its broad applications across nearly all manufacturing sectors. This chapter delves into the foundational aspects of the ultrashort pulse laser-material interaction and elucidates the intricacies of the underlying ablation mechanisms. Due to peculiarities between the metal energy absorption in contrast to the semiconductor or dielectric, the first section provides an in-depth exploration of laser-material dynamics, emphasizing the unique responses of various substrates under ultrashort pulse irradiation. A theoretical analysis of ultrashort laser-matter interaction can be represented by the two-temperature model, which describes the temperature of the electron or carrier and lattice in non-equilibrium conditions when ultrashort laser pulses are applied. As the narrative progresses, the spotlight shifts to one of the most interesting phenomena associated with these interactions: the formation of Laser-Induced Periodic Surface Structures (LIPSS). The second section unravels the genesis and evolution of LIPSS, demystifying LIPSS formation mechanisms and the pivotal role played by the ultrashort pulse duration.

1. Introduction

The study of ultrashort pulse laser interactions with materials has become increasingly significant in recent years, driven by its wide-ranging applications in various manufacturing sectors [1, 2]. To optimize laser processes and improve efficiency and quality, it is essential to have a deep understanding of the underlying physics and material-specific responses when laser pulses interact with material. Moreover, this knowledge enables precise customization of laser parameters for applications like micro and nanofabrication and surface modification. Fundamental studies also drive innovation, helping develop new techniques and pushing the boundaries of what ultrashort pulse lasers can achieve.

Figure 1 demonstrates the laser processing workflow, divided into four distinct parts, each playing a crucial role in the precision and efficiency of the laser-based manufacturing process. Single laser pulse width cannot be done with desired micromachining with all materials; a choice of laser (nanosecond, picosecond, and femtosecond) and their parameter are essential for the process’s quality, throughput, and cost-effectiveness. In nanosecond laser-material processing, the precision and quality of micromachining are not as high as those achieved in femtosecond and picosecond laser micromachining, primarily due to the presence of a heat-affected zone (HAZ) and re-solidification of the ablated feature. Lasers with their excellent beam quality promised noticeable advantages and improvements in high precision and material processing at the micron scale. Thus, a new generation of laser beam sources with ultrashort pulses and high repetition rates has been used in vast industrial applications, and it offers excellent improvements, especially in the fields of laser processing and micro-manufacturing. Ultrashort laser pulses in the range of picoseconds and femtoseconds have high pulse intensities and enable high-resolution, high-quality micromachining of almost all solid materials with minimal thermal and mechanical damage and structure sizes down to the submicron range. It is an excellent and universal tool for very fine, direct ablative microstructuring of solid materials. It has been demonstrated that ultrashort pulses bear the potential for precise micromachining (laterally and vertically) in transparent dielectrics as well as metal and semiconductors [3, 4].

Figure 1.

Comprehensive illustration showcasing laser-material processing.

The first section provides a fundamental aspect of ultrashort laser-material processing, driven by the peculiarities inherent in the energy absorption of metals compared to semiconductors or dielectrics. This section offers an insight into laser-material dynamics and the response of various substrates while irradiation of ultrashort laser pulses. A two-temperature model is used to analyze the intricacies of ultrashort laser-matter interactions, shedding light on the non-equilibrium conditions that arise within the electron or carrier and lattice temperature. The second section is devoted to the description of the LIPSS and the potential mechanisms of their formation.

2. Two-temperature model (TTM)

In the realm of ultrashort laser-material interaction, the material response can be described as a result of elevated temperatures. Therefore, it is important to understand the flow of heat inside a material. The two-temperature model represents the temporal and spatial evolution of the temperature inside a material.

2.1 Metal

Figure 2 depicts a schematic diagram of ultrashort laser pulses acting on the metal surfaces. It is divided into five parts—absorption, heating, energy transfer, thermomechanical response of the material, and ablation. When the laser pulses irradiate the substrate or material, energy transfers from the laser pulses to the material; this energy is absorbed by free electrons, which increases the temperature of the electron (absorption). At room temperature, the lattice’s and electron’s temperatures are in thermal equilibrium. Once an electron gets energy from laser pulses, an electron-electron collision occurs. As a result, there is a rapid increase in the electron temperature (heating), and these energetic electron transfers their energy to the lattice by electron-lattice collision (energy transfer). Numerous energetic electrons are present during pulsed laser irradiation of the material, requiring multiple electron-lattice collisions to transfer a significant amount of energy. Due to the transfer of energy from electron to lattice system, heat diffusion in material or substrate occurs (thermomechanical response), and material is ablated (ablation). The evolution of electron and lattice temperatures over time is determined by the two-temperature model (TTM) and governing equations of two-temperatures are given below [5].

Figure 2.

Schematic diagram of ultrashort pulse laser interaction with metal. Where $T_l$ and $T_e$ are temperatures of lattice and electron and $T_0$ is the room temperature.

$$C_e\frac{\partial T_e}{\partial t}=\nabla \left(k_e\nabla T_e\right)-k\left(T_e-T_i\right)+Q_{\mathit{\text{total}}}$$E1

$$C_l\frac{\partial T_l}{\partial t}=\nabla \left(k_l\nabla T_l\right)-G\left(T_e-T_l\right)$$E2

where $T_e$ and $T_l$ are the temperature of the electron and lattice, $k_l$ and $k_e$ are the thermal conductivity of the lattice and electron, $C_e$ and $C_l$ are the heat capacity of the electron and lattice. $Q_{\mathit{\text{total}}}$ represents the absorbed laser heating source and G is the electron-lattice coupling. During the ultrafast heating of the material, the temperature of electrons and lattices rises so that temperature-dependent materials’ properties have a pivotal role during the process.

As can be seen in Figure 2, two mechanisms of energy transfer, from laser to electron and from electron to lattice, involve two different temporal time scales driven by the electron relaxation time (${\tau }_e$) and electron-lattice relaxation time (${\tau }_{\mathit{ep}}$). In metal, the electron cooling time is around a hundred femtoseconds, while the electron-lattice relaxation time corresponds to several picoseconds. The electron-lattice coupling factor represents the energy exchange rate between the two subsystems (electron and lattice), and research groups suggest that it depends on the electron temperature, which is linear or nonlinear [6, 7]. Drastic changes in electron temperature and lattice temperature during and after irradiation of ultrashort laser pulses create a decisive influence on the material’s optical properties, such as absorptivity and reflectivity. The laser heat source can be delineated by the following equation, and it gives the absorption of laser energy by free electron [7].

$$Q_{\mathit{\text{total}}}=\left(1-R\right)\times F\times \alpha \times exp\left(-2\frac{r^2}{{\omega }_0^2}\right)\times exp\left(-4ln2\frac{{\left(t-t_0\right)}^2}{{\tau }^2}\right)\times exp\left(\mathit{\alpha z}\right)$$E3

where $R$ representing the surface reflectively, $F$ is the laser fluence, $\tau$ is the pulse width, ${\omega }_0$ is the beam radius at the laser focal plane and the pulse peak arrives at $t_0$. $R$ and $\alpha$ are the reflectivity and absorption coefficient of the material which have a significant influence on the laser energy distribution on the material transition. The reflectivity and absorption coefficient can be derived in terms of the dielectric constant ${\epsilon }_1$ and ${\epsilon }_2$. Generally, the Drude model is used to determine the dielectric constant and intraband absorption in the metal. The dielectric constant based on the Drude model is described by [8]:

$${\epsilon }_D={\epsilon }_{\infty }-\frac{{\omega }_p^2}{\omega \left(\omega +i{\gamma }_D\right)}={\epsilon }_1+i{\epsilon }_2$$E4

where ${\epsilon }_{\infty }$ is a the dielectric constant of the material and ${\omega }_{\mathrm{p}}$ is the plasma frequency, $\omega$ is the laser frequency, and ${\gamma }_D$ is the damping coefficient that is equal to the reciprocal of electron relaxation time ${\tau }_e$. It can be expressed as follows

$${\tau }_e=\frac{1}{A_e{T}_e^2+B_l{T}_l}$$E5

where $A_e$ and $B_l$ are the material constant for electron relaxation time. Based on the Drude model, refractive index $n=\sqrt{\frac{{\epsilon }_1+\sqrt{{\epsilon }_1^2+{\epsilon }_2^2}}{2}}$ and extinction coefficient $k=\sqrt{\frac{-{\epsilon }_1+\sqrt{{\epsilon }_1^2+{\epsilon }_2^2}}{2}}$ can be determined. According to the Fresnel equation, the reflectivity($R$) and absorption coefficient ($\alpha$) is obtained by [9].

$$R=\frac{{\left(n-1\right)}^2+{\kappa }^2}{{\left(n+1\right)}^2+{\kappa }^2}$$E6

$$\alpha =\frac{4\mathit{\pi \kappa }}{\lambda }$$E7

In metals, the absorption of laser light becomes more intricate due to the involvement of interband absorption mechanisms. For instance, in polyvalent materials like aluminum, nearly parallel bands lead to an increased absorption at certain laser frequencies. On the other hand, noble metals present a challenge due to their complex energy band structure. When sufficient high photon energies are applied to the noble metal, d-electrons may be excited into the s-band above the Fermi level, which contradicts our predictions made using the simply Drude model. Hence, in order to provide an accurate description of such phenomena, more advanced theoretical approaches are required. In noble metal, experimental work has shown that the effective penetration depth of the laser pulse in the material is larger than the optical penetration depth because of the ballistically moving electrons, and this is called the ballistic effect. Considering the ballistic effect, the free carrier absorption coefficient can be derived as follows:

$${\alpha }_{\mathit{abs}}=\frac{1}{\delta +{\delta }_{\text{ball}}}$$E8

With $\delta$ denoting the optical penetration depth, which is the inverse of the absorption coefficient ($\alpha$). The ${\delta }_{\text{ball}}$ is the ballistic range because of the ballistic motion and diffusion of the electrons. The previous research work demonstrated a ballistic range of about 15 nm for copper [10], 50 nm [10] for silver, and 100 nm for gold [11]. Researchers used advanced diagnostic techniques such as ultrafast pump-probe spectroscopy and time-resolved electron diffraction to measure electron and lattice temperatures in real time as well as find the basic length. These experiments not only confirm the theoretical predictions of the two-temperature model but also provide valuable insights into the transient nature of metal response during ultrashort laser ablation. By studying the evolution of the electron and lattice temperature, researchers can predict material responses, optimize laser parameters, and advance the precision and efficiency of material processing.

A numerical simulation based on the TTM model for the gold sample is shown in Figure 3 [12]. The electron temperature increases quickly and reaches a peak value of around 31,200 K at t = 2 ps, as shown in Figure 3. The lattice temperature begins to increase quickly after t = 1 ps due to the transferred energy from the electrons to lattices, and then reaches a maximum value of 3880 K at t = 26 ps. Afterward, the temperature of the electron and lattice is almost the same.

Figure 3.

Time evolution of electron temperature () and lattice temperature ($T_l$) of the gold sample irradiated by the 180 fs laser with the wavelength of 515 nm at fluence of F = $0.50J/{\mathit{cm}}^2$.

2.2 Semiconductors and dielectrics

Until now, only laser ablation with material that has free electrons (metal) has been discussed in two-temperature models, but materials like semiconductors and dielectric material ablation processes differ as compared to metals. During ultrashort pulse irradiation in semiconductors and dielectric materials, the crucial processes of electron-hole pair generation and relaxation are facilitated through multiphoton ionization and tunneling effects. While ultrashort laser pulses interact with high band gap materials, the pulse duration is shorter than the carrier-lattice interaction time. This leads to a non-equilibrium state between the carrier and lattice systems throughout the irradiation. The energy transfer within the material can be accurately described by the carrier density, denoted as n-TTM [13]. Figure 4 shows a schematic diagram of ultrashort laser pulses acting on the surface of large band gap materials. It is divided into five parts: absorption, heating, energy transfer, thermomechanical response of the material, and ablation. When the laser pulses irradiate the semiconductor, energy is transferred from the laser pulses to the material. This energy is absorbed by electrons and excited from the valence band to the conduction band via single-photon or multiphoton absorption depending on the laser energy and bandgap of the material, resulting in the creation of electron-hole pairs. In dielectric materials, electron-hole pairs are generated through two key processes: photoionization and avalanche ionization. Photoionization involves electrons moving from the valence to the conduction band via multiphoton or tunneling processes. Multiphotoionization or tunneling ionization mainly occurs at a high intensity and power density. When a single photon does not have enough energy to overcome a binding energy gap between the valance band and conduction band, a multiphoton is necessary to overcome this binding energy gap. Alternatively, when the electric field induced by the laser effectively suppresses the Coulomb wall, electrons can liberate themselves by tunneling from the valence to the conduction band—this phenomenon is termed tunneling ionization. Moreover, under certain conditions, multiphotoionization can be further intensified by the irradiating laser pulse, leading to the generation of multiple free electrons in the valence band. This intricate process, known as avalanche ionization, plays a pivotal role in plasma formation during ultrashort laser ablation of dielectric materials. New electron-hole pairs are generated by the energetic charge carrier via the impact ionization process, and the carrier density increases with the carrier temperature (heating). Afterward, these free electrons and holes recombine mainly via the Auger recombination process and transfer the excess energy to another free electron-hole pair. Simultaneously, the carrier system couples to the lattice system and transfers the energy from the carrier to the lattice until thermal equilibrium (energy transfer). Because of the energy transfer from the carrier to the lattice, the top surface of the material reaches the other state (thermomechanical response). Eventually, the temperature of the top surface reaches the vaporization temperature of the material, causing ablation (ablation).

Figure 4.

Schematic diagram of ultrashort pulse laser interaction with high band gap materials. Where $T_l$ and $T_c$ are the temperature of the lattice and carrier, and $n_0$ is the initial carrier density of a material.

To understand the physical phenomenon of ultrashort laser light absorption in high bandgap material, one has to take into account the changes in the density of the free electron in the conduction band of material. The formation of electron-hole pairs (carrier) during irradiation is critical, as it significantly influences the absorption dynamics and subsequent material responses in high band gap materials. The rate of the change of carrier density due to laser excitation processes can be expressed as follows [8]:

$$\frac{\partial n}{\partial t}=\frac{\mathit{\alpha I}}{\mathit{h\nu }}+\frac{\beta I^2}{\mathit{h\nu }}$$E9

Impact ionization and auger recombination processes significantly influence the generation of carrier density in semiconductors. By including them, the generation rate of the carrier density in semiconductors can be defined as follows [13]:

$$\frac{\partial n}{\partial t}=\nabla \left(D_0\nabla n\right)-\gamma n^3+\mathit{\eta n}+\frac{{\alpha }_{a}I}{\mathit{h\nu }}+\frac{\beta I^2}{\mathit{h\nu }}$$E10

where $n$ is the number of carrier density, ${\alpha }_a$ is the one-photon absorption coefficient, $\beta$ is the two-photon absorption coefficient, $I$ is the laser intensity, $h$ is the Planck constant, $\nu$ is the photon frequency, $\gamma$ is the auger recombination coefficient, $\eta$ is the impact ionization coefficient, and $D_0$ is the ambipolar diffusivity which represents the electron-hole pair mobility and transport from a valence band to a conduction band.

In wide bandgap dielectrics, the primary mechanisms involved in generating free carriers during ultrashort laser pulse irradiation are multiphoton and avalanche ionization. The process that takes place during ultrafast laser ablation of dielectric material, as represented by the Keldysh parameter (${\gamma }_{\mathrm{K}}$), includes multiphotonionization, tunneling ionization, and avalanche ionization [14, 15].

$$\begin{array}{l}{\gamma }_{\mathrm{K}}=\frac{{\omega }_{\mathrm{L}}\sqrt{m_{\mathrm{r}}{\epsilon }_{\mathrm{gap}}}}{{\mathit{eE}}_{\mathrm{L}}}\end{array}$$E11

where $e$ signifies the elementary (positive) charge, $m_r$ refers to the reduced mass of electrons and holes, $E_l$ represents the electric field of the laser wave, and ${\epsilon }_{\mathrm{gap}}$ is the band gap of dielectric materials or the ionization potential of individual atoms or molecules. Using the Keldysh parameter, the transition between two ionization (multiphoton ionization and tunneling ionization) can be estimated. There are three distinct cases based on the value of (${\gamma }_{\mathrm{K}}$). When ${\gamma }_{\mathrm{K}}>1$, multiphoton ionization prevails, signifying that the tunneling time of the electron is greater than the periodic oscillation of the laser. On the other hand, when ${\gamma }_{\mathrm{K}})<1$, tunnel ionization dominates under very high electric fields and low frequencies. When the Keldysh parameter equals 1, both multiphoton and tunnel ionization processes contribute to the electron excitation.

The generation of carrier density due to the photoionization and impact ionization in dielectric material can be described by [16].

$$\begin{array}{l}\frac{\partial n}{\partial t}={\sigma }_k{I}^k+\mathit{\delta In}\end{array}$$E12

where ${\sigma }_k$ is the multiphoton ionization cross section, $\delta$ is the the avalanche coefficient, and $k$ is the number of photons required for multiphoton ionization process. This equation provides a straightforward approach to estimating experimental conditions, considering non-uniform carrier density profiles in the surface of dielectric material and variations in optical response. The excitation process is characterized by two stages: initial multiphoton ionization generating free electrons, followed by avalanche ionization once a critical carrier density is reached. At high fluence, tunneling ionization may prevail over multiphoton ionization, as indicated by the earlier mention of the Keldysh parameter.

The excitation of the free electron density mainly depends upon the ultrashort laser pulse intensity. In wide band gap materials, it becomes essential to consider both one-photon absorptions and two-photon absorption across the band gap. The significance of three-photon absorption may also vary depending on photon energy, but it can be neglected as compared to single-photon absorptions and two-photon absorption. The attenuation of laser intensity due to single and two-photon absorption, as well as free carrier absorption, is described by the following expression [13]:

$$\frac{\partial I\left(z,t,r\right)}{\partial z}=-\left({\alpha }_a+{\alpha }_{\mathrm{FCA}}\right)I-\beta I^2.$$E13

where ${\alpha }_{\mathrm{FCA}}$ is the free carrier absorption. ${\alpha }_{\mathrm{FCA}}$ can be associated with Drude absorption and can be determined with Eqs. (4) and (7). Moreover, the dielectric function $\epsilon$ may comprise more terms than the simplified Eq. (4) typically used for describing excitation in high band gap materials. It is essential to note that the dielectric function $\epsilon$ may comprise more terms than the simplified Eq. (4) typically used for describing excited semiconductors [17, 18]. Most of the time, the two-photon absorption coefficient is neglected because the photon energy is greater than the bandgap of material. Assuming a negligible two-photon absorption coefficient, the Lambert-Beer law can be applied, where $a_{\mathrm{abs}}={\alpha }_a+{\alpha }_{\mathrm{fca}}$.

The laser beam is Gaussian, and the temporal and spatial evolution of the laser intensity at the top surface (z = 0) can be expressed as [13]:

$$\begin{array}{lll}{I}_0\left(r,t,z=0\right)=& \sqrt{\frac{4ln2}{\mathrm{\Pi }}}\left(\frac{F}{{\tau }_p}\right)exp\left(-2\frac{r^2}{w_0^2}\right)& \times \left(1-\mathrm{R}\right)exp\left(-4ln2\frac{{\left(t-t_0\right)}^2}{{\tau }_p^2}\right)\end{array}$$E14

For the carrier energy balance equation, the spatial and temporal evolution of carrier temperature and lattice temperature can be defined as follows [13]:

$$\begin{array}{ll}{C}_c\frac{\partial T_c}{\partial t}=\nabla \left(k_c\nabla T_c\right)-k\left(T_c-\right.& \left.T_l\right)+\left(\alpha +\mathit{\beta I}+\mathrm{\Theta }n\right)I-\frac{\partial n}{\partial t}\left(E_g+\right.\\ & \left.3K_B{T}_c\right)-n\left(\frac{\partial E_g}{\partial n}\frac{\partial n}{\partial t}+\frac{\partial E_g}{\partial T_c}\frac{\partial T_c}{\partial t}\right)\end{array}$$E15

$$\begin{array}{ll}{C}_l\frac{\partial T_l}{\partial t}=\nabla \left(k_l\nabla T_l\right)+G\left(T_c-T_l\right)& \end{array}$$E16

where $T_c$ and $T_l$ are the temperatures of carrier and lattice, respectively, $k_c$ and $k_l$ are the thermal conductivity of the carrier and lattice, respectively, $C_c$ and $C_l$ are the heat capacity of the carrier and lattice, respectively, $K_b$ is the Boltzmann constant, $t$ is the time, $\mathrm{\Theta }$ is the carrier absorption coefficient, $E_g$ is the bandgap of material, $G$ is a coupling constant.

Figure 5 shows the evolution of the carrier density, carrier temperature, and lattice temperature for femtosecond laser-silicon interaction [12]. The carrier temperature and lattice temperature rise as free carriers are generated. It is interesting to note that the peak carrier temperature occurs at t = 0.3 ps and 4600 K, while the peak carrier density occurs at 1.2 ps around $0.29\times {10}^{27}{m}^{-3}$, much later than the carrier temperature. This is due to the fact that the heat source of the carrier temperature and the energy change need that time to uplift carrier density. The carrier number density increases dramatically as time passes due to laser light excitation of electrons from the valance band to the conduction band via single-photon absorption, as shown by numerical results in Figure 5. The Auger recombination process causes it to decline after that. Simultaneously, due to energy transfer from the carrier to the lattice, the carrier temperature continues to fall as time passes after reaching a peak. Through the process of electron-lattice energy relaxation, the carrier and lattice temperatures reach equilibrium at 8 ps as time passes.

Figure 5.

Time evolution of carrier density(n), carrier temperature ($T_c$), and lattice temperature ($T_l$) of silicon sample irradiated by the 180 fs laser with the wavelength of 515 nm at fluence of $0.020J/{\mathit{cm}}^2$.

In recent studies investigating the non-equilibrium energy transfer dynamics in matter under ultrashort laser irradiation, researchers have employed advanced models to elucidate the complex interplay of energy absorption and thermal relaxation processes. For that purpose, two-temperature models have been further refined and extended through various modifications, including considerations of parabolic, hyperbolic, dual-hyperbolic, and temperature-dependent optical properties [19, 20, 21]. Additionally, the development of alternative models, such as the Hyperbolic Two-Temperature Model (HTTM) and the Nonlocal Two-Temperature Model (NTTM), has provided deeper insights into energy transfer dynamics, incorporating relaxation time and space nonlocal effects based on extended irreversible thermodynamics principles [22]. Moreover, several research groups have combined the molecular dynamics (MD) simulation with TTM to investigate ultrashort laser-matter interactions, providing detailed atomic-level insights into morphological changes induced by laser irradiation [23, 24].

3. Ablation mechanism

Laser ablation occurs through a series of complex physical processes. When a high-intensity laser beam interacts with a solid material, several phenomena take place, such as the absorption of laser energy, heating, and melting, depending upon the type of laser and material. To disintegrate some amount of matter from a substrate, the material should undergo some change in phase, such as the vaporization of material, phase change, or plasma formation. Figure 6 illustrates the phenomena and processes occurring during the laser irradiation of a solid. In nanosecond laser ablation, the pulse duration is relatively long so that it does not directly ionize or excite electrons from the material. Instead, the longer pulse duration allows for gradual energy absorption by the material, leading to thermal processes such as vaporization and melting, which eventually result in material removal. Sometimes boiling can also occur, but only when the vapor pressure of the liquid phase exceeds the ambient pressure [25].

Figure 6.

Laser ablation dynamics in metal, semiconductor, and dielectric.

Upon the ultrashort laser irradiation, the strongly excited electrons can be created within a few femtoseconds. These excited electrons interact with the lattice on timescales ranging from 1 to 20 picoseconds, transferring energy through electron-lattice interactions. Subsequently, the lattice of the material experiences heating over a period of 20 to 100 picoseconds, leading to thermal expansion and non-equilibrium conditions. This thermal energy accumulation ultimately drives nonthermal melting and ablation processes, occurring within picoseconds to nanoseconds, where the material is removed through mechanisms such as phase explosion, Coulomb explosion, and spallation, rather than traditional thermal processes like vaporization or melting.

3.1 Spallation

Spallation occurs when the laser energy or fluence is low but still sufficient to induce stress within the material. This ablation mechanism involves the rapid generation of stress waves within the material due to the sudden absorption of laser energy. These stress waves propagate through the material and cause it to fracture and eject material layers from the surface. This dynamic fracture or ejection is called “spallation” and is usually caused by stress and shock waves.

3.2 Phase explosion

When fluence is high, a direct transition of solid material into metastable liquid near its critical state occurs without boiling because of the short heating time. Subsequent bubble nucleation causes a rapid transition of the superheated liquid to a mixture of vapor and liquid droplets being ejected from the bulk material called phase explosion. In numerical solution, it is assumed that heterogeneous nucleation occurs due to phase explosion when the lattice temperature reaches 0.9Tcr (critical temperature) [7].

3.3 Coulomb explosion

In dielectric materials, the bandgap between the conduction band and valence band is typically high, inhibiting the generation of free electrons through processes like multiphoton and avalanche ionization, as discussed in the early section. At a low fluence regime, laser pulses do not have enough energy to excite electrons from the valence band, and at that time, material abated because of the Coulomb explosion. It is an electronic mechanism of material disintegrated from a solid by a charged particle. When a laser beam irradiates on the wide band gap dielectric material, at that time, ions get this energy, and the irradiated surface becomes extremely ionized. The repulsive force between these ionized charge particles exceeds the lattice binding strength, and the atomic bond is broken so that the material is ablated. In metals, coulomb explosion does not occur because the surface charge accumulation is effectively quenched by electronic mobility and suppresses the positive ion explosion [26].

Lewis et al. investigated the dynamics of ultrashort pulses in highly absorbing materials, revealing that ablation occurs through one of three mechanisms: spallation, phase explosion, or fragmentation, depending upon fluence [27]. Zhigilei et al. studied the complex interplay between melting, spallation, and phase explosion during laser pulse ablation, highlighting their simultaneous occurrence and intimate relationship [28]. Patrick et al. developed a phase explosion model that uniquely couples carrier and atom dynamics within a unified Monte Carlo and molecular dynamics scheme [29]. Experimental time-of-flight measurements of wide band gap material have found monoenergetic ion beams emitted from irradiated surfaces, favoring Coulomb explosion over phase explosion [30]. Moreover, Bulgakova et al. explored electrostatic disintegration of surface layers in metals, semiconductors, and dielectrics through the modeling of electronic transport and also concluded that Coulomb explosion is possible in dielectrics [31].

4. Origins and formation mechanisms of LIPSS

The periodic features that appear on the surface of materials after irradiation with one or more laser pulses with fluences approaching the material ablation threshold are known as ripples or LIPSS (laser-induced periodic surface structures). Since Birnbaum discovered LIPSS by irradiating semiconductors with a pulsed ruby laser, LIPSS has gained significant attention due to their ability to modify the surface morphology of materials at the micro-nanoscale and show great promise for surface functionalization applications [32, 33]. LIPSS can be generated on various materials, irrespective of their class, including metals [34], semiconductors [35], dielectrics [36], and polymers [37]. Due to its distinctive characteristics, LIPSS finds applications in various fields, including medicine, optics, tribology, biology, and more [38]. Generally, LIPSS is categorized based on their spatial period and orientation. They are broadly categorized into two main types: low-spatial frequency LIPSS (LSFL) and high-spatial frequency LIPSS (HSFL). Distinguishing between the two, LSFL is characterized by periods larger than half of the laser irradiation wavelength, while HSFL exhibits periods smaller than half of the incident wavelength [39]. Generally, under low fluence conditions, HSFLs are observed, aligned parallel to the polarization of the laser beam. However, as the fluence is increased to a higher regime, LSFL becomes more prominent and exhibits a perpendicular orientation to the laser beam polarization. This transition from HSFL to LSFL occurs as the fluence increases and the number of laser pulses decreases [35, 40]. Moreover, The polarization of the laser beam affects not only the LIPSS orientation but also their periodicity. Figure 7 illustrates the formation of LSFL and HSFL on silicon. Notably, LSFL aligns parallel to the electric field, while HSFL exhibits a perpendicular orientation to the electric field.

Figure 7.

SEM image showing integrated high-spatial frequency LIPSS (HSFL) and low-spatial frequency LIPSS (LSFL) on silicon at a fluence of $0.90J/{\mathit{cm}}^2$ and 20 laser pulses. The 2D-FFT analysis is presented in the top right corner of the image.

The periodicity and orientation of LIPSS are affected by irradiation parameters such as laser wavelength [41], angle of incidence [42], polarization [43], the number of pulses [44], and laser fluence [45], as well as by environmental circumstances like pressure, temperature [46], and by material properties such as surface roughness [47]. Experimental results have shown that the LSFL periodicity is proportional to the laser wavelength but can be further tuned with the angle of incidence at which the laser beam hits the target surface. In semiconductors, the periodicity decreases with increasing fluence, a behavior attributed to Surface Plasmon Polaritons (SPPs) [35]. This is in contrast to metals, where an opposite trend is observed—periodicity increases with rising fluence [39, 45]. The larger periodicity of LIPSS at higher fluence in metals is attributed to the induction of surface plasma waves through the parametric decay of laser light [48]. Given the multitude of applications and widespread interest in LIPSS, it has become crucial to understand and confirm the origin of these micro-nanostructures. The first hypothesis on the LIPSS formation was proposed by Birnbaum [32], who attributed their formation to a diffraction effect. Several experimental and theoretical studies have extensively investigated the formation of LIPSS by varying laser and process parameters [44, 49, 50, 51]. However, LIPSS formation mechanisms are not yet fully understood. Several mechanisms have been discussed in this section to understand the core principle behind the generation of LIPSS.

4.1 The sipe diffraction model

The first theory based on the formation of LIPSS was given by Sipe, and it has been widely accepted for classical low-spatial frequency LIPSS [50]. Based on this model, LIPSS formed because of the interference between the incident laser beam and Scatter electromagnetic wave (SEW). Sipe theory describes how surface roughness alters the electric field intensity distribution of a plane wave incident on a thin surface with a self-edge region, the height of which is much smaller than the incident laser wavelength (Figure 8).

Figure 8.

Schematic representation of laser beam irradiation on a rough surface at an incident angle θ, depicting K_i as the wave-vector component parallel to the surface and Is as the thickness of the rough region. This illustration complements the discussion of laser interaction with rough surfaces in the context of Sipe theory.

In this theoretical framework, an incident either $s$ or $p$ polarized laser on a rough surface of material with a wave vector $K$ at an angle of incidence $\theta$, projecting a component in the horizontal plane $K_i$. Sipe’s theory predicts the possible wave vectors ($k$) of LIPSS, related to their period ($\mathrm{\Lambda }$) through $\mid k\mid =\frac{2\pi }{\mathrm{\Lambda }}$ [52]. The inhomogeneous energy deposition is directly proportional to $\eta \left(k,k_i\right)\cdot \mid b\left(k\right)\mid$, where $\eta \left(k,k_i\right)$ characterizes the efficacy of roughness in contributing to inhomogeneous energy absorption at $K$, and $\mid b\left(k\right)\mid$ represents a measure of surface roughness amplitude at $k$ [52, 53].

The efficacy factor $\eta$ may exhibit sharp peaks at specific $k$ values, allowing evaluation of associated spatial periods $\mathrm{\Lambda }$. For a surface with uniformly distributed roughness, $\mid b\left(k\right)\mid$ varies slowly. The Sipe Theory thus provides a comprehensive understanding of how interference patterns, surface roughness, and laser parameters collectively contribute to the intricate process of LIPSS formation. The sipe model, however, has certain limitations due to its high predictive character on processing features. It is an approximation in which the longitudinal component of the electromagnetic field is treated using the variational principle, while the transverse component is treated using the perturbation series [52]. Over the years, significant advancements have been made in this theory to understand the formation of LIPSS. This enhanced theoretical framework, often referred to as the Sipe-Drude theory, successfully predicted the features of LIPSS based on irradiation parameters (wavelength, angle of incidence, polarization direction, and laser incident wave vector) as well as surface parameters (dielectric permittivity and surface roughness) [47, 54]. However, the Sipe-Drude theory is well explained for LSFL but an alternative mechanism or theory is needed to understand the HSFL formation.

4.1.1 Surface electromagnetic waves (SEWs) and surface plasmon polaritons (SPPs)

The basis of this model lies in the modulation of the electron on the irradiated surface, particularly through the interaction of the incident laser beam with surface-scattered electromagnetic waves (SEW). Due to the incidence of a laser beam on a metallic, slightly rough surface, scattered fields are generated as a result of surface irregularities. The interference between these scattered fields and the incident or refracted field leads to an inhomogeneous intensity distribution above and below the surface. These inhomogeneous intensity distributions increase the roughness, which contributes to an increase in SEW. As a result, regular patterns start forming, driven by the initial random roughness. In the case of metal-dielectric or metal-air interface, the SEW excite collective oscillations of electrons are known as surface plasmons. These surface plasmons are coupled to the incident light and propagate along the surface, as shown in Figure 9. The excitation SSPs involves the periodic modulation of the laser field and subsequent energy deposition in the free electrons [56]. This process heats, melts, or potentially vaporizes the lattice through electron-phonon interaction, subsequently prompting the emergence of LIPSS [56, 57, 58].

Figure 9.

Schematic representation illustrating the intensity distribution of the electromagnetic field components of a surface Plasmon Polariton (SPPs) supported by a metal-dielectric interface [55].

Based on SPPs theory, the periods are expressed as follows [56]:

$$\mathrm{\Lambda }=\frac{\lambda }{\frac{\lambda }{{\lambda }_{\mathrm{spp}}}\pm sin\left(\theta \right)}$$E17

$${\lambda }_{\mathrm{Spp}}=\lambda \times Re\left(\sqrt{\frac{{\epsilon }_{\mathrm{m}}+{\epsilon }_{\mathrm{d}}}{{\epsilon }_{\mathrm{m}}{\epsilon }_{\mathrm{d}}}}\right),$$E18

where ${\lambda }_{\mathrm{SPP}}$ is the Surface Plasmon Polariton (SPP) wavelength, $\theta$ is the angle of incidence, ${\epsilon }_m$ is the dielectric constant of the metal, and ${\epsilon }_d$ is the dielectric constant of the dielectric.

4.2 Self-organization model based on material instability

The foundation of these models rests upon the existing formation theory of ion-beam-induced ripples, which is closely related to laser polarization dependence and ionized kinetic energy distribution [59]. In contrast to previous models, the presented self-organization model places emphasis on the role of hydrodynamics in the formation of LIPSS. Figure 10 depicts LIPSS formation using the interference model and the self-organization model. In the interference model, spatially modulated energy deposition creates an “interference” pattern, resulting in periodic pattern formation. On the other hand, in the self-organization model, the surface experiences a high degree of instability induced by a femtosecond laser beam, leading to self-organized periodic pattern formation during surface relaxation.

Figure 10.

LIPSS formation occurs via two distinct models: (a) the interference model and (b) the self-organization model [60].

The key concept in hydrodynamic theories is the formation of ripples through melting flow, triggered by the irradiation of laser pulses on the sample surface. It is crucial to highlight that each proposed instability mechanism, such as Marangoni instability [61], recoil-force-driven instability [62], Rayleigh-Taylor instability [63], and evaporation-driven instability [60], requires an initial perturbation to act as the seed for the ensuing LIPSS formation. The self-organization model has effectively estimated LIPSS formation, considering interaction times and the number of incident pulses. It has also evaluated the relative influence of input energy on the resulting ripple period.

4.3 Finite difference time domain (FTDT) model

The simulation of light propagation, scattering, and diffraction phenomena can be effectively carried out through the finite difference time domain (FDTD) method by solving Maxwell’s equation [64]. In this context, Skolski et al. proposed a numerical method based on the FDTD technique to qualitatively investigate LIPSS formation on surfaces, considering factors such as roughness and inhomogeneous energy absorption in the irradiated surface [65]. It has been modified further by employing the inter-pulse feedback effect [66]. Following the initial laser pulse, absorbed electromagnetic energy in the surface layer modifies the material, prompting subsequent material removal. After subsequent laser pulses, the newly morphed surface is utilized for further FDTD simulations, resulting in a new absorbed energy profile and further modification of the surface morphology [66]. The FDTD method simulates the periodicity of LIPSS in semiconductors [66], plasmonic materials [67], and metals [67]. Additionally, it provides the theoretical foundation for the formation of HSFL. However, it does not include incubation effects or thermodynamics of molten materials. There are several other theories on the development of LIPSS, such as matter organization theories [53, 56], including second harmonic generation [52], or transient optical coupling [52].

5. Conclusion

The complex phenomena of ultrashort laser ablation involve a multitude of factors, including the spatial distribution of laser energy, absorption dynamics on the irradiated surface, transient changes in optical response, and the subsequent ablation process. Throughout this chapter, we have thoroughly studied these complexities in the context of metals, dielectrics, and semiconductors. Moreover, we also explore various ablation mechanisms specific to different materials and lasers. Additionally, we provided a description of the LIPSS and their classification in LSFL and HSFL according to the spatial period, along with a discussion on the potential mechanism of LIPSS formation. In summary, this chapter illustrates the basic physical phenomena occurring during the laser-matter interaction.