Laser machining fundamentals: micro, nano, atomic and close-to-atomic scales

With the rapid development in advanced industries, such as microelectronics and optics sectors, the functional feature size of devises/components has been decreasing from micro to nanometric, and even ACS for higher performance, smaller volume and lower energy consumption. By this time, a great many quantum structures are proposed, with not only an extreme scale of several or even single atom, but also a nearly ideal lattice structure with no material defect. It is almost no doubt that such structures play critical role in the next generation products, which shows an urgent demand for the ACSM. Laser machining is one of the most important approaches widely used in engineering and scientific research. It is high-efficient and applicable for most kinds of materials. Moreover, the processing scale covers a huge range from millimeters to nanometers, and has already touched the atomic level. Laser–material interaction mechanism, as the foundation of laser machining, determines the machining accuracy and surface quality. It becomes much more sophisticated and dominant with a decrease in processing scale, which is systematically reviewed in this article. In general, the mechanisms of laser-induced material removal are classified into ablation, CE and atomic desorption, with a decrease in the scale from above microns to angstroms. The effects of processing parameters on both fundamental material response and machined surface quality are discussed, as well as theoretical methods to simulate and understand the underlying mechanisms. Examples at nanometric to atomic scale are provided, which demonstrate the capability of laser machining in achieving the ultimate precision and becoming a promising approach to ACSM.


Abbreviations
Vector potential of electromagnetic field AR Aspect ratio c Light speed Ce, C l Specific heat of electron and lattice C 1 Material parameter in equation (2) C 2 Constant in equation (5) C 3 Parameter in equation (6) C 4 -C 6 Phenomenological constants in equation (7)

Introduction
Since being invented in 1960s, laser has been a prominent tool of manufacturing and found wide applications in scientific research and engineering development. In addition to the advantages of simple processing and high efficiency, laser machining is flexible to manipulate materials in both additive and subtractive manners, as well as by modifying physical and chemical properties. It is also an important solution to the workpieces, such as hard and brittle alloys, crystals and ceramics, which are difficult to process using mechanical approaches. In early stage, laser machining, including cutting, drilling, welding, and surface heating is performed at macroscale. With the rapid development in laser source technology, the precision of laser machining has been continuously increasing. In 1983, lens array was fabricated by He-Cd laser on photoresist with the unit width and depth of 20 µm and 4 µm respectively [1], which demonstrated laser can be an effective tool for micro-machining. The fast development of laser micro/nano-machining should be attributed to the invention of ultrafast laser (<10 ps pulse width). Based on the two photopolymerization effect, true three-dimensional manufacturing beyond the diffraction limit has been realized by femtosecond laser. It was first verified by the sculpture of 'micro/nano-bull' with an achievable resolution of 120 nm [2], and structures with greater complexity, such as bichiral plasmonic crystal [3] and magnetically driven micromachine [4], have been realized. Similarly, the lattice structure of inorganic crystals can also be changed by femtosecond pulse and the target structure is obtained after chemical etching [5,6]. Utilizing the highly localized non-linear effect, the feature size can be reduced in laser ablation [7], and micro/nano-structures are fabricated inside transparent materials (e.g. modification the refractive index of waveguide [8], micro channel for biochip [9]). Another kind of process is the formation of surface texture via spontaneous material response to the irradiation. One pioneer research is the 'black silicon', which has low reflectance due to the surface micro cones induced by femtosecond pulse [10], and hierarchical structures covering micro and nanometric scales have been realized on metal and glass surface to modify the optical or wetting property [11,12]. Laser is also capable of inducing periodic surface structures, in which the pattern and spatial frequency can be tuned and are sensitive to material behavior [13]. In addition, efforts have been made to improve the efficiency, flexibility and controllability of the process, such as multi-beam interference fabrication [14], laser field shaping by spatial light modulator [15] and ultrafast imaging technique [16]. Up to now, laser machining using various wavelengths and pulse widths gains many great achievements in the production of micro/nano-structures [17][18][19][20] or surface textures [13,[21][22][23][24], which are critical for optoelectronic devices, functional surfaces and biomedical microrobot [25]. Meanwhile, demands for smaller feature size at ACS are emerging. In nanoelectronic and quantum devices, many functional structures consist of few or even single atomic layer of traditional semiconductors and 2D materials [26][27][28]. It is just the goal of ACSM [29][30][31], which is the fundamentally transformative technology of the new manufacturing paradigm, namely manufacturing III. ACSM aims at achieving atomic precision, atomic scale feature size and material modification, and nearly zero damage on lattice structure, finally leading to the mass production of critical devices and components with functionalities from atomic scale natures of material. There have already been some candidates, such as STM manipulation, atomic force microscopybased electrochemical etching [32], atomic layer deposition, and ALE, but the era of ACSM is still in the infant stage because it is difficult to accommodate the ultimate precision, extreme surface integrity and high efficiency [33]. Therefore, it is necessary to explore novel methods and laser machining is one of the most potential approaches. As will be shown in the following sections, laser machining has been capable of processing the material at the monolayer scale. Compared with other approaches [29], laser machining has almost no limit on workpiece materials, much larger throughput than STM, and could even avoid the issue of subsurface lattice damage occurring in ALE. It is convenient to obtain a high controllability by enhancing the monochromaticity of photons, and avoid the surface pollution during photolithography processes. On the other hand, no matter which scale the process happens at, laser-matter interaction is a critical fundamental issue which directly influences the machining results. This review focuses on the subtractive laser machining, especially the processes during which the material is removed in a definite manner with high controllability rather than spontaneous deformation or chemical modification. The article tries to outline the material removal mechanisms from micro to nanometric and even down to atomic scale, in order to prompt the realization of atomic scale patterns and atomically smooth surface by laser technology.
In general, the photon energy is first absorbed by electrons, then transmitted to lattice atoms. The degree of lattice deformation determines the achievable precision, limit of feature size and surface integrity. The simplest mechanism is thermalinduced material removal, which always happens under the irradiation of large power and long pulse duration (or continuous laser). In metals, countless free electrons are accelerated by the electric field of the laser (inverse bremsstrahlung), while in semiconductors and insulators the free electrons are firstly generated via various types of ionization (avalanche, tunneling, etc). At last, hot and dense plasma is formed, which expands and erupts outwards under the large thermal gradient and stress, accompanied with the occurrence of a plume over the surface. Material removal in this way is usually above sub-micro scale, with obvious influence on the material structure (phase transition, amorphization, etc) due to the violent thermal process. It is apparently not expected for a highprecision machining, and the surface damage is not allowable for advanced optoelectronic devices. The non-thermal process can be realized via CE in laser machining. During the irradiation, atoms are ionized by incident photons and net charge state occurs in the surface layer. Because the distance between atoms is only several angstroms, strong repulsive force would emit the particles near the surface. Such a process happens in a smaller space/time scale, reducing the material removal to nanoscale. However, the recoil action in CE could also destroy the lattice, at least covering several atomic layers. For an ideal atomic scale removal, only the bonds in the topmost layer(s) are broken and nearly no lattice defect is left on the machined surface. The mechanism is based on the excitation and dynamic evolution of electronic state which is highly quantum mechanical, and depends on many factors including band gap, crystal orientation, surface reconstruction, defect and doping. Currently, there are some terminologies describing the laser-induced material removal at atomic scale (desorption, photoexfoliation, photoemission, photoetching, etc) and LID will be adopted in this review. The three processes at various scales mentioned above are schematic illustrated in figure 1. It should be pointed out that this classification is to make the discussion convenient. Although reasonable in most cases, it may still be ambiguous sometime due to the great complexity of the laser-matter interaction. For example, the removal scales by thermal plasma and CE can be similar. The phrase 'thermal effect' should also be carefully considered. Strictly speaking, thermal effect is related to phonons and always exists as long as there is electron-phonon coupling. However, it does not necessarily lead to material removal. From this perspective, thermal effect can occur during atomic layer desorption, and traditional femtosecond laser machining is not a true 'cold process' because it is likely to form hot plasma at the focus center.
In next section, laser machining mechanisms at the various scales are discussed in detail. Among them, material removal at nanometric and atomic scales are emphasized, covering metals, dielectrics and 2D materials. In section 3, specific issues are considered from the material and laser aspects, including electronic excitation, the role of material defect, effects of pulse width/number and reducing the wavelength. Three kinds of numerical methods used in theoretical analysis are introduced in section 4. From continuum equations to molecular dynamics to quantum mechanical model, the simulations make great contribution to revealing the highly dynamic process of laser machining. In section 5, several examples about nanometric/atomic scale structures are provided, which are realized by direct writing, interference irradiation and auxiliary methods. Finally, the contents of this review are summarized in section 6, accompanied with future perspectives on laser machining facing the coming of ACSM era.

Ablation at micro/sub-micro scale
The word 'ablation' is always used to identify the laserinduced material removal dominated by thermal effect. For metals, the photon energy is firstly absorbed by numerous free electrons via inverse bremsstrahlung, then is transferred to lattice via electron-phonon coupling. Under high-intensity or long pulse width irradiation, the surface layer would be melted or even evaporated, termed as phase explosion or explosive boiling [34]. In this situation, the specific enthalpy of evaporation can be used as a criterion for material removal [35]. Another mechanism is the photomechanical spallation for short pulse duration, which is caused by the stress confinement in the shallow surface before the lattice thermal expansion takes place. This process is accompanied by the tensile stress wave and void formation in the subsurface layer [34]. The mechanical-induced removal is further classified into shortand long-term ablation, which are dominated by the electronic pressure relaxation and shock/unloading wave, respectively [36]. Using the sub-picosecond pulse, a high electronic pressure can be sustained in the shallow surface to form a negative pressure region, making it possible to reduce the material removal to tens of nanometers under a moderate fluence (∼20-100 mJ cm −2 ) [37].
For semiconductors and insulators, the first step of the laser impacting on work materials is the photon excitation of valence electrons to conduction band, and the stronger electron-phonon coupling could result in a temperature rise as fast as 10 14 K s −1 [34]. It makes the surface layer plasma-like with the characteristic frequency (ω p ) as [38] where n ex , m e , ε are the number density of excited electrons, electron mass and dielectric constant, respectively. As the excitation increases, this frequency gets close to the laser frequency and violent absorption happens at resonance. Meanwhile, the surface layer would behave like conductors (optical breakdown), where the Drude model has been employed to describe the substantial change of optical properties (e.g. absorption coefficient, reflectivity) [39]. The plasma model can also interpret the formation of laser-induced periodic surface structures when irradiation fluence is just above the ablation threshold. It indicates that the interference between the laser field and surface plasmons is important for the sub-wavelength ripples orthogonal to the polarization direction [39]. In addition, plasma plume over the irradiated region is a typical phenomenon during the ablation, which contains ejected particles having similar kinetic energy and broad angular distribution [40]. The material removal depth (d) can be expressed as below when the fluence (F) is just above the ablation threshold (F th ) [41,42] where α is linear absorption coefficient, A is the Arrhenius parameter and C 1 is material parameter. The second term in equation (2) stands for the contribution of thermal effect to the removal. By optimizing the scan speed, a surface roughness of tens of nanometers can be realized on dielectrics. For multiphoton process, non-linear absorption should be considered which modifies the expression. For example, the depth and radius of the ablation crater formed by two-photon absorption of a Gaussian beam are [43] where α is now the second order absorption coefficient, I is laser intensity, E P is pulse energy, and δ is beam radius.

CE at nanometric scale
Although the phase explosion, photomechanical spallation and plasma models have been extensively investigated and employed to understand laser ablation, both the material removal and surface integrity are difficult to be controlled at nanometric level. The key is to diminish lattice deformation and thermal effect as much as possible, invoking another fundamental process of CE mentioned in the introduction. The atoms are positive-charged temporarily after being ionized by photons, then strong Coulomb repulsion arises due to the small particle distance and the surface layer would be repelled from the substrate. CE happens rapidly (<1 ps) in prior to the electron-lattice coupling, so it is considered as a non-thermal process and an ultrashort pulse (0.1-1 ps) is preferred to avoid the ablation phenomenon under long-time irradiation. Because the surface charge accumulation is crucial, CE is sometimes thought hardly to occur for metals and semiconductors as the ionization could be easily compensated, but there have been opposite evidences supporting its generality [44,45]. Material removal through CE is actually the breaking of atomic bonds by Coulomb force, so the critical charge density determining the electric field intensity and the material bond strength are two fundamental factors. Because the ejected particles are accelerated by electric field normal to the surface, they have a narrow angular distribution, momentums proportional to the charge (momentum scaling, figure 2), and velocities (can be 10 4 m s −1 ) larger than those in the plasma plume, which are remarkable distinctions from ablation [40,46]. As a dominant mechanism of low fluence irradiation, characterization of the ejected particles is always conducted to understand the process. There are two kinds of kinetic energy distributions in the femtosecond infrared laser irradiation of CaF 2 [47]. The fast peak stands for cations ejection via CE, followed by the slow peak which represents the hyperthermal state of ablation plume containing considerable neutral particles and some anions as laser fluence increases. According to the Maxwell-Boltzmann law, the velocity of fast cations and surface temperature are estimated about 10 4 m s −1 and 10 5 K respectively. In detail, electrons are firstly excited via multiphoton absorption, then escape from the surface temporarily. Due to the strong electron-phonon coupling of brittle materials, the holes would not be compensated immediately and the surface becomes positive charged. After an incubation time during which the surface charge and lattice imperfection increase, CE happens and cations are ejected. Under higher fluence, those excited electrons confined in the material begin to heat the surface layer leading to the thermal emission of slow neutral particles, and the anions are considered as a result of capturing the escaping electrons. Successive emission of fast and slow cations (Si + , Si 2+ ) with increasing fluence is also detected above the Si (111) surface irradiated by femtosecond laser, and the thresholds of CE and phase explosion are 1.2 J cm −2 and 3 J cm −2 respectively [48]. (CE and phase explosion have also been termed as gentle and strong ablation, respectively [40]. In this article, CE is not treated as an ablation process to emphasize its non-thermal nature.) The critical fractional charge per atom is estimated about 0.1 to overcome the local mechanical bonding stress and trigger CE, while the precise band structure should have no significant effect because the ejected ions energy can reach 64 eV, much higher than the band gap of typical semiconductors and insulators. Neutral Si particles are observed too [49]. Instead of thermal emission, they come from the fast cations after catching electrons near the surface. With the reduction of laser pulse duration, multiphoton absorption, ionization, and particle emission yield are enhanced. Similar phenomenon also occurs on Fe, where the 'fast peak' disappears as the pulse width increases from 25 fs to 400 fs. As another type of conductor, graphite has distinctive lattice structure that the current flowing between carbon layers is hindered. Therefore, charge accumulation is more prone to happen. The CE of graphite is verified by the emitted cations (C 1 + , C 1 2+ , C 1 3+ ) under gentle fluence (0.13 J cm −2 ), where the fast surface charge/decay time and the lack of thermal plasma confirm the absence of ablation [50].
CE can be formulated through two ways for dielectric materials [51]. The hydrodynamics-based model is suitable for nanosecond pulse, which consists of the continuity equations of electrons and ion cores, two-temperature equations for the charged particle distribution, and Poisson equation for the electric field. For femtosecond pulse, the kinetic model based on the nonequilibrium transport theory, such as Vlasov equation, should be used because the laser-material interaction is faster than thermal relaxation. Considering the ion motion and multiphoton/avalanche ionization of SiO 2 irradiated by 674 nm, 800 fs pulse, the model can give a good prediction for the material removal depth larger than 300 nm, but overestimates the depth at smaller scale. For semiconductors such as Si [44], carrier dynamics should be considered by the drift-diffusion model, and the electron emission is attributed to thermal excitation and photoionization. The theoretical removal depth per pulse fits well with experimental results in a range from several nanometers to microns. The simulation also indicates that the thickness of surface layer with sufficient electric field for CE (2.65 × 10 10 V m −1 ) can be as low as 1.5 nm, which is beneficial for improving the precision of laser machining. For metals, thermionic emission takes part in the build of critical field (1 × 10 10 V m −1 ), and CE is critical for interpreting the experimental data of low material removal (<10 nm) under small fluence (<0.5 J cm −2 ). The emitted electrons, which are simulated using the particle in cell method, can induce an additional outwards pointing electric field preventing the electron flow from inner region to surface layer, then facilitate the charge accumulation [52]. CE is also considered to happen in a so-called 'double electrical layer' region that consists of a positive charged surface layer (∼1 nm) and a subsurface with superdense electron gas (10 23 -10 25 cm −3 ) [53]. In addition, a group of comprehensive models for various kinds of solid are established, in which the critical electric field is derived using the atomic latent heat of sublimation, and the threshold fluence and ion emission yield are formulized. It also reveals that the surface charge increases from conductor (Au) to semiconductor (Si) to insulator (sapphire). Despite the weakest photoelectron emission, dielectric material has the strongest surface electric field [54].

Atomic layer removal and surface atom ejection
Despite the non-thermal feature of CE that is much gentler than ablation, it is difficult to further reduce the minimum material removal below nanoscale. In addition, lattice damage may still be formed via non-thermal manner, such as by the strong Coulomb force. Another issue is that the destructive phase explosion would happen with more and more defects introduced by CE under multi-pulse [40]. For the applications involving strong quantum effect, both material removal and surface integrity should be controlled at atomic scale in order to realize the preferred electronic and optical properties. Therefore, more fundamental and sophisticated process other than ablation and CE is required.
The Si(111)-7 × 7 surface is one representative of LID [55,56]. The most distinctive phenomenon is that the energy distribution of emitted particles is independent of laser parameters. For example, there are always peaks at 0.06 eV and an onset energy of 0.02 eV under the femtosecond/nanosecond pulse at 266-532 nm, as shown in figure 3. Different from the CE and ablation plasma, the ejected Si atoms are mainly in the electronic ground state because no cation signal is detected before the particles are ionized by an extra laser. In addition, the desorption yield has a maximum at 620 nm under the fluence of 150 mJ cm −2 , where the photon energy (2 eV) does not correspond to any spectral line of Si. Therefore, optical absorption associated with bulk electronic transitions is not considered as the reason for the desorption. Instead, laser-induced surface electronic transition should be dominant, and a model of two-hole localization followed by phonon-kick is proposed to interpret the bond breaking. The desorption yield not only depends superlinearly on the fluence (<200 mJ cm −2 ), but also is very sensitive to the site of adatoms. Atoms in the center of the 7 × 7 surface unit have a much larger yield than those at the boundaries (figure 4(a)), and using a femtosecond laser can reduce the fluence by one order of magnitude than using a nanosecond laser. Under the 28 ns laser at 500 nm, the threshold fluence of desorption is estimated about 100 mJ cm −2 and the desorption rate is almost constant [57]. An interesting phenomenon was observed during the irradiation of Si(100) surface using 7 ns laser at 532 nm (figure 4(b)) [58]. After single pulse, about 20% of the measured area is covered by vacancies, and the residual atoms in the top layer remain the dimer reconstruction structure. Although the underlying atomic layer can be seen, the atoms, however, exhibit the bulk lattice arrangement with neither reconstruction nor removal. This is reconfirmed as the pulse number increases to 17 and 37 corresponding to the vacancy occupation (in the topmost layer) of 60% and 90%, respectively. The reason of the high sensitivity to vacancies is that after photoexcitation, the holes diffuse to the surface and are trapped by the vacancies, then multi-hole atoms and anti-bonding state are formed. As a result, the underlying material would be 'protected' before the topmost layer is totally removed which starts from vacancy sites. It provides a possibility to control the surface integrity at atomic scale in ACSM. In the study using a wider wavelength range of 355-800 nm, the removal of dimers on Si(100)-2 × 1 surface increases superlinearly with laser power density and is attributed to the nonlinear localization of the holes which are optically injected in the Si-dimer backbond states [59]. The ultimate limit of LID is the removal of individual atom/cluster without obvious influence on the surrounding lattice structure. Such an extremely process is possible through localized excited state where the localized electrons or holes exist, so is site selective. For insulators such as alkali halides or alkaline earth flourides, the localization can be formed by the coupling of excitons and lattice that results in the self-trapped state. The self-trapping further evolves into neutral halogen vacancy (F center) or interstitial (H center), and finally the bulk defect and surface atom emission [60]. Another interpretation indicates that the exciton consists of a hole in the surface backbond and an electron in the conduction band, and atom removal is attributed to the electron relaxation to the anti-bonding state [61]. For semiconductors such as Si(111)-7 × 7, exciton becomes not dominant at room temperature, so the source of localization state is thought as the wiggle structure of the valence band top and conduction band bottom, and atom emission could be realized without extra defects [62]. The LID of 2D material is also investigated in the recent years. For graphite, this process is observed by time-resolved electron crystallography [63,64]. Under 120 fs pulses at 800 nm, graphite surface is firstly compressed in 0.5-3 ps, then springs back non-thermally in the following 7 ps (figure 5). The carbon layer vibrates along the surface normal direction when the fluence is less than 21 mJ cm −2 , and the sp 3 transient structure occurs as the interlayer distance decreases to 1.9 Å. Under larger laser fluences, the topmost  carbon layer is removed through a group of strong-coupled optical phonons stimulated by the photon excited carriers. Furthermore, an interesting phenomenon is discovered that the threshold fluence dramatically increases with a decrease in the removed layer number as shown in figure 6 [65]. This size effect at atomic scale originates from the dimensional crossover of the specific heat: The flexural mode specific heat gives rise to a threshold strongly dependent on the reciprocal of layer number, when graphite is in 2D form consisting of less than seven layers. In contrast, graphite turns into a 3D material with an increase in thickness (much more than seven layers). The acoustic mode specific heat becomes dominant and the threshold saturates. Based on these characteristic fluence windows, it is therefore possible to obtain a layer number selectivity in the LID of graphite. Experiment indicates that with an increase in fluence, the carbon layers are firstly desorbed as a whole sheet in non-thermal mode, then destroyed into small pieces or atoms in thermal mode. The transition fluence between the two modes is 400 mJ cm −2 for 800 nm femtosecond pulse [66]. For MoS 2 , surface bump occurs before atomic layer removal at sufficient laser power, which is sensitive to the degree of thermal conduction [67]. LID happens at lower power on the freestanding MoS 2 film than one supported by SiO 2 /Si substrate as a heat sink. Detailed analysis reveals an anisotropic behavior that the atomic layer is etched along a zigzag direction terminated by Mo-or S-edge which in turn results in a triangular pattern, and a 2 nm thick amorphous boundary is also observed around the etching zone.
LID of hetero elements from solid surfaces also attracts many research interests. In general, the final atomic removal can be realized by either direct excitation of the adsorbate, or the indirect excitation wherein the substrate is excited in prior. Desorption of H atoms from Si surface under 157 nm laser is an example of direct excitation [68]. The absence of dangling bond pairs (signal of thermal desorption) and the linear relation between the irradiation fluence and dangling bond number density confirm the mechanism of single photon absorption. Atomic removal can occur at a low fluence of 2.8 mJ cm −2 per pulse, which, however, shows a dispersed pattern (figure 7(a)).
In addition, the doping shows a non-negligible effect that positive charging of p-type surface reduces the H emission due to the bonding of photo-ionized H with B atoms. For the Si(111)-Cl system [69], experiment under a wide wavelength range (24.8-248 nm) reveals a threshold photon energy of 17 eV (figure 7(b)), which is just the energy for exciting the Cl 3s state. This can be explained using the Knotek-Feibelman (KF) model: the Cl 3s electron is firstly excited, then the hole left is filled by one electron from Si to Cl bond and another bond electron is emitted (Auger process). This leads to two holes of Si-Cl bonding state and a pair of Si + -Cl + cations. Finally, the Cl + is ejected from the surface via Coulomb repulsion, which has a maximum desorption yield at 22 eV photon energy. The electron in Cl 3p or Si 3s/3p state could also be excited by a photon less than 17 eV, but the energy is not enough to form the two-hole pair in the bonding level so there is no particle emission. Indirect excitation could happen for highenergy photons [70]. In this case, the 2p hole of bulk Si would occur at first, which in turn excites the Cl 3s electron by secondary electron cascade. This indicates a unique desorption mechanism and explains why the kinetic energy distribution of Cl + is independent of photon energy (figure 7(c)). Similar to CE, material is removed by Coulomb force in the KF model. However, it is a much milder process that only the top atomic layers are involved. In the study of Si(111)-H/Cl system [71], it is found that the polyhydrides would decompose to monohydrides under 263 nm, 4.5 ns irradiation, and H atoms emission happens via multiple-vibrational excitation of the substrate rather than the direct excitation of surface states. In contrast, the polychlorides would be removed because the backbond to the substrate is more sensitive to the ultraviolet photon. Other investigation reveals that the Cl atoms first gather together by hopping motion to form SiCl 2-4 composite which is then desorbed from the surface [72], while monochlorides are stable against the irradiation and remain on the surface [73]. The removal rate of Cl-adsorbed Si (111) surface is 3.4 × 10 −8 atoms/photon by using 193 nm, 12 ns pulse, which is faster than the process on bare Si. Besides, the removal rate linearly changes with fluence irrespective of whether Cl-adsorption exists, neither influenced by temperature from ∼20 • C to 1000 • C [62]. Discussions above imply a potential approach to ACSM, named as CALID: first weaken the bonds between the topmost and the second atom layers by surface adsorption, then use a specific photon energy so that only the backbonds of the topmost layer are broken without destroying the subsurface bonding state. Such a process in fact introduces a selectivity or self-limited mechanism which may significantly improve the resolution and controllability of LID.
CALID has attracted research interests from late 1980s. For GaAs(100) surface [74], Cl 2 gas adsorption results in arsenic and gallium chlorides. The arsenic chlorides are volatile to be desorbed, but the gallium chlorides are nonvolatile and passivate the surface. This passivation layer is removed by 193 nm excimer laser, during which a distinctive nature of CALID is shown (figure 8): The etch rate increases with laser fluence and saturates at ∼4.5 Å s −1 under 13-18 mJ cm −2 fluence, 0.5 Hz repetition rate and 5 × 10 −3 Torr Cl 2 pressure. The saturation indicates a complete removal of the chloride layer, and the surface abruptly becomes rough as the fluence excesses 18 mJ cm −2 due to thermal effect. However, the etch rate stays very low (<0.5 Å s −1 ) when Cl 2 pressure is reduced to 1 × 10 −4 Torr even though a much higher repetition rate of 80 Hz is used. In addition, the etch rate would also saturate with an increase in repetition rate, because there is not enough time to form the passivation layer before the next pulse arrives. All these have clearly illustrated the critical role of Cl 2 adsorption, and three chemical reactions are adopted to explain the mechanism. Further investigation [75] using 248 nm laser finds the threshold fluence of 13 mJ cm −2 and a saturation etch rate of 2 Å in each adsorption-removal cycle, which is independent of laser fluence, repetition rate and Cl 2 pressure. It indicates the self-limiting feature of CALID, also termed as 'digital etching', which is promising for ACSM. Assisted with tunable UV laser (198-300 nm) and TOF analysis [76], it is found that the arsenic and gallium chlorides are determined by the surface coverage of Cl 2 and the laser wavelength respectively. As the TOF spectrum shows no obvious dependence on the wavelength, the desorbed species of GaCl and As 2 are considered to be formed via photothermal process. To improve the controllability in atomic layer removal, reducing  (111):Cl surface is apparent when photon energy is larger than 17 eV, where the electrons of adsorbate are directly excited (Reproduced from [69]. © IOP Publishing Ltd. All rights reserved). (c) For photons with larger energy, the kinetic energy distribution of Cl + desorbed from Si(111) to 7 × 7:Cl 2 is independent of laser wavelength, as the bulk Si electrons would be excited before the adsorbate, i.e. indirect excitation (Reprinted from [70], Copyright (1994), with permission from Elsevier). the consumption of chemisorbed Cl is suggested. Similar results are observed for Br 2 adsorption, which has smaller electronegativity than Cl 2 . Meanwhile, a novel method combining CALID and traditional LID is proposed as shown in figure 9 [77]. Firstly, distributed Br islands are adsorbed on the GaAs surface, followed by the removal of molecular As and GaBr 3 converted from GaBr via photon-induced electron excitation. After the CALID, monolayer pits composed of pair vacancies are left on the surface. Then, atom emission happens from the boundaries of the pits by LID, which finally leads to the complete removal of the topmost layer. Desorption yield in this stage is about two orders of magnitude smaller than that in the first stage of CALID, and the crystal anisotropy shows an influence on the pattern of pits evolution. Theoretical analysis indicates that although photochemical mechanism dominates at low laser intensity, the role of photothermal process must be considered with an increase in the intensity even though there is no 'thermal damage' in terms of traditional laser machining. Laser fluence can be increased for a higher efficiency in the LID stage, but it may also induce small defects, with a dimension of 1-4 surface unit cells on the second layer [78]. More details about the halogen-based CALID of GaAs have been reviewed in 1998 [79]. This method is currently investigated in the frame of quantum theory, and the calculation shows that the desorption probability would saturate within hundreds of femtoseconds after excitation and has a superlinear dependence on the lifetime of excited states [80]. Experimental investigation has also been conducted on diamond (001) surface terminated by oxygen atoms [81]. After 4 min exposure to 266 nm, 5 ns laser with the fluence of 10 mJ cm −2 , material removal depth about only one lattice constant (0.357 nm) is achieved. It should be noticed that the photon energy (4.7 eV) is less than the band gap of bare diamond (5.5 eV), so no material would be removed without chemical adsorption. It should be pointed out that CALID aims at modifying the bonding state directly at ACS, which is different from traditional chemical assisted laser ablation. For example, Cl 2 atmosphere has been used to react with Si wafer to form SiCl 2 and SiCl 4 gas [82]. The role of laser is heating the surface to near-melting or melting temperature for chemical reaction, rather than cutting the backbonds of the adsorbed layer.
Features of the three laser machining mechanisms at various scales are summarized in table 1.

Electronic excitation
Electronic excitation is the first step of all kinds of laser processing discussed above, and becomes more and more critical as the material removal decreases to atomic scale. In general, numerous free electrons in conductors can be excited via inverse bremsstrahlung in a skin layer of ∼10 nm [54], and inter-band transition is necessary for semiconductors and insulators. Currently, micro/nano manufacturing by femtosecond laser utilizes multiphoton absorption effect to achieve small feature size (down to 10 nm), where the laser wavelength usually lies in the visible to near-infrared range. Quantum theory indicates that the possibility of inter-band transition becomes smaller with an increase in the photon number required, so it is necessary to improve the (instantaneous) power by shortening the pulse width. The Keldysh parameter (γ) is always used to characterize the excitation induced by ultra-short pulse [83] where ω, U I , E are the laser frequency, ionization potential, and peak electric field strength, respectively. If γ is much larger than one and laser intensity exceeds 10 13 W cm −2 , multiphoton absorption would occur; if γ is much smaller than one and the intensity exceeds 10 15 W cm −2 , tunnel ionization would be dominant in which the atomic potential is heavily distorted by the strong electric field so that electron tunneling can happen [84]. For multiphoton absorption, the average absorbed energy per excited electron has a linear relationship to the Keldysh parameter and is proportional to the power of laser intensity [84]. In addition, more photons than those for inter-band transition could be absorbed, which gives extra energy to the excited electrons and is revealed by the characteristic peaks of energy distribution in conduction band. Those peaks disappear with an increase in laser intensity when tunnel ionization arises [85]. As an important plasma parameter, the electron relaxation time, which influences energy transport and dielectric function, is inversely proportional to the electron density (<10 21 cm −3 ), and the decay time is estimated to be tens of femtoseconds [86]. The multiphoton excitation is also determinant in the formation and accumulation of surface defects, which are critical for atom emission by subgap photons. Avalanche ionization (or impact ionization) is another approach during which the electrons in conduction band collide with those in valance band via inverse bremsstrahlung and free carriers increase exponentially. This requires a longer pulse width (picosecond) and could damage the lattice integrity. When large number of free carriers are formed, collective plasma oscillation happens near the surface, and once the optical breakdown (see section 2.1) occurs, energy absorption is enhanced abruptly accompanied with a broadening of conduction band occupation and a phase difference between the total electric field and laser field [38]. Although optical breakdown has been employed as a criterion of ablation of dielectric material [87], it is difficult to expect the atomic layer removal via such an extensive excitation, so optical breakdown should be avoided in material removal at ACS which in fact could serve as a restraint condition of laser parameters.

The role of material defect
For crystalline solids, material defect can be generally considered as the imperfect atom arrangements that have apparent deviation from the ideal lattice structure (void, dislocation, grain/phase boundary, surface reconstruction, atomic layer step, etc). It influences electronic state (defect level and cascade excitation) and plays important roles in material removal and surface integrity. A typical example of micro laser processing is the reduction of threshold fluence. For example, the grain boundaries can prompt the melting of polycrystals although the irradiation makes no phase change in its single crystal form [88]. At small scale, defect can reduce bond strength, serve as localization site, improve cascade excitation and reduce the possibility of electron tunneling back to the valance band. As a result, those atoms near defects are more prone to be removed, and defect type influences the threshold fluence [61].
For insulators with large band gap, electronic excitation induces tight binding exciton that localizes at atom site, causes lattice distorsion, and finally forms the self-trapping state [89]. This enhances the absorption and would lead to permanent defect in picoseconds [34]. For example, the F/F + center (oxygen vacancy) of MgO induces Mg + emission below the threshold of ablation, and its photoionization is decisive to CE [90]. It should be noted that these microscopic defects are formed during polishing, so the result of the previous finishing still has significant influence on the atomic process even though an atomically flat surface can be obtained. Selftrapping becomes difficult for semiconductors due to the weak electron-lattice coupling, so the pre-existing defects enhance the atom emission. The atom removal rate near vacancies on the Si(111)-7 × 7 surface is two orders of magnitude higher than that of defect-free surface [62]. Another illustration is the LID of GaAs(110) surface with defects after electron beam irradiation [91]. Atomic layer removal starts from the defect sites and the removal rate depends on the pit edge length and defect level. Furthermore, no photo-induced pit occurs on the pristine surface without defects. Noting the laser wavelength (539 nm, 2.3 eV) and band gap (1.42 eV), this means the atom emission is not solely determined by the single photon energy although it can be large enough to stimulate inter-band transition. On the other hand, defects determine the ablation threshold and nonlinear yield-fluence dependence when the photon energy is less than the band gap, since the free electrons generated below the threshold fluence via multiphoton absorption are not enough for surface melting unless an ultrashort pulse (∼10 fs) is used. The electron-hole pairs at defect sites are also the origin of particle emission in the early stage of ablation [61]. In the infrared (1064 nm, 1.16 eV) nanosecond laser irradiation on large band gap crystal (NaNO 3 , 10 eV band gap) [92], the highly nonlinear emission of Na + and electrons is caused by the multiphoton process at specific defect sites where the energy of Na + (2-5 eV) can be much higher than the photon energy. The number of emitted ions (N em : /cm 2 pulse) is formulated as [92] N em = C 2 n df F β (5) where n df , β and C 2 are the surface defect density, photon number for ion emission at defect, and a constant, respectively. Defects can also be generated through overdense plasma (>10 22 cm −3 ) as electrons move away from holes, which builds up surface charge and breaks the softened chemical bonds [50]. Finally, there should be a critical density for specific defect type, above which is not preferred for ACSM because the energy transported from electron to lattice may be excessively enhanced by defects [40] and severe subsurface deformation may occur.

Short wavelength
Photon energy significantly influences the electronic excitation process. As the wavelength decreases, valance electrons would be excited by single photon, which does not require a large peak power as in the multiphoton excitation (infrared femtosecond laser) [62]. Therefore, the risk of thermal damage could be reduced, and CE or atom emission becomes possible for longer (nanosecond) pulse width [54]. For example, the decline of Na + /electron emission under infrared laser discussed above [92] can be re-enhanced by ultraviolet photons (248 nm, 30 ns). For such material with large band gap, the stronger the electron trapping, the more rapid the lattice thermal spike [46], so reducing laser power is more critical to improving surface quality. The LID yield of Si is lower when the wavelength changes from 532 nm to 266 nm, which may be caused by the weaker optical absorption or other deexcitation processes [55] and implies a merit of reducing the minimum material removal. Calculations show that the continued ionization under low fluence 193 nm irradiation on Si induces surface charge accumulation and higher hole density than using an 800 nm femtosecond pulse. The theoretical range of surface charging is 5-6 atomic layers, within which the CE is confined to only the topmost zone of 0.4 nm thickness [54]. Short wavelength is able to depress the thermal effect in the large fluence ablation process as well. For the irradiation of 157 nm, 20 ns laser on GaN, a Ga-rich layer will be formed and, due to its restriction in thermal diffusion, a surface roughness of ∼4 nm Ra could be achieved [42]. In contrast, the surface becomes rougher (Root mean square roughness: 15 nm) using a 248 nm, 20 ns laser, attributed to the nonuniform covering of Ga droplets [93]. To further reduce the roughness below 5 nm Ra, the fluence has to be improved, which is a particular phenomenon of GaN [94]. Furthermore, multiwavelength method is developed to improve the surface quality, wherein shorter wavelengths are employed to ionize the atoms then the ionized layer is removed by longer wavelength photons [95,96]. It is considered that the interband excitation is not enough for bond breakage if the photon energy is less than the sum of band gap and electron affinity energy. In this case, bond breakage (material removal) has to be realized via cascade excitation of localized electron states, which emits phonons during the relaxation to the conduction band bottom and causes thermal effect. With the assistance of higher energy photons, such a process can be depressed because the ionized layer has a stronger absorption than the substrate. As a result, the machined surface becomes smoother and the edge wall becomes sharper, as shown in figure 10.
Raman and fluorescence spectrums also indicate a reduction in the lattice damage. Machining of GaN using 157-248 nm double wavelengths shows an etching rate between the rates by using only single wavelength, and the side-wall angle of the etched structure can be controlled by adjusting the incidence angle of the laser beam [97]. EUV light (EUV) or soft x-ray is another representative of short wavelength irradiation that covers a range from 5 nm to 80 nm. Because the photon energy is much larger than the bonding energy of valence or even core electrons, strong absorption occurs in a shallow surface layer for almost all kinds of materials. This leads to a dramatic decrease in the ablation threshold of dielectrics, which can be two orders of magnitude less than that at infrared wavelengths. For example, the threshold of LiF is 35 J cm −2 under the irradiation of 1053 nm laser with 1 ns pulse width, which decreases to 10.2 (single shot) or 5 (three shots) J cm −2 after the wavelength and pulse width are reduced to 13.9 nm and 7 ps respectively. The ablation depth of tens of nanometers can be realized and the absorption length is estimated about 28 nm [98]. The threshold fluences of LiF and CaF 2 decrease from 20 to 40 J cm −2 under nanosecond 248 nm laser to 0.11 and 0.06 J cm −2 under 1.7 ns, 46.9 nm pulses. Dependence of the ablation rate on the fluence exhibits as equation (2) indicates without the thermal term, which means an effective absorption length as small as 14-20 nm [99]. For femtosecond pulse, a 'spallative ablation' process based on thermo-mechanical stress is proposed, wherein the surface would be changed to a two-temperature warm dense matter by the ultrashort pulse then negative stress region and material removal would occur [100]. Theoretical calculation on LiF indicates the occurrence of negative stress 10 nm under the surface for the near threshold ablation (61.5 nm, 300 fs, ∼10 mJ cm −2 ), which is in good accordance with the experimental ablation depth of 10-15 nm. For larger fluence, the negative stress comes later and moves deeper into the subsurface, and material removal is transformed from mechanical to thermal manner. It has been proved in the early 2000s that high-quality nanometric pattern can be achieved on inorganic crystals via EUV direct writing with mask ( figure 11). There is a linear relation between the shot number and ablation depth (0-2 µm), and machined surface roughness can reach 10 nm [101]. Monitor of the dynamic process by the pump-probe technique [102] reveals a rapid increase in the reflectivity of Si under 32.5 nm, 25 fs pulses. It happens in 10 ps and is caused by the nonthermal melting via electronically induced phase transition. In the following nanoseconds, solidification begins at the boundary of the irradiated zone, and circular patterns occur in the central area by the large pressure gradient as the fluence increases ( figure 12(a)). A most difference between the GaAs surfaces irradiated by optical and EUV laser is also observed ( figure 12(b)). For the optical wavelength, the peak power density at the beam center stimulates dense plasma and triggers optical breakdown, which in turn leads to the strong absorption, reduces the energy deposit depth, and finally forms a bulge at the central zone. It is also an evidence of thermal induced ablation for the heat transported to the workpiece abruptly drops due to the strong absorption by plasma plume over the solid surface. This does not occur for EUV laser because the great photon energy maintains the electronic excitation and transition from solid to plasma state. Measurement on Si indicates a spherical profile of the plasma front emitted via thermal ablation, while it changes to a planar shape for the EUV irradiation. The reason is considered as that the plasma formed by EUV laser is denser, colder and confined to a shallower zone than by longer wavelength laser, which results in the convergent emission [103]. By contrast, the reduction in ablation threshold in metals is not as obvious as that in dielectrics when the wavelength decreases. For example, the threshold of Au decreases from 50 mJ cm −2 for visible pulse to 20 mJ cm −2 for 13.9 nm pulse, and the attenuation distance has no significant change. The reason is considered as the numerous free electrons in metals which make the electronic pressure dominant [104]. The influence of EUV light on organic materials is also much concerned in photolithography. Study on the 1.2 ns, 46.9 nm irradiation on PMMA [105] indicates that only one EUV photon could induce material damage without threshold fluence. As the wavelength decreases from UV to EUV band, both the material removal rate and attenuation distance are reduced nearly one order of magnitude. Besides, the strong influence of pulse width from UV to infrared laser is not found for EUV irradiation, and the low removal rate seems to imply the failure of the model based on linear absorption coefficient [106].

Effect of pulse width and pulse number
It is well known that reducing the pulse width is beneficial for achieving smaller feature size and better surface quality. For dielectrics, the acoustics relaxation time is about 10 ps, so thermal effect would not be obvious when the pulse width Figure 11. Nanometric pattern on silica machined by 10 nm EUV light (Reproduced from [101]. © IOP Publishing Ltd. All rights reserved).
is less than that typical time and would be dominant for nanosecond pulse [104]. The x-ray photoelectron spectroscopy analysis on GaN [107] indicates that the Ga-rich layer formed by thermal decomposition during 248 nm, 30 ns laser irradiation disappears after using 150 fs pulses, even though the wavelength increases to 790 nm. A removal rate as small as 5 nm/pulse can be obtained when the threshold is down to 0.1 J cm −2 .
Although it is convenient to understand the laser-matter interaction by single pulse irradiation, multi-pulse is actually widely used in practice to enhance the efficiency. One effect of multi-pulse processing is that the threshold fluence would be reduced because defects are introduced by the front pulses which makes electronic excitation easier. This can be formulated as [108] F th-m = F th-s N C3−1 p (6) where the subscript 'th-m' and 'th-s' stand for the threshold fluence of multi-and single pulse respectively, N p is the pulse number, and C 3 is 1 for single shot. On the other hand, pulse train can achieve smaller ablation depth when the total fluence keeps constant [87]. Calculation on fused silica using plasma model shows that the ablation threshold increases with the number and separation of the pulses (780 nm, 50 fs) in a train, and the spacing and height of sub-wavelength rippled structure exhibit a decreasing tendency [39]. A uniform ablation shape and surface ripples can be expected when low fluence trains containing two pulses with the same energy are employed. Similar tendency also occurs on diamond and the reason is attributed to the reduction in the number of excited electrons and the average energy absorbed by each of them [109]. Detailed experiment on Si reveals that the first infrared femtosecond pulse induces the emission of monovalence ions and a liquid layer, then high-valence ions and material removal occur during following pulses. Using a separation of 22 ps, a smoother machined surface is realized by double-pulse with the total fluence constant (figure 13) [110]. This division of energy into each pulse not only increases the controllability of material removal, but also gets a convergent ablation depth with an increase in fluence and reduces the damage size, which is preferred for high-precision machining (especially for the materials having fast electron trapping) [46]. The threshold fluence of oxides under single pulse shot has been described as a function of band gap (E g ) and pulse width (τ ) [111] F th = (C 4 + C 5 E g )τ C 6 (7) where C 4 , C 5 and C 6 are phenomenological constants. However, such a dependence on the band gap does not hold for multi-pulse threshold, implying a distinctive fatigue mechanism. Experiment on In-doped GaN shows an obvious change in the machined surface morphology when the photon number for inter-band excitation decreases from 3 to 2. Surface stress and fracture after multi-shot are alleviated when the wavelength is reduced from 1030 nm to 343 nm. It should be noticed that all those aspects mentioned above influence the laser machining at micro and nanometric scale. However, the first two issues appear to be more crucial for the process at ACS. Data from literatures indicates the atom desorption does not apparently depend on the wavelength and pulse width. For example, LID could happen under the irradiation of 160-800 nm, 100 fs-30 ns pulses, and this range should be larger as believed.

Simulation approaches
There are three approaches mainly used to simulate laser processing. The first is solving a group of differential equations accompanied with the models of photoelectric properties of material. Two of the most important formulas are named as TTM. The 'two-temperature' refers to the fact that the laser pulse energy is rapidly absorbed by electrons at first then transported to lattice, resulting in a temperature difference between them. For metals, the electron-lattice relaxation time is 10-100 ps, which is much longer than that for electron-electron relaxation. In a time-scale of ∼100 fs, electrons, rather than lattice, dominate the heat conduction [54]. The two coupled heat conduction equations of TTM are [35] where C, K, G, S are specific heat, thermal conductivity, electron-lattice coupling constant, thermal source term of laser energy deposition, and the subscript 'e' and 'l' stands for electron and lattice respectively. Generally, most of these parameters vary with temperature and may have significant influence on the simulation result. For example, using a temperature-dependent electron-lattice coupling constant is important for low fluence irradiation, where the linear relationship between ablation depth and fluence would change to a logarithmic type [35]. When TTM is applied to semiconductors and dielectrics, more mechanisms should be included in the model, such as single-/multi-photon excitation and free electron density [112]. While for intensive excitation, metals, semiconductors and dielectrics are considered to have similar plasma behaviors, so it is possible to describe the carrier dynamics by a uniform model. In addition to TTM, other equations are necessary which include: continuity equation, Figure 13. Machined surface of Si by single and double-pulse irradiation (800 nm, 180 fs) (Reprinted from [110], with the permission of AIP Publishing). current density equation for the drift and diffusion of carriers, and Poisson equation to solve the electric field. Along with the Fowler-DuBridge theory of electron photoemission and a precise formula of complex dielectric function, such a sophisticated model is built to investigate the carrier mobility, charge redistribution, surface electric field and effect of process parameters [54]. TTM can also be combined with the equations for ionization degree and fluid dynamics of material particle to calculate the mechanical stress [100]. It is natural that a large number of material parameters would be required as the number of equations involved increases. In addition, there exists argument about the validity of electron temperature, and TTM should be safely used at least for a picosecond pulse which is longer than electron relaxation but not enough for lattice evolution [113].
As the scale of process decreases to nanometric level, the continuity of material becomes unreasonable and microscopic evolution of the lattice is not able to be studied via differential equations. Then, one can discretize the material into atoms, and MD-TTM is a widely used method. In MD-TTM, the first equation for electrons in equation (8) is solved by a finite difference grid, while the lattice temperature is directly obtained from atomic velocities. Energy transferred from electrons to lattice is accounted via modifying the Newton's equation of atoms, i.e. using the inhomogeneous Langevin thermostat [114] and electronic pressure [115]. Efforts have been made to improve the accuracy and efficiency of the simulation. For example, a dynamic pressure transmitting boundary condition can be applied to the bottom of material to eliminate the artificial reflection of elastic wave [116]. Thermal excitation of electrons below the Fermi level is considered to make the electron-lattice coupling constant more accurate [117]. Sinusoidal thermal source and surface reflection are considered to reflect the non-uniform energy distribution of laser beam [118]. Multiscale electron grid and atomic-continuum coupled description of the lattice are also employed to speed up the calculation [116]. For metals irradiated by femtosecond to picosecond laser at the fluence of tens to hundreds of mJ cm −2 , MD-TTM has successfully revealed the formation of void in the subsurface and the ablation when subsequent pulses arrive, as well as surface bulge deformation ( figure 14). Different from mechanical processes, electronic state experiences remarkable changes that influence atomic bond, so there are also some studies on modifying the empirical potential function. An electronic temperature dependent potential is developed to investigate the effect of electron heating on the lattice physical properties [36] and electronic pressure induced material removal [104]. For short wavelength laser, the attraction term in the potential is removed according to the degree of ionization. Differences between the material removal dominated by thermal and non-thermal processes are clearly revealed, and a potential of atomic layer removal with high surface integrity by large photon energy is predicted [119].
Because the laser is imposed only by a heat source term and the potential function is highly empirical, MD-TTM will be infeasible if we focus on the processes at ACS. Instead, TDDFT is widely used to simulate the laser-material interaction based on quantum mechanics. To evaluate the eigenvalues and eigenstates of a system, the time-dependent Kohn-Sham equation needs to be solved [84] iℏ (9) where the first term in the Hamiltonian contains the vector potential of electromagnetic field (A) and electron momentum (p), and the remains are the interactions between electrons (V e-e ), electron and ion core (V e-i ), and the exchangecorrelation energy (V xc ). Evolution of the state at any time is accomplished by constructing the propagator (U) which has the form as below [84] ψ(r, Strictly speaking, TDDFT is a semi-quantum or semiclassical method because only the material is quantized, and the spatial fluctuation of the laser field is always neglected for the wavelength considered here is much larger than the model size. Limited by the computation efficiency, the pulse width for TDDFT simulation always lies in the range of tens of femtoseconds to attoseconds. It has been used to calculate the dielectric function, number and energy of electron excitation, evolution of density of state, and charge distribution during the laser-matter interaction. As shown in figure 15, a movement of Si electrons (virtual excitation) occurs when the electric field of a 16 fs pulse reaches its maximum. As the photon energy is just higher than the band gap, electronhole excitation finally happens after the pulse, indicated by a decrease in the electron density between Si atoms and the density increase away from bond region [120]. In the study of multiphoton and tunnel ionization of diamond under high peak intensity up to 10 15 W cm −2 [38,84], the results show that the phase difference between laser field and total field, a signal of optical breakdown, occurs earlier for larger laser intensity. The plasma in conduction band can oscillate at a frequency higher than the laser frequency even after the pulse, so shorter wavelength light could be emitted. Based on the number of excited electrons under different intensities, the cross section of multiphoton absorption can be obtained [121]. Cohesive energy is selected as another criterion for laser-induced damage when the average energy absorbed by each atom exceeds it. It is also found that the absorbed energy is influenced by laser intensity, rather than pulse duration, while the irradiation is sustained longer than 2 fs [122], which implies controlling the laser power may be more important in the ACSM using femtosecond laser. In case of multi-pulse, simulation shows that both a large pulse separation and unequal pulse energy can increase excited electrons and excitation energy [109]. Energy desorption can also be enhanced by using dual-color pulses simultaneously. Different from the discussion in section 3.3 (multiwavelength machining) where both photon energies are larger than band gap, here one of them can be less than band gap and the longer this wavelength, the more significant the effect [123]. The calculation shows that electron dynamics in the valence band driven by the small energy photon plays a critical role, and more carrier generation, instead of more energy absorbed by each carrier, leads to an increase in energy desorption. Keeping the total pulse energy constant, the enhancement reaches a maximum when two color components are roughly equally mixed. For the CALID process of Oterminated diamond, TDDFT reveals that carbon atom emission is realized via the excitation of surface carbonyl into a triply bonded CO like state, accompanied by the scission of C-C backbond [81]. Large laser intensity and short wavelength facilitate the desorption of Cl-adsorbed Si atoms on the top layer, on which the force would oscillate rapidly then become repulsive about several nano-newtons [124]. In addition, the energy barrier for desorption can be effectively reduced from 6.2 eV to 2.5 eV after chlorination of Si [125]. Currently, the ion cores are fixed in many studies and bulk model with periodic boundary condition in all directions is applied. This is due to the heavy computing burden of TDDFT making a direct observation of material removal from surface difficult. However, a full dynamic simulation, where the motions of both electrons and ion cores are considered, becomes possible for ACSM, and there have been reports on the atomic layer removal of 2D-material and atom emission of molecules. For example, single carbon layer LID of graphite by femtosecond infrared laser is observed, where the velocity of the removed layer can reach kilometers per second [126]. Rather than photoionization or plasma process, the mechanism is that the surface electrons are heated and spilt out, which increases the hole and Coulomb repulsion in the topmost layer. Then, atomic layer desorption happens before the expanded electron gas reheats the lattice. Using a laser resonant with the out-of-surface plane optical phonon mode, an 11.3% transient interlayer compression of hexagonal BN is observed. The excited phonon mode invokes a dipole-dipole attraction between atomic layers, and the duration of lattice contraction is at least 1 ps [127]. For metal Cu(111) surface irradiated by 800 nm, 30-50 fs pulse, the simulation shows a threshold fluence between 0.1 and 0.2 J cm −2 according to the movement of lattice atoms [128]. This result is dependent on the polarization direction. When the electric field changes from parallel to normal to the surface, no material removal occurs even the fluence increases higher than 1 J cm −2 . In addition, the Ni(111) surface, which has higher absorption coefficient but smaller thermal expansion coefficient than Cu, undergoes larger volume expansion. This reflects the fact that optical properties are more critical at small time scale, during which thermal effect is less dominant. Full dynamic simulation also reveals a mechanism of self-amplified local instability for nonthermal melting in semiconductors [129]: Electron-hole pairs are firstly excited by photons. Free energy increases with antibonding electrons, and there is a tendency of bond elongation to reduce the energy of anti-bonding state. If the carriers uniformly distribute in the lattice, the net forces on atoms are zero. However, once the small vibration of ion cores makes some bonds longer, the anti-bonding level would become lower which in turn traps more electron-hole pairs locally and leads to a non-zero net force on the atoms. As a result, bond elongation is prompted and self-amplified. Because the local density of carriers is easy to exceed the threshold of phonon softening, extensive thermal process would not happen. In addition, the larger the photon energy, the higher level the electrons are excited to, where the difference between bonding and antibonding levels becomes weaker. Therefore, nonthermal melting happens faster for longer wavelength, which again implies the merit of using a short wavelength laser to improve the machined surface quality.

Nanoscale structures
Laser fabrication of micro/nano structures has already been systematically reviewed by literatures, which cover a number of typical applications, such as improving interfacial adhesion for microelectronic device packages [20], bioinspired surface for superhydrophobic, structural color, oil-water separation [13], and textures on electrode to enhance battery performance [21]. The aim of this section is presenting an intuitive cognition about the capability of laser machining by several typical examples, especially those with small size and high precision. Large-scale nanostructure arrays are always required to optimize the surface functionality, e.g. to enhance the light output of light-emitting diodes. Compared with photolithography or electron beam lithography, laser direct writing and interference irradiation have higher efficiency because of the maskless characteristic and simpler procedure [14]. The minimum feature size and period are determined by the superresolution effect and half the laser wavelength, respectively. For example, nano-holes, nano-grooves and grating structure are fabricated on GaAs by direct writing [130]. By reducing the pulse width and fluence, the groove width reaches nearly 1/10 of the focused laser spot diameter ( figure 16(a)). Coherent beams of 266 nm, 10 ns pulse at 10 Hz repetition rate have been used to fabricate the nano-hole array on GaN epitaxial layer ( figure 16(b)), and an exposure area of 0.78 cm 2 is realized via expanding the laser beam diameter to 10 mm. It achieves a 20% enhancement in the output power without damaging the electrical properties of the electrodes [131]. By increasing the angle spanned by the interfering beams, the array period can be reduced and a higher output can be expected [132]. Onedimensional grating structure can also be fabricated via surface plasmon polaritons, which is a self-organized process and possible to break the diffraction limit. In a 'two-step' method [133], single intense femtosecond pulse first induces interference pattern with size of several hundred nanometers, then the period is downsized by ∼80% by multiple shots of lower fluence at second step. Using this method, 50 nm period is realized by 266 nm, 300 fs laser.
As the critical wavelength for the most advanced photolithography technology, coherent and incoherent EUV light has also been employed as a tool for subtractive machining. Despite the advantage of the short wavelength in reducing thermal effect and feature size, it is impossible to use conventional lens to shape the beam due to the strong absorption, and reflective mirrors have to be fabricated with ultimate accuracy and surface quality. Another approach is to use transmission diffractive elements. For example, the Fresnel zone plate is employed to focus the 46.9 nm laser and make nano-holes on PMMA [134]. Thermal effect may happen because the hole depth could be much larger than the attenuation length (19 nm) at high fluences. By placing the workpiece 7 µm away from the third diffraction-order focal plane, smooth hole with 82 nm diameter and 8 nm depth is formed ( figure 17). It indicates that attenuation medium and reducing the outer band width of the Fresnel plate can further minimize the hole size. This method is also applicable to machining nano-slots by moving the sample stage [135]. Periodic surface structures would occur when mask grid is placed in front of the material. Instead of the capillary wave, melting, and interference between incident and reflected light, the reason is considered as the diffraction at the edges of mask [136]. These structures are difficult to erase under low fluence, but disappear at high fluence when  [130]. Diameter of the focused spot is 270-304 nm, and a groove width of 32 nm is realized (Reprinted from [130], Copyright (2018), with permission from Elsevier). (b) Nano-holes array on GaN layer fabricated by three-beam interference irradiation [131]. The periodicity is 1 µm (Reprinted from [131], with the permission of AIP Publishing). ablation happens [137]. They are also influenced by the distance between the mask grid and sample surface, and are sensitive to material type [138].
For those materials resisting wet chemical etching, photons with energy higher than band gap are introduced to assist the process. The photoexcited holes would diffuse to surface then trigger chemical reactions such as oxidization and etching process, and selectivity can be introduced by adjusting the wavelength. This method has been used to polish the heavily doped GaN to achieve a subnanometric roughness [139]. On the other hand, a liquid environment can enhance the aspect ratio of nano-hole. With an increase in material removal, the surface moves out of the zone where the laser fluence is higher than the threshold, so the process is ceased and the aspect ratio would not change. Dealing with this intrinsic issue of focused laser machining, a medium with larger refractivity (n) than air can be placed over the workpiece surface, in order to enhance the aspect ratio (AR) according to the following expression [140] AR = (11) where 2r 0 is the spot size at focus and I 0 is the intensity at the beam center. Chemical solution, such as HCl, could remove the ablation debris in time as well, so that the crater shape is improved ( figure 18). This so-called 'wet chemical assisted' approach has a lower threshold fluence than that of traditional process in air. More interestingly, the removal depth becomes saturated with the increase in pulse energy, which makes the crater bottom flat and is possible to precisely control the machined surface quality [141]. As the chemical reaction only happens between the solution and debris, the substrate where material composition has not been changed by the laser beam would not be etched, and this method is also capable of fabricating microchannels passing through subsurface [142].

ACS structures
As early as 1990s, atomic scale manipulation has been considered as a powerful tool for developing nanoelectronic devices [60]. A nanometric or even atomic surface integrity is always required for electronic and optoelectronic devices, in order to reduce the scattering of carriers or photons and the recombination at surface. High-quality structures at ACS are more crucial for quantum devices. For example, nanopatterned substrates with depth of several or only single atomic layer are important template for the growth of quantum dots. An ordered pattern is necessary to fabricate single-photon emitters, nano-photonic waveguides and quantum computing devices. Recently, progress has been made on InAs/GaAs system [143]. As shown in figure 19(a), monolayer InAs is first deposited on the epitaxial GaAs(001) surface. Driven by the inter-diffusion of In and Ga atoms, an InGaAs mixing wetting layer is formed in which the threshold of LID is lower than that of the GaAs substrate. Under the irradiation of 405 nm, 10 ns pulses, In atoms are preferentially desorbed with vacancies left on the surface, which in turn triggers atom emission around these vacancies. By controlling the fluence in the range of 110-125 mJ cm −2 , atomic removal depth of 3-6 Å and micro/nano patterns are successfully achieved via laser direct writing. Moreover, it has been demonstrated that periodic nano-island can be formed via interference irradiation which is much more efficient than direct writing, and the randomness of quantum dots distribution is significantly reduced. Because the laser source is integrated into the molecular beam epitaxy system, the ultrahigh vacuum ensures a very clean surface during the whole process. Further investigation shows that the quantum dots can be completely erased by 355 nm, 10 ns and 10 mJ single pulse, without damaging the underlying GaAs substrate ( figure 19(b)), and there is no deterioration in the optical quality of subsequent quantum dots regrowth [144]. To prevent the diffusion of InAs nano-island which blurs the GaAs atomic layer pattern template, the temperature should be elevated to 525 • C during the LID. These may be a prototype of editing the 'ACS code'.
Layer-by-layer removal seems to be more popular for 2D materials. For example, mechanical exfoliation is a widely used approach to obtaining graphene. Due to the lack of efficiency and resolution, as well as the glue pollution, LID has become a promising method. Irradiated by a 532 nm, 7 ns laser under the fluence of 5 J cm −2 , ten carbon layers are removed from the bulk graphite [145]. The removal of graphene can be accurately controlled at only one carbon layer with the help of a FWM system [146]. Such an atomic precision is based on the linear dependence of graphene thickness on the FWM signal intensity as shown in figure 20(a). In addition to LID, the functions of both the in-situ monitoring and assessment of the layer number are integrated into the FWM system. Nano-patterns of single atomic layer are also critical for ultra-compact optics with integrated functionalities. One typical example is the laser direct writing of monolayer TMDs to form ultrathin flat lens. Using 780 nm, 80 fs laser, concentric circular grooves are machined on monolayer MoS 2 deposited on ZnO/Si substrate (figure 20(b)) [147]. Such an Figure 19. Atomic layer step patterns on InAs/GaAs. (a) Schematic illustration of the principle and the machined surface. The white spots are quantum dots growing on a template with periodic atomic steps fabricated by interference irradiation (Reproduced from [143]. © IOP Publishing Ltd. All rights reserved). (b) Erasion of quantum dots (white spots) via LID which keeps the atomic template undestroyed (Reprinted from [144], with the permission of AIP Publishing). atomic lens achieves a sub-diffraction-limited focal spots of 0.7 Airy units from 435 nm to 585 nm. Meta-holograms and Fresnel zone plate are also fabricated on 5-6 layers PtSe 2 , realizing the manipulation of light field at atomic scale [148]. The correlation between reconstructed and source images reaches 70% in the wavelength range of 473-671 nm. It is surprising to note that the atomic layer removal of graphene and MoS 2 has also been realized by using a continuous laser in the confocal Raman spectrometer. To achieve single carbon layer, it is critical to use a substrate, such as SiO 2 /Si, to effectively dissipate the heat and prevent the graphene from being completely removed [149]. The MoS 2 monolayer left on the substrate is confirmed by the 1.8 eV fluorescence peak which is the same as the band gap, and the successive reduction in the layer number is identified by Raman shift. By tuning the laser power and exposure time, layer number can be controlled and the lateral precision of 0.26 µm can be realized [150]. Field effect transistor is further built using the laser machined monolayer, whose electronic property is comparable to that made of pristine MoS 2 monolayer. Ribbon-like patterns are also generated on the monolayer with the lateral feature size at nanoscale (figure 20(c)) [151]. It is also possible to thin 2D materials in liquid environment. Infrared femtosecond laser has been employed to break the monocrystalline TMDs (in deionized water) into pieces with submicron size and nanometric height [152]. For graphite immersed in liquid nitrogen at −196 • C [153], energy contributing to the heat plasma can be reduced. Nitrogen molecules would penetrate into the space between carbon layers and expand to gas phase under the great temperature gradient at the focus. The weak Van der Waals bonds of graphite are then broken, which realizes the atomic layer exfoliation. Following the laser process, ultrasonic vibration can further minimize the products and improve the functional groups decorating the surface [154]. Using this method, MoS 2 and WS 2 quantum dots with 1-2 layers and 2-4 nm lateral size are fabricated.  [147]. Copyright (2021)). (c) Laser machined MoS 2 monolayer, ribbon-like pattern on it and the developed field effect transistor (Reprinted with permission from [151]. Copyright (2012) American Chemical Society).

Summary and future perspectives
Laser is one of the most important tools for scientific research and advanced engineering due to its power in material processing, precision measurement and detection of microscopic information. For laser machining, the interaction mechanism with materials plays more and more critical role with the increasing precision and decreasing feature size. This article serves as a review on the topic, in particular the subtractive process, and the main contents can be summarized as follows: (a) Laser induced material removal at a scale larger than micro/sub-micro level is realized via thermal effect or mechanical spallation such as stress confinement and electronic pressure. Immense electrons in metals dominate the absorption and transmission of energy from photons, while photon excitation is necessary for dielectrics. The removal depth can be determined by an empirical formula (which is also adopted at smaller scale) and the criteria can be thermal parameters, critical tensile stress or plasma frequency of optical breakdown. (b) CE is a mechanism which happens more rapidly, leaves less surface damage than thermal ablation, and can realize a nanoscale material removal. It is a dominant process under low fluence irradiation, or takes place prior to ablation. The emitted particles have a very different nature, such as velocity distribution, charge state and propagation front, compared with the plasma plume. Although more prone to occur on insulators, CE has been observed on semiconductors and metals as well. Critical electric field intensity is the criterion of material removal. (c) It is confirmed theoretically and experimentally that single atomic layer removal with a perfect subsurface lattice can be achieved by laser induced desorption. The sophisticated process is highly quantum mechanical and material dependent, which finally leads to the breakage of atomic bonds between the first and second layers. For 2D material, there is an interesting atomic scale size effect influencing the threshold fluence based on removed layer number. Furthermore, creating a mechanism of selectivity and selflimiting is much preferred to improve the controllability. This is realized by chemical adsorption that weakens the backbonds of the topmost layer, and has been successfully validated on dielectric crystals. (d) Important issues on laser-matter interaction are discussed, from basic material properties to laser parameters. In particular, material defect has significant influence on electronic excitation and the following lattice evolution. It can be formed via self-trapping or induced during manufacturing processes. Defects make the particle emission easier and site-sensitive. Reducing laser wavelength is beneficial to depress thermal effect and improve machined surface quality, due to the enhanced ionization by high energy photons. Although having not been studied as widely as commonly used wavelengths, EUV light shows the advantage in high-precision processing and has remarkable distinctions to visible/infrared laser. (e) Three kinds of numerical method are mainly employed to simulate laser machining. Ablation and CE can be studied by using both the sophisticated differential equations and the TTM-MD coupling approach. However, laser desorption at atomic scale and accurate description of electrons require a quantum model, such as TDDFT. A 'full dynamic' simulation in which the motions of electrons and ion cores are all concerned provides valuable details to understand the mechanism. (f) Examples of nanostructures machined by direct writing and interference irradiation are presented to demonstrate the capability in minimizing the feature size and gaining preferred surface quality. With special environment medium, laser machining can realize larger aspect ratio, chemical-based selectivity, or act as catalyst for etching reactions. More importantly, it has achieved atomic scale removal and monolayer patterns on semiconductor and 2D materials, indicating a promising solution to the manufacturing of next-generation optoelectronic devices.
It has been clear that laser machining has great potential to be an efficient method of ACSM. To further develop the laserbased ACSM, the challenging issues can be summarized as follows: (a) How to determine suitable laser parameters? It is always considered that reducing the pulse width is necessary for precision laser machining. However, according to the study in this review, atomic scale removal happens in a wide range of pulse width covering hundreds of femtoseconds to tens of nanoseconds (five orders of magnitude). In contrast, most of them use a photon energy larger than band gap, as well as a moderate fluence less than about 300 mJ cm −2 which is lower than that for ablation or CE. This implies that sufficient excitation by single photon but not excessive photon number is more essential. The final goal is to establish a methodology for the design and optimization of those parameters, which is based on further understanding of the process from atomic scale.
Although there have been many researches, the large divergence in the machining conditions makes a comprehensive comparison difficult, and systematic studies from the perspective of manufacturing are lacking. (b) How would material properties dominate the atomic scale process? This fundamental issue still needs clarifying. For example, should the electron affinity energy be taken into account in addition to inter-band excitation? Is thermal damage prone to occur for indirect band gap materials due to phonon activity during electron jumping between energy levels? Is atomic layer removal possible for metals which is rarely reported in experiment? For the ultimate surface integrity, there might be critical densities of phonon and surface defect for a material, under which the lattice damage can be eliminated. On the other hand, it seems that phonons also take part in the bond breakage and atom emission, accompanied with electronic excitation/state localization. Such theoretical questions have great significance in predicting the minimum removal in the depth and lateral dimensions. (c) How to improve the controllability of the material layers to be removed at ACS? High controllability and repeatability are crucial for production, which may be an important difference between manufacturing technology and scientific research. Despite the experimental validations, removing atomic layers in a definite manner is still very difficult, because only a small perturbation in laser fluence or surface state may change the atomic bond evolution and machining result. Therefore, the selectivity and selflimiting mechanism plays a central role, which can obviously enhance the robustness. In principle, it could be realized by any approach that modifies electronic states or band structure in topmost layers. For the adsorption assisted method in this review, whether physical adsorption is feasible is of practical interest. It has shown that defect seeds are the origin of total layer etching, so it is possible to fabricate 'defect fence' to facilitate the formation of precise atomic step patterns. (d) There is no doubt that laser-based ACSM is highly dependent on the development in the laser micro/nanomanufacturing technology. Firstly, femtosecond laser has achieved great success in fabricating high-quality micro/nano-structures into/on polymers or some transparent materials using near-infrared wavelengths, based on two photopolymerization or other chemical modification approaches. However, it is still difficult to obtain a good surface integrity on crystalline solids via subtractive ablation. According to the analysis in this review, it is necessary to explore the potential by using the laser with shorter wavelengths. Secondly, there is a need to further clarify material removal process under ultrafast laser, which requires advanced numerical method integrating the information from atomic to micro scale. Multiscale simulation coupling density functional theory, molecular dynamics and mesh-based method may be one solution to balancing the accuracy and efficiency. Finally, laser field control becomes critical when the process happens at decreasing scale and near the threshold condition.
Advanced beam shaping technology is demanded, such as freeform optics for imaging and illumination, simultaneous spatio-temporal focusing for enhanced resolution.