Removal of Nanoparticles With Laser Induced Plasma

Transcription

1 Journal of Adhesion Science and Technology 22 (2008) Removal of Nanoparticles With Laser Induced Plasma Ivin Varghese, M. D. Murthy Peri, Thomas Dunbar, Brian Maynard, Derek A. Thomas and Cetin Cetinkaya Dept. of Mechanical and Aeronautical Engineering, Center for Advanced Materials Processing, Wallace H. Coulter School of Engineering, Clarkson University, Potsdam, NY , USA Abstract A review of the recent progress in the understanding of the laser induced plasma (LIP) technique utilized for nanoparticle removal is presented. LIP nanoparticle removal technique has been successfully demonstrated for removal of nm polystyrene latex (PSL) particles from silicon substrates. The motivation for LIP technique stems from the requirement for defect-free cleaning of wafers and lithography photomasks in the semiconductor and microelectronic fabrication industries as well as nanotechnology. The principle of LIP nanoparticle removal technique and progress in its applications as well as the LIP blast wave propagation are reviewed. In recent computational studies, the effects of the two consequences of LIP application, namely, radiation heating from the plasma core and the LIP shockwave thermo-mechanical (pressure and temperature) loading on the substrate and subsequent potential damage are investigated. Removal thresholds for polystyrene latex (PSL) nanoparticles from chromium (Cr) nanofilms using the LIP technique in air are reported. Rolling resistance moment as a particle removal mechanism is discussed and the main results and its implications in nanoparticle removal are summarized. For removal of smaller particles, pressure amplification techniques are employed to replace the in-air LIP. To achieve this purpose, shock tubes in air, wet-lip and shock tubes submerged in water were investigated for obtaining maximized pressure levels. It is reported that the shockwave pressure can be substantially increased so that submerged shock tubes can generate pressure levels sufficient to remove particles as small as sub-10 nm. Koninklijke Brill NV, Leiden, 2008 Keywords Laser induced plasma, nanoparticle removal, shockwaves, radiation intensity heating, pressure amplification, shock tubes, wet-lip, submerged shock tubes 1. Introduction The LIP is an emerging particle cleaning technology for sub-100 nm particle removal from nanofilms, wafers, photomasks and extreme ultraviolet lithography (EUVL) masks. It is a rapid, dry, chemical-free, effective, non-contact and selective method for micro- and nano-particle detachment in which cleaning is carried out by the shockwaves generated by the expansion of the LIP [1 8]. Currently, dam- * To whom all correspondence should be addressed. Tel.: (315) ; Fax: (315) ; cetin@clarkson.edu Koninklijke Brill NV, Leiden, 2008 DOI: / X305561

2 652 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) age risk is the main concern in laser-based nanoparticle removal techniques. Laser induced plasma (LIP) technique has been investigated for its sources of damage, particle removal thresholds and LIP pressure amplification techniques that might assist removal of smaller particles than those possible with LIP in air. It is known that the use of direct laser cleaning, as opposed to LIP, is rather limited for nanoparticle removal due to high thermoelastic loading of the substrate and, consequently, potential damage mechanisms such as peeling of top layers due to localized stress, micro-cracks and surface breakage [9]. Material alterations such as peeling-off, mosaic patterned cracks, melting, and partial/complete removal were observed on Cr (chromium) nanofilms due to excimer laser ablation [10]. Single-shot direct laser ablation applied to a Cr nanofilm (248 nm) on fused silica substrate resulted in Cr film rupture at low fluence, followed by melting and vaporization at increasing fluence [11]. The 2006 update of the International Technology Roadmap for Semiconductors (ITRS) prescribes for optical and extreme ultraviolet lithography (EUVL) masks requirements the specified defect sizes (I ) of 36 nm for 2010, 20 nm for 2015 and 11 nm for 2020, while the substrate defect sizes (L) of 35 nm for 2010, 27 nm for 2015 and 18 nm for 2020 [12]. The minimum diameter spherical defect (in polystyrene latex (PSL) sphere equivalent dimensions), i.e., maximum front surface particle size for starting materials that can be tolerated is 45 nm by 2012, 32 nm by 2015 and 22 nm by 2018 [12]. It is a challenge to ensure that these EUVL masks, photomasks and wafers are free of nano-scale contamination, since damage/material alteration might result in fabrication of faulty integrated circuits (ICs) by printing of distorted images during the lithography process, resulting in possible rejection of the mask/wafer [13]. Brush scrubbing [14 16], megasonic cleaning [17 19] and cryogenic (CO 2 snow) cleaning [20, 21] are some of the current sub-100 nm particle removal techniques from silicon substrates that are being utilized. Particle re-deposition [15, 20] and efficiency of cleaning [19] as well as substrate damage [18] are chief concerns in all current industrial cleaning techniques. It is reported that brush cleaning also suffers from problems such as post-cleaning damage and possible structural damage to the substrate, while cryogenic cleaning faces problems of limited availability of high purity CO 2, and megasonic cleaning from potential localized damage on the silicon substrate due to gas cavitation, and drying without leaving any watermarks [18]. So an efficient, precision cleaning technique for removal of sub-100 nm particles is still needed [13]. The emerging cleaning approach based on LIP generated shockwaves has experimentally been demonstrated to be an effective, non-contact, dry, fast and chemical-free method for micro- and nano-particle detachment [1, 3 7, 22], and is especially capable of cleaning selective areas, but entire wafers and lithography photomasks can also be cleaned with the help of a scanning system [13]. As the size of the particle, with a characteristic length scale L (e.g. diameter), to be removed decreases, the force of adhesion reduces by O(L), while fluid and

3 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) electrostatic forces acting on the particle diminish by O(L 2 ) and body forces (e.g. gravity) decrease by O(L 3 ). As the particle size decreases, the volume (body) and area proportional forces are dominated by the intermolecular adhesion force, causing serious difficulty in damage free nanoparticle removal in the sub-100 nm range [5]. 2. LIP Nanoparticle Removal Technique The schematic for a typical LIP nanoparticle removal setup is shown in Fig. 1a, while the instrumentation diagram and the photograph of the experimental setup are presented in Fig. 1b and 1c, respectively. In the LIP particle removal technique, a convex lens focuses the pulsed-laser beam to its focal point resulting in plasma core formation due to dielectric breakdown of air [3] that expands to a stable limiting diameter before saturating. At some time after the plasma core expansion halts, the hot compressed layer of the air surrounding the plasma core becomes detached as a shockwave front [2], which is directed onto the nanoparticle to break the adhesion bond between the particle and the substrate [8]. In the basic LIP cleaning setup, the two key interdependent and critical process parameters that have been identified are the firing distance (d) and the laser pulse energy (E) available for nanoparticle removal. These two parameters govern the initiation and form of damage on the substrate. Provided there is no direct contact of the LIP plasma core with the substrate, the two possible sources of damage are identified as the thermo-mechanical loading from the LIP shockwaves due to gas convection heating and the radiation intensity heating from the plasma core [13, 23]. The timescale for radiation heating is in nanoseconds while those for LIP shockwaves are in microseconds, resulting in laser radiation heating effects showing up earlier than those due to the LIP shockwaves on the substrate [13]. It is important to note that the expansion of the plasma core is mainly a mass transfer phenomenon while the motion of a shockwave front is a traveling pressure wave without mass transfer. The removal of smaller particles requires higher pressure levels which can be attained at a lower LIP firing distance (d) for a given pulse energy, but, as the plasma core gets closer to the surface, there is an increased risk of material alteration and/or damage [3]. For removal of smallest possible particle and maximizing particle removal efficiency, it is desirable to increase the available pressure without damage concern and determine the thresholds for LIP particle removal. It is, therefore, required to mitigate the pressure (P ) and temperature (T ) fields generated on the substrate, obtained from LIP at small firing distances d, to ensure damage-free particle removal in the sub-100 nm range. A prediction of the temperature [24] experienced by the photomask and wafer surfaces due to LIP is thus needed to predict damage risk and the type of damage. For practical applications of the LIP technique, the determination of a design space (optimized parameters) for damage-free nanoparticle removal utilizing the

4 654 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) (a) (b) (c) Figure 1. Laser induced plasma (LIP) nanoparticle removal technique: (a) schematic, (b) instrumentation diagram and (c) photograph of experimental setup showing the LIP being measured by a pressure transducer (inset). LIP removal technique is essential. In [5], transient LIP shockwave pressure measurements were conducted utilizing a piezoelectric transducer to characterize the transient pressure field of an LIP shockwave front (Fig. 1c). Optimized parameters for 60 nm PSL particle removal were determined to be a firing distance of

5 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) d = 1.4 mm, and 10 laser pulses for the 370 mj, 1064 nm Nd: YAG pulsed-laser [3]. Silicon wafer being thick and crystalline is mechanically stronger (less susceptible to material alterations and/or damage due to thermo-mechanical loading) compared to the photomasks that contain delicate patterns and thin nanometer-scale films. Determination of the onset of material alterations and/or damage, rather than the extent of damage, is critical and sufficient to ensure damage-free cleaning of wafers and photomasks. Results of some preliminary experiments conducted to investigate the onset of material alterations in nanofilms (photomasks) due to LIP loading are reported [13, 23]. Thermo-mechanical loading from LIP shockwaves, i.e., the combination of the thermal (shockwave temperature) and the mechanical (shockwave pressure) effects, as well as the thermal effects due to the laser radiation intensity (I 0 ) heating from the LIP plasma core were considered for material alterations studies on nanofilms deposited on photomasks substrates. For damage-free cleaning, the critical firing distance d cr (namely, the minimum safe LIP firing distance), the firing distance d beyond which there will be no material alterations, needs to be identified for a given pulse energy. When d<d cr the load experienced by the nanofilm on the photomask would result in either temperature greater than the melting point or stresses larger than the yield and/or rupture stress, resulting in material alterations like melting, cracking, channeling, peeling, film stripping and discoloration [13]. 3. Propagation of LIP Blast Wave Laser-induced breakdown in air, first discovered in 1963 [25], is realized in four successive stages [26]: (i) multi-photon collision with the gas molecules resulting in the initial release of electrons, (ii) initiation of ionization of the gas in the focal region and plasma formation due to the cascade release of electrons, (iii) absorption of laser energy by the plasma leading to formation of the blast wave and (iv) blast wave propagation into the surrounding gas. A primary observation obtained from experiments [27, 28] is the formation of a vortex ring in the focal region due to the asymmetric shape of the plasma region. To better understand the essential features of the blast wave propagation phenomenon, several analytical and numerical models have been developed and investigated [27, 29 40]. Taylor [29] and von Neumann [32] proposed similarity laws to accurately describe the initial motion of the blast wave when it remains strong. Reportedly, Taylor s similarity laws were independently derived by Sedov [31]. Bach and Lee [41] proposed a weak blast waves approximation assuming a power-law density profile behind the shockwaves. Brode [30] performed a numerical simulation study of spherical blast waves for both a point source and an isothermal sphere. It is noted that in air for shock pressures less than 10 atm the ideal gas assumption is reasonably valid. Jiang et al. [36] studied a micro-blast wave with the initial condition described by the similarity law by performing experiments and numerical simulations [29]. A computational model based on the asymmetry of the laser energy deposition as well as ionization

6 656 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) and dissociation effects on fluid properties was presented by Dors et al. [38]. Three outward-moving weaker shockwaves were observed by Liang et al. [39] behind the main shockwave in the propagation of a weak spherical blast wave, created by rupture of a high pressure isothermal sphere. The assumptions of the blast waves produced by an intense explosion described by the best-known similarity solution (found independently by Taylor [29], Sedov [31] and von Neumann [32]) are: (i) explosion results in sudden release of an amount of energy (E) concentrated at a point and (ii) pressures and velocities produced in the resultant strongly disturbed flow fully dominate the initial pressure and sound speed of the ambient air. E and ρ 0 are the only dimensional parameters introduced by the explosion and ambient air [29, 31] Blast Wave Theory Relations Blast wave theory (BWT) is based on similarity transformations [29, 31, 32]. The shockwave front radius R(t) as a function of propagation time t is given by [29, 31]: ( ) E 1/5 R(t) = k t 2/5. (1) ρ 0 In [42], the transient pressure (P ) and velocity (u) behind the shockwave are given by: P(t)= 8 k 2 ( ) ρ 0 E 2/5 t 6/5, (2) 25 γ + 1 ρ 0 u(t) = 4 ( ) k E 1/5 t 3/5, (3) 5 γ + 1 ρ 0 where t is the shockwave propagation time, E is the net released energy, ρ 0 is the density of the ambient air, k is a constant, and γ is the specific heat ratio of ambient air (=1.4). The particles to be removed by LIP shockwaves are in the sub-100 nm range, while the shockwave propagation is in the millimeter range, thus the nanoparticles would experience the spherical shockwave to be a plane wavefront. Therefore, the LIP shockwave loading could be modeled using the one-dimensional unsteady compression equations for normal incident shocks. Utilizing the ambient conditions i.e., kpa for pressure P 1 and 298 K for temperature T 1, the pressure behind the shockwave (P 2 ) based on the BWT can be determined from equation (2). The temperature behind the shockwave (T 2 ) can be obtained based on gas dynamics relationships [43] as: T 2 (t) T 1 = ((γ + 1)/(γ 1)) + P 2(t)/P 1 ((γ + 1)/(γ 1)) + P 1 /P 2 (t), (4)

7 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) where indices 1 and 2 correspond to properties of the ambient air and behind the incident shockwave, respectively. The pressure behind the reflected shockwave (P 5 ) based on equations for normal incident shocks is given by ( ), (5) P 5 (t) P 1 2γ /(γ 1) = 1 + P 2 (t) P 1 1 +[((γ + 1)/(γ 1))(P 1 /P 2 (t))] where indices 1, 2 and 5 correspond to properties of the ambient air, behind the incident shockwave and behind the reflected shockwave, respectively. The corresponding temperature behind the reflected shockwave (T 5 ) is obtained from gas dynamic relationships [43] as: T 5 (t) T 2 (t) = ((γ + 1)/(γ 1)) + P 5(t)/P 2 (t) ((γ + 1)/(γ 1)) + P 2 (t)/p 5 (t), (6) where indices 2 and 5 correspond to properties behind the incident shockwave and behind the reflected shockwave, respectively. The pressure and temperature that the substrate would experience due to the LIP shockwaves can be obtained from the pressure (P 5 ) and temperature (T 5 ) behind the reflected shockwave as given by equations (5) and (6), respectively. 4. LIP Radiation Intensity Heating To assess the damage potential of an LIP radiation field (one of the LIP damage sources identified [13]), prediction of the surface temperature rise due to the radiation intensity heating was required for computation of the resulting stresses in the nanofilms on the photomasks. The film surface temperature response due to radiation heating by the plasma core is a nanosecond-scale excitation that requires measurement sensors that operate in the GHz frequency range [44]. Therefore, a direct temperature measurement in the nanosecond range for nanofilms on photomasks is considered as a non-trivial technical task. No such commercially available temperature sensor (nanosecond-scale response) suitable to this temperature measurement application was found. Radiation energy (E rad ) deposited on the surface of the substrate leads to radiation heating and thermo-mechanical stresses in the substrate. For single-shot laser pulses utilizing a volume absorber type radiant power meter with a sensor area of mm 2 (S meter ), the radiation energy (E rad ) deposited on the substrate was approximated (indirect measurement) [44]. A fully-coupled thermo-elastic model based finite element (FE) investigation to predict the transient temperature (T ) experienced by the substrate due to radiation exposure was conducted with the obtained radiation intensity as load. The photomask prototype (as the substrate) utilized in FE was a 100 nm Cr nanofilm on a quartz substrate [13]. Radiation energy levels (E rad ) obtained for different firing distances (d) revealed exponential decrease in the radiation energy for larger firing distances d. The radiation intensity

8 658 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) level I 0 (profile assumed to be the same for any d) and its dependence on the firing distance d was obtained as: I 0 = a + be d/β, (7) where a = 160 MW/m 2, b = GW/m 2 and β = 4.46 mm for the 370 mj Nd: YAG pulsed-laser. The radiation intensity level I 0 = 9.09 GW/m 2 at the experimental damage threshold firing distance d = 2.5 mm was the amplitude of the normalized radiation intensity profile that was assumed for the FE analysis [13]. This radiation intensity was uniformly applied on the entire Cr film surface as heat flux, by utilizing the dynamic temperature-displacement case with distributed surface flux loading in the computational analysis. The radiation intensity level (I 0 ) is obtained as GW/m 2 for a firing distance of d = 2 mm from equation (7) for which experimentally damage was observed. For both the film and the substrate an axisymmetric solid thermo-mechanical element was utilized, while at the free boundary of the model infinite element type was used. A surface temperature rise of 450 K, a maximum radial stress of 1.93 GPa, an axial maximum stress of 46.4 kpa and a maximum shear stress of 0.8 kpa were obtained for the Cr film. Based on the analysis of the FE results, it is found that the magnitudes of the radial stress components are observed to dominate those of the axial and shear stresses. The FE analysis results were obtained for both 20% reflectivity of the Cr film as well as no reflectivity, and the corresponding temperature and maximum stress for the different firing distances d were reported [13]. 5. LIP Shockwaves A schematic for the propagation and reflection of a shockwave front is depicted in Fig. 2a. To characterize the LIP generated shockwaves, transient pressure (P ) measurements were conducted in air utilizing a dynamic pressure transducer at various firing distances d above the LIP core, while the shockwave temperature (T ) was estimated using gas dynamics relationships and the measured pressure data [8]. Air was chosen, since the medium in between the plasma core and the substrate surface during the LIP application for particle removal is usually air. The laser utilized in the reported experiments was a Spectra Physics Nd: YAG INDI-series pulsed-laser with a rated pulse energy of 450 mj, a pulse width of 5 8 ns, a repetitive rate of 10 Hz, a beam diameter of mm, and a wavelength of 1064 nm. The pressure transducer used in the reported experiments was a Kistler 603B1 (with a resonance frequency of 500 khz, a rise time of 1 µs and a surface diameter of 5.54 mm). The LIP shockwave transient pressure is observed to decrease as the firing distance (d) is increased as shown in Fig. 2b. The shockwave velocity (v) and shockwave radius (R) as a function of the shockwave propagation time (t) are depicted in Fig. 2c (where R is the set of firing distances (d) utilized in the experiments and t is the corresponding shockwave arrival time ( t) for each d). The various shockwave propagation distances (r) (the location of the shockwave front on the substrate as

9 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) (a) (b) Figure 2. (a) LIP shockwave propagation schematic, (b) LIP pressure measurements in air at different firing distances d, (c) shockwave velocity (v) and radius (R) as a function of shockwave propagation time (t), and (d) LIP shockwave propagation distance (r) for 450 mj Nd: YAG laser compared to literature values.

10 660 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) (c) (d) Figure 2. (Continued.)

11 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) a function of the arrival time) reported in the literature [29, 36, 45, 46] along with the obtained experimental results [8] are compared in Fig. 2d. Since different laser pulse energies were utilized, slight offsets are observed in the various shockwave propagations. The shockwave pressure was measured utilizing a microsecond rise-time sensor (MHz frequency range) since the shockwave expansion was in the micro-seconds time range. Finite element (FE) analysis using a linear, fully-coupled thermomechanical analysis implemented in ABAQUS was conducted to study the effect of the shockwave thermo-mechanical loading (shockwave pressure and temperature) by obtaining the stresses and surface temperature (T ) experienced by a photomask (100 nm Cr film on quartz substrate), and to determine whether the surface temperature exceeded the melting temperature and/or the maximum stresses exceeded the dynamic yield stress of the materials [8]. A temperature rise ( T ) of 152 K, a maximum radial stress (σ rr ) of 649 MPa, a maximum axial stress (σ zz ) of 195 kpa and a maximum shear stress (τ rz ) of 172 kpa were obtained on the Cr film surface due to thermo-mechanical loading of LIP shockwaves. The radial and shear stress components were predominantly created by the thermal loading (shockwave temperature) while the mechanical loading due to the shockwave pressure is responsible for the significant portion of the axial stress component in the substrate [8]. From the FE computational results [8] for LIP shockwave thermo-mechanical loading (combination of shockwave pressure (P ) and temperature (T )) of a 100 nm Cr film on a quartz substrate at a firing distance d = 2 mm, the obtained film surface temperature rise T, and the maximum values of the radial σ rr,axialσ zz and shear τ rz stress components are listed in Table 1. Table 1 also summarizes the FE results for obtained film surface temperature rise T,radialσ rr,axialσ zz and shear τ rz stress components experienced due to laser radiation intensity loading (I 0 = GW/m 2 ) from the LIP core for a 100 nm Cr film on a quartz substrate at a firing distance of d = 2 mm, to compare the effects of both loading conditions [8]. Table 1. Summary of the FE computational results for Cr film surface temperature rise T,radialσ rr,axialσ zz and shear τ rz stress components due to various LIP loading conditions on 100 nm Cr film on a quartz substrate at a firing distance of d = 2 mm. The loading conditions are: (i) radiation intensity from LIP core, (ii) LIP shockwaves and (iii) the combined effect of both. The LIP shockwave loading denotes thermo-mechanical loading due to combination of shockwave pressure (P ) and temperature (T ), while the radiation heating is for a radiation intensity level of I 0 = GW/m 2 Cr film surface LIP radiation LIP shockwave LIP total effect responses intensity level (I 0 ) (P + T ) (I 0 + P + T ) T (K) σ rr (MPa) σ zz (MPa) τ rz (MPa)

12 662 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) It is concluded that, based on FE analysis results of radiation intensity heating and the thermo-mechanical loading of LIP shockwaves (heat convection), radiation heating and subsequent thermal stresses appear to be the dominant damage sources during LIP particle removal [8, 13, 23]. 6. PSL Particle Removal Threshold For a given particle substrate materials pair, the nanoparticle removal threshold obtainable from the LIP shockwave pressure in air needs to be determined, as this would be the limiting particle removal size. If particles smaller than this limit need to be removed, then by some technique the amplification of the LIP pressure is required. The Johnson, Kendall and Roberts (JKR) model of particle adhesion approximates the pull-off force F Pull-off (in the surface normal direction needed to remove the particle) between a spherical particle and a flat substrate [3] as: F Pull-off = 3 πwd, (8) 4 where W is the work of adhesion between the particle and the substrate and D is the diameter of the spherical particle. From Derjaguin approximation, the adhesion force for two spheres of radii R 1 and R 2 [47] is given as: F = ew g, (9) where, e = 2πR 1 R 2 and g = R 1 + R 2. The adhesion force between a spherical particle (radius R 1 = R) and a flat surface (R 2 = ) can be obtained by substituting R 1 = R and R 2 = for e and g, in equation (9) as: F = 2πRW. (10) From the van der Waals interaction free energies, the adhesion force for a sphere and a flat surface (separated by a distance z 0 ) is obtained as: F = AR 6z0 2. (11) Equating the forces in equations (10) and (11), the work of adhesion is: W = A 12πz0 2, (12) where A is the Hamaker constant. Equation (12) is used to obtain the work of adhesion for spherical particles deposited on a flat substrate. The radius of the contact circle between the substrate and the particle at the onset of detachment, a, is given as: ( 3πWD 2 ) 1/3 a =, (13) 8K

13 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) with K = 4/3((1 ν 2 1 )/E 1 + (1 ν 2 2 )/E 2) 1,andwhereν 1 and E 1 are, respectively, the Poisson s ratio and the Young s modulus of the particle material, and ν 2 and E 2 are, respectively, the Poisson s ratio and the Young s modulus of the substrate material [3]. During the reported nanoparticle removal experiments with LIP, PSL particles were deposited on the silicon substrate and removal was carried out in air. The separation distance (z 0 ) between the PSL particle and the silicon substrate has been assumed to be 4 Å. In the sub-100 nm range, the van der Waals attraction forces would dominate any existing double-layer repulsion forces at this separation distance of 4 Å. The intermolecular force between the particle and the substrate for critical particle removal pressure calculation will be considered to be only the van der Waals attraction (F Pull-off ). As reported in [48], in the LIP removal technique as with any other technique, for spherical particles the dominant removal mode is rolling, under a transient pressure field generated by a shock wavefront, while other removal modes (e.g. sliding, lifting or combination of these) might also contribute to the removal [49]. To analyze the rolling mode of removal, the simplest detachment model is based on a moment balance about point O (Fig. 3a), from which the critical removal pressure [3], p c, needed for detachment of a particle with diameter D (pressure available due to LIP should exceed p c ) can be approximated as: p c = 2a(F Pull-off + mg) A s (D cos θ 2asin θ), (14) where A s = πd 2 /2 is the effective particle surface area perpendicular to the pressure field, m the particle mass, g the gravitational acceleration (often negligible in LIP), θ the angle between the force vector and a plane parallel to the substrate surface and α is the contact depth shown in Fig. 3a [9]. Since the pull-off force F Pull-off is several orders ( 8) of magnitude higher than mg, when dealing with nano-particles, the term mg in equation (14) can be neglected. The pull-off forces and the required pressures for removal can be approximated from equations (8) and (14), respectively. The simplified expression for critical pressure, p c,required for the initiation of detachment can be expressed as: p c = 4aF Pull-off πd 3. (15) The work of adhesion W (equation (12)), the pull-off force F Pull-off (equation (8)) and the removal pressure p c (equation (15)) required for polystyrene latex (PSL) particles on a Cr substrate were calculated based on material properties [13] for rolling detachment utilizing the JKR model with PSL considered as a soft particle [3]. For a 60 nm (D) PSL particle on a Cr substrate, the contact radius a is 3.24 nm, work of adhesion W is mj/m 2, pull-off force F Pull-off is 5.04 nn and the required critical pressure for removal p c is approximately 96.3 kpa when θ (the angle of approach of the shock wavefront to the particle adhered on the film/substrate) approaches 0 or π.

14 664 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) (a) (b) Figure 3. (a) Schematic of LIP shockwave interaction with particle adhered to a substrate and (b) available LIP pressure in air at various firing distances and the minimum removable PSL particle size from the Cr substrate. The maximum available shockwave pressure (P ) generated by the LIP in air at the various firing distances (d) and the corresponding PSL particle diameter (D) that can be removed from the Cr film surface with that pressure level P is reported in Fig. 3b. The LIP application on 100 nm Cr on a quartz substrate at firing distances d<2.5 mm resulted in material alterations, but no damage was observed at d = 2.5 mm and above [13, 23]. Thus in Fig. 3b, d<2.5 mmismarkedas

15 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) the experimental damage zone and d = 2.5 mm is indicated as the experimental damage threshold. Further, the PSL particle removal threshold corresponding to the experimental damage threshold has been also marked. It is observed from Fig. 3b that for the LIP shockwave pressure of 138 kpa in air at the safe firing distance of d = 2.5 mm (without any material alterations), 46 nm PSL is the smallest particle that can be removed from Cr film and/or substrate. Thus, D = 46 nm is indicated as the PSL particle removal threshold corresponding to the experimental damage threshold and D<46 nm has been marked as no particle removal zone in Fig. 3b [13] Rolling Resistance Moment The simplest detachment model is based on the balance of moments at the leading edge of the contact area of a rolling particle as discussed above (equation (14)). This model ignores the particle s initial resistance to rolling. Another potential detachment mechanism for nanoparticles is particle resonance rocking motion excited by a transient pressure field, based on the rolling resistance moment theory which takes into account the rolling resistance and the vibrational motion of the particle. This mode of motion can be excited in nanoparticles since the mean free path of the gas is comparable to the diameter of the particle, and, as a result, the continuum assumption fails. Exerting an external pressure field on a flat film-substrate system results in a moment associated with the spherical particle s rocking motion leading to change in the contact area (shifting) between the particle and the film/substrate, due to which the particle experiences asymmetric pressure field. The rolling resistance moment is proportional to the pull-off force (JKR) and the shift of the center of the contact area [50]. The critical rolling resistance moment (M y ) in static equilibrium about a particle s center point can be approximated [50] by M y 6πWr 2 θ critical, (16) where according to [8], θ critical can be approximated in the range of (1 5) 10 9 θ critical = rad. (17) r Considering removal of a 60 nm (radius r = 30 nm) PSL spherical particle from a flat Cr film/substrate, the rolling resistance moment (M y ) is in the range of nn-nm, while the work of adhesion is mj/m 2. If the rolling resistance moment of a particle is greater than the critical rolling resistance moment, then the particle would become detached from the substrate. Utilizing the equation of motion of a spherical particle in free-rotational oscillation on a flat surface: I θ + M y = 0, (18)

16 666 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) where I is the moment of inertia of the PSL spherical particle and θ is the angular acceleration. The resonance frequency of the rocking motion [51] for the spherical particle is determined as: f rocking = 1 2πr 3/2 45W 4ρ = MHz, (19) where ρ = 1040 kg/m 3. The rocking resonance frequency for the 60 nm PSL particle (r = 30 nm) is calculated as MHz from equation (19). In [51], the resonance frequency of the axial motion is given by f axial = 3α 1/6 2π π2 11/6 r, (20) ρβ1/3 where α = 3πrW,β = r/k,k = 4/3[(1 ν 2 PSL )/E PSL +(1 ν 2 Cr )/E Cr] 1, E and ν are the Young s modulus and the Poisson s ratio of the materials. For the 60 nm PSL particle (r = 30 nm) on Cr substrate the resonance frequency of the axial motion is calculated as 1.92 GHz. Thus for the PSL particle-cr substrate system, the resonance frequency of the rocking motion (601.8 MHz) is much lower than that of the axial motion (1.92 GHz), implying that the PSL particles can more easily be removed by exciting the particles in rocking motion. Direct Simulation Monte Carlo (DSMC) method was utilized for studying the shockwave-nanoparticle interactions (due to invalidity of the continuity assumption in this length scale), by applying the incident LIP shockwave properties as initial conditions (velocity and number density of molecules) [5, 6]. For a 60 nm cylindrical particle, with length equal to diameter, the transient forces and moments exerted due to the LIP shockwaves were obtained [6]. As the pressure of the LIP shockwave field available for particle removal decays exponentially as the propagation distance (r) is increased, there is a critical distance beyond which no particle removal would occur. Beyond this critical distance, the moment exerted on the particle would not exceed the rolling resistance moment [7]. The LIP shockwave pressure field exerted on a particle is a statistical distribution of the gas-particle interaction based on the kinetic gas theory [7]. If the frequency of the fluctuations in the moment exerted on the particle by gas molecules approaches the rocking resonance frequency (given by equation (19)), the amplitude of rocking motion keeps increasing until the magnitude of θ reaches θ critical, thereby resulting in the rolling and possible detachment of the particle, which could occur even beyond the vicinity of the critical distance [5 7]. The expansion of the plasma core is mainly a mass transfer phenomenon while the motion of a shockwave front is a traveling pressure wave without mass transfer. Therefore, in the LIP cleaning, no direct plasma surface interaction occurs and the particles and/or substrates are not expected to become electrically charged. By exerting a moment on the particle due to the collisions of the gas molecules with the particle the generated shockwave plays the critical role of breaking the adhesion

17 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) bond between the particle and the substrate. The shockwave front-substrate interaction and associated momentum transfer to the particles are not weakened by the formation of a boundary layer as in the case of fluid flow over a surface. The exerted moment causes particle rolling and rocking motions and if the moment exceeds the particle critical resistance moment, it results in particle detachment from the substrate. Based on the rolling mode of particle detachment, 60 nm PSL particle on a Si substrate can be removed in a circular area defined by 0.5 mm r p 4mm (where r p is the particle position on the substrate), as the peak moments obtained would be greater than the critical rolling resistance moment [6]. If the particle is in the region of 4 mm <r p 16 mm, removal may occur [6]. For the 60 nm PSL particle, 60.5 nn-nm (M crit = 66.4 nn-nm) was the peak value of the transient moment while the mean value of the fluctuations was 41.7 nn-nm at r p = 4mm[6]. The frequency spectrum of the exerted rolling moment fluctuations due to the gas molecule-particle interactions covers the rocking resonance frequency of 488 MHz. Thus, detachment might occur due to the resonance frequency of the rocking motion becoming dominant even in zones where r p > 4mm[6]. The shockwave front-particle interaction can be considered as individual gas molecules colliding with the particle. Due to the discrete nature of gas molecules, the rolling moment exerted on a particle by the shockwave is stochastic in nature. Thus the moment exerted on the particle due to the shockwave as well as the stochastic transient rolling moment act as LIP particle detachment mechanisms [5]. Rolling resistance moment and rocking resonance of the particle (due to elastic restitution effect) are the two potential particle detachment mechanisms that were introduced for LIP shockwave cleaning. Based on DSMC, it is demonstrated that a 60 nm PSL particle can be detached with the aid of a shockwave induced by a pulsed laser [6]. Thus, detachment of nanoparticles due to the laser induced shockwaves was investigated on the molecular level [6]. 7. Pressure Amplification Techniques Removal of 60 nm [3] as well as nm [52] PSL particles from silicon substrates has been successfully demonstrated utilizing the LIP removal technique in air. The instrumentation diagram for the pressure measurement setup for LIP in air is depicted in Fig. 4a. The maximum pressure that was obtained from LIP in air for a 370 mj, 1064 nm Q-switched Nd: YAG pulsed laser was 156 kpa at a firing distance d = 2 mm. It is reported that damage occurs on 100 nm Cr film on quartz substrate at a firing distance d = 2 mm [13]. Smaller particles require higher removal pressures as inferred from equation (15). Reducing the firing distance results in higher pressure field generated from the laser induced plasma (LIP), thereby increasing the removal effectiveness and reducing the limiting size of the particle that can be removed. However, if the firing distance (d) is too short, material alterations of the film or particle or substrate could occur due to the radiation heating and LIP shockwaves resulting in

18 668 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) (a) (b) Figure 4. Instrumentation diagrams for (a) LIP in air, (b) LIP utilizing a shock tube in air, (c) wet-lip and (d) submerged shock tube (in water). either surface temperatures greater than the melting point and/or resultant stresses exceeding the dynamic yield stress of the material. From the FE analyses conducted/reported in [8, 13] it is seen that the radial, circumferential and shear stresses all are dominated by the thermal effects. Radiation heating of the particle or film or substrate was determined as the major concern for material alterations [13]. Therefore, higher pressures (P ) for better removal effectiveness without any material alterations (lower radiation exposure to the surface) are required.

19 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) (c) 7.1. Shock Tubes in Air (d) Figure 4. (Continued.) If particles smaller than the threshold limit possible by the LIP in air at the critical firing distance (d cr ) need to be removed then some LIP pressure amplification technique is required. It is advantageous if higher pressures can be achieved at larger firing distances in order to mitigate/eliminate the thermal effects due to radiation

20 670 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) heating from the plasma core, determined as critical LIP damage source. A novel method for the amplification of the pressure (P ) obtained from the shockwaves at a distance away from the LIP was introduced by utilizing shock tubes [53]. This can be achieved by constraining the volume available for the expansion of the LIP by focusing the laser beam inside a cylindrical shock tube. Shock tubes can also be utilized to increase the firing distance d while obtaining the same pressure levels, resulting in reduced temperatures (T ) on the surface and, therefore, lesser damage concern. The instrumentation diagram for shock tubes in air is depicted in Fig. 4b. The objective is to optimize a shock tube for its two-fold potential for either amplifying the pressure field (for better particle removal) or to mitigate the temperature (T ) experienced on the surface (to reduce material alteration/damage concern). As the distance from the LIP core to the substrate (firing distance d) decreases the thermal load on the substrate increases. A pressure decrease of an order of magnitude per every 5 mm firing distance is observed for LIP shockwaves in air. Higher pressures at firing distances significantly further from the core of LIP are obtained with the shock tube technique. Shock tube effectiveness is quantified by its pressure amplification factor, which is the ratio of the pressures obtained with and without a shock tube in a particular medium. A pressure amplification factor of 11 was obtained at a firing distance d = 10 mm, since the shock tube in air generated transient pressure of 523 kpa while the LIP transient pressure in air without the shock tube was 47.5 kpa [53] Wet-LIP Wet-LIP is another technique in which the LIP is created inside water to utilize the larger density of water than air (a factor of approx. 775) for pressure amplification purpose [54]. Experiments are conducted in an immersion tank for wet-lip cleaning. Experiments indicate that the pressure levels are much higher for the shockwaves in water than in air. Another advantage is that the thermal effects of the LIP are reduced to an extent, because of heat loss to water and further LIP is formed as a long streak (compared to the in-air elliptical plume) in water medium, thus the applied thermal load at the target is restricted, and thus mainly the mechanical effect of the shockwave is utilized. The threshold irradiance for laser-induced breakdown for 1064 nm laser in pure water for a 5 ns pulse is approx. 70 GW/cm 2 [55]. The instrumentation diagram for wet-lip is depicted in Fig. 4c. A pressure amplification factor of 5 was observed, from 110 to 550 kpa, when the LIP was created in water as opposed to in air, at the same firing distance d = 4 mm. A peak pressure of 1030 kpa was obtained by wet-lip at a firing distance d = 0.5 mm. Thus utilizing wet-lip, a potential pressure amplification technique, higher pressures (1030 kpa) [54] are obtained compared to shock tubes [53] in air (523 kpa) Submerged Shock Tubes Underwater LIP transient pressure amplification utilizing shock tubes (submerged shock tubes) to assist non-contact particle removal was investigated [54, 56]. This

21 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) amplification approach can reduce radiation exposure of the substrate which was identified as the leading cause of LIP damage during nanoparticle removal. The instrumentation diagram for submerged shock tubes (in water) is depicted in Fig. 4d. With the aid of a submerged shock tube, maximum pressure amplitude of 6.48 MPa is observed, which demonstrates significant LIP shockwave front pressure amplification and, as a result, can remove particles with smaller sizes and/or stronger adhesion bonds. It is predicted that with wet-lip one could remove down to 10 nm particles while with submerged shock tubes, removal of well below 10 nm sized PSL particles from a silicon substrate is theoretically possible. These LIP pressure amplification techniques thus could be utilized for damage-free particle removal from substrates such as patterned silicon wafers and EUVL photomasks [56]. The experimental LIP pressures obtained at various firing distances (d) utilizing LIP in air, shock tubes in air, wet-lip and submerged shock tubes in water are shown in Fig. 5. Peak pressures of 156, 523, 1030 and 6480 kpa, were obtained utilizing LIP in air, shock tube in air, wet-lip and submerged shock tube, respectively [53, 54]. Thus it is determined that the maximum LIP pressure amplification is obtained with submerged shock tubes with peak transient pressure of 6.48 MPa and a pressure amplification factor of 8.95 obtained at a firing distance of d = 2.5 mm, when compared to the transient pressure of 724 kpa without the shock tube in wet- LIP [54]. Figure 5. Available LIP pressures P max at various firing distances d for (i) in-air LIP, (ii) in-air shock tubes, (iii) wet-lip and (iv) submerged shock tubes (in water).

22 672 I. Varghese et al. / Journal of Adhesion Science and Technology 22 (2008) Conclusions and Remarks Damage-free and effective removal of sub-100 nm particles is a challenge in semiconductor manufacture and nanotechnology for assurance of nano-scale cleanliness of lithography masks, as the minimum tolerable particle on the substrates is shrinking to sub-100 nm levels with each technological node. The laser induced plasma (LIP) technique is a fast, dry, chemical-free, non-contact precision and selective cleaning technology, in which damage is a concern as with other techniques in the sub-100 nm range. The two possible LIP damage sources excluding direct contact of the LIP with the photomask/wafer surface that have been identified are (i) the laser radiation heating (due to the very high plasma temperature) from the plasma core, and (ii) the thermo-mechanical load from the LIP shockwaves from hot gas (convection heating). Based on thermoelastic analyses (FE), the laser radiation heating (due to the very high plasma temperature) is observed to dominate LIP shockwave thermo-mechanical (convection heating) load by a factor of approx. 3. Thus radiation heating (nanosecond-scale excitation) leading to thermal expansion of the nanofilm has been determined as the chief source of LIP damage, compared to the LIP shockwave loading (microsecond-scale excitation). It was found that the film surface radial stress component σ rr was the most critical damage parameter in both radiation heating and LIP shockwave loading. The damage limits for maximum radial stress amplitude (σ rr,max ) and surface temperature (T max ) are 1.93 GPa and 725 K for no reflectivity of the Cr film, whereas 1.54 GPa and 635 K, respectively, for the case of 20% reflectivity, at the experimental damage threshold firing distance of 2.5 mm (d cr ) due to LIP radiation intensity heating. Since compressive stresses are applied due to LIP loading, residual tension in the film might help extend the damage threshold of the Cr film by lowering the resultant stresses that will be experienced. The minimum size PSL particle (soft particle) that can be removed from Cr film (photomask) utilizing LIP at the safe firing distance of d = 2.5 mm, with the 138 kpa available shockwave pressure in air, was estimated as 46 nm (JKR rolling detachment). The risk of thermo-mechanical damage due to the radiation heating and LIP shockwaves can be substantially reduced by moving the LIP core away from the substrate while generating the same pressure by utilizing shock tubes. Peak transient pressure of 523 kpa was measured at a gap distance of 10 mm, which resulted in a peak pressure amplification factor of 11 compared to in-air LIP. Wet-LIP is another LIP pressure amplification technique that resulted in a peak pressure of 1030 kpa, proving to be better than shock tubes in air (523 kpa). Submerged shock tubes (in water) with a peak pressure of 6.48 MPa, resulted in maximum pressure amplification. Particle removal down to 10 nm particles is predicted by wet-lip and theoretically removal of well below 10 nm sized PSL particles from silicon substrate utilizing submerged shock tubes is expected.

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