Method and system of liquid-assisted laser micromachining using laser repetition rate based on surface tension of liquid-assist medium

Abstract

Embodiments of methods and systems for liquid-assisted laser micromachining of a substrate are provided. A laser beam of a laser is directed at a substrate disposed in a liquid-assist medium. The substrate has a first major surface, a second major surface, and a body extending from the first major surface to the second major surface. The liquid-assist medium at least partially covers the second major surface. A focal point of the laser beam is moved along a path through the body from the second major surface toward the first major surface. The body of the substrate is removed along the path to define a cavity. The liquid-assist medium has a surface tension, and the laser pulses the laser beam at a repetition rate (F), in kHz, based on the surface tension (σ), in dyn / cm, according to F = [3.52 + 0.085σ + 0.002e 0,21(σ-37.8)] ± 0.8.

Description

Attorney Docket No.: SP24-222PCTMETHOD AND SYSTEM OF LIQUID-ASSISTED LASER MICROMACHINING USING LASER REPETITION RATE BASED ON SURFACE TENSION OF LIQUID- ASSIST MEDIUMCROSS-REFERENCE TO REEATED APPLICATIONS

[0001] This application claims the benefit of priority under 35 U.S.C. § 119 of U.S. Provisional Application No. 63 / 702,002 filed October 1, 2024, the content of which is incorporated herein by reference in its entirety.FIELD

[0002] The disclosure relates to methods and systems for machining substrates and, more particularly, to a method and system for liquid-assisted laser micromachining substrates.BACKGROUND

[0003] Precision machining of materials is used for many applications. Precision machining allows for the formation of miniature features in materials. Such features include holes, slots, grooves, and chamfers. Traditional techniques for precision machining involve mechanical methods (e.g., cutting, sawing, drilling, and scoring) or chemical methods (e.g., etching). Adaptation of traditional techniques to more demanding applications, however, has proven to be challenging. There is increasing demand for machining finer features and for forming features in a wider variety of materials. There is currently great interest in the precision machining of hard dielectric materials and in forming high aspect ratio features with a high degree of precision. Computer numerical control (CNC) machining, for example, has challenges in drilling holes with a diameter smaller than 100-200 pm in glass, especially when the aspect ratio exceeds 10-20.SUMMARY

[0004] According to an aspect, embodiments of the disclosure relate to a method. In the method, a laser beam of a laser is directed at a substrate disposed in a liquid-assist medium. The substrate has a first major surface, a second major surface that is opposite to the first major surface, and a body extending from the first major surface to the second major surface. The liquid-assist medium at least partially covers the second major surface. A focal point of the laser beam is moved along a path through the body of the substrate from the second major surface toward the first major surface. The body of the substrate is removed along the path to define a cavity extending from the second major surface toward the first major surface. TheAttorney Docket No.: SP24-222PCT liquid-assist medium comprises a surface tension, and the laser pulses the laser beam at a repetition rate (F), in kHz, based on the surface tension (o), in dyn / cm, according to F = [3.52 + 0.085o- + 0.002eo'21Cff-37'8)] ± 0.8.

[0005] According to another aspect, embodiments of the disclosure relate to a system. The system includes a laser configured to emit a laser beam along a system axis. A focusing optical system is configured to focus the laser beam to a focal point. A substrate holder contains a substrate and a liquid-assist medium. The substrate has a first major surface, a second major surface that is opposite to the first major surface, and a body extending from the first major surface to the second major surface. The liquid-assist medium at least partially covers the second major surface. The focusing optical system and the substrate holder are configured to move relative to each other along the system axis and over a plane perpendicular to the system axis so that a focal point of the laser beam is able to trace a path through the body of the substrate from the second major surface toward the first major surface. Relative movement of the focusing optical system and the substrate holder along the system axis is at a feed rate of at least 1 pm / s at a laser power of 150 mW or less.

[0006] Additional features and advantages will be set forth in the detailed description which follows, and in part will be readily apparent to those skilled in the art from that description or recognized by practicing the embodiments as described herein, including the detailed description which follows, the claims, as well as the appended drawings.

[0007] It is to be understood that both the foregoing general description and the following detailed description are merely exemplary, and are intended to provide an overview or framework to understanding the nature and character of the claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0008] The accompanying drawings are included to provide a further understanding, and are incorporated in and constitute a part of this specification. The drawings illustrate one or more embodiment s), and together with the description serve to explain principles and operation of the various embodiments. In the drawings:

[0009] FIG. 1 depicts a system for liquid-assisted laser micromachining, according to an exemplary embodiment;

[0010] FIG. 2 depicts a substrate holder containing a substrate undergoing liquid-assisted laser micromachining, according to an exemplary embodiment;Attorney Docket No.: SP24-222PCT

[0011] FIG. 3 schematically represents a laser path through a substrate during liquid-assisted laser micromachining, according to an exemplary embodiment; and

[0012] FIG. 4 is a graph of optimized laser repetition rate based on surface tension of the liquidassist medium, according to an exemplary embodiment.DETAILED DESCRIPTION

[0013] Reference will now be made in detail to various embodiments of a method and system for liquid-assisted laser micromachining in which the laser repetition rate is optimized based on the surface tension of the liquid-assist medium, examples of which are illustrated in the accompanying drawings. Liquid-assisted laser micromachining is a process in which material is removed from a substrate through acoustic shock and laser ablation at the interface between the liquid-assist medium and the substrate. As will be discussed more fully below, Applicant has found that the process of liquid-assisted laser micromachining can be enhanced by selecting the laser repetition rate based on the surface tension of the liquid-assist medium. In particular, when a relationship between the laser repetition rate and the surface tension of the liquid-assist medium was satisfied, it was found that the liquid-assisted laser micromachining process could be stabilized at a reasonable power while providing a relatively high machining rate. These and other aspects and advantages of the disclosed method and system of liquid-assisted laser micromachining will be described in relation to the embodiments provided below and in the drawings. These embodiments are presented by way of example and not by way of limitation.

[0014] FIG. 1 is a schematic view of an example liquid-assisted laser-based micromachining system (“system”) 10 according to embodiments of the present disclosure. In one or more embodiments, the system 10 can be used for processing a transparent dielectric to form an article, such as an optical interconnection device for optical fibers, amongst other possibilities. The system 10 includes a laser 20, which produces a substantially collimated laser beam 22. The laser beam 22 passes in a direction of propagation along a system axis AZ that runs in the z-direction. In an example, the laser 20 can include beam collimating optics (not shown) to form the substantially collimated laser beam 22. The wavelength of the laser 20 can be any wavelength at which the dielectric material of the substrate 100 is transparent. In one or more embodiments, the laser 20 emits a laser beam 22 having a wavelength in the UV, visible, or infrared portions of the electromagnetic spectrum. In one or more embodiments, the wavelength of the laser beam is in a range of 350 nm to 1700 nm. In one or more embodiments, the material of the substrate may have an internal transmittance at the laser wavelength of 70%Attorney Docket No.: SP24-222PCT or greater, in particular 80% or greater, most particularly 90% or greater. As used herein, unless otherwise specified, the term “internal transmittance” is used to refer to the transmittance through a glass sample that is corrected for Fresnel losses.

[0015] In one or more embodiments, the laser 20 is operable to produce a pulsed laser beam 22. As shown in FIG. 1, the laser beam 22 comprises a train of laser pulses 22P. The duration of the laser pulses 22P may be in the picosecond (ps) regime. In one or more embodiments, the laser beam pulses 22P have a duration in a range from 0.5 ps to 50 ps. In one or more embodiments, the laser 20 has a repetition rate for emitting the pulses of 2 kHz to 15 kHz, and as will be discussed more fully below, the specific repetition rate is based on the surface tension of the liquid-assist medium using in the liquid-assisted laser micromachining process. In one or more embodiments, the laser 20 is operated at a power in a range of 150 mW or less, in particular in a range of 50 mW to 150 mW.

[0016] In one or more embodiments, the system 10 includes a focusing optical system 40 downstream of the laser source 20 and along the system axis AZ. The focusing optical system 40 may comprise one or more optical elements such as one or more focusing lenses or focusing optics. In one or more embodiments, the focusing optical system 40 may also include one or more elements that provide beam conditioning (e.g., spatial filtering) and may also include one or more elements for beam steering (e.g., rotatable mirrors, etc.) and / or masking. In one or more embodiments, the focusing optical system 40 can be operably supported by a movable stage 44, providing precision linear and / or rotational movement along any one or more of the x-axis, y-axis, or z-axis.

[0017] In one or more embodiments, the system 10 also includes a substrate holder 50 having an interior 56 configured to contain a liquid-assist medium 60. In an example, the substrate holder 50 can be operably supported by a movable stage 70, providing precision linear and / or rotational movement along any one or more of the x-axis, y-axis, or z-axis. In an example, the system 10 only includes the movable precision stage 70 and the laser 20 is substantially stationary (e.g., is movable for coarse alignment). In one or more embodiments, the laser 20, the focusing optical system 40, and the substrate holder 50 are operably supported by a support base 75, such as an optical bench or another similar stable platform.

[0018] In one or more embodiments, including the embodiment shown in FIG. 1, a computer controller 80 is operably connected to at least one of the movable stage 70 of the substrate holder 50 or the movable stage 44 of the focusing optical system 40 to control the movementAttorney Docket No.: SP24-222PCT of one or both of the movable precision stages in operating the system 10 to carry out the micromachining process described herein.

[0019] The system 10 is configured to process a transparent dielectric substrate 100 having a body 101 that defines a first major surface 102 and a second major surface 104. In one or more embodiments, the transparent dielectric substrate 100 comprises a dielectric material, which may be, for example, a glass material, a glass-ceramic material, or a crystalline material. In one or more embodiments in which the dielectric substrate 100 is a glass material, the glass material may be an oxide glass or a non-oxide glass. Example of suitable glass materials include silica glasses, alkali silica glasses, alkaline earth silica glasses, borosilicate glasses, soda-lime glasses, alkaline earth boro-aluminosilicate glasses, and alkali-aluminosilicate glasses. Such glass materials may be strengthened by ion exchange or thermal tempering. A commercially available glass suitable for use as the dielectric substrate 100 is Iris™ glass (Coming Incorporated, Corning, NY). Example crystalline materials include oxide crystals, such as metal oxides (e.g., sapphire), and non-oxide crystals.

[0020] In one or more embodiments, the transparent dielectric substrate (hereinafter, “substrate”) 100 substantially planar such that the first major surface 102 is substantially parallel with the second major surface 104. In one or more embodiments, the substrate 100 has substantially constant thickness T (as shown in FIG. 2) defined as a distance between the first major surface 102 and the second major surface 104. In one or more embodiments, the thickness T is in a range from 0.03 mm to 5 mm. In one or more embodiments, the substrate 100 is rectangular in shape; although, shapes other than rectangular may also be used.

[0021] FIG. 2 is a cross-sectional side view of an assembled substrate holder 50. In one or more embodiments, the substrate holder 50 includes a holder body 5 land a cover 53. The cover 53 can be attached to an open side of the holder body 51 by any of a variety of means, such as fasteners. The cover 53 includes a transparent window-substrate 57. The windowsubstrate 57 is transparent to the wavelength of the laser beam 22. In one or more embodiments, the window-substrate 57 has an internal transmittance at the wavelength of the laser beam 22 of greater than or equal to 80%, greater than or equal to 90%, greater than or equal to 95%, or up to 100%.

[0022] In one or more embodiments, one or more spacers 58 are attached to a surface of the window-substrate 57 that faces the interior 56 of the substrate holder 50. The one or more spacers 58 are operable to provide a gap G between the window-substrate 57 and the working substrate 100. The material of the spacers 58 is such that the substrate 100 is releasablyAttorney Docket No.: SP24-222PCT attached to the spacers 58. As a non-limiting example, pottery clay may be used for the one or more spacers 58. In one or more embodiments, the spacer or spacers 58 allow the substrate 100 to be disposed in the substrate holder 50 so that both the first major surface 102 and the second major surface 104 are at least partially in direct contact with the liquid-assist medium 60. Providing the liquid-assist medium at the first major surface 102 of the substrate 100 reduces contamination of the first major surface 102 with process byproducts, reduces chipping of the first major surface 102 by reducing acoustic shock at the first major surface 102, decreases the minimum distance between cavities formed in the substrate 100, provides the ability to place cavities close to the edge of the substrate 100, and provides the ability to create precision features on an edge of the substrate 100. Notwithstanding, the liquid-assist medium 60 may be provided only in contact (at least partially) with one of the first major surface 102 or the second major surface 104 where machining is initiated.

[0023] In one or more embodiments, the gap G between an inner surface of the windowsubstrate 57 and the first major surface 102 of the substrate 100 is within a range from 0.06 mm to 1.6 mm. In particular, the gap G is selected so as not to be too small such that convection is insufficient and air bubbles become stuck between the window-substrate 57 and on the substrate 100. On the other hand, the gap G is selected so as not to be too thick to cause laser beam distortion and poor focusing because of turbulent convection.

[0024] In one or more embodiments, including the embodiment shown in FIG. 2, the substrate 100 is maintained within the interior 56 of the substrate holder 50 in a vertical orientation relative to gravity. In one or more embodiments, the substrate 100 is maintained within ten degrees of the vertical orientation. This vertical or nearly vertical orientation allows for air bubbles to quickly rise as a result of liquid convection and not become trapped and occlude the focused laser beam 22F. Additionally, the vertical or nearly vertical orientation allows debris from the laser process to drop away from the substrate 100 so that it too does not occlude the focused laser beam 22F. Notwithstanding, in one or more other embodiments, the substrate 100 may be oriented in a direction other than vertical, such as horizontal relative to gravity.

[0025] As mentioned above, the liquid-assist medium 60 is disposed on the interior 56 of the substrate holder 50. A variety of liquid-assist mediums may be used according to embodiments of the present disclosure. In one or more embodiments, the liquid-assist medium 60 is selected to have a surface tension in a range of 20 dyn / cm to 75 dyn / cm.

[0026] Water is one example of a liquid-assist medium 60 for liquid-assisted laser micromachining and high ablation rates. When water is used, a surfactant can be added toAttorney Docket No.: SP24-222PCT reduce surface tension and to prevent byproduct accumulation on the surface of the substrate 100 and to reduce the acoustic shock effect. As a non-limiting example, sodium dodecyl sulfate may be used as a surfactant. Other common surfactants known in the art may also be utilized.

[0027] Other example liquid-assist media 60 include fluorinated alkanes, fluorinated alcohols, fluorinated amines, methanol, ethanol, acetic acid, acetone, dimethyl sulfoxide (DMSO), ethylene glycol, and perfluorinated compounds. Commercially available examples of liquidassist media include Fluorinert™ FC-70 and Novec™ 7500 and 7700 (each available from 3M, St. Paul, MN). Preferable attributes of the liquid-assist medium 60 include low viscosity, high boiling point (e.g., greater than or equal to 80° C), high specific heat, low surface tension (for improved precision, e.g., a surface tension of less than 50 dyn / cm at 25° C) and high surface tension for high material removal rate (e.g., a surface tension of more than 50 dyn / cm at 25° C). Further, in one or more embodiments, the difference between the refractive index of the substrate 100 and the refractive index of the liquid-assist medium 60 is selected to be 0.2 or less. For instance, DMSO has a refractive index of about 1.48, which differs from a typical glass refractive index of 1.45 by 0.03.

[0028] With reference to both FIGS. 1 and 2, the operation of the system 10 to carry out the liquid-assisted laser micromachining process is now described. Initially, the substrate 100 is moved into a desired position relative to the system axis AZ, for example, using the movable stage 70. Once in position, the laser 20 is activated to form the substantially collimated beam 22, which is received by the focusing optical system 40. Using the substantially collimated beam 22, the focusing optical system 40 forms a focused laser beam 22F that is focused to a focus spot FS at a focus position FP along the system axis AZ. The focus spot FS has a diameter defined by a Gaussian beam waist. In one or more embodiments, the Gaussian beam waist is in a range from 2 pm to 10 pm.

[0029] In one or more embodiments, the focused laser beam 22F initially passes through the window substrate 57, the gap G, and the substrate 100 and forms the focus spot FS within the liquid- assist medium 60. FIGS. 1 and 2 show an initial focus position FP of the focus spot FS within the liquid-assist medium 60 and adjacent the second major surface 104. In one or more embodiments, adjacent to the second major surface 104 may be, e.g., in the liquid-assist medium 60 within about 10 pm of the second major surface 104.

[0030] The focus spot FS is subsequently moved forward to be at or near the second major surface 104. The focus spot FS has sufficient intensity to alter, in particular weaken, the structure of the material that makes up the body 101 of the substrate 100. The laser 20 is movedAttorney Docket No.: SP24-222PCT relative to the substrate 100 in the x, y and / or z directions to control the position of the focus spot FS. The path traveled by the focus spot FS will determine a shape of a cavity formed in the body of the substrate 100. In one or more embodiments, the substrate holder 50 with the substrate 100 is moved using the movable stage 70 while the focused laser beam 22F remains stationary to define the path of the focus spot FS. In one or more other embodiments, the focusing optical system 40 is moved using movable stage 44 while the substrate 100 and substrate holder 50 remain stationary to define the path of the focus spot FS. In still one or more other embodiments, both the substrate holder 50 with the substrate 100 and the focusing optical system 40 are moved using the movable stages 70, 44 to define the path of the focus spot FS.

[0031] FIG. 3 depicts an example motion path MP to produce a modification 121 of the substrate 100. As shown in FIG. 3, the focus spot FS is traced along a helical motion path MP that includes a motion component along the z-axis. In one or more embodiments, the helical motion path MP can have a pitch in the range from 0.1 pm to 30 pm.

[0032] The modification 121 in the substrate may have a maximum cross-sectional dimension (e.g., diameter) D controlled through motion of the focus spot FS over the motion path MP in the x and y directions, and the depth of the modification 121 can be controlled by movement of the focus spot over the motion path in the z direction. In one or more embodiments, including the embodiment shown in FIG. 3, the formation of the modification 121 begins at the second major surface 104 and continues through the body 101 in the direction of the first major surface 102. The modification 121 is ultimately used to form at least one cavity 150 in the substrate 100. In this regard, the modification 121 may extend through the entire body 101 of the substrate 100 from the second major surface 104 to the first major surface 102 (e.g., to define a through hole cavity 150) or only a part of the body 101 of the substrate 100.

[0033] In one or more embodiments, formation of the modification 121 includes ablation of the material that makes up the body 101 of the substrate 100. As material is removed from the second major surface 104, the liquid-assist medium 60 from the substrate holder 50 flows to occupy the evacuated space to maintain a wetted surface for heat removal and further micromachining. Micromachining at different depths relative to the second major surface 104 is achieved by moving the focus spot FS of the focused laser beam 22F (either through variation in the focusing optical system 40 or relative motion of the laser 20 and substrate 100) in the direction from the second major surface 104 toward the first major surface 102 of the substrate 100 over a select motion path MP. In one or more embodiments, the size (diameter) of theAttomey Docket No.: SP24-222PCT focus spot FS is selected to facilitate the flow of the liquid-assist medium 60 through the micromachined regions that define a tube-like modification 121.

[0034] Localized micromachining occurs in the vicinity of each position of the focus spot FS within the body 101 of the substrate 100 when forming the modification 121. For the helical modification 121, a helical arrangement of micromachined regions 123 is formed in the body 101 of the substrate 100. The micromachined regions 123 define the modification 121 and constitute regions of mechanical weakness which represent a trajectory for separation of the modification 121 from the rest of the body 101 of the substrate 100. Thus, in an example, the modification 121 can comprise micromachined regions 123 in the form of microcavities created by ablation and that form contiguous channels within the material that makes up the body 101 of the substrate 100. In this way, a core portion 121C of the body 101 as defined by the modification 121 is separated from the rest of the body 101 to form the cavity 150.

[0035] A given modification 121 traced using a particular motion path MP can be used to form a given cavity 150. A variety of different cavities 150 may be formed in the substrate 100 to define isolated features or, by intersecting cavities, to form complex features. The modifications 121 can have a variety of shapes to form a corresponding variety of cavities 150. Cross-sectional shapes of cavities 150 include circular, elliptical, round, square, and rectangular, and as discussed above, the cavities 150 may extend through part of or the entire thickness of the substrate 100 to form recesses, pits, slots, surface grooves, surface channels, or through-holes, amongst other possibilities. In one or more embodiments, the cavity has a maximum cross-sectional dimension in a range from 15 pm to 1000 pm. Further, the diameter or shape of the cavity 150 may change at different depths within the body 101 of the substrate 100.

[0036] As mentioned above, the disclosed liquid-assisted laser micromachining process provides increased material removal rate as well as making the process overall more consistent, robust, and stable. Specifically, as will be discussed more fully in the Experimental Example section below, these benefits are achieved by pulsing the laser at a repetition rate based on the surface tension of the liquid-assist medium according to Equation 1, below:F = [3.52 + 0.085o- + 0.002eo'21Cff-37'8)] ± 0.8. (1) in which F is the repetition rate (in kHz) and c is the surface tension of the liquid-assist medium (in dyn / cm). When the relationship of Equation 1 was satisfied, Applicant found that the liquid- assisted laser micromachining process was stable, operated at relatively low power, and provided a high axial feed rate. In one or more embodiments, the axial feed rate for the liquid-Attorney Docket No.: SP24-222PCT assisted laser micromachining process can be at least 1 pm / s, in particular at least 10 pm / s, more particularly at least 15 pm / s, and most particularly up to 30 pm / s. While the disclosed relationship provides a stable process at low power, which can maximize axial feed rate, the ultimate feed rate may depend on other factors, such as the particular motion path of the laser focal spot, laser scan speed, depth of the cavity, and desired cavity wall roughness, amongst other factors.

[0037] EXPERIMENTAL EXAMPLE

[0038] Material removal during liquid-assisted laser micromachining occurs because of nonlinear absorption of the intense laser beam in transparent dielectrics. Laser absorption leads to material breakdown (i.e., laser ablation) and to generation of oscillating micro-bubbles on the interface between the substrate and the liquid-assist medium. As has been reported in the literature (X. Liu et al., Optics & Laser Technology 41 (2009) pages 21- 24, the entire contents of which is incorporated herein by reference thereto), the oscillation frequency and collapse time (which is inverse of the frequency) of these micro-bubbles depends on the surface tension of the liquid-assist medium. For example, the collapse time of micro-bubbles in water (c ~ 72 dyn / cm) is has been found to be around 80 ps, which corresponds to an oscillation frequency of 12.5 kHz.

[0039] In view of the relationship between micro-bubble collapse time and surface tension, Applicants investigated the effect of matching the laser pulse repetition rate to the oscillation frequency. To this end, experiments were performed in which holes having a diameter of about 125 pm were drilled in a 2 mm thick fused silica substrate in contact with deionized water. The laser operated at 1030 nm wavelength, generating 10 ps long pulses. The beam was steered by a scanning galvanometer (Scanlab GmbH, Puchheim, Germany) with a lens having a numerical aperture (NA) of 0.15. The scanning galvanometer traced a pattern having the diameter of 125 pm and pulled the pattern through the sample along the system axis. In embodiments, the motion path MP generated by the scanning galvanometer for these experiments can be formed by the following steps: (i) the focus spot FS is configured to be positioned proximate to a surface of the substrate (e.g., the second major surface 104), (ii) the focus spot FS is then traced in a closed or near-closed (e.g., circular) path in a plane (e.g., the x-y plane illustrated in FIGS. 1-3), (iii) the focus spot FS is then incremented in a direction transverse or perpendicular (e.g., the z-direction illustrated in FIGS. 1-3) to the plane, and (iv) steps (ii) and (iii) are repeated until the focus spot FS passes substantially through or entirely through the thickness of the substrate. The repetition rate was varied from 5 kHz to 20 kHz,Attorney Docket No.: SP24-222PCT and the conditions were selected to achieve the fastest drilling (maximum feed rate) at minimal laser power. The operation was deemed to pass if three consecutive holes were able to be drilled. The results are summarized in Table 1 below.Table 1. Optimized Process Conditions for Different Repetition Rates

[0040] As can be seen from Table 1, drilling at 5 and 10 kHz was successful in producing the three consecutive holes, but the process was unstable, experiencing short interruptions and small defects on walls of the holes. In particular, the side wall defects were the result of incomplete cutting, and instead of round, smooth sidewalls, parts of the sidewall exhibited unfinished cutting that reduced the cross-sectional area, producing flat spots on an otherwise circular diameter of the hole. The 20 kHz repetition rate did not allow for through-hole drilling even at a reduced feed rate and comparatively high power (50-100 % higher than the other repetition rates). The 12.5 kHz condition, however, provided a significantly faster axial feed rate (almost 2x higher than at 5 and 10 kHz), and lower power (the required laser power is proportional to the repetition rate to keep the pulse energy the same). Accordingly, the optimum laser repetition rate corresponds to inverse of the micro-bubbles’ collapse time (i.e., to the micro-bubbles’ oscillation frequency).

[0041] With the knowledge that the optimum laser repetition rate corresponds to the oscillation frequency of the bubbles, which in turn depends on the surface tension of the liquid-assist medium, Table 2 provides surface tension information for various liquid-assist mediums. In the table below, two of the deionized water samples included a surfactant, in particular sodium dodecyl sulfate (“SDS”).Table 2. Surface Tension of Various Li quid- Assist MediaAttorney Docket No.: SP24-222PCT

[0042] Using the information, FIG. 4 provides a graph of optimum repetition rate based on surface tension. The curve in FIG. 4 was fitted with an equation, which is Equation 1 above. Based on Applicant’s observation, satisfactory results were still achieved when small deviations (± 0.8 kHz) were made to the laser repetition rate.

[0043] Unless otherwise expressly stated, it is in no way intended that any method set forth herein be construed as requiring that its steps be performed in a specific order. Accordingly, where a method claim does not actually recite an order to be followed by its steps or it is not otherwise specifically stated in the claims or descriptions that the steps are to be limited to a specific order, it is in no way intended that any particular order be inferred. In addition, as used herein, the article "a" is intended to include one or more than one component or element, and is not intended to be construed as meaning only one.

[0044] It will be apparent to those skilled in the art that various modifications and variations can be made without departing from the spirit or scope of the disclosed embodiments. Since modifications, combinations, sub-combinations and variations of the disclosed embodiments incorporating the spirit and substance of the embodiments may occur to persons skilled in the art, the disclosed embodiments should be construed to include everything within the scope of the appended claims and their equivalents.

Claims

Attorney Docket No.: SP24-222PCTWhat is claimed is:

1. A method, comprising: directing a laser beam of a laser at a substrate disposed in a liquid-assist medium comprising a surface tension, the substrate comprising a first major surface, a second major surface opposite the first major surface, and a body extending from the first major surface to the second major surface, the liquid-assist medium at least partially covering the second major surface; moving a focal point of the laser beam along a path through the body of the substrate from the second major surface toward the first major surface; removing the body of the substrate along the path to define a cavity extending from the second major surface toward the first major surface; and wherein the laser pulses the laser beam at a repetition rate (F), in kHz, based on the surface tension (o), in dyn / cm, according toF = [3.52 + 0.085o- + 0.002eo'21Cff-37'8)] ± 0.8.

2. The method of claim 1, wherein the liquid-assist medium comprises at least one of water, water and added surfactants, fluorinated alkanes, fluorinated alcohols, fluorinated amines, methanol, ethanol, acetic acid, acetone, dimethyl sulfoxide, ethylene glycol, or perfluorinated compounds.

3. The method of claim 1 or claim 2, wherein the surface tension is in a range from 20 dyn / cm to 75 dyn / cm.

4. The method of any of claims 1-3, wherein the repetition rate is in a range of 2 kHz to 15 kHz.

5. The method of any of claims 1-4, wherein the laser pulses the laser beam for pulse durations in a range from 0.5 ps to 50 ps.

6. The method of any of claims 1-5, wherein the laser beam has a wavelength in a range from 350 nm to 1700 nm.Attorney Docket No.: SP24-222PCT7. The method of any of claims 1-6, wherein the laser is operated at a power in a range from 50 mW to 150 mW.

8. The method of any of claims 1-7, wherein the focal point of the laser beam has a diameter as defined by Gaussian beam waist in a range from 2 pm to 10 pm.

9. The method of any of claims 1-8, wherein the path the focal point is moved through the body is a helical path.

10. The method of any of claims 1-9, wherein the cavity has a maximum cross-sectional dimension in a range from 15 pm to 1000 pm.

11. The method of any of claims 1-10, wherein the substrate comprises a thickness between the first major surface and the second major surface of 5 mm or less.

12. The method of any of claims 1-11, wherein the substrate has an internal transmittance of at least 70% at a wavelength of the laser beam.

13. The method of any of claims 1-12, wherein the substrate is a transparent dielectric.

14. A system, comprising: a laser configured to emit a laser beam along a system axis; a focusing optical system configured to focus the laser beam to a focal point; and a substrate holder containing a substrate and a liquid-assist medium, the substrate comprising a first major surface, a second major surface opposite the first major surface, and a body extending from the first major surface to the second major surface, the liquid-assist medium at least partially covering the second major surface; wherein the focusing optical system and the substrate holder are configured to move relative to each other along the system axis and over a plane perpendicular to the system axis so that a focal point of the laser beam is able to trace a path through the body of the substrate from the second major surface toward the first major surface; and wherein relative movement of the focusing optical system and the substrate holder along the system axis is at a feed rate of at least 1 pm / s at a laser power of 150 mW or less.Attorney Docket No.: SP24-222PCT15. The system of claim 14, wherein the liquid-assist medium comprises a surface tension (G) in dyn / cm and the laser is configured to pulse the laser beam at a repetition rate (F) in kHz based on the surface tension according toF = [3.52 + 0.085o- + 0.002eo'21Cff-37'8)] ± 0.8.

16. The system of claim 15, wherein the surface tension is in a range from 20 dyn / cm to 75 dyn / cm.

17. The system of claim 15 or claim 16, wherein the repetition rate is in a range from 2 kHz to 15 kHz.

18. The system of any of claims 14-17, wherein the laser is configured to pulse the laser beam for pulse durations in a range from 0.5 ps to 50 ps.

19. The system of any of claims 14-18, wherein the laser beam has a wavelength in a range from 350 nm to 1700 nm.

20. The system of any of claims 14-19, wherein the focal point of the laser beam has a diameter as defined by Gaussian beam waist in a range from 2 pm to 10 pm.

21. The system of any of claims 14-20, wherein the path that the focal point is traced through the body is a helical path.

22. The system of any of claims 14-21, wherein the substrate comprises a thickness between the first major surface and the second major surface of 5 mm or less.

23. The system of any of claims 14-22, wherein the substrate has an internal transmittance of at least 70% at a wavelength of the laser beam.

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