Apparatus such as a liquid lens and methods of manufacturing apparatus, wherein the junction is configured to fracture at the same burst pressure

Abstract

An apparatus comprising: a first substrate; and a second substrate bonded with the first substrate via an innermost bond, an outermost bond, and a bond between the innermost bond and the outermost bond, the second substrate comprising a via and a shaft extending through the via. Each of the bonds has a strength, and the strengths of the bonds sequentially increase from the innermost bond to the outermost bond. The strength of each bond is sufficiently low such that the bond, rather than the first substrate, fails in response to a liquid (within a cavity defined by the first substrate, a third substrate, and the via of the second substrate) exerting pressure on the first substrate. Each of the bonds is configured to fail at approximately the same pressure exerted on the first substrate by the liquid. Methods of manufacturing the apparatus are additionally disclosed.

Description

[0001] Cross-references to related applications

[0002] This application claims the benefit of priority to U.S. Provisional Application No. 63 / 104753, filed October 23, 2020, under 35 U.S.SC §119, the contents of which are incorporated herein by reference in their entirety. Background Technology

[0003] In some cases, liquid lenses comprise layered substrates, wherein a first (top) substrate is disposed on a second (center) substrate, the second (center) substrate including a through-hole and disposed on a third (bottom) substrate. The first and third substrates sandwich a second substrate, forming a cavity defined by the through-hole and two distinct liquids within the cavity. In some cases, the liquid lens comprises two distinct liquids that are generally immiscible and thus form a meniscus between the two liquids. The meniscus can be used as a lens to manipulate electromagnetic radiation (such as visible or infrared radiation) passing through it. The meniscus contacts the through-hole of the second substrate at an angle relative to the through-hole. Changing the angle at which the meniscus contacts the through-hole alters the shape or position of the meniscus, or both, thereby changing the way the meniscus manipulates the electromagnetic radiation passing through. Subjecting the liquid to an electric field can change the angle at which the meniscus contacts the through-hole; this is known as electrowetting.

[0004] The layered substrates of the liquid lens are hermetically sealed to prevent liquid escape. In other words, the first substrate is bonded to the second substrate, and the second substrate is bonded to the third substrate. In some cases, a laser is used to impart heat at the interface between the substrates, which forms a strong inorganic bond between the substrates upon cooling. The imparted heat is highly localized and dissipates rapidly, thus not degrading the potentially heat-sensitive liquid. In some cases, the laser forms concentric bonds centered on vias. For example, the laser can form as many concentric bonds as possible within a allocated space. The concentric bonds are closed-loop to provide a hermetically sealed seal. More than one concentric bond is used to create redundancy in case any given concentric bond has a defect that could otherwise prevent a hermetically sealed seal. The process of forming such a bond via a laser is sometimes referred to as "laser-assisted welding."

[0005] Liquid lenses are particularly suitable for electronic devices such as tablets and smartphones. In some cases, the liquid within the cavity of the liquid lens exerts pressure on a first substrate, a third substrate, or both. For example, an increase in liquid temperature can cause the liquid to expand. As another example, if an electronic device is dropped and impacts a surface, the resulting jolt can cause the liquid to exert pressure on the substrate. Electronic device manufacturers sometimes specify the burst pressure of the liquid lens. The burst pressure can represent the minimum internal pressure (e.g., exerted by the liquid) at which the first substrate and / or the bond between the first and second substrates is expected to fail. In other words, the first substrate and / or the bond should not fail in response to internal pressures below the burst pressure exerted by the liquid.

[0006] However, the problem is that the properties of the bonding can cause the liquid to (i) cause the first substrate to break at the internal bonding line, or (ii) cause all concentric bonds between the first and second substrates to break in a rapid sequence in the same event. In either case, the liquid lens becomes inoperable. These problems extend beyond liquid lenses to devices other than liquid lenses, including liquids disposed between bonded substrates (e.g., hermetic sealing devices). Summary of the Invention

[0007] This disclosure solves the problem of joints formed concentrically around an axis via laser, wherein each joint has a different joint strength, and the joint strength increases sequentially with respect to distance from the axis. In other words, the joint strength increases with outward movement from the axis. The joint strength is configured such that an increase in pressure from a liquid within a cavity of a device (such as a liquid lens) causes the joint to fail rather than the first substrate to burst. Furthermore, the strength and radius of each joint cooperate such that all joints in the joint fail under the same or substantially the same pressure.

[0008] According to a first aspect of the present disclosure, an apparatus includes: a first substrate; and a second substrate, the second substrate being joined to the first substrate via a plurality of joints, the plurality of joints including an innermost joint, an outermost joint, and at least one intermediate joint between the innermost joint and the outermost joint; wherein the strength of the joints increases sequentially from the innermost joint to the outermost joint.

[0009] According to the second aspect, the first aspect, wherein: each joint includes a different effective fracture toughness (K IC The innermost joint includes the minimum effective fracture toughness (K). IC The outermost joint includes the maximum effective fracture toughness (K). IC ); and the effective fracture toughness (K) of each joint in at least one intermediate joint. IC The engagement increases toward the outermost side.

[0010] According to the third aspect, the device of any one of the first to second aspects further includes: a third substrate, which is bonded to the second substrate relative to the first substrate; a cavity defined by through-holes in the first substrate, the third substrate, and the second substrate; and a liquid disposed within the cavity; wherein the strength of each bond is low enough that the bond, rather than the first substrate, fails in response to pressure applied to the first substrate by the liquid.

[0011] According to the fourth aspect, the apparatus of any one of the first to second aspects further includes: a third substrate bonded to the second substrate relative to the first substrate; a cavity defined by through-holes in the first substrate, the third substrate, and the second substrate; and a liquid disposed within the cavity; wherein each of the bonding components is configured to fail under substantially the same pressure applied to the first substrate by the liquid.

[0012] According to the fifth aspect, any one of the third to fourth aspects, wherein: each joint includes a radius; and the radius and strength of the joint are co-configured such that each joint fails under substantially the same pressure applied by the liquid to the first substrate.

[0013] According to the sixth aspect, any one of the third to fifth aspects, wherein the pressure at the joint failure point is 1 MPa to 3 MPa.

[0014] According to the seventh aspect, any one of the first to sixth aspects, wherein each of the first substrate and the second substrate includes a coefficient of thermal expansion greater than 5 ppm / ℃ from 20℃ to 300℃.

[0015] According to the eighth aspect, any one of the first to seventh aspects, wherein: each joint includes a width, and all joints have widths that are at least substantially equal; adjacent joints are separated by a spacing, and the spacing between all adjacent joints is at least substantially equal; and the ratio of the spacing to the width is 1 to 5.

[0016] According to the ninth aspect, or any one of the first to eighth aspects, wherein the device is a liquid lens.

[0017] According to a tenth aspect, an apparatus includes: a first substrate; a second substrate joined to the first substrate via a plurality of joints, the plurality of joints including an innermost joint, an outermost joint, and at least one intermediate joint between the innermost joint and the outermost joint, the second substrate including a through-hole; a third substrate joined to the second substrate opposite to the first substrate; a cavity defined by the through-hole of the first substrate, the third substrate, and the second substrate; and a liquid disposed within the cavity; wherein each of the joints is configured to fail under substantially the same pressure applied to the first substrate by the liquid.

[0018] According to the eleventh aspect, the tenth aspect, the strength of the joint increases sequentially from the innermost joint to the outermost joint; and the radius and strength of the joint are co-configured such that each joint fails under approximately the same pressure applied by the liquid to the first substrate.

[0019] According to the twelfth aspect, any one of the tenth to eleventh aspects, wherein: each joint has a substantially equal width; each pair of adjacent joints is separated by a substantially equal spacing; and the ratio of spacing to width is 1 to 5.

[0020] According to a thirteenth aspect of this disclosure, a method of manufacturing an apparatus includes: assigning a minimum burst pressure; determining a range of incident laser energy densities ranging from a minimum incident laser energy density sufficient to form a bond between a first substrate and a second substrate to a maximum incident laser energy density sufficient to form a bond weaker than that between the first substrate and the second substrate; determining a range of bond strength ranging from a minimum bond strength formed using the minimum incident laser energy density to a maximum bond strength formed using the maximum incident laser energy density; determining a range of bond radii varying from the assigned minimum burst pressure and the determined range of bond strengths, the range of bond radii ranging from the minimum radius of the innermost bond to the maximum radius of the outermost bond; and determining the number of bonds, each... Each joint has an equal width and an equal spacing between adjacent joints, such that the ratio of spacing to width is 1 to 5; the radius of each of at least one intermediate joint between the innermost joint and the outermost joint is determined, the radius varying depending on the number of joints determined and the spacing between adjacent joints; the intensity of each intermediate joint varying depending on the determined radius of each intermediate joint is determined; the incident laser energy density corresponding to the determined intensity of each intermediate joint within the range of incident laser energy density is determined; and the innermost joint is formed at the minimum radius using the minimum incident laser energy density, the outermost joint is formed at the maximum radius using the maximum incident laser energy density, and each intermediate joint is formed at the determined radius using the determined incident laser energy density.

[0021] According to the fourteenth aspect and the thirteenth aspect, wherein: (a) determining the range of incident laser energy density from the minimum incident laser energy density sufficient to form a bond between the first substrate and the second substrate to the maximum incident laser energy density sufficient to form a bond weaker than that between the first substrate and the second substrate includes: determining the range of laser power from the minimum laser power sufficient to form a bond between the first substrate and the second substrate to the maximum laser power sufficient to form a bond weaker than that between the first substrate and the second substrate; (b) determining the range of bonding strength from the minimum bonding strength formed using the minimum incident laser energy density to the maximum bonding strength formed using the maximum incident laser energy density includes: determining the range of bonding strength from the minimum bonding strength formed using the minimum laser power to the maximum bonding strength formed using the maximum laser power. (c) Determining the incident laser energy density corresponding to each intermediate joint within the range of the maximum joint strength; (d) Forming the innermost joint at the minimum radius using the minimum incident laser energy density, forming the outermost joint at the maximum radius using the maximum incident laser energy density, and forming each intermediate joint at the determined radius using the determined incident laser energy density includes: forming the innermost joint at the minimum radius using the minimum laser power, forming the outermost joint at the maximum radius using the maximum laser power, and forming each intermediate joint at the determined radius using the determined laser power.

[0022] According to the fifteenth aspect and the fourteenth aspect, determining the minimum laser power includes attempting to form a joint with various laser powers, wherein at least one laser power is insufficient to form a joint, and the minimum laser power for forming a joint is the minimum laser power.

[0023] According to any one of the sixteenth, fourteenth, and fifteenth aspects, determining the maximum laser power includes (a) preparing a sample pair of a first substrate and a second substrate, (b) stacking each sample pair to form an interface between the first substrate and the second substrate, and the interface of each sample pair is subjected to different laser powers from the minimum laser power upward, thereby forming a series of parallel and spaced-apart joints at the interface of each pair between the first substrate and the second substrate, (c) for each sample pair, placing a wedge between the first substrate and the second substrate, and (d) for each sample pair, pushing the wedge closer to the series of joints until (i) the joint closest to the wedge becomes unjoined, or (ii) the first substrate breaks; and the highest laser power that causes the joint closest to the wedge to become unjoined rather than the first substrate to break is the maximum laser power.

[0024] According to the seventeenth aspect, or any one of the fourteenth to sixteenth aspects, determining the range of bonding strength includes (a) preparing sample pairs of the first substrate and the second substrate, (b) stacking each sample pair to form an interface between the first substrate and the second substrate, and subjecting the interface of each sample pair to different laser powers within a range of laser powers to form a series of parallel and spaced bondings between the first substrate and the second substrate, (c) for each sample, placing a wedge between the first substrate and the second substrate, (d) pushing the wedge closer to a series of bondings formed by a specific laser power, (e) determining the distance between the wedge at the point of bonding breakage and the bonding closest to the wedge, and (f) relating the determined distance to a function of laser power; wherein the determined distance is within a range from a minimum distance associated with a bonding formed by the maximum laser power to a maximum distance associated with a bonding formed by the minimum laser power.

[0025] According to the eighteenth and seventeenth aspects, the distance determined therein decreases as the laser power increases.

[0026] According to aspect nineteen, or any one of aspects sixteen to eighteen, wherein the wedge-shaped member includes a razor blade.

[0027] According to aspect 20, or any one of aspects 17 to 19, wherein determining the range of joint strength includes the effective fracture toughness (K) of the joint. IC It is quantized as a function of the determined distance.

[0028] According to aspect 21, aspect 20, the effective fracture toughness (K) of the joint will be... IC Quantification into a function of the determined distance includes using a numerical model, which will combine the effective fracture toughness (K) of the joint. IC It is quantified as a function of the distance at the joint fracture point caused by the modeled wedge.

[0029] According to aspects 22 and 21, the numerical model uses the thickness of the modeled wedge, the width of the joint, the spacing between adjacent joints, the thickness of the first substrate, the thickness of the second substrate, the Young's modulus of the first substrate, the Young's modulus of the second substrate, the Poisson's ratio of the first substrate, the Poisson's ratio of the second substrate, the shear modulus of the first substrate, and the shear modulus of the second substrate as variables.

[0030] According to aspects 23 and 22, the numerical model quantifies the stress intensity factors of longitudinal opening and in-plane shear for the range of assumed distances at the crack initiation point, as well as the effective fracture toughness (K) from the stress intensity factors of longitudinal opening and in-plane shear. IC ).

[0031] According to the 24th aspect and the 23rd aspect, wherein (a) determining the range of incident laser energy density from the minimum incident laser energy density sufficient to form a bond between the first substrate and the second substrate to the maximum incident laser energy density for forming a bond weaker than the first substrate between the first substrate and the second substrate includes: determining the range of laser velocity from the maximum laser velocity sufficient to form a bond between the first substrate and the second substrate to the minimum laser velocity for forming a bond weaker than the first substrate between the first substrate and the second substrate; (b) determining the range of bonding strength from the minimum bonding strength formed using the minimum incident laser energy density to the maximum bonding strength formed using the maximum incident laser energy density includes: determining the range of bonding strength from the minimum bonding strength formed using the maximum laser velocity to the minimum bonding strength formed using the maximum laser velocity. (c) Determining the incident laser energy density, which varies with the determined intensity, for each intermediate bond within the range of the maximum bond strength; and (d) forming the innermost bond at the minimum radius using the minimum incident laser energy density, forming the outermost bond at the maximum radius using the maximum incident laser energy density, and forming each intermediate bond at the determined radius using the determined incident laser energy density, which includes forming the innermost bond at the minimum radius using the maximum laser velocity, forming the outermost bond at the maximum radius using the minimum laser velocity, and forming each intermediate bond at the determined radius using the determined laser velocity.

[0032] According to aspect 25, or any one of aspects 13 to 24, wherein the range for determining the joint radius includes the effective fracture toughness (K) for the joint. IC The range quantifies the pressure at each joint burst as a function of the joint radius.

[0033] According to aspects 26 and 25, the numerical model is for the effective fracture toughness (K) of the joint. IC The range quantifies the pressure at each joint burst as a function of the joint radius.

[0034] According to aspect 27, any one of aspects 13 to 26, wherein the ratio of the spacing to the width of the joints is 1.75 to 3.5; and the number of joints is at least 5.

[0035] According to aspect 28, or any one of aspects 13 to 27, wherein determining the strength of each intermediate joint includes determining the effective fracture toughness (K) of each of the intermediate joints. IC It is quantified as a function of the determined radius and assigned burst pressure of each in the intermediate joint.

[0036] According to aspects 29 and 28, the numerical model is for the effective fracture toughness (K) of the joint. IC The range quantifies the pressure at each joint burst as a function of the joint radius, and according to the model, the effective fracture toughness (K) of each in the intermediate joint is... IC It is quantified as a function of the determined radius and the assigned burst pressure.

[0037] According to aspects 30 and 29, determining the strength of each intermediate joint includes interpolating a graph for a given effective fracture toughness (K) of the joint. IC The burst pressure is plotted as a function of the radius of the joint.

[0038] According to aspect 31, any one of aspects 13 to 30, wherein determining the incident laser energy density corresponding to each intermediate joint includes (a) using a numerical model, the numerical model determining the effective fracture toughness (K0) of the joint. IC ) is quantified as a function of the joint radius and burst pressure to determine the fracture toughness (K) of each intermediate joint. IC (b) Using a numerical model, the distance at which the modeled wedge causes the joint to fracture is quantified as the effective fracture toughness (K) of the joint. IC The function of ) is used to determine the dependence on the determined fracture toughness (K). IC (c) the distance of each of the intermediate junctions, and experimentally correlate the distance as a function of the incident laser energy density to determine the incident laser energy density of each intermediate junction that varies with the determined distance of each intermediate junction.

[0039] According to the thirty-second aspect, the thirty-first aspect, wherein relating the distance as a function of the incident laser energy density includes (a) preparing a sample pair of a first substrate and a second substrate, (b) stacking each sample pair to form an interface between the first substrate and the second substrate, and the interface of each sample pair being subjected to different incident laser energy densities within a range of incident laser energy densities to form a series of parallel and spaced-apart joints between the first substrate and the second substrate, (c) for each sample, placing a wedge between the first substrate and the second substrate, (d) pushing the wedge closer to the series of joints formed by a specific incident laser energy density, (e) determining the distance between the wedge at the joint break and the joint closest to the wedge, and (f) relating the determined distance as a function of the incident laser energy density.

[0040] According to aspect 33, any one of aspects 13 to 32, wherein the minimum burst pressure is at least 1 MPa.

[0041] According to aspect 34, any one of aspects 13 to 32, wherein the minimum burst pressure is at least 2 MPa.

[0042] According to aspect 35, any one of aspects 13 to 32, wherein the minimum burst pressure is 2 MPa to 3 MPa.

[0043] According to aspect thirty-six, any one of aspects thirteen to thirty-five, wherein the incident laser energy density increases sequentially for each joint from the innermost joint to the outermost joint.

[0044] According to aspect thirty-seven, or any one of aspects thirteen to thirty-six, the resulting joint is concentric around the axis.

[0045] According to aspect thirty-eight, any one of aspects thirteen to thirty-seven, wherein the strength of the joint increases sequentially from the innermost joint with the minimum strength to the outermost joint with the maximum strength.

[0046] According to any one of the thirty-nine aspects, from the thirteenth to the thirty-eighth aspect, the device is a liquid lens; and both the first substrate and the second substrate are glass.

[0047] The following detailed description will describe additional features and advantages, which will be apparent in part to those skilled in the art, or may be recognized by practicing the embodiments described herein, including the following detailed description, claims, and drawings.

[0048] It should be understood that both the above general description and the following detailed description are merely exemplary and intended to provide an overview or framework for understanding the nature and characteristics of the claims. The accompanying drawings are included to provide further understanding and are incorporated into and form part of this specification. The drawings illustrate one or more embodiments and, together with the description, are used to explain the principles and operation of the embodiments. Attached Figure Description

[0049] Figure 1 This is an exploded perspective view of some embodiments of the device (specifically a liquid lens), showing a second substrate having a through-hole, and the second substrate being disposed between a first substrate and a third substrate;

[0050] Figure 2 yes Figure 1 A perspective view of the device shows the joining of a first substrate and a second substrate, the joining being concentrically arranged about an axis extending through a through hole, and including an innermost joining and an outermost joining.

[0051] Figure 3 Is it through Figure 2 The line III-III intercepted Figure 1 A cross-sectional view of the device shows adjacent joints separated by equal spacing, and each joint has the same width;

[0052] Figure 4 It is manufacturing Figure 1 Flowcharts of some embodiments of the device's method;

[0053] Figure 5 This is a sample of a first and second substrate joined together using a series of joints, and a cross-sectional view of a wedge inserted between the first and second substrates, the wedge being pushed toward the nearest joint in the series of joints to determine the distance between the wedge and the nearest joint at the point of breakage of the nearest joint, or alternatively, whether the first substrate is based on... Figure 4 The method breaks down due to several steps;

[0054] Figure 6 yes Figure 5 A top view of the sample;

[0055] Figure 7 The graph plots the experimentally determined distance between the wedge at the joint fracture point and the nearest joint as a function of the laser energy density used to form the joint (here, specifically, the laser power at a constant laser speed and a constant laser spot size). It shows that this distance decreases from a maximum distance associated with the minimum incident laser energy density that can form the joint (here, the minimum laser power at a given laser speed and spot size) to a minimum distance associated with the maximum incident laser energy density that can form the joint (here, the maximum laser power at a given laser speed and spot size), which has insufficient strength to cause the first substrate to fracture before the joint fails.

[0056] Figure 8 This is a schematic cross-sectional view of a wedge-shaped component used in numerical modeling, which causes [the following text appears to be incomplete and requires further context: "from the representation"] Figure 5 The displacement of the double cantilever extending from the joint of the first and second substrates.

[0057] Figure 9 It is by Figure 8 The graphs generated by the numerical modeling of the wedge scenario show the effective fracture toughness K, which varies with the distance between the modeled wedge and the joint. IC At this distance, the joint fractures under several assumed joint widths, where the effective fracture toughness K IC It increases as the distance decreases;

[0058] Figure 10 This is a cross-sectional schematic diagram illustrating numerical modeling of some embodiments of bonding a first substrate to a second substrate, wherein pressure is applied to the first substrate through a through-hole in the second substrate;

[0059] Figure 11 It is by Figure 10 The graphs generated by the numerical modeling scenario show the effective fracture toughness K for various fixed values. IC The value, which varies with the critical burst pressure of the joint radius (e.g., the pressure at the joint fracture point between the first and second substrates), shows the effective fracture toughness K of the joint in order for joints of different radii to burst at the same assigned burst pressure. IC It must increase with the increase of the radius of the joint;

[0060] Figure 12 It is a graph determined experimentally by the distance between the nearest joint in a series of joints, where the joint breaks, showing that the distance decreases as the spacing decreases (and thus the joint strength increases) until a certain point.

[0061] Figure 13 It is an experimentally determined graph of the distance between the wedge, which varies with the incident laser energy density (here, specifically, the laser power in watts at constant laser speed and spot size), and the nearest junction in a series of junctions generated by the laser. It shows that the minimum incident laser energy density (i.e., the minimum laser power) provides the maximum distance, and the maximum incident laser energy density (i.e., the maximum laser power) provides the minimum distance.

[0062] Figure 14 The effective fracture toughness K of the joint is determined by the distance between the wedge and the joint at the fracture point. IC The numerical modeling curves show the curves from... Figure 13 The minimum distance provides the maximum effective fracture toughness K IC And from Figure 13 The maximum distance provides the minimum effective fracture toughness K IC ;

[0063] Figure 15 It is for various fixed effective fracture toughness K IC The numerical modeling curve of the burst pressure varying with the radius of the joint shows the value derived from the assumed assigned burst pressure. Figure 14 Minimum effective fracture toughness value K IC Provide a minimum radius value (e.g., Figure 1 The innermost engagement radius of the device), and from Figure 14 Maximum effective fracture toughness K IC The value provides the maximum radius value (e.g., Figure 1 (the radius of the outermost junction of the device);

[0064] Figure 16 yes Figure 15 The magnified portion of the graph shows Figure 1 The radius of each joint in the device's joints is such that the joints have a spacing-to-width ratio between 1 and 5 (e.g., between 1 and 3.5), and each joint must have an effective fracture toughness K that detonates under the same assigned blast pressure. IC value;

[0065] Figure 17 yes Figure 14 The magnified portion of the graph shows the dependent variable from Figure 16 The obtained effective fracture toughness K IC Value Figure 1 The distance value of each joint in the device's connection; and

[0066] Figure 18 yes Figure 13 The magnified portion of the graph shows the dependent variable from Figure 17 The obtained distance values ​​are to be used to form Figure 1 The incident laser energy density of each junction in the device (here, specifically, laser power in watts at constant laser speed and spot size). Detailed Implementation

[0067] Reference will now be made in detail to these embodiments, examples of which are illustrated in the accompanying drawings. Where possible, the same reference numerals will be used throughout the drawings to indicate the same or similar parts.

[0068] refer to Figures 1-3This document discloses an apparatus 10 having a first substrate 12 and a second substrate 16. In one embodiment, the apparatus 10 is a liquid lens. In other embodiments, the apparatus 10 is an OLED, a MEMS device (such as a projector moving mirror chip or a miniaturized radar glass package), or a microfluidic device (such as a flow cell or microreactor). In one embodiment, the apparatus 10 includes a first substrate 12, a third substrate 14, and a second substrate 16 disposed between the first substrate 12 and the third substrate 14. In one embodiment, the first substrate 12, the third substrate 14, and the second substrate 16 are all glass (e.g., having a glass composition primarily comprising oxide-based SiO2). The second substrate 16 includes a through-hole 18. The through-hole 18 of the first substrate 12, the third substrate 14, and the second substrate 16 defines a cavity 20. In one embodiment, a liquid 22 comprising a first liquid 22a and a second liquid 22b is disposed in the cavity 20. An axis 24 extends through the cavity 20. The first substrate 12 and the second substrate 16 are attached to each other via a plurality of joints 26, which are concentric about the axis 24 in this embodiment. The plurality of joints 26 includes an innermost joint 26a and an outermost joint 26b. The innermost joint 26a may be the joint 26 positioned closest to the cavity 20 and / or the axis 24. The outermost joint 26b may be the joint 26 positioned furthest from the cavity 20 and / or the axis 24. In an embodiment, the plurality of joints 26 includes at least one intermediate joint 26 disposed between the innermost joint 26a and the outermost joint 26b. Similarly, the third substrate 14 and the second substrate 16 are attached to each other via similar joints 26. This disclosure specifically discusses only the joints 26 that join the first substrate 12 and the second substrate 16, but this disclosure is equally applicable to the joints 26 between the second substrate 16 and the third substrate 14. The joints 26 have a width 30. Each joint 26 is spaced apart from the next adjacent joint by a pitch 32 (e.g., the center-to-center spacing or pitch between adjacent joints). In an embodiment, each joint 26 is centered on the axis 24 and spaced apart from the axis 24 by a radius 36. The properties and characteristics of the device 10 will be discussed further below.

[0069] I. Methods for manufacturing equipment

[0070] Now for reference Figure 4 The method 34 for manufacturing equipment 10 is described.

[0071] A. Determine the minimum burst pressure. At step 35, method 34 includes assigning a minimum burst pressure. The minimum burst pressure is the minimum pressure within cavity 20 that the device 10 is designed and manufactured to fail according to method 34 (e.g., the minimum fluid pressure 56 from the liquid 22 within cavity 20). Figure 10For example, the device 10 designed and manufactured according to method 34 is configured to withstand all fluid pressure 56 from liquid 22 up to a minimum burst pressure without causing the first substrate 12 to fracture (e.g., fracture causing a crack to extend completely through the thickness of the first substrate 12) or rendering the joint 26 between the first substrate 12 and the second substrate 16 unjoined. In an embodiment, the minimum burst pressure is a purchaser requirement (e.g., specification). The liquid 22 within the cavity 20 of the device 10 imparts a fluid pressure 56, and the device 10 manufactured according to method 34 is configured to withstand this fluid pressure 56. In an embodiment, the minimum burst pressure is at least 1 MPa, at least 2 MPa, between 1 MPa and 3 MPa, or between 2 MPa and 3 MPa.

[0072] B. Determine the range of incident laser energy densities used to form the bond. (Reference) Figures 5-7 In step 38, method 34 includes determining a range of incident laser energy densities, from a minimum incident laser energy density sufficient to form a bond 26 between the first substrate 12 and the second substrate 16 to a maximum incident laser energy density sufficient to form a bond 26 between the first substrate 12 and the second substrate 16, which is weaker than the first substrate 12. That is, the maximum incident laser energy density forms a bond 26 with insufficient strength to cause the first substrate 12, rather than the bond 26, to fracture in response to a force (such as pressure 56) separating the first substrate 12 from the second substrate 16. For example, the maximum incident laser energy density could be the highest incident laser energy density forming the bond 26, which has sufficiently low strength such that the bond 26 becomes unbonded before the first substrate 12 fractures when an increased force is applied to separate the first substrate 12 from the second substrate 16. The strength of the bond 26 is referred to herein as “effective fracture toughness K”. IC "To quantify, although other quantifications and measurements of the intensity of the junction 26 can be used. Incident laser energy density is the laser energy per unit area (i.e., spot size) of the incident laser spot incident on the interface between the first substrate 12 and the second substrate 16. Therefore, at a constant spot size and constant laser velocity, the incident laser energy density increases with increasing laser power (wattage). At a constant spot size and constant laser power, the incident laser energy density increases with decreasing laser velocity. At a constant laser power and constant laser velocity, the incident laser energy density increases with decreasing spot size."

[0073] In an embodiment, at least one of the first substrate 12 or the second substrate 16 is substantially transparent to the laser emission wavelength(s) (e.g., transmittance greater than 75%), and a laser-absorbing film is disposed between the first substrate 12 and the second substrate 16 to facilitate the emission of laser light from which a bond 26 is formed between the first substrate 12 and the second substrate 16. The laser-absorbing film absorbs the emission from the laser light, which causes localized heating and softening of the first substrate 12 and the second substrate 16. The first substrate 12 and the second substrate 16 then cool and form the bond 26. At relatively low incident laser energy densities (e.g., relatively low laser power or relatively high laser velocity), the laser-absorbing film can withstand heating and act as a conductive path for controlling the device 10. At relatively high incident laser energy densities (e.g., relatively high laser power or relatively low laser velocity), the laser-absorbing film can diffuse throughout the bond 26 into the first substrate 12 and the second substrate 16. Example laser-absorbing films include chromium oxynitride and chromium metal, although other metals, metal oxides, polymers, or other materials may also be used.

[0074] In an embodiment, to determine the minimum incident laser energy density, the laser attempts to bond the first substrate 12 and the second substrate 16 at various incident laser energy densities. Some incident laser energy densities will be insufficient to form a bond 26 between the first substrate 12 and the second substrate 16. The lowest incident laser energy density that results in the formation of a bond 26 between the first substrate 12 and the second substrate 16 can be designated as the minimum incident laser energy density.

[0075] In an embodiment, to determine the maximum incident laser energy density, (a) a sample pair of the first substrate 12 and the second substrate 16 is prepared, (b) each sample pair is stacked to form an interface between the first substrate 12 and the second substrate 16, and the interface of each pair is subjected to different incident laser energy densities from the minimum incident laser energy density upwards, and a series 40 of parallel and spaced joints 26 are formed between the first substrate 12 and the second substrate 16 at the interface of each pair, (c) a wedge 42 is placed between the first substrate 12 and the second substrate 16, and (d) the wedge 42 is pushed closer to the series 40 of joints 26 until (i) the joint 26 closest to the wedge 42 fails (e.g., becomes unjoined) or (b) the first substrate 12 breaks.

[0076] For (a), the sample pair can be generally rectangular and have a width 52 that is narrower than the width of the wedge 42 (see Figure 6 For example, the thickness of the first substrate 12 of the sample is 48 and the thickness of the second substrate 16 of the sample is 50 (see...). Figure 5The widths can be the same, such as 0.5 mm. Each substrate 12, 16 has an identical example width 52 of 1 inch and an example length (orthogonal to the width 52) of 3 inches. At least one of the first substrate 12 and the second substrate 16 is coated with a film that absorbs at the incident laser wavelength to provide interfacial heating.

[0077] For (b), the joints 26 are all straight and parallel to each other, and are center-to-center spaced at a pitch 32 such that the pitch-to-width ratio is greater than 5. The joints 26 extend across the entire width 42 of the now-joined substrates 12, 16. The first joint 26 in the series 40 of joints 26 may be approximately 0.5 inches from the edge of the stacked substrates 12, 16, thereby allowing space to insert the wedge 42 and move the wedge 42 closer to the first joint 26 in the series 40 of joints 26. For one sample, the minimum incident laser energy density is selected to form the series 40 of joints 26. For the next sample, the series 40 of joints 26 is formed with an increased incident laser energy density, and so on for each subsequent sample. Assuming that the laser power is increased to increase the incident laser energy density, the laser can be configured to provide a constant spot size (e.g., 10-15 μm spot size) at a constant laser velocity (e.g., 50 to 300 mm / s). Lasers can be pulses with repetition frequencies ranging from 10 kHz to 500 kHz, or they can be continuous waves. The pulse duration of a pulsed laser is typically 5 to 20 ns.

[0078] For (c) and (d), the wedge 42 is a #60 0.15-0.14mm thick razor blade from Lutz Blades (Sorlingen, Germany). For (d), the razor blade wedge 42 is slowly translated toward the nearest joint 26 at a speed of approximately 1 mm per minute using a plunger-type digital micrometer (Mitutoyo, MHD-2”MB-164-164, Japan). The highest incident laser energy density of the series 40 forming the joint 26 can be designated as the maximum incident laser energy density, where the joint 26 closest to the wedge 42 fails before the first substrate 12 breaks. A camera can be used to monitor when the first substrate 12 of the joint 26 breaks.

[0079] In one embodiment, the incident laser energy density is a function of the laser power (i.e., the power of the laser, typically expressed in watts or milliwatts) and the laser velocity (i.e., the velocity at which the laser is emitted and the substrates 12, 16 translate relative to each other). In another embodiment, the incident laser energy density is varied by changing the laser power using a constant laser velocity and a constant spot size. Higher laser power results in a higher incident laser energy density. Lower laser power results in a lower incident laser energy density. In yet another embodiment, the incident laser energy density is varied by changing the laser velocity using a constant laser power and a constant spot size. Slower laser velocity results in a higher incident laser energy density. Faster laser velocity results in a lower incident laser energy density. In yet another embodiment, the incident laser energy density is varied by changing the spot size using a constant laser velocity and a constant laser power. Smaller spot size results in a higher incident laser energy density. Larger spot size results in a lower incident laser energy density.

[0080] Therefore, in the embodiment, step 38 of determining the range of incident laser energy density includes: determining the range of laser power (e.g., in watts or milliwatts at a constant laser speed and a constant spot size), which ranges from the minimum laser power sufficient to form a bond 26 between the first substrate 12 and the second substrate 16 to the maximum laser power sufficient to form a bond 26 between the first substrate 12 and the second substrate 16, which is weaker than the first substrate 12.

[0081] In these embodiments, to determine the minimum laser power, the laser attempts to bond the first substrate 12 and the second substrate 16 at various laser powers. Some laser powers will be insufficient to form a bond 26 between the first substrate 12 and the second substrate 16. The lowest laser power that results in the formation of a bond 26 between the first substrate 12 and the second substrate 16 can be designated as the minimum laser power. For example, the laser may attempt to form the bond 26 with laser powers of 0.4W, 0.5W, 0.6W, and 0.7W. If 0.4W of laser energy is insufficient to form the bond 26, but 0.5W, 0.6W, and 0.7W of laser power do form the bond 26, then 0.5W will be the minimum laser power.

[0082] In an embodiment, to determine the maximum laser power, (a) a sample pair of the first substrate 12 and the second substrate 16 is prepared, (b) each sample pair is stacked to form an interface between the first substrate 12 and the second substrate 16, and the interface of each pair is subjected to different laser powers from the minimum laser power upwards, forming a series 40 of parallel and spaced-apart joints 26 at the interface of each pair between the first substrate 12 and the second substrate 16, (c) a wedge 42 is placed between the first substrate 12 and the second substrate 16, and (d) the wedge 42 is pushed closer to the series 40 of joints 26 until (i) the joint 26 closest to the wedge 42 fails (e.g., becomes unjoined) or (b) the first substrate 12 breaks. The highest laser power forming the series 40 of joints 26 can be designated as the maximum laser power, wherein the joint 26 closest to the wedge 42 fails before the first substrate 12 breaks. For example, if laser powers of 0.6W, 0.7W, and 0.8W all form a series 40 of joints 26, where the joint 26 closest to the wedge 42 fails before the first substrate 12 breaks in response to the wedge 42, but a laser power of 0.9W forms a series 40 of joints 26, where the first substrate 12 breaks in response to the wedge 42 before the joint 26 closest to the wedge 42 fails, then 0.8W is the maximum laser power. Experimental details are otherwise described above for determining the maximum incident laser energy density.

[0083] In other embodiments, step 38 of determining the range of incident laser energy density includes determining a range of laser speeds (e.g., in watts or milliwatts at constant laser power and constant spot size), ranging from a maximum laser speed sufficient to form a bond 26 between the first substrate 12 and the second substrate 16 to a minimum laser speed sufficient to form a bond 26 between the first substrate 12 and the second substrate 16, which is weaker than the first substrate 12. The same protocol used to determine the laser power range described above can be used to determine the laser speed range, but with varying the laser speed at a constant laser power instead of varying the laser power at a constant laser speed.

[0084] C. Determine the range of bonding strength formed by the range of incident laser energy densities. In step 44, method 34 includes determining the range of bonding strength of bonding 26, from the minimum bonding strength formed using the minimum incident laser energy density to the maximum bonding strength formed using the maximum incident laser energy density. In an embodiment, step 44 includes determining the range of bonding strength, which ranges from the minimum bonding strength formed using the minimum laser power to the maximum bonding strength formed using the maximum laser power (assuming a constant laser speed and a constant spot size). In other embodiments, step 44 includes determining the range of bonding strength, which ranges from the minimum bonding strength formed using the maximum laser speed to the maximum bonding strength formed using the minimum laser speed (assuming a constant laser power and a constant spot size).

[0085] i. The distance at which the wedge causes the joint to break is correlated with the incident laser energy density that produces the joint. In an embodiment, determining the range of the joint strength of the joint 26 includes: (a) preparing samples of the first substrate 12 and the second substrate 16, (b) stacking each sample pair to form an interface between the first substrate 12 and the second substrate 16, and subjecting the interface of each sample pair to different incident laser energy densities within a range of incident laser energy to form a series 40 of parallel and spaced joints 26 between the first substrate 12 and the second substrate 16, (c) for each sample pair, placing a wedge 42 between the first substrate 12 and the second substrate 16, (d) pushing the wedge 42 close to the series 40 of joints 26 formed by a specific incident laser energy density, (e) determining a distance 46(a*) between the wedge 42 and the joint 26 closest to the wedge 42 at the joint 26 break, and (f) correlating the determined distance 46(a*) as a function of the incident laser energy density. The experimental details (a) through (d) are as described above to determine the maximum incident laser energy density. As will become apparent, the distance 46(a*) and the strength of the joint 26 (e.g., by the effective fracture toughness (K) of the joint 26) are related. IC The energy density is related to the incident laser energy density used to form the joint 26 and varies depending on the incident laser energy density. For this related range of incident laser energy densities between the minimum and maximum incident laser energy densities, the wedge 42 is pushed close to the joint 26 in a series 40 until the joint 26 closest to the wedge 42 fails, and the distance 46a* between the wedge 42 and the nearest joint 26 is recorded when the nearest joint 26 fails. The distance 46(a*) may be referred to herein as the “crack length”, for example, the length between the nearest joint 26 and the wedge 42 at the crack in the joint 26.

[0086] In embodiments where the incident laser energy density is varied by changing the laser power at a constant laser velocity and a constant spot size, determining the range of the bonding strength of the joint 26 includes: (a) preparing samples of the first substrate 12 and the second substrate 16; (b) stacking each sample pair to form an interface between the first substrate 12 and the second substrate 16, with each sample pair's interface subjected to different laser powers within a laser power range to form a series 40 of parallel and spaced-apart joints 26 between the first substrate 12 and the second substrate 16; (c) for each sample pair, placing a wedge 42 between the first substrate 12 and the second substrate 16; (d) pushing the wedge 42 closer to the series 40 of joints 26 formed by a specific laser power; (e) determining the distance 46(a*) between the wedge 42 and the joint 26 closest to the wedge 42 at the point of breakage of the joint 26; and (f) relating the determined distance 46(a*) to a function of the laser power. The experimental details of (a) to (d) are as described above to determine the maximum incident laser energy density. As will become apparent, the distance 46(a*) and the strength of the joint 26 (e.g., the effective fracture toughness (K) of the joint 26) IC The value is related to (to quantify) and varies depending on the laser power used to form the joint 26. For this related range of laser power between the minimum and maximum laser power, the wedge 42 is pushed close to the joint 26 in a series 40 until the joint 26 closest to the wedge 42 fails, and the distance 46(a*) between the wedge 42 and the nearest joint 26 is recorded when the nearest joint 26 fails. The distance 46(a*) may be referred to herein as the “crack length”, for example, the length between the nearest joint 26 and the wedge 42 at the crack in the joint 26.

[0087] In embodiments where the incident laser energy density is varied by changing the laser velocity at constant laser power and constant spot size, determining the bonding strength range of the joint 26 includes the same steps (a) to (f) as described above, except that in (b), the interface of each sample pair is subjected to different laser velocities within the laser velocity range to form a series 40 of parallel and spaced-apart joints 26 between the first substrate 12 and the second substrate 16; in (d), the wedge 42 is pushed close to the series 40 of joints 26 formed by a specific laser velocity; and in (f), the determined distance 46(a*) is related to the laser velocity. The experimental details of (a) to (d) are as described above to determine the maximum incident laser energy density. As will become apparent, the distance 46(a*) is related to the strength of the joint 26 (e.g., by the effective fracture toughness (K) of the joint 26). ICThe value is related to (to be quantified) and varies depending on the laser speed used to form the joint 26. For this related range of laser speeds between the maximum and minimum laser speeds, the wedge 42 is pushed close to the series 40 of joints 26 until the joint 26 closest to the wedge 42 fails, and the distance 46(a*) between the wedge 42 and the nearest joint 26 is recorded when the nearest joint 26 fails. The distance 46(a*) may be referred to herein as the “crack length”, for example, the length between the nearest joint 26 and the wedge 42 at the crack in the joint 26.

[0088] Figure 7This is a graph showing the distance 46(a*) varying with the incident laser energy density (here, specifically, the laser power at a constant laser velocity and a constant spot size), which forms the junction 26 that breaks at this distance 46(a*) in the hypothetical example. The determined distance 46(a*) ranges from the minimum distance 46(a*) associated with the junction 26 formed by the maximum laser power (i.e., the maximum incident laser energy density) to the maximum distance 46(a*) associated with the junction 26 formed by the minimum laser power (i.e., the minimum incident laser energy density). More specifically, the minimum laser power forms the junction 26 that breaks at the maximum distance 46(a*). A higher power LP1 results in the junction 26 breaking at a smaller distance 46(a*) a1, and the same applies to laser power increasing from LP2 to LP5 and distance decreasing from a1 to a5. The maximum laser power forms the junction 26 that breaks at the minimum distance 46(a*). As shown in the figure, the determined distance 46(a*) decreases with increasing laser power (i.e., incident laser energy density) forming the joint 26. Without being bound by theory, it is assumed that the higher the incident laser energy density used to form the joint 26, the stronger the joint 26. In other words, the stronger the joint 26, the more it can withstand the separation force caused by the wedge 42, and the greater the decrease in distance 46(a*) between the wedge 42 and the joint 26. As described above, the joint 26 is formed at an incident laser energy density higher than the maximum incident laser energy density (and therefore outside the range of incident laser energy densities), which has a strength relative to the first substrate 12 such that the wedge 42 causes the first substrate 12 to break rather than fail (e.g., the joint 26 corresponding to an incident laser energy density greater than the maximum incident laser energy density is stronger than the first substrate 12). The strength of the joint 26 is generally less than that of the first substrate 12 because the laser emission forming the joint 26 can cause damage to the substrates 12, 16 joined at the joint 26. An incident laser energy density between the minimum and maximum incident laser energy densities creates a bond 26, which has a strength relative to the first substrate 12 such that the wedge 42 causes the bond 26 to break rather than the first substrate 12. An incident laser energy density between the minimum and maximum incident laser energy densities, and including both, defines the range of incident laser energy densities used to form the bond 26 of the apparatus 10 according to method 34.

[0089] In an embodiment, when performing the experiment with the wedge 42 to determine the distance 46(a*) at the break of the joint 26, which varies with the incident laser energy density used to form the joint 26, preferably, the thickness 48 of the first substrate 12 and the thickness 50 of the second substrate 16 are equal for each sample. This helps to ensure that the wedge 42 is testing the strength of the joint 26, rather than the strength of the first substrate 12.

[0090] ii. Quantify the effective fracture toughness of the joint resulting from the range of incident laser energy densities. In an embodiment, determining the range of strength of the joint 26 formed using the range of incident laser energy densities includes quantifying the effective fracture toughness (K0) of the joint 26. IC The effective fracture toughness is quantified as a function of the determined distance (a*). In this paper, K is used to represent the effective fracture toughness. IC This represents, and is a quantification of, the strength of joint 26. The effective fracture toughness (K0) of joint 26... IC ) is a material property that is a function of the incident laser energy density used to generate the junction 26.

[0091] Now for reference Figure 8 and Figure 9 In the embodiment, the effective fracture toughness (K) of the joint 26 will be... IC The quantification of the determined distance 46(a*) as a function includes the use of a numerical model that incorporates the effective fracture toughness (K) of 26. IC The numerical model is quantified as a function of the assumed distance 46(a*) at the joint fracture caused by the modeled wedge 42. In one embodiment, the numerical model utilizes boundary element modeling (“BEM”). In other embodiments, the numerical model utilizes the finite difference method.

[0092] In another embodiment, the numerical model utilizes finite element modeling (“FEM”). The finite element modeling disclosed herein uses the wedge 42, explained above using the principles of linear elastic fracture mechanics (“LEFM”), to model the experimental test. This modeling utilizes the thickness (Δ) of the wedge 42, the width 30 (w) of the joint 26, the spacing 32 (s) between adjacent joints, the thickness 48 (t1) of the first substrate 12, the thickness 50 (t2) of the second substrate 16, the Young's modulus (E1) of the first substrate 12, the Young's modulus (E2) of the second substrate 16, the Poisson's ratio (v1) of the first substrate 12, the Poisson's ratio (v2) of the second substrate 16, the shear modulus (μ1) of the first substrate 12, and the shear modulus (μ2) of the second substrate 16 as variables. The model assumes that the joint 26 is uniform. This modeling models the wedge 42 inserted between the first substrate 12 and the second substrate 16, which causes displacements (Δ1 and Δ2) at a distance 46 (a*) from the nearest joint 26. Displacements (Δ1 and Δ2) result in finite loads (P1 and P2) on the first substrate 12 and the second substrate 16, where stress is concentrated at the nearest joint 26. The model assumes that joint 26 fractures at various distances 46 (a*), and calculates the effective fracture toughness (K) of joint 26 for each of the assumed distances 46 (a*). IC This model can produce, for example... Figure 9 The graph shown here is a hypothetical curve, which illustrates different curves for several different widths 30 of the joint 26. Note that, generally, the wider the width 30 of the joint 26, the shorter the distance 46(a*) that the wedge 42 can move toward the joint 26 before the joint 26 breaks.

[0093] More specifically, the model begins with the premise that the first substrate 12 and the second substrate 16 form a double cantilever extending away from the joint 26, such as Figure 8 As shown in the diagram. The joint 26 has a specific fracture energy (Γ), and the wedge 42, which causes displacements (Δ1, Δ2) of the first substrate 12 and the second substrate 16, causes the crack to propagate through the joint 26 only if the crack will release potential energy (U) greater than the specific fracture energy (Γ) of the joint 26. This change in potential energy (U) per unit crack extension is quantified as the Griffith energy release rate:

[0094]

[0095] Assuming there is no energy exchange between the wedge 42 and the substrates 12 and 16 during the virtual crack propagation (e.g., the wedge 42 is under displacement control), the potential energy (U) from the wedge 42 placed between the first substrate 12 and the second substrate 16 is:

[0096]

[0097] Where (P) is the force applied by the wedge to the substrates 12 and 16. After inserting equation (2) into equation (1), for a fixed width (B) of substrates 12 and 16, the Griffith energy release rate (G) becomes:

[0098]

[0099] in,

[0100]

[0101]

[0102] Applying the moment of a double cantilever beam, we can derive:

[0103]

[0104]

[0105] in,

[0106]

[0107]

[0108] thus,

[0109]

[0110] Ultimately, the equation for Griffith's energy release rate (G) becomes:

[0111]

[0112] Effective fracture toughness (K) of joint 26 resisting potential energy (U) changes IC It is related to the Griffith energy release rate (G), as follows:

[0113]

[0114] With the thickness (t1, t2), Young's modulus (E1, E2), and combined displacement (Δ) (as the thickness of the modeled wedge 42) known, the effective fracture toughness (K) of the joint 26 can be calculated for any specific assumed distance 46 at the crack initiation site (as a*). IC It should be noted that the above model assumes that the crack extends parallel to the interface between the first substrate 12 and the second substrate 16 (e.g., via the joint 26), although the crack can occur in directions other than parallel.

[0115] Although the wedge 42 can cause crack propagation through the joint 26, the crack can alternatively propagate through the first substrate 12 at a different angle (θ), or between the joint 26 and the first substrate 12. In another numerical model, three failure modes are considered to determine the angle (θ), each with an associated stress intensity factor. The three failure modes are: (i) Mode I – longitudinal opening with a stress intensity factor K I (ii) Mode II – in-plane shear, which has a stress intensity factor K II ; and (iii) Mode III – out-of-plane shear, which has a stress intensity factor K III In terms of the Griffith energy release rate (G) balance:

[0116]

[0117] Stress intensity factor K I K II and K III Determine the direction θ of the crack propagation. The stress field at the edge of joint 26 is:

[0118]

[0119] Where i, j = x, y and k = x, y. The model can assume that Mode III (out-of-plane shear) is negligible, and therefore the associated stress intensity factor K can be ignored. III For mode I—longitudinal opening—the stress field has a stress component (σ). x σ y σ xy ) and tip displacement (u x u y And the stress field is:

[0120]

[0121]

[0122] For Mode II – in-plane shear – the stress field has a stress component (σ). x σ y σ xy ) and tip displacement (u x u y And the stress field is:

[0123]

[0124]

[0125] In the above using polar coordinates, r is the radius (length) of the virtual crack, θ is the angle of the virtual crack, κ = 3 - 4ν for the plane strain condition, and κ = (3 – ν) / (1 + ν) for the plane stress condition. The symbol O in equations 15-18 above refers to higher-order terms in the series expansion, which can be ignored because the contribution of higher-order terms to the overall result is negligible.

[0126] T is the "T-stress" value, a known measure that drives fracture initiation events in brittle materials. The T-stress value is used as the displacement vector (u) for crack propagation in the xy plane. x u y The driving force of ). The stress T is formally defined as:

[0127]

[0128] Where σ xx and σ yy The current FEM stress field is taken from the area closest to the crack tip (e.g., the edge of joint 26). A fitting operation is needed to determine K at a given displacement point. I and K II Value. This stems from the definition of the stress intensity factor:

[0129]

[0130] Therefore, σ is obtained from the stress field calculated under a given virtual crack length a. yy (r, θ = 0) or σ xy The value of (r, θ = 0) can determine K. I and K II value:

[0131]

[0132] Where L is the sample length, b is the width 52 of the bonded substrates 12 and 16, and F is a geometric factor defined as follows:

[0133]

[0134] The crack propagates in a direction θ, which is determined using the following expression:

[0135]

[0136] Therefore, the virtual crack length 'a' can vary, and is assumed to be the distance 46(a*) at the crack formation point, and K I and K II The value can be determined as explained. K has the assumed distance a = a*. I and K IIThe Griffith energy release rate (G) is balanced as follows:

[0137] (K I 2 +K II 2 )·(1-v 2 ) = K IC 2 (twenty four)

[0138] Therefore, the effective fracture value K can be determined for any given distance 46(a*). IC And can form such as Figure 9 The curve shown at the location.

[0139] Curve plots that can be created from these models (such as...) Figure 9 The intensity range of the junction 26 formed by the incident laser energy density range can be determined either directly from the model calculations or at the location of the incident laser energy density, ranging from the minimum intensity formed using the minimum incident laser energy density to the maximum intensity formed using the maximum incident laser energy density. For example, the junction 26 (with a specific width 30) formed using the minimum incident laser energy density (here, specifically, the minimum laser energy at a constant laser velocity and a constant spot size) in... Figure 7 and Figure 9 The crack broke at the maximum (“maximum”) distance of 46 (a*) indicated in the middle. From Figure 9 The reproduced curves can determine the effective fracture toughness (K) of this joint 26 (generated using minimum incident laser energy density). IC ), and this effective fracture toughness is Figure 9 The minimum (“minimum”) effective fracture toughness (K) of the joint formed using the incident laser energy density range is identified. IC Similarly, the junction 26 (with a specific width 30) produced using the maximum incident laser energy density (here, specifically, the maximum laser power at a constant laser velocity) is in Figure 7 and Figure 9 The crack broke at the minimum (“minimum”) distance of 46 (a*) indicated in the middle. From Figure 9 The reproduced curves can determine the effective fracture toughness (K) of this joint 26 (generated by the maximum incident laser energy density). IC ), and Figure 9 The location is marked as the maximum effective fracture toughness (K). IC Therefore, the minimum incident laser energy density produces a specific minimum effective fracture toughness (K). IC The junction 26, and the maximum incident laser energy density produces a specific maximum effective fracture toughness (K). ICThe strength range of the joint 26 formed using the incident laser energy density range is thus determined, which range is formed using the minimum incident laser energy density and quantified as the minimum effective fracture toughness (K). IC The minimum strength of the laser is formed using the maximum incident laser energy density and quantified as the maximum effective fracture toughness (K). IC (the maximum strength of)

[0140] The effective fracture toughness (K) of each joint 26 formed using each incident laser energy density within the incident laser energy density range IC Quantization can be determined in the same way. In other words, each joint 26 breaks at a specific distance 46(a*), and based on each of these specific distances 46(a*), a graph generated using a numerical model can be obtained (e.g., Figure 9 To determine a specific effective fracture toughness (K) IC In other words, each incident laser energy density produces a specific joint 26, and each joint 26 has a specific effective fracture toughness (K). IC This quantifies the strength of the joint 26. In other words, each incident laser energy density from the minimum to the maximum produces a joint 26 that fractures at a specific distance 46 (a*) between the wedge 42 and the joint 26, and from this distance 46 (a*), the selected model can be used to calculate the effective fracture toughness (K) of the joint 26. IC ).

[0141] Furthermore, it is worth noting that, as emphasized in the model above, the effective fracture toughness (K) IC The modulus varies with the composition of the bonded substrates 12 and 16 (e.g., Young's modulus (E1 and E2), Poisson's ratio (v1 and v2), and shear modulus (μ1 and μ2) of the substrates 12 and 16). For reference, borosilicate glass compositions (such as BK7) typically have an effective fracture toughness (K0) close to 0.7 MPa·m1 / 2. IC The well-separated bond between the layers of this glass results in a lower effective fracture toughness (K). IC The value is typically in the range of 0.3 to 0.5 MPa·m1 / 2.

[0142] E. Determine the radius range of the joint to meet the minimum burst pressure. Now refer to Figure 10 and Figure 11In step 54, method 34 includes determining a range of radius 36 of the joint 26 that varies with the assigned minimum burst pressure 56 (from step 35) and the determined strength of the joint 26 (from step 44), the range being from the minimum radius 36 of the innermost joint 26a to the maximum radius 36 of the outermost joint 26b. In an embodiment, determining the range of radius 36 that varies with the determined strength of the joint 26 includes determining the quantified effective fracture toughness (K) of the joint 26. IC The range of radius 36 of the joint 26. In an embodiment, determining the range of radius 36 includes: for the effective fracture toughness (K) of the joint 26. IC The range of values ​​is quantified for the pressure 56, which is dependent on the radius 36 of the joint 26, under which each joint 26 will burst.

[0143] In the embodiment, for the quantified effective fracture toughness (K) of the joint 26 described above IC The range of stress 56, dependent on the radius 36 of the joint 26, is quantified using a numerical model to determine the effective fracture toughness (K) of the joint 26 dependent on the distance 46 (a*). In this embodiment, the numerical model considers a different stress field (e.g., a more distributed one) than the numerical model described above to determine the effective fracture toughness (K) of the joint 26 dependent on the distance 46 (a*). IC In this embodiment, the model applies the following equation to a fluid pressure 56 at which the engagement 26 will burst, which may be referred to as the "critical burst pressure" (P). burst ):

[0144]

[0145] Where v is the Poisson's ratio of the first substrate 12, t1 is the thickness of the first substrate 12 (48), E is the Young's modulus of the first substrate 12, r is the radius of the bond 26 (36), and K IC This refers to the selected effective fracture toughness of the joint 26 used in the numerical model. The above equation assumes an infinitely wide joint 26 between the first substrate 12 and the second substrate 14. In other embodiments, step 54 utilizes a numerical model that takes into account a joint 26 with a defined width of 30.

[0146] from Figure 11 The conceptual diagram shown indicates that as the radius 36 of the joint 26 decreases, for any given effective fracture toughness (K... IC The higher the pressure 56 that joint 26 can withstand before joint 26 fractures (i.e., the greater the burst pressure 56), the better. Furthermore, note that to meet a specified burst pressure 56 (e.g., as indicated by the horizontal dashed line), the effective fracture toughness (K0) of the joint increases with the radius of joint 26. IC (This must be added separately.)

[0147] As described above, at step 38 of method 34, the minimum incident laser energy density and the maximum incident laser energy density can be determined. Subsequently, an embodiment of step 44 of method 34 includes determining the effective fracture toughness (K... IC ) Quantify the strength range of these joints 26, which ranges from the minimum fracture toughness (K0) of the joints 26 generated using the minimum incident laser energy density and the maximum incident laser energy density, respectively. IC ) to maximum fracture toughness (K IC Using the minimum burst pressure from step 35, it is possible to achieve a pressure similar to... Figure 11 The minimum and maximum radii 36 of the joint 26 are determined either from the graph shown or directly from the numerical model that generated the graph. For example, refer to... Figure 11 If the horizontal dashed line represents the allocated pressure 56 from step 35, then the horizontal dashed line corresponds to the quantified minimum and maximum fracture toughness (K) from step 44. IC The vertical dashed line "minimum" indicates a minimum radius of 36, where the horizontal dashed line intersects with the minimum fracture toughness value (K) from step 54. IC The vertical dashed line "maximum" indicates a maximum radius of 36, where the horizontal dashed line intersects with the maximum fracture toughness value (K) from step 54. IC The two joints intersect. In other words, if the joint 26 with the minimum radius 36 determined from step 54 is formed with the minimum incident laser energy density from step 38, and the joint 26 with the maximum radius 36 determined from step 54 is formed with the maximum incident laser energy density from step 38, then both joints 26 will have the effective fracture toughness (K0) that fails under the same fluid pressure 56 assigned at step 35. IC The radius 36 of the joint 26 for device 10 is thus determined. The range of radius 36 determined at step 54 represents the range of radius 36 of the joint 26, which is designed to burst under the same pressure 56 distributed at step 35 and not cause device 10 to fail on the first substrate 12 rather than at the joint 26. The joint 26 formed at the minimum radius 36 (e.g., the innermost joint 26a) is formed with the minimum incident laser energy density and therefore has the minimum strength (quantified as minimum effective fracture toughness (K)). IC Subsequently, the joint 26 formed at the maximum radius 36 (e.g., the outermost joint 26b) is formed with the maximum incident laser energy density and therefore has the maximum strength (quantified as the maximum effective fracture toughness (K)). IC )).

[0148] Note that the range of radius 36 varies depending on the assigned pressure 56 from step 35 and the composition of substrates 12, 16. For example, in step 35, a constant minimum and maximum effective fracture toughness (K) is assumed. IC The assigned pressure 56 is increased to reduce the minimum and maximum radii 36 of the joint 26 to achieve the assigned pressure 56. Similarly, if the composition of the substrates 12 and 16 is changed so that the resulting joint 26 has increased effective fracture toughness (K0), the assigned pressure 56 is reduced. IC If the range of values ​​is constant and the distributed pressure 56 remains unchanged, then the radius 36 of the range defining the radius 36 of the joint 26 increases.

[0149] As further explained below, each of the joints 26 between the innermost joint 26a and the outermost joint 26b (e.g., the intermediate joint 26) will have an increased strength (e.g., the quantified effective fracture toughness (K)) as it moves outward sequentially from the innermost joint 26a to the outermost joint 26b. IC This design ensures that each of the joints 26 is designed to burst under the same pressure 56 allocated at step 35. Therefore, when forming the joints 26 with a laser, the incident laser energy density sequentially increases for each joint 26 moving outward from the innermost joint 26a, to sequentially increase the strength (e.g., effective fracture toughness (K)) of each successive outward-moving joint 26. IC For example, using a constant laser velocity, when forming the joint 26 with a laser, the laser power is sequentially increased for each joint 26 moving outward from the innermost joint 26a, in order to sequentially increase the strength (e.g., effective fracture toughness (K)) of each joint 26. IC Alternatively, using a constant laser power, when forming the joint 26 with the laser, the laser speed is sequentially reduced for each joint 26 moving outward from the innermost joint 26a, in order to sequentially increase the strength (e.g., effective fracture toughness (K)) of each joint 26. IC )).

[0150] F determines the number of joints and the spacing between them. Now refer to... Figure 12 In step 58, method 34 includes determining the number of joints 26, each joint 26 having an equal width 30 and an equal spacing 32 between adjacent joints 26, such that the ratio of the spacing 32 to the width 30 of the joint 26 is 1 to 5 (such as 1 to 3.5).

[0151] It has been found that as the spacing 32 between the joints 26 decreases, the joints 26 appear to fit together to maximize their respective strengths (e.g., effective fracture toughness (K)). IC The strength of each joint 26 would increase to more than what it would have if the joints 26 were spaced further apart. This concept is... Figure 12The graph shown is experimentally illustrated, where the distance 46(a*) (directly related to the strength of the bond 26) is plotted as a function of the center-to-center spacing 32 between the bonds 26. The experiment utilized samples bonded to a first substrate 12 and a second substrate 16, the first substrate 12 having a thickness 48 of 500 μm and the second substrate 16 having a thickness 50 of 50 of 50. Numerous bonds 26 were formed between the first substrate 12 and the second substrate 16 using a laser. Each bond 26 has a width 30 of approximately 15 μm. The center-to-center spacing 32 between the bonds 26 is constant for each individual sample but varies between samples within the range of 20 μm to 100 μm. All other laser conditions (such as laser power, laser speed, and spot size) were constant. Note the significant change in distance 46(a*) as the center-to-center spacing 32 between the joints 26 decreases to below 60 μm, with the inflection point occurring somewhere around 50 μm (e.g., at a spacing-to-width ratio of approximately 3.5 (50 μm / 15 μm ≈ 3.5)). As mentioned above, the lower the distance 46(a*), the lower the strength of the joint 26 (e.g., as determined by the effective fracture toughness (K)). IC The higher the quantification, the better. Without theoretical constraints, it is believed that when the joints 26 are spaced sufficiently close to each other (such as by a ratio of 5 or less, or 3.5 or less), the residual stress fields of adjacent joints 26 exhibit significant cooperation. In other words, as the center-to-center spacing 32 between joints 26 decreases, the morphology of each joint 26 transforms from isolated compressive-tensile stresses to a larger cascaded cooperative joint structure.

[0152] However, there is a limit—a minimum spacing 32 at which this synergistic effect occurs. Spacing the joints 26 closer than this minimum spacing 32 causes the intensity of each joint 26 to decrease as the spacing 32 between the joints 26 decreases. This can be seen in the increase of distance (a*) as the spacing 32 decreases to below 5 μm and at the inflection point at approximately 15 μm. For example, overwriting a joint 26—that is, laser-forming a joint 26 that overlaps with another joint 26—does not result in this synergistic effect of increasing the intensity of each joint 26, or the increase in intensity of each joint is less compared to joints 26 with a larger spacing 32. Without being bound by theory, it is assumed that when a laser overwrites an already formed joint 26 to create a new joint 26 overlapping the already formed joint 26, the laser damages the already formed joint 26, thereby reducing the intensity of the already formed joint 26.

[0153] In an embodiment, the center-to-center spacing 32 between the joints 26 varies with the width 30 of the joints 26. In an embodiment, the ratio of spacing 32 to width 30 is in the range of 1 to 5, 1 to 3.5, 1.5 to 2.5, 1.75 to 2.25, 1.75 to 3.5, about 2, or 2. It has been found that the aforementioned synergistic effect occurs within the aforementioned range. Above the upper limit of 5, or even above 3.5, the joints 26 no longer cooperate to the extent that they significantly increase the strength of each of the joints 26. Below the lower limit of 1, laser overwriting of the joints 26 results in internal damage, which reduces the strength of the joints 26. In an embodiment, the number of joints 26 is at least 5.

[0154] G. Determine the specific radius of each of the joints. In step 60, method 34 includes determining the radius 36 of each joint 26 (i.e., intermediate joints 26) between the innermost joint 26a and the outermost joint 26b. The range of the radius 36 of the joint 26 from the minimum radius 36 to the maximum radius 36 can be determined in the previous step 54, and the spacing 32 between the joints 26 and the number of joints 26 can be determined in the previous step 58. Therefore, the specific radius 36 of all intermediate joints 26 can be determined by starting with the minimum radius 36 and determining the next adjacent joint 26 as the minimum radius 36 plus the determined spacing 32, and so on, up to the joint 26 before the outermost joint 26b at the maximum radius 36.

[0155] H. Determine the strength of each joint between the innermost and outermost joints, depending on the determined radius. In step 62, method 34 includes determining the strength of each joint 26 (i.e., intermediate joint 26) between the innermost joint 26a and the outermost joint 26b, which varies with the determined radius 36 (from step 60) of each of the joints 26 (i.e., intermediate joint 26) between the innermost joint 26a and the outermost joint 26b and the assigned burst pressure 56 (from step 35).

[0156] In an embodiment, determining the strength of each joint 26 between the innermost joint 26a and the outermost joint 26b, which vary with each of the joints 26, includes: determining the effective fracture toughness (K0) of each joint 26 between the innermost joint 26a and the outermost joint 26b. IC The effective fracture toughness (Ka) is quantified as a function of the determined radius 36 (from step 60) and the assigned burst pressure 56 (from step 35). In an embodiment, the effective fracture toughness (Ka) of each intermediate joint 26 between the innermost joint 26a and the outermost joint 26b is... IC The value is determined directly based on the numerical model described above, and its dependence is on the allocated burst pressure 56 and the determined radius 36.

[0157] In the embodiment, the effective fracture toughness (K) of each intermediate joint 26 between the innermost joint 26a and the outermost joint 26b is... IC ) by curves (such as Figure 11 The interpolation of the curve (the curve plotting the burst pressure 56 as a given effective fracture toughness (K) for joint 26) is determined, and the curve plots the burst pressure 56 as a given effective fracture toughness (K) for joint 26. IC The value is a function of radius 36. For example, and refer to... Figure 11 Assuming that the radius 36 determined between the minimum radius 36 and the maximum radius 36 at step 60, r2 to r6, can determine the effective fracture toughness (K) of each intermediate joint 26 at the intersection of a specific radius 36 and the burst pressure 56 allocated from step 35. IC Interpolation is performed. The effective fracture toughness (K) of each intermediate joint 26 is calculated. IC The radius increases as the radius increases from the minimum radius 36 to the maximum radius 36.

[0158] J. Determine the incident laser energy density for each intermediate joint. In step 66, method 34 includes determining the incident laser energy density for forming each intermediate joint 26 between the innermost joint 26a and the outermost joint 26b, the incident laser energy density being dependent on the determined intensity of each joint 26 (from step 66). In an embodiment, step 66 includes determining a laser power corresponding to each intermediate joint 26 within a range of laser power (using a constant laser speed and a constant spot size), the laser power being dependent on the determined intensity of each intermediate joint 26. In an embodiment, step 66 includes determining a laser speed corresponding to each intermediate joint 26 within a range of laser speed (using a constant laser power and a constant spot size), the laser speed being dependent on the determined intensity of each intermediate joint 26.

[0159] i. Determine the distance a* for each joint. In an embodiment, determining the incident laser energy density for forming each joint 26 between the innermost joint 26a and the outermost joint 26b includes: using a numerical model that quantifies the distance 46(a*) at which the modeled wedge 42 causes the joint 26 to fracture as the effective fracture toughness (K) of the joint. IC ), to determine the distance 46(a*) of each of the intermediate joints 26, which varies with the effective fracture toughness (K) of each intermediate joint 26 as determined above. IC In the embodiment, the distance 46(a*) between each intermediate joint 26 between the innermost joint 26a and the outermost joint 26b is obtained from a graph (such as...). Figure 9 The curve (K) is determined by which the effective fracture toughness (K) will be determined for a given width 30 of joint 26. IC This is plotted as a function with a distance of 46(a*). For example, refer to... Figure 9 The effective fracture toughness (K) of each intermediate joint 26 between the innermost joint 26a and the outermost joint 26b as defined above. IC The joint 26 intersects the width 30 of the joint 26 at a specific distance 46(a*), which is therefore the determined distance 46(a*) of that specific intermediate joint. For each intermediate joint 26 determined in step 62, the effective fracture toughness (K) is... IC This process is repeated to obtain the determined distance (a*) for each intermediate joint 26. Distances 46(a*)a1, a2, a3, a4, and a5 correspond to the effective fracture toughness (K) of each of the intermediate joints 26. IC Values ​​1, 2, 3, 4, and 5.

[0160] ii. The incident laser energy density is determined from an experimental plot of the distance a* varying with respect to the incident laser energy density. In the embodiment, as described above, the incident laser energy density is determined from the experimental correlation of the distance 46(a*) varying with respect to the incident laser energy density, such as from a graph (such as... Figure 7 The graph shows that the distance 46(a*) is experimentally plotted as a function of the incident laser energy density (specifically, the laser power at constant laser velocity and spot size). Therefore, the incident laser energy density (specifically, the laser power) at any given distance (a*) determined in step 66 can be determined from the graph. Distances 46(a*) a1, a2, a3, a4, a5 intersect the lines experimentally determined at laser powers LP1, LP2, LP3, LP4, and LP5, respectively.

[0161] K. Forming the joint using the determined incident laser energy. In step 68, method 34 includes: forming the innermost joint 26a at a minimum radius 36 using the minimum incident laser energy density, forming the outermost joint 26b at a maximum radius using the maximum incident laser energy density, and forming each intermediate joint 26 at a determined radius (from steps 60 and 66) using the determined incident laser energy density. As described above, for each joint 26 moving outward (away from axis 24) from the innermost joint 26a, the incident laser energy density increases sequentially. The innermost joint 26a is formed at a minimum radius 36 using the minimum incident laser energy density. The outermost joint 26b is formed at a maximum radius 36 using the maximum incident laser energy density. Each joint 26 has, in the embodiment, effective fracture toughness (K IC The strength is quantified by a force that is configured to cause joint 26 to fail under the assigned burst pressure 56. Joint 26 is concentric about axis 24. The strength of joint 26 increases sequentially from the innermost joint 26a with the lowest strength to the outermost joint 26b with the highest strength.

[0162] In an embodiment, step 68 includes: forming the innermost joint 26a at a minimum radius 36 using minimum laser power, forming the outermost joint 26b at a maximum radius using maximum laser power, and forming each intermediate joint 26 at a determined radius (from steps 60 and 66) using a determined laser power (all at a constant laser speed and spot size). As described above, for each joint 26 moving outward (away from axis 24) from the innermost joint 26a, the laser power increases sequentially. The innermost joint 26a is formed at a minimum radius 36 using minimum laser power. The outermost joint 26b is formed at a maximum radius 36 using maximum laser power. Each joint 26 has, in the embodiment, effective fracture toughness (K). IC The strength is quantified by a force that is configured to cause joint 26 to fail under the assigned burst pressure 56. Joint 26 is concentric about axis 24. The strength of joint 26 increases sequentially from the innermost joint 26a with the lowest strength to the outermost joint 26b with the highest strength.

[0163] In an embodiment, step 68 includes: forming the innermost joint 26a at a minimum radius 36 using the maximum laser speed, forming the outermost joint 26b at a maximum radius using the minimum laser speed, and forming each intermediate joint 26 at a determined radius (from steps 60 and 66) using a determined laser speed (all at constant laser power and spot size). As described above, for each joint 26 moving outward (away from axis 24) from the innermost joint 26a, the laser speed decreases sequentially. The innermost joint 26a is formed at a minimum radius 36 using the maximum laser speed. The outermost joint 26b is formed at a maximum radius 36 using the minimum laser speed. Each joint 26 has, in the embodiment, effective fracture toughness (K). IC The strength is quantified by a force that is configured to cause joint 26 to fail under the assigned burst pressure 56. Joint 26 is concentric about axis 24. The strength of joint 26 increases sequentially from the innermost joint 26a with the lowest strength to the outermost joint 26b with the highest strength.

[0164] Some devices (such as liquid lenses) are manufactured by forming concentric joints using a constant incident laser energy density (e.g., using constant laser power and constant laser velocity), where as many concentric joints as possible are formed within a given space. This can lead to a waste of electricity and / or time, because only the innermost joint of the manufactured liquid lens is a result of resisting fluid pressure. If the fluid pressure is sufficient to cause the innermost joint to fail, then the fluid pressure is sufficient to cause all concentric joints to fail, leading to the failure of the liquid lens. Therefore, the electricity and time spent forming the remaining joints may not be entirely beneficial. This method 34 enables the formation of a limited number of joints 26, where each joint is designed to fail under an assigned burst pressure 56, which is more economical in terms of time and electricity.

[0165] II Equipment

[0166] The device 10 (such as a liquid lens) manufactured using method 34 can exhibit various improved properties. First, each concentric joint 26 of the device 10 has sufficiently low strength (e.g., effective fracture toughness (K)). IC This strength causes joint 26, rather than the first substrate 12, to fail in response to the increased fluid pressure 56. Failure of the first substrate 12 results in failure of the device 10. Failure of the innermost joint 26a (and any subsequent joints 26 other than the outermost joint 26b) may not result in failure of the device 10 because at least one joint 26 remains to seal the liquid 22 within the cavity 20. This is particularly important in embodiments where each of the first substrate 12 and the second substrate 16 has a relatively high coefficient of thermal expansion (e.g., greater than about 5 ppm / °C), because the width 30 of the joints 26 is typically narrow, resulting in the use of more joints 26. Conversely, when made with the highest possible effective fracture toughness (K... IC When a liquid lens is exposed to increased fluid pressure, the first substrate, rather than the bond, may fail, leading to the failure of the entire liquid lens. The "coefficient of thermal expansion" is the average linear expansion of a substrate over a temperature range of approximately 20°C to approximately 300°C. For example, the coefficient of thermal expansion can be determined using the procedure described in ASTM E228, "Standard Test Method for Linear Thermal Expansion of Solid Materials With a Push-Rod Dilatometer."

[0167] Second, the strength of each joint 26 (e.g., effective fracture toughness (K) IC The joints 26 sequentially increase outward from the innermost joint 26a to the outermost joint 26b. Each of the joints 26 has a different toughness (e.g., effective fracture toughness (K)).IC The innermost joint 26a is the weakest (e.g., with the lowest effective fracture toughness (K)). IC The outermost joint 26b is the strongest (e.g., the largest effective fracture toughness (K)). IC Conversely, liquid lenses manufactured using other methods can result in all joints having the same strength (e.g., the same effective fracture toughness (K)). IC This is the result of forming each one in the joint using the same incident laser energy density.

[0168] Third, each joint 26 of the device 10 is configured to fail under the same fluid pressure 56. Therefore, if the fluid pressure 56 is temporarily at a level that would cause the innermost joint 26a to fail, the failure of the innermost joint 26a increases the volume occupied by the liquid 22 and thus reduces the fluid pressure 56 exerted by the liquid 22, allowing the next joint 26 to remain intact against the fluid pressure 56, and so on toward the outermost joint 26b. In other words, resistance to the assigned burst pressure is distributed throughout all joints 26. Conversely, in a liquid lens in which all joints are formed with the same incident laser energy density, all joints have the same effective fracture toughness (K0). IC Since the burst pressure is inversely proportional to the square of the joint radius (see Equation 25 above), it is assumed that all joints have the same effective fracture toughness (K). IC If the fluid pressure is sufficient to cause failure of the innermost joint, then the fluid pressure is likely sufficient to cause failure of all concentric joints and thus failure of the liquid lens. The device 10 of this disclosure avoids such catastrophic failure by resisting the burst pressure 56 through all joints distributed throughout the joints 26, which have effective fracture toughness (Ka) that increases sequentially from the innermost joint 26a to the outermost joint 26b. IC The radius 36 and strength of each joint 26 are cooperatively configured such that each joint 26 fails under the same pressure 56 or at least approximately the same pressure 56 (e.g., an average pressure 56 calculated from the pressure 56 at the point of failure of each joint 26, and each pressure 56 deviating from the average pressure 56 by at most 10%), which is applied to the first substrate 12 by liquid 22. In an embodiment, the pressure 56 at the point of failure of the joint 26 is from 1 MPa to 3 MPa.

[0169] Fourth, the spacing 32 between the joints 26 of the device 10 is optimized as a spacing-to-width ratio within the range of 1 to 5 (such as 1 to 3.5, 1.5 to 3, 2 to 2.5, 1.75 to 2.25, and 1.75 to 3.5). With such a spacing 32, the stress field cooperates to maximize the effective fracture toughness (K0) of each joint 26. IC Increase to the designed effective fracture toughness (K)IC The above, and therefore, each joint 26 will have a higher fluid pressure 56 at the actual burst point than the allocated fluid pressure 56. This results in a more robust device 10. Conversely, liquid lenses formed using other manufacturing processes typically include as many joints as space allows, and the joints are spaced as close as possible, even overwriting adjacent joints. As mentioned above, this approach reduces the effective fracture toughness (K) of each overwritten joint. IC It is worth noting that the effective fracture toughness (K) will be in the range of 1 to 5 (such as 1 to 3.5). IC The designed effective fracture toughness (K) is increased to that of a single joint 26. IC The ratio of the spacing to the width above the first substrate 12 is unlikely to cause failure of any given joint 26 other than the outermost joint 26b. Furthermore, failure of the outermost joint 26b is without consequence because failure of the outermost joint 26b presupposes failure of every other joint 26, and therefore would cause failure of the device 10 anyway. In embodiments, the widths 30 of the joints 26 are equal or at least approximately equal (e.g., an average width 30 calculated from the width 30, and each width 30 deviates from the average width 30 by at most 10%). In embodiments, each pair of adjacent joints 26 is separated by the same spacing 32 or substantially the same spacing 32 (e.g., an average spacing 32 calculated from the spacing 32, and each spacing 32 deviates from the average spacing 32 by at most 10%).

[0170] III. Example

[0171] Now for reference Figures 13-17 An example of the device 10 prepared according to method 34 is described. To perform steps 38 and 44 of method 34, a sample of a first substrate 12 having a thickness 48 of 500 μm and a sample of a second substrate 16 having a thickness 50 of 500 μm are prepared. The samples of the first substrate 12 and the second substrate 16 have a composition of BK7, which is a high-purity borosilicate glass distributed by Schott AG (Mainz, Germany). A laser-absorbing interface film composed of 50 nm chromium oxynitride and 150 nm chromium metal is disposed between the first substrate 12 and the second substrate 16. The laser selected for method 34 is a 355 nm pulsed ultraviolet (UV) laser configured with a laser velocity of 50 mm / s, a spot size of 15 μm, a repetition rate of 80 kHz, and a pulse width of 10 ns. Therefore, the incident laser energy density is varied by changing the laser power while maintaining a constant laser velocity and spot size.

[0172] In preparing to perform step 38 of method 34, samples of the first substrate 12 and the second substrate 16 are stacked together, and a laser is used to attempt to bond the two substrates 12, 16 to a series 40 of fifty (50) individual straight joints 26, each 15 μm wide and spaced at a 100 μm pitch 32. The 100 μm pitch 32 is too wide to allow the stress fields of the joints 26 to cooperate as detailed above, thereby significantly increasing the effective fracture toughness (K0) of each joint 26. IC According to step 38 of method 34, for each sample of the stacked first substrate 12 and second substrate 16, the laser power is sequentially increased, wherein the laser power is in the range of 0.45W to 1.1W, while other laser parameters remain the same (including laser velocity and spot size), thereby changing the incident laser energy density. The minimum laser power resulting in the formation of the bond 26 between the first substrate 12 and the second substrate 16 is identified as 0.52W.

[0173] According to steps 38 and 44 of method 34, the experiment including the aforementioned wedge 42 was performed on each sample of the joined first substrate 12 and second substrate 16. More specifically, the sample was placed in the field of view of the camera. A flat razor blade (Lutz Blades, German #60.15-0.14mm thick) representing the wedge 42 was inserted into the gap between the first substrate 12 and the second substrate 16. The flat razor blade (e.g., wedge 42) was then slowly translated toward the series 40 of the joint 26 at a rate of about 1mm per minute using a plunger-type digital micrometer (Mitutoyo, Japanese MHD-2”MB-164-164), while the camera monitored for signs of initial crack formation at the nearest joint 26 or the first substrate 12.

[0174] The maximum laser power for forming the joint 26 is determined to be 0.9 W, which breaks at the joint 26 in response to the wedge 42, rather than breaking at the first substrate 12. Therefore, the maximum laser power range determined according to step 38 is 0.9 W. Thus, the range of laser power via step 38 is 0.52 W to 0.9 W. This is the range of laser power to be used in the fabrication of the apparatus 10 according to method 34 using the selected 355 nm wavelength laser.

[0175] Preparing to Figure 13The plotted curves were reproduced to show the distance 46(a*) as a function of laser power within the range of laser power. The range of the distance 46(a*) at the break of joint 26 was determined to be approximately 11 mm (associated with a maximum laser power of 0.9 W) to approximately 15 mm (associated with a minimum laser power of 0.52 W). Therefore, the range of distance 46(a*) is approximately 11 mm to approximately 15 mm. Note that the wedge 42 causes the distance 46(a*) from the break of joint 26 to be variable with the laser power forming the joint 26.

[0176] Numerical models were used to determine the effective fracture toughness (K) dependent on distance 46(a*). IC At a distance of 46 (a*), a modeled wedge 42 with a thickness (△) of 0.14 mm causes joint 26 to fracture. The model assumes a width 30 of joint 26 of 0.01 mm. Model (FEM model) generation Figure 14 The curves at the point are shown. The curves reveal that the joint 26, formed by a maximum laser power of 0.9 W and fractured at a minimum distance (a*) of approximately 11 mm, has an effective fracture toughness (K0) of 0.55 MPa·m1 / 2. IC Furthermore, the graphs reveal that the joint 26, formed with a minimum laser power of 0.52 W and fractured at a maximum distance (a*) of approximately 15 mm, possesses an effective fracture toughness (K0) of 0.31 MPa·m1 / 2. IC Therefore, the joint 26 of the device 10 manufactured via method 34 will be formed by a laser power in the range of 0.52W to 0.9W, and is designed to have an effective fracture toughness (K) in the range of 0.31MPa·m1 / 2 to 0.55MPa·m1 / 2. IC ).

[0177] According to step 35 of method 34, a minimum burst pressure of 300 psi (≈2.1 MPa) is applied. This is the minimum fluid pressure 56 applied by liquid 22, at which device 10 is designed to fail.

[0178] According to step 54 of method 34, the range of radius 36 of the joint 26 that satisfies the allocated minimum burst pressure of 300 psi (≈2.1 MPa) is determined, the range of radius 36 being dependent on the effective fracture toughness (K). IC The range of values. More specifically, for the effective fracture toughness (K) of joint 26. IC The range of values ​​was determined using a numerical model to quantify the pressure 56, which is dependent on the radius 36 of the joint 26, at which the joint 26 will burst. The results of the numerical model are... Figure 15The curves are reproduced at the specified points. The horizontal dashed line represents the distributed burst pressure of 300 psi (≈2.1 MPa). At a minimum radius of 36 mm (0.75 mm), the horizontal line intersects with the minimum effective fracture toughness (K, C) interpolated at 0.31 MPa·m1 / 2 (between 0.3 MPa·m1 / 2 and 0.4 MPa·m1 / 2). Furthermore, at a maximum radius of 36 mm (1.04 mm), the horizontal line intersects with the maximum effective fracture toughness (K) interpolated at 0.55 MPa·m1 / 2. IC (Between 0.5 MPa·m1 / 2 and 0.6 MPa·m1 / 2) intersects. The numerical model could have been used to directly determine the minimum radius 36 and the maximum radius 36, instead of using... Figure 15 Interpolating the curves, the minimum radius 36 and the maximum radius 36 vary with the assigned burst pressure and the minimum effective fracture toughness (K). IC ) and maximum effective fracture toughness (K IC The known value of ). Therefore, the radius 36 of the concentric joint 26 of the device 10 formed according to method 34 will be in the range of 0.75 mm to 1.04 mm. More specifically, a laser will be used to form the innermost joint 26a at a laser power of 0.52 W at a radius 36 of 0.75 mm and the outermost joint 26b at a laser power of 0.90 W at a radius 36 of 1.04 mm, such that the innermost joint 26a will have an effective fracture toughness (K) of 0.31 MPa·m1 / 2. IC Furthermore, the outermost joint 26b will have an effective fracture toughness of 0.55 MPa·m1 / 2 (K). IC Both the innermost joint 26a and the outermost joint 26b are designed to fail under the same assigned burst pressure of 300 psi (≈2.1 MPa). Note that any radius 36 greater than 1.04 mm will have an effective fracture toughness (K1 / 2) exceeding the maximum value of 0.55 MPa·m1 / 2. IC This will therefore cause the first substrate 12, rather than the outermost joint 26b, to fracture in response to the allocated burst pressure 56 of 300 psi (≈2.1 MPa). Any radius 36 less than 0.75 mm will have an effective fracture toughness (K1 / 2) of less than 0.31 MPa·m1 / 2. ICThis corresponds to a laser power below 0.52W, which would be insufficient to form a bond 26 between the first substrate 12 and the second substrate 16. Any expectation of increasing the laser power above 0.52W at the innermost bond 26a or at a smaller radius 36 would cause the innermost bond 26a to fail above the burst pressure 56 assigned at step 35, making the remainder of the bond 26 substantially susceptible to failure as well (because any pressure 56 sufficient to cause the innermost bond 26a to fail would also cause each of the other bonds 26 to fail, since these other bonds 26 are designed to fail at lower pressures 56). The example now turns to the intermediate bond 26 between the innermost bond 26a and the outermost bond 26b.

[0179] According to step 58 of method 34, the number of joints 26 and the spacing 32 between joints 26 are determined. As explained, if the ratio of the spacing to the width of the joints 26 is between 1 and 3.5, then the effective fracture toughness (K0) of the joints 26 is... IC The reinforcement is enhanced to exceed the design value. As mentioned above, the joint 26 has a width 30 of 15 μm and a radius 36 spanning a range of 0.29 mm (290 μm) from 0.75 mm to 1.04 mm. The 29 μm spacing 32 will allow for eleven (11) joints 26 and a spacing-to-width ratio of 1.93 (e.g., 29 μm / 15 μm = 1.93), which is within the desired range of 1 to 5 (and even 1 to 3.5, and 1.75 to 2.25).

[0180] According to step 60 of method 34, the radius 36 of each intermediate joint 26 (i.e., those joints 26 between the innermost joint 26a and the outermost joint 26b) is determined. With the spacing 32 between the joints 26 already determined, the joints 26 will correspondingly have the following radius 36:

[0181] 1 (innermost side) 0.75 2 ～0.78 3 ～0.81 4 ～0.84 5 ～0.87 6 ～0.90 7 ～0.92 8 ～0.95 9 ～0.98 10 ～1.01 11 (outermost) 1.04

[0182] According to step 62 of method 34, the effective fracture toughness (K) of each intermediate joint 26 between the innermost joint 26a and the outermost joint 26b is determined. IC It is determined to be a function of the determined radius 36 and the assigned burst pressure 56. Now refer to Figure 16 , it is Figure 15 In the enlarged portion, vertical lines of radius 36 for joints 26 (i.e., intermediate joints 26), numbered 2 to 10, are added between the innermost joint 26a and the outermost joint 26b, between radii 36. All vertical lines intersect the assigned target pressure 56 of 2.1 MPa (~300 psi). The effective fracture toughness (K0) on the graph is shown below. IC Interpolating between the values, the vertical radius 36 line intersects the horizontal line with the assigned burst pressure 56 at the following values:

[0183] 1 (innermost side) 0.75 0.31 2 ～0.78 0.33 3 ～0.81 0.36 4 ～0.84 0.38 5 ～0.87 0.40 6 ～0.90 0.43 7 ～0.92 0.45 8 ～0.95 0.47 9 ～0.98 0.49 10 ～1.01 0.52 11 (outermost) 1.04 0.55

[0184] Numerical models can be used to directly determine the effective fracture toughness (K) of each intermediate joint 26. IC ), instead of using Figure 16 The curve graph.

[0185] from Figure 17 The curve (which is) Figure 14 The magnified portion of the graph (of which the distance 46(a*) between each intermediate joint 26 between the innermost joint 26a and the outermost joint 26b is determined, and this distance 46(a*) varies with the determined effective fracture toughness (K). IC The value and the assigned blasting pressure are 56. Figure 17 The curve will effectively determine the fracture toughness (K) for a given width of joint 26. IC The value is plotted as a function of distance 46(a*). This represents the effective fracture toughness (K) of each intermediate joint 26 determined above. IC The horizontal line of the value intersects the curve, and then the vertical line is drawn downwards to the axis at a distance of 46 (a*). Therefore, the effective fracture toughness (K) of each intermediate joint 26 is... IC The value of ) is assigned a distance of 46(a*). Therefore, junction 26 has the following distance of 46(a*):

[0186]

[0187]

[0188] Numerical models can be used to directly determine the distance 46(a*) of each intermediate joint 26 between the innermost joint 26a and the outermost joint 26b, without using Figure 17 The curve graph.

[0189] According to step 66 of method 34, from Figure 18 The curve at the location (which is) Figure 13 The laser power to be used to form each intermediate joint 26 between the innermost joint 26a and the outermost joint 26b is determined by magnifying the relevant portion and plotting the distance 46(a*) as a function of laser power. This laser power is dependent on the determined distance 46(a*) for each joint 26. The distance 46(a*) for each intermediate joint 26 determined above is horizontally traced to the laser power dependent on the distance (a*) line and then plotted as a vertical line to the laser power axis to determine the laser power used to form each of the intermediate joints 26 between the innermost joint 26a and the outermost joint 26b.

[0190] 1 (innermost side) 0.75 0.31 15.0 0.52 2 ～0.78 0.33 14.3 0.55 3 ～0.81 0.36 13.8 0.60 4 ～0.84 0.38 13.4 0.63 5 ～0.87 0.40 12.9 0.69 6 ～0.90 0.43 12.5 0.74 7 ～0.92 0.45 12.1 0.78 8 ～0.95 0.47 11.8 0.82 9 ～0.98 0.49 11.5 0.85 10 ～1.01 0.52 11.2 0.89 11 (outermost) 1.04 0.55 11.0 0.90

[0191] Finally, according to step 68 of method 34, a bond 26 is formed between the first substrate 12 and the second substrate 16 using a laser, each bond 26 being formed with a determined laser power. At a constant laser speed and spot size, the laser power is sequentially increased for each bond 26 moving outward from the innermost bond 26a. Liquid 22 can be deposited in the cavity, and the third substrate 14 can be bonded to the second substrate 16 before or after the first substrate 12 is bonded to the second substrate 16.

[0192] It will be apparent to those skilled in the art that various modifications and variations may be made without departing from the spirit or scope of the claims.

Claims

1. A liquid lens device, comprising: First substrate; as well as A second substrate is joined to the first substrate via a plurality of concentric joints, the plurality of concentric joints including an innermost joint, an outermost joint and at least one intermediate joint between the innermost joint and the outermost joint, the at least one intermediate joint being radially spaced from the innermost joint and the outermost joint. The strength of the concentric joints increases sequentially from the innermost joint to the outermost joint.

2. The liquid lens device as described in claim 1, characterized in that: Each of the plurality of concentric joints includes a different effective fracture toughness ( ); The innermost joint includes the minimum effective fracture toughness ( ); The outermost joint includes the maximum effective fracture toughness ( );as well as The effective fracture toughness of each of the at least one intermediate joint. Increase toward the outermost engagement.

3. The liquid lens device of claim 1, further comprising: A third substrate, wherein the third substrate is bonded to the second substrate opposite to the first substrate; A cavity defined by through-holes in the first substrate, the third substrate, and the second substrate; as well as Fluid disposed within the cavity; The strength of each of the plurality of concentric joints is low enough that the plurality of concentric joints, rather than the first substrate, fail in response to pressure applied to the first substrate by the fluid.

4. The liquid lens device of claim 1, further comprising: A third substrate, wherein the third substrate is bonded to the second substrate opposite to the first substrate; A cavity defined by through-holes in the first substrate, the third substrate, and the second substrate; as well as Fluid disposed within the cavity; Each of the plurality of concentric joints is configured to fail under approximately the same pressure applied to the first substrate by the fluid.

5. The liquid lens device according to any one of claims 3-4, characterized in that: Each of the plurality of concentric joints includes a radius; and The radius and strength of the plurality of concentric joints are configured in a coordinated manner such that each of the plurality of concentric joints fails under approximately the same pressure applied by the fluid to the first substrate.

6. The liquid lens device according to any one of claims 3-4, characterized in that, The pressure at the point of joint failure is between 1 MPa and 3 MPa.

7. The liquid lens device according to any one of claims 1-4, characterized in that, Each of the first substrate and the second substrate has a coefficient of thermal expansion greater than 5 ppm / °C from 20°C to 300°C.

8. The liquid lens device according to any one of claims 1-4, characterized in that: Each of the plurality of concentric joints includes a width, and the widths of the plurality of concentric joints are at least substantially equal; Adjacent joints are separated by a spacing, and the spacing between all adjacent joints is at least approximately equal; as well as The ratio of the spacing to the width is between 1 and 5.

9. A liquid lens device, comprising: First substrate; A second substrate is joined to the first substrate via a plurality of concentric joints, the plurality of concentric joints including an innermost joint, an outermost joint and at least one intermediate joint between the innermost joint and the outermost joint, the second substrate including a through-hole; A third substrate, wherein the third substrate is bonded to the second substrate opposite to the first substrate; The cavity defined by the through-holes of the first substrate, the third substrate, and the second substrate; as well as The liquid contained within the cavity; Each of the plurality of concentric joints is configured to fail under approximately the same pressure applied by the liquid to the first substrate.

10. The liquid lens device as claimed in claim 9, characterized in that, The strength of the plurality of concentric joints increases sequentially from the innermost joint to the outermost joint; and The radii and strengths of the plurality of concentric joints are configured in a coordinated manner such that each of the plurality of concentric joints fails under approximately the same pressure applied by the liquid to the first substrate.

11. The liquid lens device according to any one of claims 9-10, characterized in that: Each of the plurality of concentric joints has approximately the same width; Each pair of adjacent joints is separated by approximately the same spacing; as well as The ratio of the spacing to the width is between 1 and 5.

12. A method for manufacturing a liquid lens device, comprising: Assign minimum blasting pressure; The range of incident laser energy densities is determined from the minimum incident laser energy density sufficient to form a bond between the first substrate and the second substrate to the maximum incident laser energy density that forms a bond between the first substrate and the second substrate weaker than that between the first substrate and the second substrate. Determine the range of bonding strength from the minimum bonding strength formed using the minimum incident laser energy density to the maximum bonding strength formed using the maximum incident laser energy density; Determine the range of the joint radius that varies with the assigned minimum burst pressure and the determined range of joint strength, the range of the joint radius being from the minimum radius of the innermost joint to the maximum radius of the outermost joint. The number of joints is determined, each joint having an equal width and an equal spacing between adjacent joints, such that the ratio of the spacing to the width is 1 to 5; Determine the radius of each of at least one intermediate joint between the innermost joint and the outermost joint, the radius depending on the number of joints determined and the spacing between adjacent joints; Determine the strength of each intermediate joint, which is dependent on the determined radius of each intermediate joint; Determine the incident laser energy density, within the range of incident laser energy density, corresponding to the incident laser energy density of each intermediate junction, which varies with the determined intensity. as well as The innermost junction is formed at the minimum radius using the minimum incident laser energy density, the outermost junction is formed at the maximum radius using the maximum incident laser energy density, and each intermediate junction is formed at the determined radius using the determined incident laser energy density.

13. The method as described in claim 12, characterized in that: The range of incident laser energy densities, defined as being from the minimum incident laser energy density sufficient to form the bond between the first substrate and the second substrate to the maximum incident laser energy density sufficient to form a bond weaker than that between the first substrate and the second substrate, includes: The range of laser power is determined from the minimum laser power sufficient to form the bond between the first substrate and the second substrate to the maximum laser power required to form a bond between the first substrate and the second substrate that is weaker than that between the first substrate and the second substrate. Determining the range of the bonding strength from the minimum bonding strength formed using the minimum incident laser energy density to the maximum bonding strength formed using the maximum incident laser energy density includes: Determine the range of the bonding strength from the minimum bonding strength formed using the minimum laser power to the maximum bonding strength formed using the maximum laser power; Determining the incident laser energy density, within the range of incident laser energy density, corresponding to the variable incident laser energy density at each intermediate junction, and varying with the determined intensity, includes: Determine the laser power within the range of the laser power corresponding to each intermediate junction, varying with the determined intensity; and The innermost junction is formed at the minimum radius using the minimum incident laser energy density, the outermost junction is formed at the maximum radius using the maximum incident laser energy density, and each intermediate junction is formed at the determined radius using the determined incident laser energy density, comprising: The innermost joint is formed at the minimum radius using the minimum laser power, the outermost joint is formed at the maximum radius using the maximum laser power, and each intermediate joint is formed at the determined radius using the determined laser power.

14. The method as described in claim 13, characterized in that: Determining the minimum laser power includes attempting to form a bond with various laser powers, where at least one laser power is insufficient to form a bond, and the minimum laser power required to form a bond is the minimum laser power.

15. The method as described in claim 13, characterized in that: Determining the maximum laser power includes (a) preparing sample pairs of the first substrate and the second substrate, (b) stacking each sample pair to form an interface between the first substrate and the second substrate, and the interface of each sample pair being subjected to different laser powers upward from the minimum laser power, thereby forming a series of parallel and spaced-apart joints between the first substrate and the second substrate at the interface of each pair, (c) for each sample pair, placing a wedge between the first substrate and the second substrate, and (d) for each sample pair, pushing the wedge closer to the series of joints until (i) the joint closest to the wedge becomes unjoined, or (ii) the first substrate breaks; as well as The highest laser power in the series of formations that causes the engagement closest to the wedge to become unengaged rather than the first substrate to break is the maximum laser power.

16. The method as described in claim 13, characterized in that: Determining the range of the bonding strength includes (a) preparing sample pairs of the first substrate and the second substrate, (b) stacking each sample pair to form an interface between the first substrate and the second substrate, and subjecting the interface of each sample pair to different laser powers within the range of the laser power to form a series of parallel and spaced bondings between the first substrate and the second substrate, (c) for each sample, placing a wedge between the first substrate and the second substrate, (d) pushing the wedge closer to the series of bondings formed by a specific laser power, (e) determining the distance between the wedge at the point of bonding breakage and the bonding closest to the wedge, and (f) relating the determined distance to a function of the laser power; The determined distance is within a range from the minimum distance associated with the junction formed by the maximum laser power to the maximum distance associated with the junction formed by the minimum laser power.

17. The method as described in claim 16, characterized in that: Determining the range of the joint strength includes the effective fracture toughness of the joint ( ) is quantized as a function of the determined distance.

18. The method as described in claim 17, characterized in that: The effective fracture toughness of the joint ( Quantifying the effective fracture toughness (a function of the determined distance) involves using a numerical model that incorporates the effective fracture toughness of the joint. The value is quantified as a function of the distance at the joint fracture point caused by the modeled wedge.

19. The method as described in claim 18, characterized in that: The numerical model uses the thickness of the modeled wedge, the width of the joint, the spacing between adjacent joints, the thickness of the first substrate, the thickness of the second substrate, the Young's modulus of the first substrate, the Young's modulus of the second substrate, the Poisson's ratio of the first substrate, the Poisson's ratio of the second substrate, the shear modulus of the first substrate, and the shear modulus of the second substrate as variables.

20. The method as described in claim 19, characterized in that: The numerical model quantifies the stress intensity factors of longitudinal opening and in-plane shear for the range of assumed distances at the crack initiation point, and the effective fracture toughness derived from the stress intensity factors of longitudinal opening and in-plane shear. ).

21. The method as described in claim 12, characterized in that: The range of incident laser energy densities, defined as being from the minimum incident laser energy density sufficient to form the bond between the first substrate and the second substrate to the maximum incident laser energy density sufficient to form a bond weaker than that between the first substrate and the second substrate, includes: The range of laser speeds is determined from the maximum laser speed sufficient to form the bonding between the first substrate and the second substrate to the minimum laser speed sufficient to form the bonding between the first substrate and the second substrate that is weaker than that between the first substrate and the second substrate. Determining the range of the bonding strength from the minimum bonding strength formed using the minimum incident laser energy density to the maximum bonding strength formed using the maximum incident laser energy density includes: Determine the range of the bonding strength within the range from the minimum bonding strength formed using the maximum laser speed to the maximum bonding strength formed using the minimum laser speed; Determining the incident laser energy density, within the range of incident laser energy density, corresponding to the variable incident laser energy density at each intermediate junction, and varying with the determined intensity, includes: Determine the laser velocity within the range of the laser velocity corresponding to the determined intensity of each intermediate joint; and The innermost junction is formed at the minimum radius using the minimum incident laser energy density, the outermost junction is formed at the maximum radius using the maximum incident laser energy density, and each intermediate junction is formed at the determined radius using the determined incident laser energy density, comprising: The innermost joint is formed at the minimum radius using the maximum laser speed, the outermost joint is formed at the maximum radius using the minimum laser speed, and each intermediate joint is formed at the determined radius using the determined laser speed.

22. The method according to any one of claims 12-21, characterized in that: Determining the range of the joint radius includes the effective fracture toughness for the joint ( The range quantifies the pressure at each joint burst as a function of the radius of the joint.

23. The method as described in claim 22, characterized in that: The numerical model is for the effective fracture toughness of the joint. The range quantifies the pressure at each joint rupture as a function of the radius of the joint.

24. The method according to any one of claims 12-21, characterized in that: The ratio of the spacing to the width of the joint is 1.75 to 3.5; and The number of joints is at least 5.

25. The method according to any one of claims 12-21, characterized in that: Determining the strength of each intermediate joint includes determining the effective fracture toughness of each of the intermediate joints. ) is quantified as a function of the determined radius and assigned burst pressure of each of the intermediate joints.

26. The method as described in claim 25, characterized in that: The numerical model is for the effective fracture toughness of the joint. The range of ) quantifies the pressure at each joint burst as a function of the radius of the joint, and according to the model, the effective fracture toughness of each of the intermediate joints ( It is quantified as a function of the determined radius and the assigned burst pressure.

27. The method as described in claim 26, characterized in that: Determining the strength of each intermediate joint includes interpolating a graph for a given effective fracture toughness of the joint. The burst pressure is plotted as a function of the radius of the joint.

28. The method according to any one of claims 12-21, characterized in that: Determining the incident laser energy density corresponding to each intermediate joint includes (a) using a numerical model that determines the effective fracture toughness of the joint. ) is quantified as a function of the radius and burst pressure of the joint to determine the fracture toughness of each intermediate joint. (b) Using a numerical model that quantifies the distance at which the modeled wedge causes the joint to fracture as the effective fracture toughness of the joint. The function of ) is used to determine the dependence on the determined fracture toughness ( (c) the distance of each of the intermediate joints, and (d) experimentally relating the distance to a function of the incident laser energy density to determine the incident laser energy density of each intermediate joint that varies with the determined distance of each intermediate joint.

29. The method as described in claim 28, characterized in that: The distance correlation as a function of incident laser energy density includes (a) preparing sample pairs of the first substrate and the second substrate, (b) stacking each sample pair to form an interface between the first substrate and the second substrate, wherein the interface of each sample pair is subjected to different incident laser energy densities within the range of the incident laser energy density to form a series of parallel and spaced-apart joints between the first substrate and the second substrate, (c) for each sample, placing a wedge between the first substrate and the second substrate, (d) pushing the wedge closer to the series of joints formed by a specific incident laser energy density, (e) determining the distance between the wedge at the joint break and the joint closest to the wedge, and (f) correlation of the determined distance as a function of incident laser energy density.

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