Particle detector, image generation device, and image generation method
11402520 · 2022-08-02
Assignee
Inventors
Cpc classification
H01L31/101
ELECTRICITY
H01L31/115
ELECTRICITY
G01T1/241
PHYSICS
A61B6/52
HUMAN NECESSITIES
G01T1/1606
PHYSICS
H10N60/84
ELECTRICITY
G01N21/17
PHYSICS
International classification
G01N21/17
PHYSICS
Abstract
According to one embodiment, a particle detector is disclosed. The particle detector includes a substrate, and detection regions provided on the substrate and insulated from the substrate. Each of the detection regions includes superconducting strips having a longitudinal direction and configured for detecting a particle, and the superconducting strips are arranged in arrangement directions differing between the detection regions. The numbers of particles detected by the respective detection regions are used to generate accumulated detection number profiles of particles in the arrangement directions of the superconducting strips of the respective detection regions, and each of the accumulated detection number profiles includes a profile obtained by accumulating the numbers of particles detected by the respective superconducting strips along the longitudinal direction.
Claims
1. A particle detector comprising: a substrate; and detection regions provided on the substrate and insulated from the substrate, each of the detection regions comprising superconducting strips having a longitudinal direction and configured for detecting a particle on a certain particle arrival region, the superconducting strips being arranged in arrangement directions differing between the detection regions, wherein: the number of the detection regions is three or more, the number of particles detected by the respective detection regions are used to generate accumulated detection number profiles of particles in the arrangement directions of the superconducting strips of the respective detection regions, each of the accumulated detection number profiles includes a profile obtained by accumulating the numbers of particles detected by the respective superconducting strips along the longitudinal direction, and the accumulated detection number profiles of the particles are used to reconstruct a two-dimensional distribution of the number of particles on the certain particle arrival region.
2. The particle detector of claim 1, wherein the two-dimensional distribution of the number of particles on the certain particle arrival region is reconstructed by using a technique of projection-slice theorem.
3. The particle detector of claim 1, wherein the respective arrangement directions of the superconducting strips are equally distributed.
4. The particle detector of claim 1, wherein the detection regions are stacked in an insulated state, or arranged in a same plane in an insulated state.
5. The particle detector of claim 1, wherein: the detection regions include a first detection region, a second detection region, a third detection region, and a fourth detection region, the first detection region includes first superconducting strips and the arrangement direction thereof is a first direction, the second detection region includes second superconducting strips and the arrangement direction thereof is a second direction different from the first direction, the third detection region includes third superconducting strips and the arrangement direction thereof is a third direction different from the first direction and the second direction, the fourth detection region includes fourth superconducting strips and the arrangement direction thereof is a fourth direction different from the first direction, the second direction, and the third direction, the number of particles detected by each of the first superconducting strips is used to generate a first accumulated detection number profile, the number of particles detected by each of the second superconducting strips is used to generate a second accumulated detection number profile, the number of particles detected by each of the third superconducting strips is used to generate a third accumulated detection number profile, and the number of particles detected by each of the fourth superconducting strips is used to generate a fourth accumulated detection number profile.
6. The particle detector of claim 1, wherein each of the superconducting strips has a linear shape.
7. The particle detector of claim 1, wherein each of the superconducting strips has a meandering shape.
8. The particle detector of claim 1, wherein the particles are those that have passed through a sample.
9. An image generation device comprising: the particle detector of claim 1; and a generator which generates the accumulated detection number profiles based on the number of particles detected by the respective detection regions of the particle detector, and reconstructs a two-dimensional distribution of the number of particles on the certain particle arrival region by using the accumulated detection number profiles.
10. The image generation device of claim 9, wherein the respective arrangement directions of the superconducting strips are equally distributed.
11. The image generation device of claim 9, wherein the detection regions are stacked in an insulated state, or arranged in a same plane in an insulated state.
12. The image generation device of claim 9, wherein the generator reconstructs the two-dimensional distribution of the number of particles on the certain particle arrival region by using the accumulated detection number profiles of the particles with a technique of projection-slice theorem.
13. An image generation method employing the particle detector of claim 1, the image generation method comprising: irradiating the particle detector with particles that passed through a sample by irradiating the sample with particles; generating the accumulated detection number profiles based on the number of particles detected by the respective detection regions of the particle detector; and reconstructing a two-dimensional distribution of the number of particles on the certain particle arrival region by using the accumulated detection number profiles.
14. The image generation method of claim 13, wherein the number of particles detected by the respective detection regions of the particle detector are those that are detected by the respective detection regions at different angles of rotation by rotating any one of the sample and the particle detector more than once at the different angles of rotation with respect to an axis parallel to the traveling direction of the particles.
15. The image generation method of claim 13, wherein reconstructing the two-dimensional distribution of the number of particles on the certain particle arrival region by using the accumulated detection number profiles is performed with a technique of projection-slice theorem.
16. The image generation method of claim 15, wherein the reconstructed two-dimensional distribution of the number of particles on the certain particle arrival region is a projection image of the sample through which the particles passed.
17. The image generation method of claim 16, wherein the reconstructed image includes a three-dimensional image, and generating the three-dimensional image comprising obtaining projection images of the sample by varying an angle formed by a plane of the sample to be irradiated with the particles and a plane perpendicular to the axis.
18. A particle detector comprising: a substrate; and detection regions provided on the substrate and insulated from the substrate, each of the detection regions comprising superconducting strips having a longitudinal direction and configured for detecting a particle on a certain particle arrival region, the superconducting strips being arranged in arrangement directions differing between the detection regions, wherein: the number of the detection regions is three or more, each of the detection regions includes the certain particle arrival region, the number of particles detected by the respective detection regions are used to generate accumulated detection number profiles of particles in the arrangement directions of the superconducting strips of the respective detection regions, each of the accumulated detection number profiles includes a profile obtained by accumulating the number of particles detected by the respective superconducting strips along the longitudinal direction, and the accumulated detection number profiles of the particles on the certain particle arrival region are used to compare with other accumulated detection number profiles of the particles on other certain particle arrival region to evaluate the similarity between the particles on the certain particle arrival region and the particles on the other certain particle arrival region.
19. The particle detector of claim 1, wherein: the detection regions include a first detection region, a second detection region and a third detection region, the first detection region includes first superconducting strips and the arrangement direction thereof is a first direction, the second detection region includes second superconducting strips and the arrangement direction thereof is a second direction different from the first direction, the third detection region includes third superconducting strips and the arrangement direction thereof is a third direction different from the first direction and the second direction, the number of particles detected by each of the first superconducting strips is used to generate a first accumulated detection number profile, the number of particles detected by each of the second superconducting strips is used to generate a second accumulated detection number profile, and the number of particles detected by each of the third superconducting strips is used to generate a third accumulated detection number profile.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
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DETAILED DESCRIPTION
(16) In general, according to one embodiment, a particle detector is disclosed. The particle detector comprises a substrate, and detection regions provided on the substrate and insulated from the substrate. Each of the detection regions comprises superconducting strips having a longitudinal direction and configured for detecting a particle, and the superconducting strips are arranged in arrangement directions differing between the detection regions. The numbers of particles detected by the respective detection regions are used to generate accumulated detection number profiles of particles in the arrangement directions of the superconducting strips of the respective detection regions, and each of the accumulated detection number profiles includes a profile obtained by accumulating the numbers of particles detected by the respective superconducting strips along the longitudinal direction.
(17) Embodiments will be described hereinafter with reference to the accompanying drawings. The drawings are schematic or conceptual drawings, and dimensions and ratios are not necessarily the same as those in reality. Further, in the drawings, the same reference symbols (including those having different subscripts) denote the same or corresponding parts, and overlapping explanations thereof will be made as necessary. In addition, as used in the description and the appended claims, what is expressed by a singular form shall include the meaning of “more than one”.
First Embodiment
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(19) The particle detector of the present embodiment includes a substrate 10, a first detection region 11.sub.1 provided on the substrate 10, a second detection region 11.sub.2 provided on the first detection region 11.sub.1, a third detection region 11.sub.3 provided on the second detection region 11.sub.2, and a fourth detection region 11.sub.4 provided on the third detection region 11.sub.3. Although the number of detection regions (the number of stacked layers) is four in the present embodiment, the number may be two, three, five or more.
(20) As shown in the sectional view of
(21) The first detection region 11.sub.1 to the fourth detection region 11.sub.4 are provided in order on the insulating layer 10b. As a result, the first detection region 11.sub.1 to the fourth detection region 11.sub.4 are stacked on the substrate 10 in the state of being insulated from the substrate 10.
(22) The first detection region 11.sub.1 includes first superconducting strips 20.sub.1. An arrangement direction of the first superconducting strips 20.sub.1 is a first direction D1. A longitudinal direction of the first superconducting strips 20.sub.1 is a direction perpendicular to the first direction D1. The first superconducting strips 20.sub.1 are, for example, arranged periodically.
(23) The width and the thickness of the first superconducting strips 20.sub.1 are less than or equal to 200 nm. This is because the sectional areas of the first superconducting strips 20.sub.1 are made smaller to the extent that superconducting regions are divided. A well-known material can be selected as appropriate as the materials of the first superconducting strips 20.sub.1. As in the case of a material including tantalum, the greater the absorptance of X-rays is, the greater the detection efficiency of X-ray photons is.
(24) Although the number of first superconducting strips 20.sub.1 is five in the present embodiment, the number may be four, three, two, six or more.
(25) As shown in the sectional view of
(26) The second detection region 11.sub.2 includes second superconducting strips 20.sub.2 of which arrangement direction is a second direction D2 different from the first direction D1. A longitudinal direction of the second superconducting strips 20.sub.2 is a direction perpendicular to the second direction D2. The second superconducting strips 20.sub.2 are, for example, arranged periodically.
(27) The second superconducting strips 20.sub.2 are provided on the first insulating layer 21 shown in
(28) The third detection region 11.sub.3 includes third superconducting strips 20.sub.3 of which arrangement direction is a third direction D3 different from the first direction D1 and the second direction D2. A longitudinal direction of the third superconducting strips 20.sub.3 is a direction perpendicular to the third direction D3. The third superconducting strips 20.sub.3 are, for example, arranged periodically.
(29) The third superconducting strips 20.sub.3 are provided on the above-described second insulating layer. The third detection region 11.sub.3 further includes a third insulating layer corresponding to the first insulating layer 21 shown in
(30) The dimensions, the number, and the superconducting materials of the third superconducting strips 20.sub.3 are the same as those of the first superconducting strips 20.sub.1.
(31) The fourth detection region 11.sub.4 includes fourth superconducting strips 20.sub.4 of which arrangement direction is a fourth direction D4 different from the first direction D1, the second direction D2, and the third direction D3. A longitudinal direction of the fourth superconducting strips 20.sub.4 is a direction perpendicular to the fourth direction D4. The fourth superconducting strips 20.sub.4 are, for example, arranged periodically.
(32) The fourth superconducting strips 20.sub.4 are provided on the above-described third insulating layer. For example, as shown in the sectional view of
(33) The number and the superconducting materials of the fourth superconducting strips 20.sub.4 are the same as those of the first superconducting strips 20.sub.1.
(34) As described above, an X-ray photon is incident on the fourth detection region 11.sub.4 (detection region in the highest layer). The incident X-ray photon is absorbed by any one of the fourth superconducting strips 20.sub.4 of the fourth detection region 11.sub.4, any one of the third superconducting strips 20.sub.3 of the third detection region 11.sub.3, any one of the second superconducting strips 20.sub.2 of the second detection region 11.sub.2 or any one of the first superconducting strips 20.sub.1 in the first detection region 11.sub.1 (detection region in the lowest layer), or the incident X-ray photon passes through the fourth detection region 11.sub.4 to the first detection region 11.sub.1, and reaches the substrate 10.
(35) By determining the number of stacked layers so that a certain number of X-ray photons are absorbed by the detection region of the lowest layer, the probability of detection of X-ray photons increases. Thus, a detection failure, i.e., a failure to detect X-ray photons, can be prevented from occurring. In addition, also in cases where X-ray photons which are incident at the same time are detected by any one of the detection region in the highest layer to the detection region in the lowest layer, all the X-ray photons can be detected.
(36) The particle detector of the present embodiment may include a slit portion 30 which is disposed above the fourth detection region 11.sub.4 and which limits a region of X-rays to be detected. Reference symbol 30s represents an opening portion of the slit portion 30 (slit opening portion). The shape of the slit-portion opening 30s is determined so that the region of X-rays pass through the slit-portion opening 30s is included in a region where superconducting strips are arranged in all of the fourth detection region 11.sub.4 to the first detection region 11.sub.1. When the slit portion 30 is not included in a part of the particle detector, the slit portion 30 is prepared when detecting an X-ray photon.
(37) The particle detector of the present embodiment may include an X-ray generator 31 which is disposed above the slit portion 30 and which generates X-rays. When the X-ray generator 31 is not included in a part of the particle detector, the X-ray generator 31 is prepared when detecting an X-ray photon.
(38) In the following description, when it is unnecessary to distinguish the first to fourth superconducting strips 20.sub.1 to 20.sub.4 in particular, they will be referred to as superconducting strips 20.sub.i. Similarly, when it is unnecessary to distinguish the first to fourth detection regions 11.sub.1 to 11.sub.4 in particular, they will be referred to as detection regions 11.sub.i.
(39) As shown in
(40) The particle detector may include an amplifier 26 connected to the one end 20.sub.iA of the superconducting strip 20.sub.i. The amplifier 26 amplifies an electrical signal generated by the superconducting strip 20.sub.i. When the amplifier 26 is not included in a part of the particle detector, the amplifier 26 is prepared when detecting an X-ray photon.
(41) The particle detector may include a measuring instrument 27 which is connected to the amplifier 26 and which is configured to monitor an electrical signal.
(42) When an X-ray photon is absorbed by the superconducting strip 20.sub.i in a superconducting state, which is cooled down to a critical temperature or less, a superconducting region of the superconducting strip 20.sub.i is divided. Thus, detecting a state in which the superconducting region is divided (divided state) corresponds to detecting the X-ray photon. Here, when the divided state arises, the superconducting strip 20.sub.i generates an electrical signal (for example, a pulsed electrical signal). Accordingly, the X-ray photon can be detected by detecting the electrical signal by using the measuring instrument 27.
(43) When the measuring instrument 27 is not included in a part of the particle detector, the measuring instrument 27 is prepared when detecting an X-ray photon.
(44) The superconducting strip 20.sub.i is cooled down to the critical temperature or less by an optional refrigerator (not shown) so as to maintain the superconducting state. The refrigerator may not be included in the particle detector as in the case of the current source 25, the amplifier 26, etc.
(45) Next, a method of detecting an X-ray photon using the particle detector of the present embodiment will be described.
(46) As shown in
(47) Since the width and the thickness of the superconducting strip 20.sub.i are less than or equal to 200 nm, the sectional area of the superconducting strip 20.sub.i is small. Thus, when an X-ray photon is absorbed in the superconducting strip 20.sub.i, a region called a hot spot (hereinafter, referred to as a hot spot region) 51, which transitions to a non-superconducting state, is generated in a superconducting region 50 of the superconducting strip 20.sub.i as shown in
(48) Then, the hot spot region 51 and the bypass region 52, which have transitioned to a non-superconducting state, rapidly disappear by being cooled, and thus, a pulsed electrical signal is generated by temporary electrical resistance generated by the division of the superconducting region 50. The pulsed electrical signal is amplified by the amplifier 26, and the number of X-ray photons is detected by counting the amplified pulsed electrical signal by using the measuring instrument 27 (step S5).
(49) Here, the number of detected X-ray photons, for example, as shown in
(50) In
(51) Note that, in
(52) A profile as shown in
(53) In this manner, according to the present embodiment, the particle detector which can be used to generate an accumulated detection number profile of X-ray photons in the directions can be provided by adopting the structure in which the detection regions 11.sub.i are stacked.
(54) As an example showing the use of an obtained accumulated detection number profile, a difference between two different samples is evaluated. That is, the difference between the two different samples in a certain direction can be evaluated by comparing accumulated detection number profiles in the direction of the two different samples, and the difference between the two different samples can be evaluated in detail by similarly making a comparative evaluation in all the directions. At this time, if the directions (in the present embodiment, the directions D1 to D4) are equally distributed (in the present embodiment, the angle formed by the direction D1 and the direction D2, the angle formed by the direction D2 and the direction D3, and the angle formed by the direction D3 and the direction D4 are equal), the difference between the two different samples can be evenly evaluated. For example, if the samples have a geometrical pattern formed of horizontal and vertical sides, a minimum comparative evaluation can be made by selecting a total of four directions including two directions extending along the sides (horizontal direction and vertical direction) and two directions extending not along the sides (direction slanting upward to the left and direction slanting upward to the right) as the directions.
(55) While the particle detector and the particle detection method for detecting X-ray photons have been described in the present embodiment, the present embodiment is also applicable to the detection of other particles. For example, the present embodiment is applicable to the detection of particles, such as extreme ultraviolet (EUV) photons, ultraviolet photons, infrared photons, visible light photons, electrons, neutrons, and ions.
Second Embodiment
(56)
(57) In
(58) When the sample 32 is irradiated with X-rays, the particle detector 1 is irradiated with X-ray photons of the X-rays which pass through the sample (steps 10).
(59) The accumulated detection number profile generator 2a generates accumulated detection number profiles, based on data measured by the measuring instrument 27 (step S11). The number of accumulated detection number profiles is equal to the number of stacked detection regions, and in the present embodiment, a first accumulated detection number profile to a fourth accumulated detection number profile are generated. More details are as follows.
(60) The accumulated detection number profile generator 2a generates a profile of an accumulated detection number with respect to the positions in the arrangement direction of the superconducting strips 20.sub.4 (fourth accumulated detection number profile) which is obtained by accumulating data measured by the measuring instrument 27, that is, by accumulating the numbers of X-ray photons detected by the respective fourth superconducting strips 20.sub.4 along the longitudinal direction thereof.
(61) The accumulated detection number profile generator 2a further generates a profile of an accumulated detection number with respect to the positions in the arrangement direction of the superconducting strips 20.sub.3 (third accumulated detection number profile) which is obtained by accumulating data measured by the measuring instrument 27, that is, by accumulating the numbers of X-ray photons detected by the respective third superconducting strips 20.sub.3 along the longitudinal direction thereof.
(62) The accumulated detection number profile generator 2a further generates a profile of an accumulated detection number with respect to the positions in the arrangement direction of the superconducting strips 20.sub.2 (second accumulated detection number profile) which is obtained by accumulating data measured by the measuring instrument 27, that is, by accumulating the numbers of X-ray photons detected by the respective second superconducting strips 20.sub.2 along the longitudinal direction thereof.
(63) The accumulated detection number profile generator 2a further generates a profile of an accumulated detection number with respect to the positions in the arrangement direction of the superconducting strips 20.sub.2 (first accumulated detection number profile) which is obtained by accumulating data measured by the measuring instrument 27, that is, by accumulating the numbers of X-ray photons detected by the respective first superconducting strips 20.sub.1 along the longitudinal direction thereof.
(64) In the following description, if it is unnecessary to distinguish the first accumulated detection number profile to the fourth accumulated detection number profile in particular, they will be referred to as accumulated detection number profiles.
(65) The first accumulated detection number profile to the fourth accumulated detection number profile are input to the Fourier transform image generator 2b. The Fourier transform image generator 2b performs Fourier transforms of the first accumulated detection number profile to the fourth accumulated detection number profile and generates a first Fourier transform image profile to a fourth Fourier transform image profile on the basis of the projection-slice theorem.
(66) The Fourier transform image of the X-ray projection image of the sample is input to the X-ray projection image generator 2c. The X-ray projection image generator 2c generates (reconstructs) an X-ray projection image of the sample by performing an inverse Fourier transform of the Fourier transform image of the X-ray projection image of the sample (step S12). This X-ray projection image is a projection image of X-rays that have passed through the sample.
(67) Here, a medical computed tomography (CT) device performs X-ray radiation more than once, i.e., radiates an X-ray from an X-ray generator to a subject from different directions. However, in the present embodiment, the value of the angle θ.sub.1 is different for each of the detection regions, and thus the projection image can be obtained by performing X-ray radiation once. This leads to a reduction in the generation time of the X-ray projection image of the sample.
(68) In the projection-slice theorem, as shown in
(69) In contrast, in the present embodiment, data of one point in the intensity profile is a value obtained by accumulating the number of X-ray photons in the longitudinal directions of the superconducting strips 20.sub.i in which the X-ray photons are those that pass through sample 32 and are incident on top surfaces of superconducting strips 20.sub.i whose inclination angle is the angle θ.sub.i, and a traveling direction of the X-ray is perpendicular to the plane of the angle θ.sub.i. The generated (reconstructed) image (reconstructed image) is a projection image of the sample 32 projected on the plane of the angle θ.sub.i. By changing the relationship between the traveling direction of the X-ray and the angle θ′ in the projection-slice theorem, not a two-dimensional sectional image but a projection image can be obtained by using a technique of the projection-slice theorem.
(70) In order to obtain intensity data of a Fourier transform image as equally as possible, the angle θ.sub.i is determined so that 0 to 180 degrees are equally divided by the number N of stacked layers.
(71) In
(72) In addition, as shown in
(73) Note that,
(74) Furthermore, as shown in
(75) It should be noted that meandering superconducting strips 20.sub.i′ shown in
(76) The superconducting strip 20.sub.i′ has a structure in which a first straight portion 20.sub.i1′ extending along the axis 43 and a second straight portion 20.sub.i2′ extending along the axis 42 are alternately arranged.
(77) A dimension along the axis 42 of the second straight portion 20.sub.i2′ is greater than a dimension along the axis 42 of the first straight portion 20.sub.i1′ Thus, the absorption probability of the X-ray photon 61 of the second straight portion 20.sub.i2′ is higher than the absorption probability of the X-ray photon 61 of the first straight portion 20.sub.i1′.
(78) As a result, as shown in
(79) An accumulated intensity profile obtained by the meandering superconducting strips 20.sub.i′ may be deformed from the accumulated intensity profile obtained by the straight superconducting strips 20.sub.i shown in
(80) The meandering superconducting strips 20.sub.i′ include the second straight portion 20.sub.i2′ having the higher absorption probability of the X-ray photon, and thus the meandering superconducting strips 20.sub.i′ absorb more X-ray photons 61 than the straight superconducting strips 20.sub.i. Consequently, when the meandering superconducting strips 20.sub.i′ are used, the photons can be more efficiently counted.
(81) Note that, the image generator 2 may constituted by using one generator, two generators, or four or more generators which have the function of accumulated detection number profile generator 2a, the function of the Fourier transform image generator 2b, and the function of the X-ray projection image generator 2c. For example, when four or more generators is used, the function of the Fourier transform image generator 2b is implemented by different generators which includes a generator having the function of generating the first Fourier transform image profile to the fourth Fourier transform image profile, and another generator having the function of generating the Fourier transform image of the X-ray projection image of the sample.
(82) In addition, if an evaluation portion (or an inspection portion) is added to the image generation device of the present embodiment, an inspection device (or an evaluation device) for evaluating (inspecting) the sample 32 also can be achieved. More specifically, an evaluation portion which evaluates the quality of the sample 32 (or an inspection portion which determines whether the sample 32 is defective or not), based on the projection image of the sample 32 generated by the image generator 2, is added. The evaluation portion (or the inspection portion) is connected to the image generator 2.
(83) In addition, if an evaluation portion for evaluating a difference between two samples is used as the evaluation portion, the difference between the two samples can be evaluated on the basis of projection images of the two samples generated by the image generator 2.
Third Embodiment
(84) When a sample 32 includes an array pattern 91 in which quadrangles 90 are periodically arranged as shown in
(85) In
(86) A spatial frequency corresponding to the period a of
(87) Thus, when the sample 32 includes the array pattern 91 (periodic pattern), the number of stacked detection regions can be reduced by adopting an angle defined by tan.sup.−1{(n.Math.a/m.Math.b)} as the angle θ.sub.4 of inclination of
(88) For example, in a case in which n and m are each any one of −1, 0 and 1, the angle θ is 0 degrees when n is 0 and m is −1 or 1, the angle θ is tan.sup.−1(a/b) degrees when n is 1 and m is 1, or n is −1 and m is −1, the angle θ is 90 degrees when n is −1 or 1 and m is 0, and the angle θ is 180−tan.sup.−1(a/b) degrees when n is −1 and m is 1, or n is 1 and m is −1.
Fourth Embodiment
(89)
(90) In the first embodiment, detection regions are stacked, whereas in the present embodiment, detection regions 11.sub.i are arranged to be in contact with a surface (common surface) of a substrate 10 as shown in
(91)
(92) First, as shown in
(93) Next, as shown in
(94) In addition, as shown in
(95)
(96) First, as shown in
(97) Next, as shown in
(98) Next, as shown in
(99) In addition, as shown in
(100) While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, the novel embodiments described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the embodiments described herein may be made without departing from the spirit of the inventions. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the inventions.