Abstract
We disclose an array of Infra-Red (IR) detectors comprising at least one dielectric membrane formed on a semiconductor substrate comprising an etched portion; at least two IR detectors, and at least one patterned layer formed within or on one or both sides of the said dielectric membrane for controlling the IR absorption of at least one of the IR detectors. The patterned layer comprises laterally spaced structures.
Claims
1. An infra-red (IR) detector array device comprising: at least one dielectric membrane formed on a semiconductor substrate comprising an etched portion; an array of IR detectors comprising at least two IR detectors, wherein said array of IR detectors are formed on or within said at least one dielectric membrane; and at least one patterned layer formed within or on said dielectric membrane for controlling the IR absorption of at least one of the said IR detectors, and wherein said at least one patterned layer comprises laterally spaced structures.
2. A device according to claim 1, wherein said at least one patterned layer is located above one of the at least two IR detectors so that said at least one patterned layer is associated with one of the at least two IR detectors.
3. A device according to claim 1, wherein said at least one patterned layer is located above all the IR detectors within the dielectric membrane so that said at least one patterned layer is associated with all of the at least two IR detectors.
4. A device according to claim 1, wherein said at least one patterned layer having the laterally spaced structures have the same pattern above at least some of the IR detectors.
5. A device according to claim 1, wherein said at least one patterned layer having the laterally spaced structures have a different pattern above at least some of the IR detectors.
6. A device according to claim 1, wherein said at least one patterned layer comprises a first set of laterally spaced structures above one of the IR detectors and a second set of laterally spaced structures above one other of the IR detectors, wherein the first and second sets of laterally spaced structures have the same pattern.
7. A device according to claim 1, wherein said at least one patterned layer comprises a first set of laterally spaced structures above one of the IR detectors and a second set of laterally spaced structures above other of the IR detectors, wherein the first and second sets of laterally spaced structures have a different pattern.
8. A device according to claim 1, wherein each laterally spaced structure comprises a metal comprising gold or platinum, or a CMOS-based metal such as aluminium, copper, titanium, molybdenum, or tungsten.
9. A device according to claim 1, wherein said structures are repeated periodically in a lateral direction forming a repeat pattern.
10. A device according to claim 9, wherein the repeat pattern comprises a hexagonal or square shape.
11. A device according to claim 1, wherein said structures comprise a circle, ellipse, rectangular, trapezoid or a combination of different shapes, or a hole of these shapes within a layer.
12. A device according to claim 1, wherein the patterned layer comprises single crystal silicon or polysilicon.
13. A device according to claim 1, wherein the IR detectors comprise any one or more of a thermopile, a resistor, transistor and a diode.
14. A device according to claim 1, wherein each IR detector comprises a thermopile comprising one or more thermocouples each coupled in series.
15. A device according to claim 14, wherein each thermocouple further comprises a first thermal junction, joins to adjacent thermocouples to form a second thermal junctions, the first thermal junction being a hot junction and the second thermal junction being a cold junction.
16. A device according to claim 15, wherein the hot junction is located inside the dielectric membrane and the cold junction is located outside the dielectric membrane.
17. A device according to claim 1, wherein each IR detector comprises at least one diode, wherein said at least one diode comprises a material comprising polysilicon or single crystal silicon.
18. A device according to claim 17, further comprising a reference diode in the cold junction region to measure substrate or ambient temperature.
19. A device according to claim 1, wherein each IR detector comprises at least one resistor, wherein said at least one resistor is located in the centre of the dielectric membrane.
20. A device according to claim 19, wherein said at least one resistor comprises a material comprising: metal comprising aluminium, tungsten, copper, titanium, and/or platinum; n or p type polysilicon; and n or p type single crystal silicon.
21. A device according to claim 20, further comprising a reference resistor located in the cold junction region to measure substrate or ambient temperature.
22. A device according to claim 1, wherein each IR detector comprises a thermopile in which Seeback effect and resistance change effect are used to determine IR radiation.
23. A device according to claim 1, wherein each comprises a thermopile coupled with a reference diode in the cold junction region to determine a cold junction temperature estimation which is used to determine an absolute hot junction temperature.
24. A device according to claim 1, wherein the dielectric membrane comprises silicon dioxide and/or silicon nitride.
25. A device according to claim 1, wherein all the IR detectors of the array are formed within or on a single membrane.
26. A device according to claim 1, wherein each IR detector of the array are formed within or on a different dielectric membrane.
27. A device according to claim 1, further comprising a plurality of dielectric membranes each comprising a plurality of IR detectors.
28. A device according to claim 1, wherein said at least one dielectric membrane further comprises further structures comprising polysilicon, single crystal silicon or metal, the further structures separating the IR detectors.
29. A device according to claim 28, wherein said further structures are embedded within, above and/or below the dielectric membrane.
30. A device according to claim 1, wherein said at least one dielectric membrane is formed by any one of: back-etching using Deep Reactive Ion Etching (DRIE) of the substrate, which results in vertical sidewalls; and using anisotropic etching such as KOH (Potassium Hydroxide) or TMAH (Tetra Methyl Ammonium Hydroxide) which results in slopping sidewalls.
31. A device according to claim 1, wherein said at least one dielectric membrane is formed by a front-side etch or a combination of a front-side and back-side etch to result in a suspended membrane structure, supported only by two or more beams.
32. A device according to claim 1, wherein said at least one dielectric membrane is circular.
33. A device according to claim 1, wherein said at least one dielectric membrane is rectangular, or rectangular shaped with rounded corners to reduce the stresses in the corners.
34. A device according to claim 1, further comprising circuitry formed on the same chip with said array of IR detectors.
35. A device according to claim 1, being formed with circuitry in the same package.
36. A device according to claim 34, wherein the circuitry comprise any one of switches, multiplexer, decoder, filter, amplifier, analogue to digital converter, and/or other circuitry.
37. A device according to claim 34, wherein the circuitry is placed outside the area of said at least one dielectric membrane area.
38. A device according to claim 34, wherein the circuitry comprises one or more of: an IR detector; a multiplexor and decoder to address each detector in the array; a temperature sensor for ambient temperature monitoring and compensation; driving and readout for said temperature sensor; and driving and readout circuitry for the IR detector.
39. A device according to claim 34, wherein the circuitry comprises analogue circuitry to improve spectral selectivity by processing the outputs from each individual IR detector within the array.
40. A device according to claim 39, wherein the circuitry comprises a differential or instrumentation amplifier to determine the differential signal between two IR detectors to extract the difference in a spectral response.
41. A device according to claim 39, further comprising digital interfacing and processing devices formed on the same chip or in the same package to allow improved processing and spectral selectivity.
42. A device according to claim 1, wherein the substrate comprises any one of: silicon; silicon on insulator; silicon carbide; gallium arsenide; gallium nitride; and/or a combination of silicon carbide, gallium arsenide, gallium nitride with silicon.
43. A device according to claim 1, wherein the device is fabricated using a CMOS-usable metal selected from a group comprising tungsten, aluminium, titanium, and molybdenum.
44. A device according to claim 1, wherein the IR detectors are formed using a CMOS-usable material selected from a group comprising Silicon, polysilicon and silicides.
45. A device according to claim 1, wherein the device is fabricated using a non-CMOS material.
46. A device according to claim 1, wherein the device is packaged using one or more of: a metal transistor output (TO) type package; a ceramic, metal or plastic surface mount package; IR filters; a reflector; a flip-chip method; a chip or wafer level package; a lens; a printed circuity board (PCB).
47. A device according to claim 46, wherein the package is hermetically or semi-hermetically sealed with air, dry air, argon, nitrogen, xenon or any other noble gas; and/or the device is packaged in vacuum.
48. A device according to claim 1, further comprising an IR emitter fabricated on the same chip.
49. A device according to claim 48, wherein said IR emitter is formed on or within a separate membrane.
50. A device according to claim 48, wherein said IR emitter comprises a heater comprising any one or more of tungsten, aluminium, copper, polysilicon, single crystal silicon, titanium, platinum, and gold.
51. A device according to claim 48, wherein said IR emitter comprises one or more plasmonic patterned layers within or on one side of the dielectric membrane.
52. A Non-Dispersive Infra-Red (NDIR) sensor system or a spectroscopic sensor system comprising the IR detector array device according to claim 1 and an IR emitter.
53. A sensor system according to claim 52, wherein the IR detector array device and the IR emitter are formed on the same chip.
54. A sensor system according to claim 52, wherein the IR detector array device and the IR emitter are formed on a different chip, or the IR emitter comprises a micro-bulb, or a diode based IR emitter.
55. A sensor system according to claim 52, further comprising at least one IR filter.
56. A sensor system according to claim 52, further comprising a reflecting device.
57. A sensor system according to claim 52, wherein said at least one patterned layer associated with each IR detector is configured to produce at least one wavelength.
58. A sensor system according to claim 57, wherein each IR detector is configured to produce a technique which extracts the output signal from one of the IR detectors from the output signal from the one other of the IR detectors to provide at least one IR absorption wavelength.
59. A sensor system according to claim 58, wherein the technique identifies a gas from the signal received by the IR detectors.
60. A sensor system according to claim 58, wherein the technique determines the gas concentration from the signal received by the detector array.
61. A sensor system according to claim 60, being configured such that the output from each IR detector is grouped or processed to extract the characteristics of the gas.
62. A method of manufacturing an infra-red (IR) detector array device, the method comprising: forming a semiconductor substrate; depositing one or more layers of polysilicon and/or metals and dielectric layers to form an array of IR detectors and at least one patterned layer; bulk etching the semiconductor substrate to form one or more dielectric membranes; wherein said at least one patterned layer is formed within or on said dielectric membrane for controlling the IR absorption of at least one of the said IR detectors, and wherein said at least one patterned layer comprises laterally spaced structures.
Description
BRIEF DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0047] Some preferred embodiments of the invention will now be described by way of example only and with reference to the accompanying drawings, in which:
[0048] FIG. 1 shows a schematic top view of a double thermopile IR detector chip, with one IR detector having a patterned layer for controlling the IR absorption;
[0049] FIG. 2 shows a schematic top view of a double diode IR detector chip, with one IR detector having a patterned layer for controlling the IR absorption. A reference diode that measure the substrate/case/ambient temperature is also placed outside the membrane areas;
[0050] FIG. 3 shows the schematic cross-section of the double thermopile IR detector chip shown in FIG. 1;
[0051] FIG. 4 shows the schematic cross-section of the double diode IR detector chip shown in FIG. 2;
[0052] FIG. 5 shows a schematic top view of a thermopile IR detector chip comprising four thermopile IR detectors. Three of the four thermopile IR detectors have a patterned layer for controlling the IR absorption. The patterned plasmonic layers are different on each device;
[0053] FIG. 6 shows a schematic top view of a double diode IR detector chip, with one IR detector having a patterned layer for controlling the IR absorption. The diodes are embedded within the same dielectric membrane and along with multiple metal tracks acting as separation;
[0054] FIG. 7 shows the schematic cross-section of the double diode IR detector chip shown in FIG. 6 where the membrane trench has sloping side-walls;
[0055] FIG. 8 shows the schematic cross section of the double thermopile IR detector chip with circuitry on the same chip;
[0056] FIG. 9 shows the schematic cross section of the double thermopile IR detector chip having an IR emitter fabricated on the same chip;
[0057] FIG. 10 shows a schematic depiction of the double thermopile IR detector chip facing an IR emitter for filter-less carbon dioxide NDIR detection;
[0058] FIG. 11 shows a schematic depiction of a double thermopile IR detector chip having an IR emitter fabricated on the same chip for filter-less carbon dioxide NDIR detection;
[0059] FIG. 12 shows a schematic top view of a double thermopile IR detector chip with circuitry on the same chip;
[0060] FIG. 13 shows the carbon dioxide detection capabilities of the chip depicted in FIG. 12 in the NDIR configuration depicted in FIG. 10; and
[0061] FIG. 14 illustrates an exemplary flow diagram outlining the manufacturing method of the IR detector array device.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0062] FIG. 1 shows a schematic top-view of a double thermopile IR detector chip 1, with two membranes 2 and 3. The membranes are dielectric membranes and may comprise one or more layers of silicon dioxide and/or silicon nitride. A thermopile, comprising one or more thermocouples connected in series, is embedded within each membrane to form two distinct thermopile IR detectors. Each thermocouple comprises of two dissimilar materials 4 and 5 which form a junction within the membrane while the other ends of the materials are outside the membrane where they are connected electrically to the adjacent thermocouple to form the cold junction. The thermocouple materials may comprise metal such as Aluminium, Tungsten, Titanium or combination of those, doped polysilicon (n or p type) or doped single crystal silicon (n or p type). In the example that both the materials are polysilicon and/or single crystal silicon, a metal link 6 might be used to form the junctions between them. A plasmonic patterned layer 7 is also embedded within membrane 3, to provide the thermopile IR detector with tailored optical properties. The plasmonic patterned layer may be made of metal such as tungsten, aluminium, titanium, molybdenum, gold or platinum, silicides or polysilicon or single crystal silicon, and are periodically repeated in a lateral direction. The pattern may be made of dots or holes of circles, ellipses, rectangular structures, trapezoidal structures, or any other shape. The repeat pattern may be hexagonal or square. The structures may be in more than one layer, within or on the top surface of the membrane.
[0063] FIG. 2 shows a schematic top-view of a double diode IR detector chip 1, with two membranes 2 and 3. The membranes are dielectric membranes and may comprise one or more layers of silicon dioxide and/or silicon nitride. A diode 8, and tracks 9, is embedded within each membrane to form to distinct diode IR detectors. The diodes may be made of polysilicon or of single crystal silicon. One or several diodes for enhanced sensitivity may be connected in series in the centre or in the proximity of the centre of the membrane. A plasmonic patterned layer 7 is also embedded within membrane 3, to provide the diode IR detector with tailored optical properties. The plasmonic patterned layer may be made of metal such as tungsten, aluminium, titanium, molybdenum, gold or platinum, silicides or polysilicon or single crystal silicon. The pattern may be made of circles, ellipses, rectangular structures, trapezoidal structures, or any other shape periodically repeated in a lateral direction. The repeat pattern may be hexagonal or square. The structures may be in more than one layer within or on the top surface of the membrane. A reference diode 10 that measures the substrate/case/ambient temperature is also placed outside the membrane areas.
[0064] FIG. 3 shows the schematic cross-section of the double thermopile IR detector chip shown in FIG. 1. The membranes 2 and 3 are supported on an etched substrate 11, and comprise dielectric layers 12 and may comprise one or more layers of silicon dioxide and/or silicon nitride. The thermopiles comprise p-doped silicon 4, and n-doped silicon 5, and a metal 6 is used to form a junction between them. The thermopile materials may comprise many other configurations, for example, n-doped silicon and metal, or p-doped silicon and metal. The silicon for the thermopiles may be polysilicon or single crystal silicon. A plasmonic patterned layer 7 is also embedded within membrane 3, to provide the thermopile IR detector with tailored optical properties. The substrate in this example is etched by Deep Reactive Ion Etching (DRIE) which results in vertical sidewalls.
[0065] FIG. 4 shows the schematic cross-section of the double diode IR detector chip shown in FIG. 2. The membranes 2 and 3 are supported on an etched substrate 11, and comprise dielectric layers 12 and may comprise one or more layers of silicon dioxide and/or silicon nitride. The diodes 8 are made of single crystal silicon and contacted via metal tracks 9. Alternatively the diodes may be made of polysilicon. A plasmonic patterned layer 7, made of multiple metal layers, is also embedded within membrane 3, to provide the diode IR detector with tailored optical properties. A reference diode 10 that measures the substrate/case/ambient temperature is also placed outside the membrane areas.
[0066] FIG. 5 shows a schematic top-view of a thermopile IR detector chip 1, with four membranes 2, 3, 13 and 14. The membranes are dielectric membranes and may comprise one or more layers of silicon dioxide and/or silicon nitride. A thermopile, comprising one or more thermocouples connected in series, is embedded within each membrane to form four distinct thermopile IR detectors. Each thermocouple comprises two dissimilar materials 4 and 5 which form a junction within the membrane while the other ends of the materials are outside the membrane where they are connected electrically to the adjacent thermocouple to form the cold junction. The thermocouple materials may comprise metal such as Aluminium, Tungsten, Titanium or combination of those, doped polysilicon (n or p type) or doped single crystal silicon (n or p type). In the example that both the materials are polysilicon and/or single crystal silicon, a metal link 6 might be used to form the junctions between them. A plasmonic patterned layer 7 is also embedded within membrane 3, to provide the thermopile IR detector with tailored optical properties. A plasmonic patterned layers 15 and 16 is also embedded within membrane 13 and 14, to provide the thermopile IR detectors with tailored optical properties different from each other and from the ones provided by layer 7. Alternatively, the patterned plasmonic layer may be identical in all the IR devices within the array. Alternately, the patterned plasmonic layer or layers may be different on each device, or may be the same across some devices, but different across others. The array may also have some devices with the same patterned plasmonic layer or layers and some without any patterned plasmonic layer.
[0067] FIG. 6 shows a schematic top-view of a double diode IR detector chip 1, with a single membrane 2. The membrane is dielectric membrane and may comprise one or more layers of silicon dioxide and/or silicon nitride. Two diode 8, and tracks 9, are embedded within the membrane along with a separation 17 to form to diode IR detectors. The diodes may be made of polysilicon or of single crystal silicon. One or several diodes for enhanced sensitivity may be connected in series in the centre or in the proximity of the centre of the membrane. A plasmonic patterned layer 7 is also embedded within membrane 2, to provide only one of the diodes IR detectors with tailored optical properties.
[0068] FIG. 7 shows the schematic cross-section of the double diode IR detector chip shown in FIG. 6. The membranes 2 are supported on an etched substrate 11, and comprise dielectric layers 12 and may comprise one or more layers of silicon dioxide and/or silicon nitride. The diodes 8 are made of single crystal silicon and contacted via metal tracks 9. Alternatively, the diodes may be made of polysilicon. A plasmonic patterned layer 7, made of multiple metal layers, is also embedded within membrane 2, to provide only one of the diode IR detectors with tailored optical properties. Metal layers 17 are used to form the separation between the diodes. This separation area also acts as a heat sink. The separation 17, while made of metal in this figure, may also be made from single crystal silicon or polysilicon, or may comprise metal and polysilicon and/or single crystal silicon. The substrate in this example is etched by KOH resulting in sloping sidewalls.
[0069] FIG. 8 shows the schematic cross-section of the double thermopile IR detector chip shown in FIG. 1 with circuitry on the same chip. The membranes 2 and 3 are supported on an etched substrate 11, and comprise dielectric layers 12 and may comprise one or more layers of silicon dioxide and/or silicon nitride. The thermopiles comprise p-doped silicon 4, and n-doped silicon 5, and a metal 6 is used to form a junction between them. The thermopile materials may comprise many other configurations, for example, n-doped silicon and metal or p-doped silicon and metal. The silicon for the thermopiles may be polysilicon or single crystal silicon. A plasmonic patterned layer 7 is also embedded within membrane 3, to provide the thermopile IR detector with tailored optical properties. The substrate in this example is etched by Deep Reactive Ion Etching (DRIE) which results in vertical sidewalls. Outside the membrane areas, as an example, a MOSFET 18 is shown, which comprises implant regions 19, a polysilicon gate and interconnect metal.
[0070] FIG. 9 shows the schematic cross-section of the double thermopile IR detector chip shown in FIG. 1 with an IR emitter on the same chip. The membranes 2 and 3 are supported on an etched substrate 11, and comprise dielectric layers 12 and may comprise one or more layers of silicon dioxide and/or silicon nitride. The thermopiles comprise p-doped silicon 4, and n-doped silicon 5, and a metal 6 is used to form a junction between them. The thermopile materials may comprise many other configurations, for example, n-doped silicon and metal, or p-doped silicon and metal. The silicon for the thermopiles may be polysilicon or single crystal silicon. A plasmonic patterned layer 7 is also embedded within membrane 3, to provide the thermopile IR detector with tailored optical properties. The substrate in this example is etched by Deep Reactive Ion Etching (DRIE) which results in vertical sidewalls. An IR emitter, in form of a microheater 20, is connected via tracks 21 and embedded within an additional membrane. A plasmonic patterned layer 22 is also embedded within the IR emitter membrane to provide the IR emitter with tailored optical properties.
[0071] FIG. 10 shows a schematic depiction of a double thermopile IR detector chip facing an IR emitter for filter-less carbon dioxide NDIR detection. The chips are both mounted on a package 23. The devices maybe packaged in a metal TO type package. The devices may also be packaged in a ceramic, metal or plastic SMD (surface mount device) package. The package may have one or more IR filters or windows, or a filter whose characteristics vary spatially. The package maybe hermetically or semi-hermetically sealed with air, dry air, argon, nitrogen, xenon or any other noble gas. The device may also be packaged in a vacuum. The device may also be packaged with a lens or a reflector. The package may also be a chip or wafer level package, formed for example, by wafer-bonding an etched wafer/chip on top, with the etched wafer/chip having a portion that is transparent to at least some wavelengths of IR. The device may also be packaged directly on a PCB, or be packaged in a flip-chip method. Even if in this example the NDIR system is for carbon dioxide detection, it may be used for detecting other gases (e.g. carbon monoxide, humidity, methane, etc.).
[0072] FIG. 11 shows a schematic depiction of a double thermopile IR detector chip having an IR emitter fabricated on the same chip for filter-less carbon dioxide NDIR detection. The device maybe packaged in a metal transistor output (TO) type package. The device may also be packaged in a ceramic, metal or plastic SMD (surface mount device) package. The package may have one or more IR filters or windows, or a filter whose characteristics vary spatially. The package maybe hermetically or semi-hermetically sealed with air, dry air, argon, nitrogen, xenon or any other noble gas. The device may also be packaged in a vacuum. The device may also be packaged with a lens or a reflector. The package may also be a chip or wafer level package, formed for example, by wafer-bonding an etched wafer/chip on top, with the etched wafer/chip having a portion that is transparent to at least some wavelengths of IR. The device may also be packaged directly on a PCB, or be packaged in a flip-chip method. Even if in this example the NDIR system is for carbon dioxide detection, it may be used for detecting other gases (e.g. carbon monoxide, humidity, methane, etc.). The IR radiation is guided from the IR emitter to the IR detector via mirrors 24. Other methods for guiding the IR radiation from the IR emitter to the IR detector may be employed.
[0073] FIG. 12 shows a schematic top-view of a double thermopile IR detector chip 1, with two membranes 2 and 3. The membranes are dielectric membranes and may comprise one or more layers of silicon dioxide and/or silicon nitride. A thermopile, comprising one or more thermocouples connected in series, is embedded within each membrane to form two distinct thermopile IR detectors. Each thermocouple comprises two dissimilar materials 4 and 5 which form a junction within the membrane while the other ends of the materials are outside the membrane where they are connected electrically to the adjacent thermocouple to form the cold junction. The thermocouple materials may comprise metal such as Aluminium, Tungsten, Titanium or combination of those, doped polysilicon (n or p type) or doped single crystal silicon (n or p type). In the example that both the materials are polysilicon and/or single crystal silicon, a metal link 6 might be used to form the junctions between them. A plasmonic patterned layer 7 is also embedded within membrane 3, to provide the thermopile IR detector with tailored optical properties. As an example, a differential amplifier 25 and circuitry for signal processing 26 are co-integrated on the same chip to provide the double thermopile IR detector chip with a single output 27, thus facilitating the integration of the chip in a system and improving the chip performance by reducing parasitic components arising from the implementation of such circuitry on a separate chip or PCB.
[0074] FIG. 13 shows the carbon dioxide detection capabilities of a chip similar to the one depicted in FIG. 12 in the NDIR configuration similar to the one depicted in FIG. 10.
[0075] FIG. 14 illustrates an exemplary flow diagram outlining the manufacturing method of the IR detector array device.
[0076] The skilled person will understand that in the preceding description and appended claims, positional terms such as ‘above’, ‘overlap’, ‘under’, ‘lateral’, etc. are made with reference to conceptual illustrations of an device, such as those showing standard cross-sectional perspectives and those shown in the appended drawings. These terms are used for ease of reference but are not intended to be of limiting nature. These terms are therefore to be understood as referring to a device when in an orientation as shown in the accompanying drawings.
[0077] It will be appreciated that all doping polarities mentioned above may be reversed, the resulting devices still being in accordance with embodiments of the present invention.
[0078] Although the invention has been described in terms of preferred embodiments as set forth above, it should be understood that these embodiments are illustrative only and that the claims are not limited to those embodiments. Those skilled in the art will be able to make modifications and alternatives in view of the disclosure which are contemplated as falling within the scope of the appended claims. Each feature disclosed or illustrated in the present specification may be incorporated in the invention, whether alone or in any appropriate combination with any other feature disclosed or illustrated herein.
