Patent ID: 12256578

Like reference numbers and designations in the various drawings indicate like elements.

DETAILED DESCRIPTION

As used herein, the terms such as “first”, “second”, “third”, “fourth” and “fifth” describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms may be only used to distinguish one element, component, region, layer or section from another. The terms such as “first”, “second”, “third”, “fourth” and “fifth” when used herein do not imply a sequence or order unless clearly indicated by the context. The terms “photo-detecting”, “photo-sensing”, “light-detecting”, “light-sensing” and any other similar terms can be used interchangeably.

Spatial descriptions, such as “above”, “top”, and “bottom” and so forth, are indicated with respect to the orientation shown in the figures unless otherwise specified. It should be understood that the spatial descriptions used herein are for purposes of illustration only, and that practical implementations of the structures described herein can be spatially arranged in any orientation or manner, provided that the merits of embodiments of this disclosure are not deviated by such arrangement.

As used herein, the term “intrinsic” means that the semiconductor material region is without intentionally adding dopants, or contains much lower dopant concentration compared to the dopant concentrations in the doping regions surrounding the semiconductor material region.

Referring toFIG.1AtoFIG.8B, the present disclosure provides an optical sensing apparatus100a,100b,200a,200b,300a,300b,400a,400b,500a,500b,600a,600b,700a,700b,800a,800b.

FIG.1Aillustrates a cross-sectional view of an optical sensing apparatus100aaccording to one or more embodiments of the present disclosure.FIG.1Billustrates a cross-sectional view of an optical sensing apparatus100baccording to one or more embodiments of the present disclosure. The optical sensing apparatus100a/100bcan be operated as an avalanche photodiode (APD) or a single-photon avalanche diode (SPAD).

Referring toFIG.1AtoFIG.1B, the optical sensing apparatus100aincludes a substrate101including a first material (e.g., Si), an absorption region109including a second material (e.g., Ge), where the absorption region109is configured to receive an optical signal and generate photo-carriers in response to receiving the optical signal. The absorption region109is supported by the substrate101and includes a first interface1091and a second interface1092opposite to the first interface1091. Referring toFIG.1A, in some embodiments, the absorption region109is formed over the first interface1011of the substrate101. Referring toFIG.1B, in some embodiments, the absorption region109is embedded in the substrate101.

In some embodiments, the substrate101includes a top layer102including a first interface1011and a second interface1012opposite to the first interface1011of the substrate101. In some embodiments, the substrate101further includes an insulating layer103formed under the top layer102. In some embodiments, the substrate101further includes a base layer10supported the insulating layer103. In some embodiments, the base layer10includes the first material. In some embodiments, the substrate101may be a silicon on insulator (SOI) substrate. The second interface1092of the absorption region109is between the first interface1091and the second interface1012of the substrate101. In some embodiments, the top layer102includes the first material.

In some embodiments, the optical sensing apparatus100afurther includes a buried-dopant region105formed in the substrate101(e.g., in the top layer102of the substrate and above the second interface1012of the substrate101) and separated from the absorption region109. The optical sensing apparatus100afurther includes an amplification region120formed in the substrate101and between the absorption region109and the buried-dopant region105, where the amplification region120is configured to collect at least a portion of the photo-carriers from the absorption region109and to amplify the portion of the photo-carriers. The buried-dopant region105is of a first conductivity type (e.g., n-type) and is configured to collect at least a portion of the amplified photo-carriers from the amplification region120. The amplification region120is formed using the first material (e.g., silicon). In some embodiments, the amplification region120may be doped with the dopants of the first conductivity type, where the doping of the amplification region120is lighter than the doping of the buried-dopant region105.

In some embodiments, the optical sensing apparatus100afurther includes an interface-dopant region107formed in the substrate101(e.g., in the top layer102of the substrate) and between the absorption region109and the buried-dopant region105. The interface-dopant region107is of a second conductivity type (e.g., p-type) different from the first conductivity type. In some embodiments, the amplification region120is between the interface-dopant region107and the buried-dopant region105.

In some embodiments, at least one of the interface-dopant region107and the buried-dopant region105includes one or more first regions (e.g., first buried-dopant regions207and first interface-dopant regions203as described inFIGS.2A and2B) and one or more second regions (e.g., second buried-dopant regions205and second interface-dopant regions201as described inFIGS.2A and2B) surrounding the one or more first regions, where a property of the one or more first regions is different from a property of the second regions so as to form, under a reverse bias breakdown voltage (e.g., a first break-down voltage as described herein after), one or more punch-through regions123and one or more blocking regions125in the amplification region120, since the electric field associated with the one or more punch-through region123is stronger than the electric field associated with the one or more blocking regions125at a reverse bias. In some embodiments, the one or more punch-through regions123are adjacent to the one or more first regions and the one or more blocking regions125are adjacent to the one or more second regions.

In some embodiments, the property includes peak doping concentration or depth. For example, a peak doping concentration of the one or more first regions (e.g., first buried-dopant regions207as described inFIGS.2A and2B) of the buried-dopant region105is greater than the than a peak doping concentration of the one or more second regions (e.g., second buried-dopant regions205as described inFIGS.2A and2B) of the buried-dopant region105. For another example, a depth of the one or more first regions (e.g., first buried-dopant regions207as described inFIGS.2A and2B) is deeper than a depth of the one or more second regions (e.g., second buried-dopant regions205as described inFIGS.2A and2B). In some embodiments, the depth of the first regions and the second regions of the buried-dopant region105is measured by a distance from the second interface1012of the substrate101to the peak doping concentration.

For another example, a peak doping concentration of the one or more first regions (e.g., first interface-dopant regions203as described inFIGS.2A and2B) of the interface-dopant region107is lower than the than a peak doping concentration of the one or more second regions (e.g., second interface-dopant regions201as described inFIGS.2A and2B) of the interface-dopant region107. For another example, a depth of the one or more first regions (e.g., first interface-dopant regions203as described inFIGS.2A and2B) of the interface-dopant region107is deeper than a depth of the one or more second regions (e.g., second interface-dopant regions201as described inFIGS.2A and2B) of the interface-dopant region107. In some embodiments, the depth of the first regions and the second regions of the interface-dopant region107is measured by a distance from the second interface1092of the absorption region109to the peak doping concentration.

As disclosed in example embodiments in reference toFIGS.2A-8B, by controlling one or more properties (e.g., dopant level, dopant depth, etc.) of the interface-dopant region107and the buried-dopant region105, one or more blocking regions125can be formed around one or more punch-through regions123. In general, the punch-through region(s)123has a first break-down voltage lower than a second break-down voltage associated with the one or more blocking regions125, such that avalanche breakdown begins to occur in the punch-through region(s)123before the one or more blocking regions125. Accordingly, the one or more punch-through regions123collect at least a portion of the photo-carriers from the absorption region109and amplify the collected photo-carriers under the first break-down voltage. Besides, the one or more blocking regions125may block at least a portion of the photo-carriers so as to guide the portion of the photo-carriers to enter the punch-through region(s)123under the first break-down voltage.

In other words, when the optical sensing apparatus100a/100bis in operation at a reverse bias, the electric field associated with the one or more punch-through regions123is stronger than the electric field associated with the one or more blocking regions125. As a result, the breakdown region can be confined in the punch-through regions123instead of the whole amplification region120. These punch-through regions123and the blocking regions125as field-controlled regions with different punch-through/breakdown voltages help to avoid premature breakdown in avalanche photodiode (APD)/single-photon avalanche diode (SPAD), which improves sensitivity and/or reduces amplification of dark current. Accordingly, the optical sensing apparatus100a,100bhas better performance such as higher sensitivity and longer detection distance.

In some embodiments, the optical sensing apparatus100a,100bfurther includes a cladding layer131formed surrounding or over the absorption region109, depending on the arrangement of the absorption region109and the substrate101. In some embodiments, the cladding layer131includes insulating material (e.g., oxide) for electrical isolation between two conductive regions (e.g., the second conductive regions121a/121band the third conductive regions127a/127bas described herein after)

In some embodiments, the optical sensing apparatus100a,100bfurther includes one or more first contacts115a/115bformed on the cladding layer131and electrically coupled to the buried-dopant region105, where the one or more first contacts115a/115bare configured to provide at least a portion of the photo-carriers from the buried-dopant region105as a readout signal. For example, a readout circuitry (not shown) may be coupled to the one or more first contacts115a/115b.

In some embodiments, the optical sensing apparatus100a,100bfurther includes one or more first conductive regions119a/119bformed in the substrate101(e.g., in the top layer102of the substrate101) and electrically coupled to the buried-dopant region105. In some embodiments, the one or more first conductive regions119a/119bcan be of the first conductivity type and doped with a dopant having a peak doping concentration not less than about 5×1018cm−3(e.g., about 1×1019cm−3). In some embodiments, the substrate101is substantially devoid of metal material between the first interface1011and the second interface1012so as to maintain the material integrity of the top layer102of the substrate101, which improves the performance of the optical sensing apparatus100a,100b.

The optical sensing apparatus100a,100bfurther includes one or more second conductive regions121a/121bformed in the cladding layer131, where each one of the one or more second conductive regions121a/121bis electrically coupled to (i) a respective one of the one or more first contacts115a/115b, and (ii) a respective one of the one or more first conductive regions119a/119b.

In some embodiments, the optical sensing apparatus100a,100bincludes a doped contact region111of the second conductivity type formed between the absorption region109and the cladding layer131or formed in the absorption region109. In some embodiments, the doping concentration of the doped contact region111can be between about 1×1018cm−3and 5×1020cm−3. The doped contact region111is configured to collect photo-carriers of a first type, and where the buried-dopant region105is configured to collect photo-carriers of a second type. For example, when the doped contact region111is of p-type and the buried-dopant region105is of n-type, the doped contact region111is configured to collect holes and the buried-dopant region105is configured to collect electrons. In some embodiments, the doped contact region111includes the first material or the second material.

In some embodiments, the optical sensing apparatus100a,100bincludes one or more second contacts117a/117bover the cladding layer131. In some embodiments, the optical sensing apparatus100a,100bincludes one or more third conductive regions127a/127bformed in the cladding layer131for electrical connection between the doped contact region111and the respective one or more second contacts117a/117b.

In some embodiments, the second conductive regions121a/121band the third conductive regions127a/127bmay be vias filled with metal.

In some embodiments, the absorption region109is p-doped, and the buried-dopant region105is n-doped. For example, the absorption region109is doped with a peak doping concentration between about 1×1017cm−3and 1×1019cm−3. The buried-dopant region105is not less than about 5×1018cm−3(e.g., about 1×1019cm−3).

In some embodiments, the absorption region109is of the second conductivity type and has a gradient doping profile. For example, the gradient doping profile can be graded from a first interface1091of the absorption region109or from a doped contact region111to a second interface1092of the absorption region109. In some embodiments, the gradient doping profile can be a gradual decrease/increase or a step-like decrease/increase depending on the moving direction of the carriers (e.g., electrons, when the buried-dopant region105is n-type). In some embodiments, the concentration of the gradient doping profile is gradually deceased/increased from the first interface1091or the doped contact region111of the absorption region109to the second interface1092of the absorption region109depending on the moving direction of the carriers.

In some embodiments, the concentration of the gradient doping profile is gradually such as radially deceased/increased from a center of the first interface1091or the doped contact region111of the absorption region109to the second interface1092and to the side interfaces1093of the absorption region109depending on the moving direction of the carriers (e.g., electrons, when the buried-dopant region105is n-type). For example, when the doped contact region111is of p-type, electrons move in the absorption region109substantially along a direction from the first interface1091to the second interface1092, the concentration of the gradient doping profile of the dopant in the absorption region109, for example, boron, is gradually deceased from the first interface1091or from the doped contact region111to the second interface1092of the absorption region109. In some embodiments, the concentration of the gradient doping profile is gradually and laterally decreased/increased from an edge of the first interface1091or the doped contact region111of the absorption region109to the side interfaces1093of the absorption region109depending on the moving direction of the carriers (e.g., electrons, when the buried-dopant region105is n-type).

Referring toFIG.1A, in some embodiments, the absorption region109is over the first interface1011of the substrate101. In some embodiments, the optical sensing apparatus100amay further include a passivation layer (not shown) covering the interface (e.g., first interface1091and side interface1093) of the absorption region109for protecting the absorption region109. Referring toFIG.1B, in some embodiments, the absorption region109is embedded in the substrate101, for example, embedded in the top layer102of the substrate101. In some embodiments, the optical sensing apparatus100bfurther includes one or more sidewall-dopant regions133surrounding the absorption region109for blocking the carriers (e.g., electrons when the buried-dopant region105is of n-type) from entering the top layer102through the side interface1093of the absorption region109, and thus the one or more sidewall-dopant regions133further facilities the carriers entering the amplification region120between the absorption region109and the buried-dopant region105. In some embodiments, the sidewall-dopant regions133is of the second conductivity type (e.g., p-type). In some embodiments, the peak doping concentration of the sidewall-dopant regions133is not less than 1×1017cm−3. In some embodiments, the passivation layer includes a material different from the second material. For example, the passivation layer may include amorphous silicon, poly silicon, epitaxial silicon, aluminum oxide (e.g., AlxOy), silicon oxide (e.g., SixOy), Ge oxide (e.g., GexOy), germanium-silicon (e.g., GeSi), silicon nitride family (e.g., SixNy), high-k materials (e.g., HfOx, ZnOx, LaOx, LaSiOx), and any combination thereof. In some embodiments, the sidewall-dopant regions133may include first material (e.g., single crystal silicon).

In some embodiments, the absorption region109of the optical sensing apparatus has a width greater than 10 μm. For example, the width of the absorption region109can be 250 μm, or 700 μm. By having the absorption region109in a large dimension, a lens over the absorption region109may not be necessary, which may reduce the cost of the optical sensing apparatus100a,100band also alleviate a problem of shielding optical signal by the lens.

In some embodiments, the absorption region109is p-doped, and where the buried-dopant region105is n-doped. For example, the absorption region109is doped with a peak doping concentration between about between 1×1017cm−3and 1×1019cm−3. The buried-dopant region105is not less than about 5×1018cm−3(e.g., about 1×1019cm−3).

FIG.2Aillustrates a cross-sectional view of an optical sensing apparatus200aaccording to one or more embodiments of the present disclosure.FIG.2Billustrates a cross-sectional view of an optical sensing apparatus200baccording to one or more embodiments of the present disclosure.

Referring toFIG.2AtoFIG.2B, in some embodiments, the buried-dopant region105includes one or more first buried-dopant regions207having a first peak doping concentration (e.g., not less than about 5×1018cm−3, such as about 1×1019cm−3) and a first depth. In some embodiments, the buried-dopant region105further includes one or more second buried-dopant regions205surrounding the one or more first buried-dopant regions207and having a second peak doping concentration and a second depth, where at least one or more of (i) the second peak doping concentration (e.g., not less than 5×1017cm−3, such as about 1×1018cm−3) is lower than the first peak doping concentration, or (ii) the second depth is shallower than the first depth. In some embodiments, the first depth of the first buried-dopant regions207is measured by a distance from the second interface1012of the substrate101to the first peak doping concentration, and the second depth of the second buried-dopant regions205is measured by a distance from the second interface1012of the substrate101to the second peak doping concentration.

Under a reverse bias breakdown voltage (e.g., the first break-down voltage as described above), one or more punch-through regions123and one or more blocking regions125in the amplification region120can be formed, where the one or more punch-through regions123are adjacent to the one or more first buried-dopant regions207and the one or more blocking regions125are adjacent to the one or more second buried-dopant regions205.

In some embodiments, the interface-dopant region107further includes one or more first interface-dopant regions203having a third peak doping concentration and a third depth. The interface-dopant region107further includes one or more second interface-dopant regions201having a fourth peak doping concentration and a fourth depth, where at least one or more of (i) the fourth peak doping concentration (e.g., not less than about 1×1017cm−3or 2×1017cm−3) is higher than the third peak doping concentration (e.g., not less than about 1×1017cm−3), or (ii) the fourth depth is shallower than the third depth. In some embodiments, the third depth of the first interface-dopant regions203is measured by a distance from the second interface1092of the absorption region109to the third peak doping concentration, and the fourth depth of the second interface-dopant regions201is measured by a distance from the second interface1092of the absorption region109to the fourth peak doping concentration. In some embodiments, a ratio of the fourth peak doping concentration to the third peak doping concentration is not more than 10.

Under a reverse bias breakdown voltage (e.g., the first break-down voltage as described above), one or more punch-through regions123and one or more blocking regions125in the amplification region120can be formed, where the one or more punch-through regions123are adjacent to the one or more first interface-dopant regions203and the one or more blocking regions125are adjacent to the one or more second interface-dopant regions201. In some embodiments, under a reverse bias breakdown voltage (e.g., the first break-down voltage as described above), one or more punch-through regions in the amplification region120can be formed between the first interface-dopant regions203and the first buried-dopant regions207, and one or more blocking regions125in the amplification region120can be formed between the second interface-dopant regions201and the second buried-dopant regions205.

In some embodiments, a difference between the first peak doping concentration of the one or more first buried-dopant regions207and the third peak doping concentration of the one or more first interface-dopant regions203is greater than a difference between the second peak doping concentration of the one or more second buried-dopant regions205and the fourth peak doping concentration of the one or more second interface-dopant regions201.

Referring toFIG.2A, in some embodiments, a first distance between the first buried-dopant regions207and the first interface-dopant regions203is less than a second distance between second buried-dopant regions205and the second interface-dopant regions201. At a reverse bias, the electric field associated with the punch-through region123is stronger than the electric field associated with the blocking regions125. As a result, a first break-down voltage associated with the one or more punch-through regions123is lower than a second break-down voltage associated with the one or more blocking regions125. In some embodiments, the first distance is measured from the distance between the first peak doping concentration and the third peak doping concentration. The second distance is measured from the distance between the second peak doping concentration and the fourth peak doping concentration.

By having the fourth peak doping concentration of the one or more second interface-dopant regions201higher than the third peak doping concentration of the one or more first interface-dopant regions203, the carriers (e.g., electrons when the buried-dopant region105is of n-type) can be guided into the punch-through regions123through the first interface-dopant regions203. As a result, an interface area where carriers passing through is confined, which reduces the dark current of the optical sensing apparatus200a,200b.

Referring toFIG.2A, in some embodiments, the absorption region109is over the first interface1011of the substrate101. In some embodiments, the optical sensing apparatus200amay further include a passivation layer (not shown) covering the interface (e.g., first interface1091and side interface) of the absorption region109for protecting the absorption region109. Referring toFIG.2B, in some embodiments, the absorption region109is embedded in the substrate101, for example, embedded in the top layer102of the substrate101. In some embodiments, the sidewall-dopant regions133has a peak doping concentration higher than the third peak doping concentration of the one or more first interface-dopant regions203for further facilitating the carriers entering the amplification region120through the one or more first interface-dopant regions203, which further confines the punch-through regions123where breakdown occurs at the first break-down voltage. In some embodiments, the peak doping concentration of the sidewall-dopant regions133is not less than 1×1017cm−3.

FIG.3Aillustrates a cross-sectional view of an optical sensing apparatus300aaccording to one or more embodiments of the present disclosure.FIG.3Billustrates a cross-sectional view of an optical sensing apparatus300baccording to one or more embodiments of the present disclosure.

Referring toFIG.3AtoFIG.3B, in some embodiments, the buried-dopant region105includes one or more first doped guard-rings303having a fifth peak doping concentration (e.g., not more than about 5×1018cm−3), the one or more first doped guard-rings303surrounding the one or more first buried-dopant regions207, where the fifth peak doping concentration of the one or more first doped guard-rings303is lower than the first peak doping concentration of the one or more first buried-dopant regions207. For example, a ratio of the first peak doping concentration to the fifth peak doping concentration is not less than 5 (e.g., about 10). The one or more first doped guard-rings303are configured to adjust an electric field associated with edges or corners of the one or more first buried-dopant regions207. For example, by having the first doped guard-rings303surrounding the one or more first buried-dopant regions207, the electric field associated with edges or corners of the one or more first buried-dopant regions207may be reduced, which further confines the punch-through regions123where breakdown occurs at the first break-down voltage.

Referring toFIG.3Aand toFIG.3B, in some embodiments, where the interface-dopant region107further includes one or more second doped guard-rings301having a sixth peak doping concentration (e.g., not more than about 1×1017cm−3), where the one or more second doped guard-rings301surround the one or more second interface-dopant regions201. In some embodiments, the sixth peak doping concentration is lower than the fourth peak doping concentration of one or more second interface-dopant regions201. For example, a ratio of the fourth peak doping concentration of the one or more second interface-dopant regions201to the sixth peak doping concentration of the one or more second doped guard-rings301is not less than 5 (e.g., about 10). The one or more second doped guard-rings301are configured to adjust an electric field associated with edges or corners of the one or more second interface-dopant regions201. For example, by having the second doped guard-rings301surrounding the one or more second interface-dopant regions201, the electric field associated with edges or corners of the one or more second interface-dopant regions201may be reduced, which alleviates the problem of break down occurring between the interface-dopant region107and the one or more first conductive regions119a/119b.

FIG.4Aillustrates a cross-sectional view of an optical sensing apparatus400aaccording to one or more embodiments of the present disclosure.FIG.4Billustrates a cross-sectional view of an optical sensing apparatus400baccording to one or more embodiments of the present disclosure.

Referring toFIG.4A,FIG.4B, in some embodiments, the interface-dopant region107includes multiple first interface-dopant regions203and multiple second interface-dopant regions201so as to form multiple punch-through regions123and multiple blocking regions125under the first break-down voltage. In some embodiments, the multiple first interface-dopant regions203are separated by the multiple second interface-dopant regions201, and thus the multiple punch-through regions123and multiple blocking regions125are alternate formed under the first break-down voltage.

By forming the multiple first interface-dopant regions separated by the multiple second interface-dopant regions, multiple breakdown routes (e.g., multiple punch-through regions123) are formed for the carriers (e.g., electrons when the buried-dopant region105is of n-type) flowing from the absorption region109to the buried-dopant region105under the first break-down voltage. As a result, the carriers can be guided into the amplification region120uniformly under reverse bias, which increases the speed and the quantum efficiency of the optical sensing apparatus400a,400b.

In some embodiments, the buried-dopant region105includes multiple first buried-dopant regions207and the buried-dopant region105includes multiple second buried-dopant regions205so as to form multiple punch-through regions123and multiple blocking regions125under the first break-down voltage. In some embodiments, the multiple first buried-dopant regions207are separated by the multiple second buried-dopant regions205, and thus the multiple punch-through regions123and multiple blocking regions125are alternate formed under the first break-down voltage.

Referring toFIGS.4C and4Das examples, in some embodiments, the multiple punch-through regions123may be formed without the first interface-dopant regions203. Specifically, when a distance between two second interface-dopant regions201is under a threshold distance d (as illustrated inFIG.4C), the corner fields formed between the second interface-dopant regions201form a punch-through region123under the first break-down voltage. As an example, the threshold distance d can be on the order of several-hundred nm (e.g., 200 nm, 300 nm, 500 nm, or a distance that provides sufficient corner fields to form the punch-through region.) or below 1 μm. Such embodiments are advantageous because removing the first interface-dopant regions203may simplify the fabrication process of the device.

By having the multiple first buried-dopant regions separated by the multiple second buried-dopant regions, multiple breakdown routes (e.g., multiple punch-through regions123s) are formed for the carriers (e.g., electrons when the buried-dopant region105is of n-type) flowing from the absorption region109to the buried-dopant region105under the first break-down voltage. As a result, the carriers can be guided into the amplification region120uniformly under reverse bias, which increases the speed and the quantum efficiency of the optical sensing apparatus.

FIG.5Aillustrates a cross-sectional view of an optical sensing apparatus500aaccording to one or more embodiments of the present disclosure.FIG.5Billustrates a cross-sectional view of an optical sensing apparatus500baccording to one or more embodiments of the present disclosure. In some embodiments, a distance between the first buried-dopant regions207and the second interface1092of the absorption region109is less than a distance between second buried-dopant regions205and the second interface1092of the absorption region109. As a result, the electric field associated with the first buried-dopant regions207is stronger than the electric field associated with the second buried-dopant regions205.

FIG.6Aillustrates a top view of an optical sensing apparatus600aaccording to one or more embodiments of the present disclosure. The optical sensing apparatus600acan be, for example, any of the optical sensing apparatus100a,100b,200a,200b,300a,300b,500a, or500b. In some embodiments, the first buried-dopant region207is surrounded by the second buried-dopant regions205such that the punch-through region123is surrounded by the blocking region125under the first break-down voltage. In some embodiments, the first interface-dopant region203is surrounded by the second interface-dopant regions201such that the punch-through region123is surrounded by the blocking region125under the first break-down voltage.

FIG.6Billustrates a top view of an optical sensing apparatus600baccording to one or more embodiments of the present disclosure. The optical sensing apparatus600acan be, for example, any of the optical sensing apparatus400a, or400b. In some embodiments, the multiple first buried-dopant regions207are surrounded by the second buried-dopant regions205such that the multiple punch-through regions123are surrounded by the blocking region125under the first break-down voltage. In some embodiments, the multiple first interface-dopant regions203are surrounded by the second interface-dopant regions201such that the multiple punch-through region123is surrounded by the blocking region125under the first break-down voltage.FIG.6AandFIG.6Billustrates some example arrangement of the punch-through regions123and the blocking region125based on different arrangements of the first interface-dopant regions203and the second interface-dopant regions201and the different arrangements of the first buried-dopant regions207and the second buried-dopant regions205. However, the present disclosure is not limited to the arrangement illustrate inFIG.6AandFIG.6B.

FIG.7Aillustrates a cross-sectional view of an optical sensing apparatus700aaccording to one or more embodiments of the present disclosure.FIG.7Billustrates a cross-sectional view of an optical sensing apparatus700baccording to one or more embodiments of the present disclosure. In some embodiments, the optical sensing apparatus700a,700bfurther includes a buffer layer170between the absorption region109and the buried-dopant region105. In some embodiments, the buffer layer170is formed between the absorption region109and the interface-dopant region107. In some embodiments, the buffer layer170is formed using the first material (e.g., single crystal silicon). In some embodiments, the buffer layer170may include a material the same as the material of the sidewall-dopant regions133. In some embodiments, the buffer layer170has a thickness between 200 nm and 400 nm. In some other embodiments, the buffer layer170has a thickness between 100 nm and 300 nm. In some embodiments, the buffer layer170is intrinsic and has a thickness for distributing electric field along a direction substantially perpendicular to a first interface1011of the substrate101. For example, the buffer layer170may have a thickness not less than 150 nm, which facilitates lowering the electric field in the absorption region109, and thus the dark current of the optical sensing apparatus700a,700bis further reduced. As another example, the buffer layer170may have a thickness not less than 50 nm. Besides, compared to a comparative optical sensing apparatus without the buffer layer170or having a buffer layer170with a thickness of a few nms or a few tens of nms, the optical sensing apparatus700a,700bof the present disclosure has a lower electric filed in the buffer layer170, which also alleviates the problem of breakdown phenomenon or carrier tunneling in the buffer layer170. Accordingly, the performance of the optical sensing apparatus700a,700bis improved. The buffer layer170may be formed in, for example, any of the optical sensing apparatus100a,100b,200a,200b,300a,300b,400a,400b,500a, or500b.

Referring toFIGS.7C-7Das example optical sensing apparatus700c/700d, in some implementations, one or more field-control regions190aand190bmay be formed around the buffer layer170. Depending on the shape of the buffer layer170, the field-control regions190aand190bmay be part of a ring at the edge of the buffer layer170that is circular, or the field-control regions190aand190bmay be of any other suitable shape surrounding the buffer layer170. The field-control regions190aand190bmay be of a second conductivity type (e.g., p-type) having a peak doping concentration that is higher than that of the buffer layer170. In some implementations, by controlling one or more properties (e.g., dopant level, dopant depth, etc.) of the field-control regions190aand190b, one or more blocking regions125can be formed around one or more punch-through regions123. For example, a peak doping concentration of the field-control regions190aand190bis greater than the peak doping concentration of the buffer layer170. For another example, a depth of the field-control regions190aand190bis deeper than a depth of the buffer layer170. In some embodiments, the depth of the field-control regions190aand190band the buffer layer170is measured by a distance from an interface1031(as shown inFIG.7Cbetween the absorption109and the buffer layer170) to the peak doping concentration.

In some embodiments, the punch-through region(s)123has a first break-down voltage similar to a second break-down voltage associated with the one or more blocking regions125, such that avalanche breakdown similarly begins to occur in the punch-through region(s)123and the blocking region(s)125, while the electrical field in the one or more punch-through regions123reaches the absorption region109but the electrical field in the one or more blocking regions125terminates on the field-control regions190aand190b. Accordingly, the one or more punch-through regions123collect at least a portion of the photo-carriers from the absorption region109and amplify the collected photo-carriers under the first break-down voltage. Besides, the one or more blocking regions125may block at least a portion of the photo-carriers so as to guide the portion of the photo-carriers to enter the punch-through region(s)123.

FIGS.8A-8Dillustrates a cross-sectional view of an optical sensing apparatus800a/800b/800c/800daccording to one or more embodiments of the present disclosure. In some embodiments, the optical sensing apparatus800a/800b/800c/800dincludes the buried-dopant region105including the first buried-dopant regions207and the second buried-dopant regions205as mentioned above. In some embodiments, the optical sensing apparatus800a/800b/800c/800dincludes the interface-dopant region107including the first interface-dopant regions203and second interface-dopant regions201as mentioned above. In some embodiments, the buried-dopant region105further includes one or more first doped guard-rings303as mentioned above. In some embodiments, the interface-dopant region107further includes one or more second doped guard-rings301as mentioned above. In some implementations, the optical sensing apparatus800a/800b/800c/800dincludes one or more field-control regions190aand190bas mentioned above.

It should be understood that the elements mentioned in the present disclosure can be combined in any manner and in any number to create additional embodiments. For example, the optical sensing apparatus300a,400a,500a,700a,800amay also include a passivation layer as mentioned inFIG.1A. The optical sensing apparatus, e.g.,200a,200b,300a,300b,400a,400b,500a,500b,600a,600b,700a,700b,800a,800b, can also be doped with a graded doping profile of the as described inFIG.1AthroughFIG.1B.

FIG.9is a block diagram of an example of a sensing system900. The sensing system900may include a sensing module910and a software module920configured to reconstruct a three-dimensional (3D) model930of a detected object. The sensing system900or the sensing module910may be implemented on a mobile device (e.g., a smartphone, a tablet, vehicle, drone, etc.), an ancillary device (e.g., a wearable device) for a mobile device, a computing system on a vehicle or in a fixed facility (e.g., a factory), a robotics system, a surveillance system, or any other suitable device and/or system.

The sensing module910includes a transmitter unit914, a receiver unit916, and a controller912. During operation, the transmitter unit914may emit an emitted light903toward a target object902. The receiver unit916may receive reflected light905reflected from the target object902. The controller912may drive at least the transmitter unit914and the receiver unit916. In some implementations, the receiver unit916and the controller912are implemented on one semiconductor chip, such as a system-on-a-chip (SoC). In some cases, the transmitter unit914is implemented by two different semiconductor chips, such a laser emitter chip on III-V substrate and a Si laser driver chip on Si substrate.

The transmitter unit914may include one or more light sources, control circuitry controlling the one or more light sources, and/or optical structures for manipulating the light emitted from the one or more light sources. In some embodiments, the light source may include one or more light emitting diodes (LEDs) or vertical-cavity surface-emitting lasers (VCSELs) emitting light that can be absorbed by the absorption region in the optical sensing apparatus. For example, the one or more LEDs or VCSEL may emit light with a peak wavelength within a visible wavelength range (e.g., a wavelength that is visible to the human eye), such as 570 nm, 670 nm, or any other applicable wavelengths. For another example, the one or more LEDs or VCSEL may emit light with a peak wavelength above the visible wavelength range, such as 850 nm, 940 nm, 1050 nm, 1064 nm, 1310 nm, 1350 nm, 1550 nm, or any other applicable wavelengths.

In some embodiments, the emitted light from the light sources may be collimated by the one or more optical structures. For example, the optical structures may include one or more collimating lens.

The receiver unit916may include one or more optical sensing apparatus, e.g.,100a,100b,200a,200b,300a,300b,400a,400b,500a,500b,600a,600b,700a,700b,800a,800b. The receiver unit916may further include a control circuitry for controlling the control circuitry and/or optical structures for manipulating the light reflected from the target object902toward the one or more optical sensing apparatus. In some implementations, the optical structures include one or more lens that receive a collimated light and focus the collimated light towards the one or more optical sensing apparatus.

In some embodiments, the controller912includes a timing generator (e.g.,1072inFIG.10) and a processing unit. The timing generator1072receives a reference clock signal and provides timing signals to the transmitter unit914for modulating the emitted light903. The timing signals are also provided to the receiver unit916for controlling the collection of the photo-carriers. The processing unit processes the photo-carriers generated and collected by the receiver unit916and determines raw data of the target object902. The processing unit may include control circuitry, one or more signal processors (e.g.,1058inFIG.10) for processing the information output from the optical sensing apparatus, and/or computer storage medium that may store instructions for determining the raw data of the target object902or store the raw data of the target object902. As an example, the controller912in an i-ToF sensor determines a distance between two points by using the phase difference between light emitted by the transmitter unit914and light received by the receiver unit916.

The software module920may be implemented to perform in applications such as facial recognition, eye-tracking, gesture recognition, 3-dimensional model scanning/video recording, motion tracking, autonomous vehicles, and/or augmented/virtual reality.

In some embodiments, the sensing system900may be implemented in a lidar system. The sensing system900may further include one or more scanning mirror arranged between the route of the one or more optical structures and the target object902. In some embodiments, the scanning mirror may include micro-electromechanical systems (MEMS) mirror. In some embodiments, the one or more scanning mirror includes multiple scanning mirrors arranged in a one-dimensional or two-dimensional array.

FIG.10shows a block diagram of an example device1000that can be a receiver unit (e.g.,916) or a controller (e.g.,912). Here, an image sensor array1052(e.g., 240×180-pixel array) may be implemented using any implementations of the optical sensing apparatus described in the present disclosure, e.g.,100a,100b,200a,200b,300a,300b,400a,400b,500a,500b,600a,600b,700a,700b,800a,800b, where the optical sensing apparatus are arranged in one dimensional or two-dimensional array. A phase-locked loop (PLL) circuit1070(e.g., an integer-N PLL) may generate a clock signal (e.g., four-phase system clocks) for modulation and demodulation. Before sending to the image sensor array1052and an external illumination driver1080, the clock signal generated by the phase-locked loop (PLL) circuit1070may be gated and/or conditioned by a timing generator1072for a preset integration time and different operation modes. A programmable delay line1068may be added in the illumination driver1080path to delay the clock signals.

A voltage regulator1062may be used to control an operating voltage of the image sensor array1052. For example, N voltage domains may be used for an image sensor. A temperature sensor1064may be implemented for the possible use of depth calibration and power control, and the inter-integrated circuit (I2C) controller1066can access the temperature information from the temperature sensor1064.

The readout circuit1054of the optical sensing apparatus bridges each of the optical sensing apparatus of the image sensor array1052to a column analog-to-digital converter (ADC)1056, where the ADC1056outputs may be further processed and integrated in the digital domain by a signal processor1058before reaching an output interface1074that is coupled to the timing generator1072. In some embodiments, the readout circuit1054may be in a three-transistor configuration including a reset gate, a source-follower, and a selection gate, or in a four-transistor configuration including an additional transfer gate, or any suitable circuitry for processing collected charges.

A memory1060may be used to store the outputs by the signal processor1058. In some implementations, the output interface1074may be implemented using a 2-lane, 1.2 Gb/s D-PHY mobile industry processor interface (MIPI) transmitter, or using complementary metal-oxide-semiconductor (CMOS) outputs for low-speed/low-cost systems. The digital data further conditioned by the signal processor1058is sent out through an MIPI interface1076for further processing.

An inter-integrated circuit (I2C) interface may be used to access all of the functional blocks described here.

In some embodiments, a bandgap of the first material, is greater than a bandgap of the second material of absorption region109. In some embodiments, the absorption region109and/or the substrate101includes or is composed of a semiconductor material. In some embodiments, the absorption region109and/or the substrate101includes or is composed of a Group III-V semiconductor material. The Group III-V semiconductor material may include, but is not limited to, GaAs/AlAs, InP/InGaAs, GaSb/InAs, or InSb. For example, in some embodiments, the absorption region109includes or is composed of InGaAs, and the substrate101include or is composed of InP. In some embodiments, the absorption region109includes or is composed of a semiconductor material including a Group IV element. For example, Ge, Si or Sn. In some embodiments, the absorption region109includes or is composed of the SixGeySn1-x-y, where 0≤x≤1, 0≤y≤1, 0x+y≤1. In some embodiments, the absorption region109includes or is composed of Ge1-aSna, where 0≤a≤0.1. In some embodiments, the absorption region109includes or is composed of GexSi1-x, where 0≤x≤1. In some embodiments, the absorption region109composed of intrinsic germanium is of p-type due to material defects formed during formation of the absorption region, where the defect density is from 1×1014cm−3to 1×1016cm−3. In some embodiments, the substrate101includes or is composed of the SixGeySn1-x-y, where 0≤x≤1, 0≤y≤1, 0≤x+y≤1. In some embodiments, the substrate101includes or is composed of Ge1-aSna, where 0≤a≤0.1. In some embodiments, the substrate101includes or is composed of GexSi1-x, where 0≤x≤1.

In some embodiments, the optical sensing apparatus further includes an optical element (not shown) over the absorption region109or substrate101. In some embodiments, the optical elements include lenses.

During packaging or assembling an optical sensor component (e.g., chip or module that includes any optical sensing apparatus described above) on a system (e.g., printed circuit board), an encapsulation layer such as epoxy may be used to cover the optical component in order to protect the optical component. The optical sensor component may include a micro-lens or a micro-lens array for guiding (e.g., focusing) light onto the sensor(s). The micro-lens may be formed using a polymer-based material, which may have an effective refractive index that is close to the effective refractive index of the encapsulation layer. As the result of the lower refractive index contrast, the designed performance (e.g., focal length) of the micro-lens may suffer. Accordingly, an optical sensing apparatus that addresses such technical issue is disclosed in reference toFIGS.11A-11EandFIGS.12A-12E.

Referring toFIG.11A, the optical sensing apparatus1100aincludes a substrate1130(e.g., Si substrate10) and one or more pixels1140supported by the substrate, where each of the pixel1140comprises an absorption region (e.g., Ge absorption region109) supported by the substrate1130. A pixel can be any one of optical sensing apparatus described above (e.g.,100a-b,200a-b,300a-b,400a-d,500a-b,600a-b,700a-d,800a-d, etc.). The absorption region1140is configured to receive an optical signal L and generate photo-carriers in response to receiving the optical signal. The optical sensing apparatus1100afurther includes one or more lenses1160over the respective pixel of the one or more pixels1140, where the one or more lenses1160are composed of a first material (e.g., Si) having a first refractive index (e.g., ≥3 at the wavelength range absorbed by the absorption region of the one or more pixels1140but not absorbed by the lenses1160). The optical sensing apparatus1100afurther includes an encapsulation layer1115over the one or more lenses1160and composed of a second material (e.g., polymer) having a second refractive index between 1.3 to 1.8, where a difference between the first refractive index and the second refractive index is above an index threshold such that a difference between an effective focal length of the one or more lenses1160and a distance between the one or more lenses1160and the one or more pixels1140is within a distance threshold (e.g., 1%, 5%, or any other threshold that is tolerable by the system). As a result, the optical signal L can be converged and focused to enter the absorption region of the one or more pixels1140.

In some embodiments, the first refractive index of the one or more lenses1160is not less than 3 (e.g., refractive index of Si is approximately 3.45), where the difference between the first refractive index and the second refractive index of the encapsulation layer1115is not less than 0.5, such that optical signal L can be converged and focused to enter the absorption region of the one or more pixels1140.

In some embodiments, the optical sensing apparatus1100afurther comprises a first planarization layer1180between the encapsulation layer1115and the one or more lenses1160, where the first planarization layer1180is composed of a third material (e.g., polymer or oxide material such as SixOy) having a third refractive index (e.g., between 1 and 2 at the wavelength range absorbed by the absorption region of the one or more pixels40) that is within a threshold (e.g., 1%, 5%, or any other threshold that is tolerable by the system) from the second refractive index so as to minimize reflection when the optical signal L passes through the interface between the encapsulation layer1115and the first planarization layer1180. In some embodiments, the first planarization layer1180provides a substantially flat surface for the subsequent layer (e.g., encapsulation layer1115, filter layer1190, second anti-reflection layer1125or one or more lenses1160) to be formed on.

In some embodiments, the optical sensing apparatus1100afurther comprises a first anti-reflection layer1170between the one or more lenses1160and the first planarization layer1180, where the first anti-reflection layer1170is composed of a fourth material (e.g., oxide material such as SixOyor nitride material such as SixNyor oxynitride material such as SiXOYNZ) having a fourth refractive index (e.g., between 1 and 2.5 at the wavelength range absorbed by the absorption region of the one or more pixels1140) between the third refractive index of the first planarization layer1180and the first refractive index of the one or more lenses1160.

In some embodiments, the optical sensing apparatus1100afurther comprises a second planarization layer1150between the one or more lenses1160and the substrate1130. The second planarization layer1150is configured to provide a substantially flat surface for the subsequent layer (e.g., filter layer1190or one or more lenses1160) to be formed on.

In some embodiments, the first planarization layer1180or the second planarization layer1150is composed of a material comprising polymer having a refractive index between 1 and 2.

Referring toFIG.11B, in some embodiments, the optical sensing apparatus1100bincludes a filter layer1190between the first planarization layer1180and the encapsulation layer1115, where the filter layer1190is configured to pass optical signal having a specific wavelength range (e.g., SWIR range).

Referring toFIGS.11A and11C, in some embodiments, the optical sensing apparatus1100a/1100cfurther includes a second anti-reflection layer1125between the first planarization layer1180and the encapsulation layer1115, where the second anti-reflection layer1125is composed of a sixth material (e.g., polymer or oxide material such as SixOy) having a sixth refractive index (between 1 and 2 at the wavelength range absorbed by the absorption region of the one or more pixels1140) between the second refractive index of the encapsulation layer1115and the third refractive index of the first planarization layer1180. In some embodiments, the sixth material of the second anti-reflection layer1125and the third material of the first planarization layer1180can be the same. In some embodiments, the sixth refractive index is within a threshold (e.g., 1%, 5%, or any other threshold that is tolerable by the system) from the second refractive index so as to minimize reflection when the optical signal L passes through the interface between the encapsulation layer1115and the second anti-reflection layer1125.

Referring toFIG.11C, in some embodiments, the optical sensing apparatus1100cfurther comprises a filter layer1190between the one or more lenses1160and the one or more pixels1140, where the filter layer1190is configured to pass optical signal having a specific wavelength range.

In some embodiments, the optical sensing apparatus1100cfurther includes a second planarization layer1150(e.g., referring toFIG.11C) between the filter layer1190and the substrate1130.

Referring toFIG.11DandFIG.11E, in some embodiments, the optical sensing apparatus1100d/1100efurther includes a spacer1135between the one or more lenses1160and the second planarization layer1150(the other layers illustrated inFIGS.11A-11Cmay be present but are not shown). The thickness (e.g., less than 10 μm) of the spacer1135is configured to provide a path for light to propagate from the one or more lenses1160to the one or more pixels1140, such that a difference between an effective focal length of the one or more lenses1160and a distance between the one or more lenses1160and the one or more pixels1140is within a distance threshold. In some implementations, the spacer1135may be composed of a material (e.g., Si, or oxide material such as SixOy, or nitride material such as SixNy, or oxynitride material such as SiXOYNZ) having a refractive index (e.g., between 1 and 4 at the wavelength range absorbed by the absorption region of the one or more pixels40) less than the first refractive index of the one or more lenses1160. In some implementations, the order of different layers may be different (e.g., the filter layer1190may be formed before or after the spacer1135).

In some embodiments, the optical sensing apparatus1100a-1100efurther comprises a carrier substrate1110and an integrated circuit layer1120between the one or more pixels1140and the carrier substrate1110, where the integrated circuit layer1120comprises a control circuit configured to control the one or more pixels1140.

In some embodiments, the absorption regions of the one or more pixels1140are at least partially embedded in a substrate1130(e.g., optical sensing apparatus100binFIG.1B).

In some embodiments, the one or more pixels1140are multiple pixels arranged in one-dimensional and two-dimensional array.

In some embodiments, the absorption region includes or is composed of GexSi1-x, where 0≤ x≤1. In some embodiments, the substrate30includes or is composed of the SixGeySn1-x-y, where 0≤x≤1, 0≤y≤1, 0≤x+y≤1. In some embodiments, the substrate1130includes or is composed of Ge1-aSna, where 0≤a≤ 0.1. In some embodiments, the substrate1130includes or is composed of GexSi1-x, where 0≤x≤1. For example, in some embodiments, the absorption region includes or is composed of Ge, and the substrate1130include or is composed of Si.

In the present disclosure, if not specifically mention, the absorption region has a thickness depending on the wavelength of photons to be detected and the material of the absorption region. In some embodiments, when the absorption region includes germanium and is designed to absorb photons having a wavelength equal to or greater than 800 nm, the absorption region has a thickness equal to or greater than 0.1 μm. In some embodiments, the absorption region includes germanium and is designed to absorb photons having a wavelength between 700 nm and 2000 nm, the absorption region has a thickness between 0.1 μm and 2.5 μm. In some embodiments, the absorption region has a thickness between 1 μm and 2.5 μm for higher quantum efficiency. In some embodiments, the absorption region may be grown using a blanket epitaxy, a selective epitaxy, or other applicable techniques.

In some implementations, to further improve planarization and/or reduce thickness of the overall device, the optical sensor component may include a metalens array for guiding (e.g., focusing) light onto the pixels1140. Referring toFIG.12Aas an example, the optical sensing apparatus1200ashown inFIG.12Ahas the same layer arrangement as the optical sensing apparatus1100ashown inFIG.11A, where the one or more lenses1160are replaced with a metalens array1260. A metalens of the metalens array1260may be formed using 1D or 2D array of surface structures that when combined, acts as an optical element with one or more functions (e.g., a diffractive lens, a filter, etc.). To achieve sufficient index contrast from the encapsulation layer1115and any other intermediate layers, the metalens array1260may be formed using Si, SixOy, SixNy, SixOyNz, Nb2O5, a-Si:H, TiO2, Ta2O5, ITO, Ag, Nb, or Cr, where 0≤x≤1, 0≤y≤1, 0≤z≤1.

As another example, the optical sensing apparatus1200b/1200cshown inFIG.12BandFIG.12Chas the same layer arrangements as the optical sensing apparatus1100b/1100cshown inFIG.11BandFIG.11C, respectively, where the one or more lenses1160are replaced with a metalens array1260. Since the surface structures that form a metalens do not form a curved surface like lens1160, a better planarization may be achieved with the encapsulation layer1115. Moreover, a smaller lens may be designed with a metalens, which can increase the density of the overall optical sensor.

Referring toFIG.12DandFIG.12E, in some embodiments, the optical sensing apparatus1200d/1200efurther comprises a spacer1235between the metalens array1260and the second planarization layer1150(the other layers illustrated inFIGS.12A-12Cmay be present but are not shown). The thickness (e.g., less than 10 μm) of the spacer1235is configured to provide a path for light to propagate from the metalens array1260to the one or more pixels1140, such that a difference between an effective focal length of the metalens array1260and a distance between the metalens array1260and the one or more pixels1140is within a distance threshold. In some implementations, the spacer1235may be composed of a material (e.g., Si, or oxide material such as SixOy, or nitride material such as SixNy, or oxynitride material such as SiXOYNZ) having a refractive index (e.g., between 1 and 4 at the wavelength range absorbed by the absorption region of the one or more pixels1140) less than the effective refractive index of the metalens array1260. In some implementations, the order of different layers may be different (e.g., the filter layer1190may be formed before or after the spacer1235).

In some embodiments, the absorption region is configured to absorb photons having a peak wavelength in an invisible wavelength range equal to or greater than 800 nm, such as 850 nm, 940 nm, 1050 nm, 1064 nm, 1310 nm, 1350 nm, or 1550 nm or any suitable wavelength range. In some embodiments, the absorption region receives an optical signal and converts the optical signal into electrical signals. The absorption region can be in any suitable shape, such as, but not limited to, cylinder, or rectangular prism.

In some embodiments, the absorption region109has a thickness depending on the wavelength of photons to be detected and the material of the absorption region. In some embodiments, when the absorption region109includes germanium and is designed to absorb photons having a wavelength equal to or greater than 800 nm, the absorption region has a thickness equal to or greater than 0.1 μm. In some embodiments, the absorption region109includes germanium and is designed to absorb photons having a wavelength between 800 nm and 2000 nm, the absorption region has a thickness between 0.1 μm and 2.5 μm. In some embodiments, the absorption region has a thickness between 1 μm and 2.5 μm for a higher quantum efficiency. In some embodiments, the absorption region may be grown using a blanket epitaxy, a selective epitaxy, or other applicable techniques.

In some embodiments, the term “contact”, includes metals or alloys. For example, the first contacts115a/115band the second contacts117a/117b, include Al, Cu, W, Ti, Ta—TaN—Cu stack, or Ti—TiN—W stack.

As used herein and not otherwise defined, the terms “substantially” and “about” are used to describe and account for small variations. When used in conjunction with an event or circumstance, the terms can encompass instances in which the event or circumstance occurs precisely as well as instances in which the event or circumstance occurs to a close approximation. For example, when used in conjunction with a numerical value, the terms can encompass a range of variation of less than or equal to ±10% of that numerical value, such as less than or equal to ±5%, less than or equal to ±4%, less than or equal to ±3%, less than or equal to ±2%, less than or equal to ±1%, less than or equal to ±0.5%, less than or equal to ±0.1%, or less than or equal to ±0.05%.

While the inventive concepts have been described by way of examples and in terms of embodiments, it is to be understood that the disclosure is not limited thereto. On the contrary, it is intended to cover various modifications and similar arrangements and procedures, and the scope of the appended claims therefore should be accorded the broadest interpretation so as to encompass all such modifications and similar arrangements and procedures.