Group III-V compound and Group II-VI compound semiconductors have particularly wide band gaps and are capable of emitting green or blue light. Recently semiconductor devices, such as photo-electric conversion devices using III-V or II-VI group compound semiconductor crystals as base materials have been developed to improve efficiency and life time of the semiconductor devices.
However, one drawback to Group III-V compound and Group II-VI compound semiconductors are their poor optical gain characteristics.
In one embodiment, a semiconductor device includes at least one active layer composed of a first compound, and at least one barrier layer composed of a second compound and disposed on at least one surface of the at least one active layer. The at least one barrier layer has an energy band gap that is wider than the energy band gap of the at least one active layer. The first and/or second compounds may be selected to reduce relaxation time of an electron or hole in the at least one active layer.
The foregoing summary is illustrative only and is not intended to be in any way limiting. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features will become apparent by reference to the drawings and the following detailed description.
a) and (b) are schematic diagrams of an illustrative embodiment of a semiconductor device.
a) and (b) are schematic diagrams showing band gaps of the semiconductor device of
a) and (b) are schematic diagrams illustrating an electron-phonon scattering and a carrier-carrier scattering, respectively.
a)-(e) are schematic diagrams illustrating an illustrative embodiment of a method for fabricating a semiconductor device.
In one embodiment, a semiconductor device includes at least one active layer composed of a first compound, and at least one barrier layer composed of a second compound and disposed on at least one surface of the at least one active layer. An energy band gap of the at least one barrier layer can be wider than an energy band gap of the at least one active layer. The first and/or second compounds can be selected to reduce a relaxation time of an electron or hole in the at least one active layer.
The compositions of the first and/or second compounds can be selected to reduce a scattering rate of the electron or hole in the at least one active layer to reduce the relaxation time. Further, the compositions of the first and/or second compounds can be selected to reduce an internal polarization field in the at least one active layer to reduce the scattering rate. Still further, the compositions of the first and/or second compounds can be selected to make a sum of piezoelectric and spontaneous polarizations in the at least one active layer and a sum of piezoelectric and spontaneous polarizations in the at least one barrier layer substantially the same to reduce the internal polarization field.
Each of the first and second compounds can include a III-V group compound semiconductor material or a II-VI group compound semiconductor material. The first compound can include, for example, GaN, InGaN, CdZnO, AlN, AlP, AlAs, GaP, GaAs, InN, InP, InAs, AlGaN, AlGaP, AlGaAs, InGaN, InGaP, InGaAs, INAlN, InAlP, InAlAs, AlGaInN, AlGaInP, AlGaInAs, ZnO, ZnS, CdO, CdS, CdZnS, CdZnO, MgZnO, MgZnS, CdMgZnO, or CdMgZnS. The second compound can include, for example, AlInGaN, InGaN, AlGaN, AlGaP, AlGaAs, InGaN, InGaP, InGaAs, InAlN, InAlP, InAlAs, AlGaInP, AlGaInAs, CdZnS, CdZnO, MgZnO, MgZnS, CdMgZnO, or CdMgZnS.
In some embodiments, the first compound can include InxGa1-xN (0≦x≦1) and the second compound can include Aly1Ga1-y1-y2Iny2N (0≦y1+y2≦1). Variable x can be in the range of about 0.05 and 0.15, variable y1 can be in the range of about 0.05 to 0.3, and variable y2 can be in the range of about 0.1 and 0.22.
In some embodiments, the first compound can include CdxZn1-xO (0≦x≦1) and the second compound can include MgyZn1-yO (0≦y≦1). Variable x can be in the range of about 0 and 0.20, and variable y can be in the range of about 0.01 and 0.80.
The at least one active layer can have a thickness of about 0.1 nm to 300 nm, and the at least one barrier layer can have a thickness of about 0.1 nm to 500 nm.
In some embodiments, the energy band gap of the at least one active layer can be in the range of about 0.7 eV and 3.4 eV, and the energy band gap of the at least one barrier layer can be in the range of about 0.7 eV and 6.3 eV. In other embodiments, the energy band gap of the at least one active layer can be in the range of about 2.2 eV and 3.35 eV, and the energy band gap of the at least one barrier layer can be in the range of about 3.35 eV and 5.3 eV.
In another embodiment, a method for fabricating a semiconductor device includes forming at least one active layer composed of a first compound on a substrate, and forming at least one barrier layer composed of a second compound on at least one surface of the at least one active layer. An energy band gap of the at least one barrier layer is wider than an energy band gap of the at least one active layer. The compositions of the first and/or second compounds can be adjusted to reduce relaxation time of an electron or hole in the at least one active layer. Further, the compositions of the first and/or second compounds can be adjusted to reduce an internal polarization field in the at least one active layer
Each of the first and second compounds can include a III-V group compound semiconductor material or a II-VI group compound semiconductor material. In some embodiments, when the first compound includes InxGa1-xN and the second compound includes Aly1Ga1-y1-y2Iny1N, the compositions of the first and/or second compounds can be adjusted by controlling a variable x in the range of 0-1, and a sum of variables y1 and y2 in the range of 0-1. In other embodiments, when the first compound includes CdxZn1-xO and the second compound includes MgyZn1-yO, the compositions of the first and/or second compounds can be adjusted by controlling each of variables x and y in the range of 0-1.
The at least one active layer can have a thickness of about 0.1 nm to 300 nm and the at least one barrier layer can have a thickness of about 0.1 nm to 500 nm Either the at least one active layer or the at least one barrier layer can be formed by employing radio-frequency (RF) magnetron sputtering, pulsed laser deposition, metal organic chemical vapor deposition (MOCVD), molecular beam epitaxy, or radio-frequency plasma-excited molecular beam epitaxy. The compositions of the first and/or second compounds can be adjusted by controlling an amount of precursor gases or by controlling a processing temperature or processing time to reduce the relaxation time of the electron or hole in the at least one active layer.
In the following detailed description, reference is made to the accompanying drawings, which form a part hereof. In the drawings, similar symbols typically identify similar components, unless context dictates otherwise. The illustrative embodiments described in the detailed description, drawings, and claims are not meant to be limiting. Other embodiments may be utilized, and other changes may be made, without departing from the spirit or scope of the subject matter presented herein. It will be readily understood that the aspects of the present disclosure, as generally described herein, and illustrated in the Figures, can be arranged, substituted, combined, separated, and designed in a wide variety of different configurations, all of which are explicitly contemplated herein.
a) and (b) are schematic diagrams of an illustrative embodiment of a semiconductor device 100.
As depicted in
As depicted in
Active layer 120 may be composed of a III-V group compound semiconductor material or a II-VI group compound semiconductor material. For example, III-V group compound semiconductor materials of active layer 120 include, without limitation, GaN, InGaN, AlN, AlP, AlAs, GaP, GaAs, InN, InP, InAs, AlGaN, AlGaP, AlGaAs, InGaN, InGaP, InGaAs, INAlN, InAlP, InAlAs, AlGaInN, AlGaInP, or AlGaInAs. The II-VI group semiconductor material of active layer 120 may include, without limitation, ZnO, ZnS, CdO, CdS, CdZnO, CdZnS, MgZnO, MgZnS, CdMgZnO, or CdMgZnS. Each of upper and lower barrier layers 110 and 130 may be composed of a III-V group compound semiconductor material or a II-VI group compound semiconductor material. In some embodiments, each of upper barrier layer 110 and lower barrier layer 130 may also be composed of a ternary compound semiconductor material or a quaternary compound semiconductor material. The ternary or quaternary III-V group compound semiconductor material of each of upper barrier layer 110 and lower barrier layer 130 may include, without limitation, AlInGaN, InGaN, AlGaN, AlGaP, AlGaAs, InGaN, InGaP, InGaAs, InAlN, InAlP, InAlAs, AlGaInP, or AlGaInAs. The ternary or quaternary II-VI group compound semiconductor material of upper barrier layer 110 and lower barrier layer 130 may include, without limitation, CdZnS, MgZnS, CdZnO, MgZnO, CdMgZnO, or CdMgZnS.
In other embodiments, semiconductor device 100 can have two or more active layers and two or more barrier layers. For example, the two or more active layers and the two or more barrier layers can be sequentially deposited to form a sandwiched configuration in which an active layer is sandwiched with two barrier layers.
A quantum efficiency is a quantity defined as the percentage of photons that produces an electron-hole pair, and can be measured by, for example, an optical gain of semiconductor device 100. The optical gain g(ω) can be calculated by using a non-Markovian model with many-body effects due to interband transitions. In some examples, the “many-body effects” refer to a band gap renormalization and an enhancement of optical gain due to attractive electron-hole interaction (Coulomb or excitonic enhancement). The optical gain g(ω) is given by Equation (1) as below. For theory on the optical gain, see Doyeol Ahn, “Theory of Non-Markovian Gain in Strained-Layer Quantum-Well Lasers with Many-Body Effects”, IEEE Journal of Quantum Electronics, Vol. 34, No. 2, p. 344-352 (1998), and Ahn et al., “Many-Body Optical Gain and Intraband Relaxation Time of Wurtzite InGaN/GaN Quantum-Well Lasers and Comparison with Experiment”: Appl. Phys. Lett. Vol. 87, p. 044103 (2005), which are incorporated by references herein in their entireties.
where ω is an angular frequency of a photon in active layer 120; μ is a vacuum permeability; nr is a refractive index of active layer 120; c is a speed of light in free space; V is a volume of active layer 120; fc and fhσ are Fermi functions for a conduction band and a valence band of 3×3 block Hamiltonian Hσ, respectively; Mlmησ({right arrow over (k)}∥) is a dipole matrix element between the conduction band with a spin state η and the valence band of the 3×3 block Hamiltonian Hσ; {circumflex over (∈)} is an unit vector in the direction of a photon polarization; and Clmησ({right arrow over (k)}∥) is a renormalized lineshape function.
The renormalized lineshape function Clmησ({right arrow over (k)}∥) is presented by Equation (2) below:
where the function g2 is presented by the Equation (3) below.
where {right arrow over (k)}∥ is an in-plane wave vector, Reqlmησ({right arrow over (k)}∥) and Imqlmησ({right arrow over (k)}∥) are the real and imaginary parts of Coulomb interaction between an electron in the conduction band with a spin state η and a hole in the valence band of 3×3 block Hamiltonian Hσ in the presence of photon fields, respectively. ReΞlmησ(0,Δlmησ({right arrow over (k)}∥)) and Imσlmησ(0,Δlmησ({right arrow over (k)}∥)) are the real and imaginary parts of the non-Markovian lineshape.
The real and imaginary parts of the non-Markovian lineshape are presented by Equations (4) and (5) below, respectively:
where τin is relaxation time of carriers, and τc is correlation time for intraband process.
As shown in Equations (4) and (5), the abstract values of the real and imaginary parts of the non-Markovian lineshape ReΞlmησ(0,Δlmησ({right arrow over (k)}∥)) and ImΞlmησ(0,Δlmησ({right arrow over (k)}∥)) increase as the relaxation time τin increases. Thus, since the renormalized lineshape function Clmησ({right arrow over (k)}∥) decreases when the non-Markovian lineshape increases according to the Equation (3), it decreases as the relaxation time increases. Accordingly, the optical gain g(ω) decreases as the relaxation time τin increases according to Equation (1). Here, the relaxation time refers to the time period during which a carrier, such as an electron or hole, transits from a steady state to an equilibrium state. A carrier emits energy in the form of, for example, light, corresponding to the band gap between the steady state and the equilibrium state in quantum well 240 while the carrier undergoes the transition. Thus, for the same band gap between the steady state and the equilibrium state, as the relaxation time τin decreases, an amount of the emitted energy per a time unit increases. Accordingly, the optical gain g(ω) will increase.
The relaxation time is related to an electron-phonon scattering and a carrier-carrier scattering in quantum well 240.
The scatterings are related to the intensity of an internal polarization field in quantum well 240. For example, when the internal polarization field exists in quantum well 240, it pushes electrons or holes to a wall of quantum well 240. Thus the effective well width is reduced, and the reduction results in the enhancement of the scattering rate. Accordingly, if the internal polarization field in quantum well 240 is reduced, the scattering rate can be decreased, and thus the relaxation time τin can be decreased. As illustrated above, this results in the enhancement of the optical gain of quantum well 240.
The internal polarization field in quantum well 240 can arise from a spontaneous polarization PSP and a piezoelectric polarization PPZ. Spontaneous polarization PSP refers to polarization that arises in ferroelectrics without external electric field. Piezoelectric polarization PPZ refers to polarization that arises from electric potential generated in response to applied mechanical stress such as strain of a layer. Although PPZ alone can be reduced by the reduction of the strain, PSP still remains in quantum well 240. For additional detail on spontaneous and piezoelectric polarizations PSP and PPZ and the internal polarization field, see Ahn et al., “Spontaneous and piezoelectric polarization effects in wurtzite ZnO/MgZnO quantum well lasers”, Appl. Phys. Lett. Vol. 87, p. 253509 (2005), which is incorporated by reference herein in its entirety.
Thus, the scattering rate is decreased and thus the optical gain g(ω) is increased when a total internal polarization field, that includes the spontaneous and piezoelectric polarizations is reduced. The total internal polarization field Fzw in quantum well 240 can be determined from the difference between the sum of PSP and PPZ in quantum well 240 and the sum of PSP and PPZ in upper barrier layer 110 or lower barrier layer 130. That is, internal polarization filed Fzw can be presented by Equation (6) below.
F
Z
W=[(PSPb+PPZb)−(PSPw+PPZw)]/(∈w+∈bLw/Lb) Equation (6)
where P is the polarization, the superscripts w and b denote quantum well 240 and upper and lower barrier layers 110 and 130, respectively, L is a thickness of quantum well 240 and upper and lower barrier layers 110 and 130, and ∈ is a static dielectric constant.
In some embodiments, internal polarization field Fzw can have a value of zero by making the sum (PSPb+PPZb) of spontaneous and piezoelectric polarizations at upper or lower barrier layer 110 or 130 and the sum (PSPw+PPZw) of spontaneous and piezoelectric polarizations at quantum well 240 the same. For example, this can be achieved by controlling the mole fractions of the compounds in upper and lower barrier layers 110 and 130, and/or active layer 120.
With reference to
In some embodiments, as depicted in
In some embodiments, AlGaInN barrier layer 410 may have a thickness of several nanometers to several hundreds nanometers (nm). In other embodiments, barrier layer 410 may have a thickness of about 0.1 nm to 500 nm or about 1 nm to 100 nm. In some embodiments, a III-V group compound semiconductor material having a band gap wider than a band gap of a III-V group compound semiconductor material of the active layer can be selected for the barrier layer.
InGaN active layer 420 has a smaller band gap than the band gap of AlGaInN barrier layer 410, thus forming a quantum well in InGaN active layer 420. For example, the band gap of InGaN active layer 420 is in the range of about 0.7 eV and 3.4 eV, and the band gap of AlGaInN barrier layer 410 is in the range of about 0.7 eV and 6.3 eV. The difference between the band gaps of InGaN active layer 420 and AlGaInN barrier layer 410 can be controlled by adjusting the composition of InGaN active layer 420, the composition of barrier layer 410, or the compositions of both InGaN active layer 420 and AlGaInN barrier layer 410. In an illustrative example, aluminum (Al) composition of AlGaInN barrier layer 410 can be controlled so that AlGaInN barrier layer 410 has a larger band gap than that of InGaN active layer 420. For example, the composition of AlGaInN barrier layer 410 can be controlled to achieve a mole fraction of Al composition of the range of about 0.05 to 0.3, assuming that the total mole value of III group compound, that is, the sum of mole fractions of Al, In, and Ga, is one.
As illustrated with respect to Equation (6) above, the internal polarization field in the quantum well formed in InGaN active layer 420 can be reduced by controlling the mole fractions of the compositions of InGaN active layer 420 and AlGaInN barrier layer 410, which will now be described in detail.
The graph shown in
As depicted in
Compositions of InGaN active layer 420 and AlGaInN barrier layer 410 can be controlled. The graph shown in
As shown in the graph of
In some embodiments, by using the linear line as shown in
In some embodiments, the mole fractions of Al, Ga, and In compositions of AlGaInN barrier layer 410 can be controlled to accomplish zero internal polarization field. For example, AlGaInN barrier layer 410 can have a composition of Aly1Ga1-y1-y2Iny2N (0≦y+y2≦1). Variables y1 and y2 denote the mole fractions of Al and In compositions, respectively. A subtraction of y1 and y2 from one, that is, 1-y1-y2 denotes the mole fraction of Ga composition of AlGaInN barrier layer 410. For example, y1 can be in the range of about 0.05 to 0.3, and y2 can be in the range of about 0.1 and 0.22, in order to reduce the internal polarization field or accomplish the zero internal polarization field.
In some embodiments, the relationship between III-V group compound semiconductor materials of an active layer and a barrier layer can show non-linear relationship, such as logarithmic or exponential relationship in accordance with the type of the III-V group compound semiconductor materials of the active layer and the barrier layer and the variety of compositions of the III-V group compound semiconductor materials.
In some embodiments, the mole fractions of In compositions of InGaN active layer 420 and AlGaInN barrier layer 410 can be selected in consideration of the compressive strain of InGaN active and AnGaInN barrier layers 420 and 410. Since the higher In composition (e.g., about 0.3 or more) results in larger compressive strain and the growth of the strained layers is limited to a critical thickness, the lower In composition (e.g., about 0.01 to 0.1) can be selected.
As illustrated above, a scattering rate in a quantum well decreases as an internal polarization field in the quantum well decreases. Accordingly, by reducing the internal polarization field, the scattering rate can be decreased, and thus the relaxation time can be decreased. This results in the enhancement of the optical gain. The change of the scattering rate for different values of internal polarization field is illustrated in
As depicted in
The graph shown in
In other embodiments, a semiconductor device may have II-VI group compound. Such a II-VI group compound semiconductor device will now be described with reference to
With reference to
In some embodiments, upper and lower MgZnO barrier layers 910 and 930 may each have a thickness of several nanometers to several hundreds nanometers. In other embodiments, upper and lower MgZnO barrier layers 910 and 930 may each have a thickness of about 0.1 nm to 500 nm or about 1 nm and to 100 nm. The II-VI group compound semiconductor material of the upper and lower barrier layers (e.g. upper and lower MgZnO barrier layers 910 and 930) have wider band gaps than that of the II-VI group compound semiconductor material of the active layer (e.g. CdZnO active layer 920), thus forming a quantum well in the active layer (e.g. CdZnO active layer 920). In other embodiments, a II-VI group compound semiconductor material having a wider band gap than that of a II-VI group semiconductor material of the active layer can be selected for the upper and lower barrier layers.
In some embodiments, CdZnO active layer 920 has a band gap of about 2.2 eV to 3.35 eV, and upper and lower MgZnO barrier layers 910 and 930 each have a band gap of about 3.35 eV to 5.3 eV. The band gaps of upper and lower MgZnO barrier layers 910 and 930 and CdZnO active layer 920 can vary depending on the compositions of Mg, Zn or Cd in upper and lower MgZnO barrier layers 910 and 920, and CdZnO active layer 930. Due to the differences between the band gaps of CdZnO active layer 920 and upper and lower MgZnO barrier layers 910 and 930, a quantum well is formed in CdZnO active layer 920. As illustrated with respect to Equation (6) above, the internal polarization field in the quantum well can be reduced by controlling the mole fractions of the compositions of CdZnO active layer 920 and/or upper and lower MgZnO barrier layers 910 and 930.
With reference to the graph shown in
As an example, when Cd composition of CdxZn1-xO active layer 920 and Mg composition of MgyZn1-yO barrier layers 910 and 930 are approximately zero and 0.1, respectively, that is, II-VI group compound semiconductor device 900 has ZnO active layer 920 and upper and lower Mg0.1Zn0.9O barrier layers 910 and 930, the internal polarization field becomes approximately zero. As another example, the internal field becomes zero when variables x and y are approximately 0.05 and 0.37, 0.1 and 0.5, 0.15 and 0.6, or 0.2 and 0.7, respectively. In the case where variables x and y are 0.2 and 0.7, respectively, II-VI group compound semiconductor device 900 has Cd0.2Zn0.80 active layer 920 and upper and lower Mg0.7Zn0.30 barrier layers 910 and 930. When Cd composition (x) in CdxZn1-xO active layer 920 is in the range of about zero (0) and 0.2, Mg composition (y) in upper and lower MgyZn1-yO barrier layers 910 and 930 can be in the range of about 0.01 and 0.8.
The relationship between Cd composition of CdZnO active layer 920 and Mg composition of each of upper and lower MgZnO barrier layers 910 and 930 is shown in graph (a) of
Graph (b) in
Graph (a) in
Graph (b) in
In some embodiments, a method for fabricating a semiconductor device is provided.
As depicted in
A lower barrier layer 1330 may be disposed on a top surface of buffer layer 1320, as depicted in
As depicted in
In some embodiments, an upper barrier layer 1350 can be disposed on a top surface of active layer 1330, as depicted in
In some embodiments, lower barrier layer 1330 or upper barrier layer 1350 can be selectively disposed on active layer 1330. For example, semiconductor device 1300 can have lower barrier layer 1330 disposed on a bottom surface of active layer 1340, upper barrier layer 1350 disposed on a top surface of active layer 1340, or both lower and upper barrier layers 1330 and 1350 disposed on bottom and top surfaces of active layer 1340, respectively.
As described above, the III-V group compound semiconductor materials or the II-VI group compound semiconductor materials for active layer 1340 and/or upper and lower barrier layers 1350 and 1330 can be selected such that active layer 1340 has a narrower band gap than that of upper and lower barrier layers 1350 and 1330. This band gap difference forms a quantum well in active layer 1340.
As depicted in
Accordingly, a II-VI or III-V group compound semiconductor device in accordance with one embodiment can an reduce internal polarization field in a quantum well by forming an upper and/or lower barrier layer of II-VI group compound on at least one active layer of II-VI group compound, or forming an upper and/or lower barrier layer of III-V group compound on at least one active layer of III-V group compound. Further, the II-VI or III-V group compound semiconductor device can reduce the internal polarization field in the quantum well by controlling the mole fractions of a II-VI group compound or III-V group compound in the active layer, the upper barrier layer, and/or the lower barrier layer. Through the reduction of the internal polarization field in the quantum well, a relaxation time of the electrons or holes in the active layer is reduced and the optical gain of the semiconductor device is enhanced.
In some embodiments, a photo-electric conversion device, an optoelectronic device, or a quantized electronic device in which the semiconductor device described above is installed can be provided. For example, a short wavelength emitter, a photo detector, a laser, a high electron mobility transistor, or a light emitting device can include a semiconductor device. The semiconductor device includes at least one active layer and at least one barrier layer formed on at least one surface of the active layer. Each of the active layer and the barrier layer is composed of a III-V or II-VI group compound semiconductor material. The barrier layer has a wider band gap than that of the active layer.
One skilled in the art will appreciate that, for this and other processes and methods disclosed herein, the functions performed in the processes and methods may be implemented in differing order. Furthermore, the outlined steps and operations are only provided as examples, and some of the steps and operations may be optional, combined into fewer steps and operations, or expanded into additional steps and operations without detracting from the essence of the disclosed embodiments.
The present disclosure is not to be limited in terms of the particular embodiments described in this application, which are intended as illustrations of various aspects. Many modifications and variations can be made without departing from its spirit and scope, as will be apparent to those skilled in the art. Functionally equivalent methods and apparatuses within the scope of the disclosure, in addition to those enumerated herein, will be apparent to those skilled in the art from the foregoing descriptions. Such modifications and variations are intended to fall within the scope of the appended claims. The present disclosure is to be limited only by the terms of the appended claims, along with the full scope of equivalents to which such claims are entitled. It is to be understood that this disclosure is not limited to particular methods, reagents, compounds compositions or biological systems, which can, of course, vary. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting.
With respect to the use of substantially any plural and/or singular terms herein, those having skill in the art can translate from the plural to the singular and/or from the singular to the plural as is appropriate to the context and/or application. The various singular/plural permutations may be expressly set forth herein for sake of clarity.
It will be understood by those within the art that, in general, terms used herein, and especially in the appended claims (e.g., bodies of the appended claims) are generally intended as “open” terms (e.g., the term “including” should be interpreted as “including but not limited to,” the term “having” should be interpreted as “having at least,” the term “includes” should be interpreted as “includes but is not limited to,” etc.). It will be further understood by those within the art that if a specific number of an introduced claim recitation is intended, such an intent will be explicitly recited in the claim, and in the absence of such recitation no such intent is present. For example, as an aid to understanding, the following appended claims may contain usage of the introductory phrases “at least one” and “one or more” to introduce claim recitations. However, the use of such phrases should not be construed to imply that the introduction of a claim recitation by the indefinite articles “a” or “an” limits any particular claim containing such introduced claim recitation to embodiments containing only one such recitation, even when the same claim includes the introductory phrases “one or more” or “at least one” and indefinite articles such as “a” or “an” (e.g., “a” and/or “an” should be interpreted to mean “at least one” or “one or more”); the same holds true for the use of definite articles used to introduce claim recitations. In addition, even if a specific number of an introduced claim recitation is explicitly recited, those skilled in the art will recognize that such recitation should be interpreted to mean at least the recited number (e.g., the bare recitation of “two recitations,” without other modifiers, means at least two recitations, or two or more recitations). Furthermore, in those instances where a convention analogous to “at least one of A, B, and C, etc.” is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., “a system having at least one of A, B, and C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc.). In those instances where a convention analogous to “at least one of A, B, or C, etc.” is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., “a system having at least one of A, B, or C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc.). It will be further understood by those within the art that virtually any disjunctive word and/or phrase presenting two or more alternative terms, whether in the description, claims, or drawings, should be understood to contemplate the possibilities of including one of the terms, either of the terms, or both terms. For example, the phrase “A or B” will be understood to include the possibilities of “A” or “B” or “A and B.”
In addition, where features or aspects of the disclosure are described in terms of Markush groups, those skilled in the art will recognize that the disclosure is also thereby described in terms of any individual member or subgroup of members of the Markush group.
As will be understood by one skilled in the art, for any and all purposes, such as in terms of providing a written description, all ranges disclosed herein also encompass any and all possible subranges and combinations of subranges thereof. Any listed range can be easily recognized as sufficiently describing and enabling the same range being broken down into at least equal halves, thirds, quarters, fifths, tenths, etc. As a non-limiting example, each range discussed herein can be readily broken down into a lower third, middle third and upper third, etc. As will also be understood by one skilled in the art all language such as “up to,” “at least,” and the like include the number recited and refer to ranges which can be subsequently broken down into subranges as discussed above. Finally, as will be understood by one skilled in the art, a range includes each individual member. Thus, for example, a group having 1-3 cells refers to groups having 1, 2, or 3 cells. Similarly, a group having 1-5 cells refers to groups having 1, 2, 3, 4, or 5 cells, and so forth.
From the foregoing, it will be appreciated that various embodiments of the present disclosure have been described herein for purposes of illustration, and that various modifications may be made without departing from the scope and spirit of the present disclosure. Accordingly, the various embodiments disclosed herein are not intended to be limiting, with the true scope and spirit being indicated by the following claims.