Systems and methods for electrodepositing manganese oxide with improved rate capabilities for electrical energy storage
10818917 ยท 2020-10-27
Assignee
Inventors
Cpc classification
H01G11/50
ELECTRICITY
Y02E60/10
GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
H01M4/13
ELECTRICITY
C25D1/006
CHEMISTRY; METALLURGY
H01G11/24
ELECTRICITY
H01M10/0525
ELECTRICITY
International classification
H01M4/36
ELECTRICITY
H01M4/13
ELECTRICITY
C25D5/10
CHEMISTRY; METALLURGY
H01G11/24
ELECTRICITY
H01G11/50
ELECTRICITY
Abstract
Systems and methods that facilitate enhancing the energy storage capabilities of MnO.sub.2 in nanowire energy storage devices such as nanowire-based capacitors or batteries.
Claims
1. A method for preparing arrays of -MnO.sub.2 based core@shell nanowires, the method comprising: a step of electrodepositing a core metal to form an array of nanowire cores; and a step of electrodepositing HMTA-doped -MnO.sub.2 onto the array of nanowire cores forming an array of core metal@shell -MnO.sub.2, core@shell nanowires.
2. The method of claim 1, wherein the core metal comprises Au.
3. The method of claim 1, wherein the array of nanowire cores is formed on a glass substrate.
4. The method of claim 1, further comprising a step of the step of depositing a photoresist layer onto a substrate; patterning the photoresist layer; and wherein the step of electrodepositing a core metal includes electrodepositing the core metal on the patterned photoresist layer forming the array of nanowire cores on the patterned photoresist layer.
5. The method of claim 1, wherein the step of electrodepositing HMTA-doped -MnO.sub.2 comprises: a step of electrodepositing an HMTA-free primer layer onto the array of nanowire cores to create an array of MnO.sub.2 primed nanowire cores; and a step of electrodepositing HMTA-doped -MnO.sub.2 onto the array of MnO.sub.2 primed nanowires cores forming the array of -MnO.sub.2 based core@shell nanowires.
6. A method for preparing arrays of -MnO.sub.2 based nanowires, the method comprising: a step of depositing a photoresist layer onto a substrate; a step of patterning the photoresist layer; and a step of electrodepositing HMTA-doped -MnO.sub.2 onto the patterned photoresist layer to produce an array of -MnO.sub.2 based nanowires.
7. The method of claim 6, wherein the substrate comprises soda lime glass.
8. The method of claim 6, wherein the photoresist layer is deposited by spin coating.
9. The method of claim 6, wherein the photoresist layer is patterned using a 36 nm UV light source combined with a shutter and photolithographic alignment fixture.
10. The method of claim 9, wherein the photoresist layer is developed for 20 s.
11. The method of claim 10, wherein the photoresist layer is rinsed using water.
12. The method of claim 6, wherein a step of electrodepositing HMTA-doped -MnO.sub.2 onto the patterned photoresist layer comprises: a step of electrodepositing an HMTA-free primer layer onto the patterned photoresist layer to create a MnO.sub.2 primed patterned photoresist; and a step of electrodepositing HMTA-doped -MnO.sub.2 onto the MnO.sub.2 primed patterned photoresist forming the array of -MnO.sub.2 based nanowires.
13. An energy storage device comprising: first and second contacts; and an array of nanowires extending between the first and second contacts, wherein individual nanowires of the array of nanowires include HMTA-doped -MnO.sub.2.
14. The energy storage device of claim 13, wherein the HMTA-doped -MnO.sub.2 is a coating characterized by petals with a thickness of 6 nm to 9 nm.
15. The energy storage device of claim 13, wherein the HMTA-doped -MnO.sub.2 includes interlayer spacing that is expanded by 30% compared to non-HMTA-doped -MnO.sub.2.
16. The energy storage device of claim 13, wherein C.sub.sp for the HMTA-doped -MnO.sub.2 with t.sub.dep=500 s is at least 15 higher at 200 mV/s than non-HMTA-doped -MnO.sub.2.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1) The details of the example embodiments, including structure and operation, may be gleaned in part by study of the accompanying figures, in which like reference numerals refer to like parts. The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. Moreover, all illustrations are intended to convey concepts, where relative sizes, shapes and other detailed attributes may be illustrated schematically rather than literally or precisely.
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(43) It should be noted that elements of similar structures or functions are generally represented by like reference numerals for illustrative purpose throughout the figures. It should also be noted that the figures are only intended to facilitate the description of the preferred embodiments.
OVERVIEW
(44) The various embodiments provided herein are generally directed to systems and methods that facilitate enhancing the energy storage capabilities of MnO.sub.2 in nanowire energy storage devices such as nanowire-based capacitors or batteries. According to embodiments, a method for preparing arrays of -MnO.sub.2 based core@shell nanowires comprises electrodepositing a core metal to form an array of nanowire cores and electrodepositing HMTA-doped -MnO.sub.2 onto the array of nanowire cores to produce an array of core metal@-MnO.sub.2, core@shell nanowires.
(45) In some embodiments, the core metal comprises Au. In some embodiments, the array of nanowire cores is formed on a glass substrate.
(46) According to embodiments, a method for preparing arrays of -MnO.sub.2 based nanowires comprises depositing a photoresist layer onto a substrate, patterning the photoresist layer, and electrodepositing HMTA-doped -MnO.sub.2 onto the patterned photoresist layer to produce an array of -MnO.sub.2 based nanowires.
(47) In some embodiments, the substrate comprises soda lime glass. In some embodiments, the photoresist layer is deposited by spin coating. In some embodiments, the photoresist layer is patterned using a 36 nm UV light source combined with a shutter and photolithographic alignment fixture. In some embodiments, the photoresist layer is developed for 20 s. In some embodiments, the photoresist layer is rinsed using Millipore water.
(48) In some embodiments, electrodepositing HMTA-doped -MnO.sub.2 onto the patterned photoresist layer comprises electrodepositing an HMTA-free primer layer onto the patterned photoresist layer to create an array of MnO.sub.2 primed gold nanowires, and electrodepositing HMTA-doped -MnO.sub.2 onto the array of MnO.sub.2 primed gold nanowires to produce the array of -MnO.sub.2 based nanowires.
(49) In some embodiments, an energy storage device comprises first and second contacts, and an array of nanowires extending between the first and second contacts. In some embodiments, individual nanowires of the array of nanowires include HMTA-doped -MnO.sub.2.
(50) In some embodiments, the HMTA-doped -MnO.sub.2 has a coating characterized by petals with a thickness of 6 nm to 9 nm.
(51) In some embodiments, the HMTA-doped -MnO.sub.2 includes interlayer spacing that is expanded by 30% compared to non-HMTA-doped -MnO.sub.2.
(52) In some embodiments, C.sub.sp for the HMTA-doped -MnO.sub.2 with t.sub.dep=500 s is at least 15 higher at 200 mV/s than non-HMTA-doped -MnO.sub.2.
DESCRIPTION
(53) The various embodiments provided herein are generally directed to systems and methods that facilitate enhancing the energy storage capabilities of MnO.sub.2 in nanowire energy storage devices such as nanowire-based capacitors or batteries.
(54) Barriers to Li+ intercalation/deintercalation at the MnO.sub.2-electrolyte interface and slow Li diffusion within the MnO.sub.2 are two contributing factors that have been proposed as potential sources of the aforementioned poor rate of performance. The influence of both of these mechanisms is minimized by increasing the level of dispersion of the MnO.sub.2 by, for example, decreasing the MnO.sub.2 particle diameter. Increased dispersion translates into a higher surface area:volume ratio and reduced diffusion path lengths within the MnO.sub.2 for Li. A significant disadvantage of Li.sub.xMnO.sub.2again shared by other metal oxidesis its low electronic conductivity which varies from 2-410-4 S/cm (x=0) increasing to 4-510-2 S/cm (for x=1.0) as compared with 105 S/cm for a metal such as silver. The low conductivity of Li.sub.xMnO.sub.2 necessitates that it be supported at high dispersion on a good conductor such as a metal or carbon, and many examples of this general paradigm have been reported (e.g., an approach disclosed by the inventors has been to embed a gold nanowire within a shell of -MnO.sub.2so-called Au@MnO.sub.2 core:shell nanowireswhere both the gold nanowires and the -MnO.sub.2 shell are prepared by electrodeposition). A key point is that the gold nanowire core does not insure facile electrical communication with the MnO.sub.2 shell when this shell increases in thickness beyond 60 nm or so. In Au@MnO.sub.2 nanowires, the MnO.sub.2 shell must still intercalate Li+ and communicate electrically with the gold nanowire core, and the strategy outlined according to the embodiments disclosed herein is intended to impact one or both of these processes.
(55) In certain embodiments, planar arrays of gold@-MnO.sub.2, core@shell nanowires, are prepared by electrodeposition with hexamethylenetetramine (hereinafter referred to as HMTA) and their electrochemical properties evaluated. HMTA alters the MnO.sub.2 in three ways: First, it changes the morphology of the MnO.sub.2 creating a more open morphology for the MnO.sub.2 coating, characterized by petals with a thickness of 6 nm to 9 nm, rather than much thinner -MnO.sub.2 sheets seen in the absence of HMTA. Second, the electronic conductivity of the -MnO.sub.2 is increased by an order of magnitude. Third, -MnO.sub.2 prepared in HMTA show a (001) interlayer spacing that is expanded by 30% possibly accelerating Li transport. The net effect of HMTA-doping is to dramatically improve high rate performance. The net result are Au@-MnO.sub.2 nanowires that better retain C.sub.sp at high charge/discharge rates, and/or at high MnO.sub.2 mass loadings. This is a large effect: C.sub.sp for the thickest -MnO.sub.2 shells, with t.sub.dep=500 s, were a factor of 15 times higher at 200 mV/s when HMTA was present in the plating solution.
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(57) Preparation of Au/MnO.sub.2 Core:Shell Nanowires.
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(59) Process flow 200 provides for fabricating Au@MnO.sub.2 core:shell nanowires. A 40 nm thick nickel film is thermally evaporated on top of precleaned 11 squares of soda lime glass (step 201). Then a positive photoresist (PR, Shipley, 51808) layer is deposited by spin-coating (step 202), followed by soft-baking at 90 C. for 30 min, and a contact mask is used to pattern the PR layer with a 365 nm UV light source combined with a shutter and photolithographic alignment fixture (Newport, 83210i-line, 2.3 s). The exposed PR region is developed for 20 s (Shipley, MF-319) and then rinsed with Millipore water (Milli-Q, p >18 M.Math.cm). The exposed nickel removed by etching for 6 min in 0.8 M nitric acid (step 203). The whole device is then dipped into commercial Au plating solution (Clean Earth Solutions) and Au is potentiostatically electrodeposited using a Gamry Series G 300 potentiostat at 0.9 V versus saturated calomel electrode (SCE) using a one-compartment, three-electrode electrochemical cell with a Pt foil counter electrode (step 204). After electrodeposition, the surface is first rinsed with acetone to remove photoresist, and then with Millipore water, revealing patterned Ni pads together with Au nanowires deposited on the edges of these pads (step 205). Nickel is then removed by immersion in nitric acid for 6 min (step 206). After etching, the device is rinsed with Millipore water and air-dried. On the unetched side of this nanowire array, the Au nanowires still attached to nickel fingers are used as electrical contacts. This completes the exemplary preparation by LPNE of a gold nanowire array.
(60) Finally, -MnO.sub.2 is electrodeposited onto these nanowires (step 207) using either of two procedures: HMTA-free Au/MnO.sub.2 nanowires are prepared using an aqueous solution of 2 mM Mn(ClO.sub.4).sub.2 and 50 mM LiClO.sub.4 by potentiostatic oxidation at +0.60 V vs. MSE. Deposition times ranging from 40 s to 500 s produced MnO.sub.2 shells between 400 nm and 2.2 m in thickness. Au/MnO.sub.2 core:shell nanowires containing HMTA are prepared using a two step procedure in which a thin HMTA-free primer layer is first electrodeposited as described above, using a t.sub.dep+10 s. Then, HMTA-doped -MnO.sub.2 is electrodeposited onto MnO.sub.2-primed gold nanowires from a solution containing 10 mM HMTA in addition to 2 nM Mn(ClO.sub.4).sub.2 and 50 mM LiClO.sub.4. A t.sub.dep ranging from 30 s to 490 s results in the unique MnO.sub.2 morphology described below. In both cases, freshly deposited Au@MnO.sub.2 nanowires are removed from plating solutions, rinsed with Millipore water, and dried in the oven at 90 C. for 30 min prior to electrochemical assessment.
(61) All three-electrode, half-cell measurements were performed on arrays of 1800 nanowires. All capacitor measurements involved a sandwich of two 1800 nanowire layers.
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(64) Preparation of -MnO.sub.2 Nanowire for Conductivity Measurements.
(65) Solid -MnO.sub.2 nanowires, prepared without a Au core nanowire, were synthesized for conductivity measurements. These -MnO.sub.2 nanowires were prepared following the lithographically patterned nanowire electrodeposition (LPNE) method discussed in a previous work. Although in this work electrodeposition of MnO.sub.2 was carried out at a constant potential of +0.6 Vvs MSE for 40 s, 100 s, 300 s, and 500 s using two different plating solutions, one with HMTA and one without HMTA, as discussed above.
(66) Preparation of the Gel Electrolyte and Sandwich Capacitor Assembly.
(67) Symmetrical, Au@-MnO.sub.2 nanowire sandwich capacitors were prepared by fabricating 1800 nanowire arrays on each of two glass substrates, and pressing these two layers together, using a 2 m thick PMMA gel electrolyte. The 1.0 M LiClO.sub.4, 20 w/w %, PMMA, PC gel electrolyte was prepared by adding 1.6 g (20 w/w %) of PMMA to 5 mL of 1.0 M LiClO.sub.4 in dry propylene carbonate (PC) with mixing at 115 C. In a desiccator, the mixed gel was permitted to cool to room temperature as it transformed to the gel state. The 1.0 M LiClO.sub.4, 20 w/w %, PMMA, PC gel electrolyte was deposited on the device by spin-coating (2500 rpm, 160 s) resulting in a layer of 1 m thickness. Two of these devices were combined to form a complete sandwich capacitor with a total PMMA gel layer thickness of 2 m. This assembly was accomplished by pressing together these nanowire layers with the electrical contacts oriented on opposite ends of the device. After assembly, sandwich capacitors were hermetically sealed to exclude moisture using hot glue prior to electrochemical characterization.
(68) Structural Characterization.
(69) Scanning electron micrographs were acquired using a FEI Magellan 400 XHR system. Energy dispersive spectroscopic (EDS) images were acquired by the same SEM system with EDS detector (Oxford Instruments, 80 mm.sup.2, with Aztec software). Accelerating voltages of incident electron beams ranged from 1 kV to 25 kV, and probe currents ranged from 13 pA to 0.8 nA. All SEM specimens were mounted on stainless stubs and held by carbon tape. Grazing-incidence X-ray diffraction (GIXRD) patterns were obtained using a Rigaku SmartLab x-ray diffractometer employing the parallel beam optics. The x-ray generator was operated at 40 kV and 44 mA with Cu K irradiation. X-ray photoelectron spectroscopy (XPS) was measured using the AXIS Supra by Kratos Analytical Inc. equipped with monochromatic Al/Ag X-ray source.
(70) Electrochemical Characterization.
(71) All electrochemical measurements were performed in a one-compartment three-electrode cell using a Gamry potentiostat. The specific capacitance, C.sub.sp, was measured in 1.0 M LiClO.sub.4 in dry acetonitrile. Prior to each measurement, the acetonitrile was presaturated with N.sub.2 gas. A Pt foil was used as a counter electrode in conduction with a saturated mercurous sulfate reference electrode (MSE). All potentials are quoted with respect to the saturated mercurous sulfate reference electrode (MSA), EMSE=+0.640 Vversus normal hydrogen electrode. A value of 0.78 g/mC was used to determine MnO.sub.2 shell masses from the deposition charge as required for the calculation of C.sub.sp.
(72) Electrodeposition of -MnO.sub.2 from HMTA-Containing and HMTA-Free Plating Solutions.
(73) Linear arrays of 1800 gold nanowires with lateral dimensions of 275 nm (w)40 nm (h) were prepared on glass surfaces using the LPNE process (
(74) Au@-MnO.sub.2 core@shell nanowires were obtained by exposing a 0.90 cm length of this array to a MnO.sub.2 plating solution. -MnO.sub.2 was electrodeposited in a hemicylindrical layer onto each of the gold nanowires in the array (
Mn.sub.2.sup.++2H.sub.2O.fwdarw.MnO.sub.2+4H.sup.++2e.sup.(1)
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(76) The unbuffered plating solution employed for this reaction had a pH=7.20.2 and the pKa of HMTA is 4.9, so it is unprotonated at this pH. The presence of 10 mM HMTA in the plating solution had a subtle influence on the kinetics of MnO.sub.2 deposition, increasing the reaction rate by 2-5% as determined from current versus time traces (
(77) Characterization of Au@-MnO.sub.2 Core@Shell Nanowires.
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(79) The -MnO.sub.2 shells obtained by electrodeposition from HMTA-free plating solution onto gold nanowires has a morphology that consists of many concentric, wrinkled MnO.sub.2 sheets wrapped one on top of another (
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(82) The apparent thickness of each MnO.sub.2 petal, however, is much thicker in the 10-30 nm range depending upon the deposition duration (
(83) This suggests that the porosity of the MnO.sub.2 shell obtained in the presence of HMTA is greater than that which is obtained in its absence.
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(85) Electron dispersive x-ray analysis (EDX) elemental maps of single -MnO.sub.2 nanowires (
(86) For nanowires and films obtained with and without HMTA, grazing incidence x-ray pow-der diffraction (GIXRD) patterns for arrays of Au@-MnO.sub.2 nanowires show weaker reflection amplitudes than patterns acquired for films, but these patterns are otherwise very similar (
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(88) The morphological, structural, and chemical changes induced in the -MnO.sub.2 by HMTA, seen in the data of
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(90) For the thickest shells (t.sub.dep=500 s) at the highest scan rate (100 mV/s), the disparity between HMTA and no-HMTA samples is pronounced with C.sub.sp 15 higher, on average, for HMTA versus no-HMTA samples (
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(92) The increase in XRD (001) layer spacing induced by the electrodeposition of -MnO.sub.2 in the presence of HMTA (
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(96) The conductance of solid -MnO.sub.2 nanowires was measured in laboratory air by recording current versus potential (I-V) traces for an array of 200 nanowires across a 10 m gap between two evaporated gold electrodes (
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(102) According to embodiments, a method 1000 for preparing planar arrays of gold@-MnO.sub.2, core@shell nanowires comprises evaporating Ni film onto a glass substrate 1001. In embodiments, the glass substrate comprises soda lime glass.
(103) In embodiments, the method 1000 continues with depositing a photoresist layer onto the Ni film 1002. In embodiments, the photoresist layer is a positive photoresist layer. In embodiments, the positive photoresist layer is deposited by spin coating.
(104) In embodiments, the method 1000 continues with soft baking the substrate having the Ni film and photoresist layer 1003. In embodiments, the substrate is soft baked for 30 mins at 90 C.
(105) In embodiments, the method 1000 continues with patterning the photoresist layer by applying a contact mask to the photoresist layer 1004. In embodiments, the photoresist layer is patterned using a 36 nm UV light source combined with a shutter and photolithographic alignment fixture.
(106) In embodiments, the method 1000 continues with developing and rinsing the photoresist layer 1005. In embodiments, the photoresist layer is developed for 20 s. In embodiments, the photoresist layer is rinsed using Millipore water.
(107) In embodiments, the method 1000 continues with etching to remove any exposed Ni from a top surface 1006. In embodiments, the exposed Ni is removed by etching for 6 min in nitric acid.
(108) In embodiments, the method 1000 continues with potentiostatically electrodepositing Au onto the top surface 1007. In embodiments, the Au is electrodeposited using a Gamry Series G 300 potentiostat at 0.9 V versus saturated calomel electrode (SCE) using a one-compartment, three-electrode electrochemical cell with a Pt foil counter electrode.
(109) In embodiments, the method 1000 continues with rinsing the top surface with acetone to remove remaining photoresist and reveal a nanowire array 1008.
(110) In embodiments, the method 1000 continues with removing any remaining Ni from the nanowire array 1009. In embodiments, any remaining Ni is removed by immersion in nitric acid.
(111) In embodiments, the method 1000 continues with electrodepositing -MnO.sub.2 onto the nanowire wire array 1010 to produce the planar array of gold@-MnO.sub.2, core@shell nanowires. In embodiments, depositing -MnO.sub.2 onto the nanowire wire array comprises electrodepositing an HMTA-free primer layer 1011 onto the nanowire array to create MnO.sub.2 primed gold nanowires, and electrodepositing HMTA-doped -MnO.sub.2 onto the MnO.sub.2 primed gold nanowires 1013.
(112) In certain embodiments, Au/MnO.sub.2 core:shell nanowires containing HMTA are prepared using a two-step procedure in which a thin HMTA-free primer layer is first electrodeposited as described above, using a t.sub.dep=10 s. Then, HMTA-doped -MnO.sub.2 is electrodeposited onto MnO.sub.2-primed gold nanowires from a solution containing 10 mM HMTA in addition to 2 mM Mn(ClO.sub.4).sub.2 and 50 mM LiClO.sub.4. A t.sub.dep ranging from 30 s to 490 s results in the unique MnO.sub.2 morphology described herein.
(113) In embodiments, HMTA-free Au/MnO.sub.2 nanowires are prepared using an aqueous solution of 2 mM Mn(ClO.sub.4).sub.2 and 50 mM LiClO.sub.4 by potentiostatic oxidation at +0.60 V vs. MSE. Deposition (1014) times ranging from 40 s to 500 s produced MnO.sub.2 shells between 400 nm and 2.2 m in thickness.
(114) In embodiments, the completed nanowire arrays are removed from the plating solution, rinsed and dried (1013, 1015).
(115) The present embodiments include the addition of the amine, HMTA, to the plating solution used to prepare the MnO.sub.2 layer for Au@-MnO.sub.2 core@shell nanowires. HMTA changes the morphology of the MnO.sub.2, increases the (001) interlayer spacing by 30%, and increases its electrical conductance by an order of magnitude. The net result are Au@-MnO.sub.2 nanowires that better retain C.sub.sp at high charge/discharge rates, and/or at high MnO.sub.2 mass loadings. This is a large effect: C.sub.sp for the thickest -MnO.sub.2 shells, with t.sub.dep=500 s, were a factor of 15 times higher at 100 mV/s when HMTA was present in the plating solution. While the rate performance of Au@-MnO.sub.2 nanowires is certainly improved by HMTA, a considerable loss of C.sub.spclose to 50%is still seen (
(116) TABLE-US-00001 TABLE 1 Summary of Metrics for Au@-MnO.sub.2 Prepared in HMTA-Containing and HMTA-Free Plating Solutions Gravimetric tdep.sup.a Thickness.sup.b Loading.sup.c C.sub.sp .sup.d C.sub.sp.HMTA/ -MnO.sub.2 (s) (nm) (ng/nanowire) (F/g) C.sub.sp.no-HMTA No-HMTA 40 380 8 1.2 0.3 60 9 100 660 20 4.3 2 39 1 300 1080 50 8.9 1 7 2 500 1800 110 11.8 0.5 3 2 HMTA 40 650 20 3.4 3 90 6 1.5 100 1070 50 4.6 3 74 2 1.9 300 1700 50 10.0 1 57 6 8.1 500 2200 300 12 0.4 45 1 5 .sup.aThe duration of the potentiostatic electrodeposition of MnO.sub.2. .sup.bMnO.sub.2 shell thickness measured using SEM. .sup.cGravimetric loading is estimated from coulometry of the MnO.sub.2 deposition. Loading pertains to nanowires 0.90 cm in length.
(117) All features, elements, components, functions, and steps described with respect to any embodiment provided herein are intended to be freely combinable and substitutable with those from any other embodiment. If a certain feature, element, component, function, or step is described with respect to only one embodiment, then it should be understood that that feature, element, component, function, or step can be used with every other embodiment described herein unless explicitly stated otherwise. This paragraph therefore serves as antecedent basis and written support for the introduction of claims, at any time, that combine features, elements, components, functions, and steps from different embodiments, or that substitute features, elements, components, functions, and steps from one embodiment with those of another, even if the following description does not explicitly state, in a particular instance, that such combinations or substitutions are possible. Express recitation of every possible combination and substitution is overly burdensome, especially given that the permissibility of each and every such combination and substitution will be readily recognized by those of ordinary skill in the art upon reading this description.
(118) In many instances entities are described herein as being coupled to other entities. It should be understood that the terms coupled and connected (or any of their forms are used interchangeably herein and, in both cases, are generic to the direct coupling of two entities (without any non-negligible (e.g., parasitic intervening entities) and the indirect coupling of two entities (with one or more non-negligible intervening entities)). Where entities are shown as being directly coupled together, or described as coupled together without description of any intervening entity, it should be understood that those entities can be indirectly coupled together as well unless the context clearly dictates otherwise.
(119) While the embodiments are susceptible to various modifications and alternative forms, specific examples thereof have been shown in the drawings and are herein described in detail. It should be understood, however, that these embodiments are not to be limited to the particular form disclosed, but to the contrary, these embodiments are to cover all modifications, equivalents, and alternatives falling within the spirit of the disclosure. Furthermore, any features, functions, steps, or elements of the embodiments may be recited in or added to the claims, as well as negative limitations that define the inventive scope of the claims by features, functions, steps, or elements that are not within that scope.