The present disclosure relates to exciton gating in organic photovoltaic cells.
Photovoltaic cells based on organic semiconductors are attractive for their inherent compatibility with lightweight substrates and high throughput processing techniques. In order to realize efficient power conversion, the tightly bound excitons generated under optical excitation must be efficiently dissociated, and the constituent electronic charges separated and collected. The excitonic character of the excited state thus introduces a challenge into the photoconversion process, namely, how to realize dissociation and maximize exciton harvesting. In many organic photovoltaic cells (OPVs), dissociation is realized at an electron donor-acceptor (D-A) interface. Consequently, the efficiency of exciton harvesting depends strongly on the ability of the exciton to reach said interface. Straightforward exciton migration is exacerbated by a short exciton diffusion length (LD) relative to the optical absorption length in most organic semiconductors.
Much effort in the optimization of OPV architecture reflects a fundamental challenge in solid-state physics, namely, how to direct the motion of the neutral exciton. In inorganic semiconductors, excitonic phenomena are often not considered at room temperature due to their low binding energy and straightforward dissociation via thermal energy. When present, the large radius of the Wannier-Mott-type excitons of these systems permits some degree of spatial manipulation via applied electric fields. In organic semiconductors, the localized Frenkel-type exciton is strongly bound, often making manipulation with an applied field more difficult.
The ability to direct exciton transport using a consistent scheme for biasing exciton motion would have broad application in a variety of optoelectronic devices, of particular note for photoconversion and exciton harvesting in an OPV.
Directed exciton transport may be achieved with the incorporation of exciton permeable interfaces. These interfaces introduce a symmetry-breaking imbalance in exciton energy transfer rates, leading to super-diffusive motion. Accordingly, among other benefits, exciton permeable interfaces may enable enhanced exciton harvesting in organic photovoltaic cells (OPVs). This disclosure demonstrates directed exciton transport in both dilute donor and energy-cascade OPVs where judicious optimization of the interface allows super-diffusive motion to be exploited for enhanced exciton transport. Generalized systems incorporating multiple exciton permeable interfaces are also described, demonstrating the ability to overcome the diffusive limit by directing exciton motion.
In general, in an aspect, an organic photovoltaic device includes an organic electron donor region, and an organic electron acceptor region. The acceptor region forms a donor-acceptor interface with the donor region. At least one of the donor region and the acceptor region includes an exciton permeable interface. An energy transfer imbalance across the exciton permeable interface is configured to bias exciton transfer towards the donor-acceptor interface.
Implementations of this aspect may include one or more of the following features.
In some implementations, the energy transfer imbalance can be due to a difference in concentration of a first material across the exciton permeable interface.
At least one of the donor region and the acceptor region can include a first organic layer including a first concentration of the first material, and a second organic layer include a second concentration of the first material. The first organic layer can be disposed between the second organic layer and the donor-acceptor interface. The first concentration can be greater than the second concentration. The exciton permeable interface can be an interface between the first organic layer and the second organic layer.
In some implementations, the first concentration can be 100%. In some implementations, the first concentration can be less than 100%.
In some implementations, the energy transfer imbalance can be due to a difference in molecular ordering across the exciton permeable interface.
In some implementations, the energy transfer imbalance can be due to a difference in photoluminescence efficiency across the exciton permeable interface.
In some implementations, the energy transfer imbalance can be due to a difference in index of refraction across the exciton permeable interface.
In some implementations, the energy transfer imbalance can be due to a difference in molecular orbital energy levels across the exciton permeable interface.
In some implementations, the energy transfer imbalance can be due to a difference in spectral overlap integral across the exciton permeable interface.
In some implementations, the acceptor region can include an optically absorbing material.
In some implementations, at least one of the donor region and the acceptor region can further include a plurality of exciton permeable interfaces. An energy transfer imbalance across each exciton permeable interface can be configured to bias exciton transfer towards the donor-acceptor interface. At least one of the donor region and the acceptor layer can include further include a plurality of organic layers. Each exciton permeable interface can be an interface between adjacent organic layers.
In some implementations, an energy transfer imbalance across the plurality of layers can be configured to bias exciton transfer towards the donor-acceptor interface.
In some implementations, each organic layer can have a respective concentration of a material such that the material concentration varies monotonically across the plurality of organic layers.
In some implementations, each organic layer can have a respective concentration of a material such that the material concentration varies continuously across the plurality of organic layers.
In some implementations, at least one organic layer can have a respective concentration of material that varies across that organic layer.
In some implementations, the organic photovoltaic device can further include one or more additional organic electron donor regions and one or more additional organic acceptor region. The additional electron donor regions and additional acceptor regions can form one or more additional donor-acceptor interfaces. At least one of the additional donor regions and acceptor regions can include an additional exciton permeable interface. An energy transfer imbalance across the additional exciton permeable interface can be configured to bias exciton transfer towards at least one of the additional donor-acceptor interfaces.
In some implementations, the energy transfer imbalance can be due to a difference in exciton radiative decay rate across the exciton permeable interface.
The details of one or more implementations are set forth in the accompanying drawings and the description below. Other features and advantages will be apparent from the description, the drawings, and the claims.
This disclosure describes implementations for directed energy transfer and enhanced exciton diffusion in organic semiconductors. In particular, this disclosure demonstrates that while gains in exciton harvesting are possible with enhanced bulk LD, a more effective approach can be achieved by introducing exciton permeable interfaces that intentionally bias energy transfer and exciton transport toward the donor-acceptor (D-A) interface. Such passive exciton gates break the symmetry associated with normal diffusion transitioning to a super-diffusive regime. In the super-diffusive regime, excitons realize large diffusion efficiencies without the need to increase the area of the dissociating interface.
As described herein, exciton permeable interfaces between material layers act as a mechanism for enhanced diffusion. Notably, an imbalance in energy transfer rates across the interface imparts directed exciton transfer towards the donor-acceptor interface, also contributing to an increase in exciton diffusion efficiency (ηD) for the device.
This effect of these interfaces can be quite general. To understand how this imbalance is derived, consider the following equation where kT is the total rate of exciton hopping, kA is the hopping rate to an individual hopping site from a set of all possible hopping sites, A, and d is the distance to that hopping site. Exemplary materials properties a, b, c, signify that the hopping rate is material dependent and can vary depending on the mechanism for exciton transport. Example material properties include molecular ordering, radiative decay rate of the exciton, index of refraction, molecular orbital energy levels (or energy gap), and exciton transfer integrals. Importantly, changes in these rates, along with d, at an interface create direction-dependent imbalances in the total hopping rate.
k
T
=Σk
A(d,a,b,c)
Although kT is shown above as depending on three example parameters a, b, and c, the actual number of parameters may vary depending on the mechanism for exciton transport.
When an exciton is in the middle of a layer, the individual hopping rates are the same in all directions and the exciton transport in the film is said to be diffusive. At an interface however, there can be an imbalance in individual hopping rates where, for instance, the hopping rate into the next layer is larger than the hopping rate to remain in the current layer. Such a situation results in anomalous diffusion.
In the case of the dilute donor OPVs containing a dilute organic donor layer directly adjacent to a neat organic layer, this imbalance is achieved through a discontinuity in molecular site density, e.g., an exciton in the dilute layer at the interface experiences more possible destination sites in the more concentrated neat layer than in the dilute layer. As such, there will be a larger probability for excitons to move into the more concentrated layer resulting in directed exciton motion.
Although an example OPV device 100 is show in
The inset 150 shows a close up of the exciton permeable interface 120 between two different donor layers 116 and 118 of the donor region 108. An exciton 122 in the dilute donor layer 118 at the exciton permeable interface 120 experiences a greater number of possible acceptor sites 124 in the more concentrated donor layer 116 than in the dilute donor layer 118. Further, the distances between acceptor sites 124 in the more concentrated donor layer 116 (e.g., distance 126) are, on average, shorter than the distances between acceptor sites 124 in the dilute donor layer 118 (e.g., distance 128). As such, there will be a larger probability for excitons to move into the more concentrated donor layer 116, resulting in directed exciton motion.
Although concentration imbalance is one mechanism of providing an imbalance in energy transfer across an interface 120, other mechanisms are also possible. For example, as an alternative or in addition to concentration imbalances between layers, an imbalance in energy transfer across an interface may be achieved by varying other molecular parameters that affect the above equation (e.g., a, b, c). The following equation describes the hopping rate of excitons that undergo Förster energy transfer, connecting the hopping rate to molecular parameters. Here, τ is the exciton lifetime, ηPL is the photoluminescence efficiency, κ is the dipole orientation factor, n is the index of refraction, λ is the wavelength, FD is the normalized fluorescence, and σA is the molecular absorption cross-section.
In the context of Förster energy transfer, a list of parameters that could possibly be varied can include:
While any or all these parameters can be used to create an imbalance, in some cases, dilution might be the most easily realized and most amenable to creating very large and tunable imbalances in exciton hopping. To demonstrate the power of this effect, as described below, we performed some simulations where we monitor the ability for an exciton to traverse a 16-nm thick layer and vary the number of permeable interfaces. We hold the bulk transport (LD) constant between the simulations to only capture the effect of the interfaces. In some implementations, we can increase the transport efficiency (ηT) and reduce the average transit time by moving from a bilayer case with one interface to an effectively graded case with nominally 15 interfaces.
In an example configuration, a passive exciton gate may be formed at the interface between two materials (e.g., as shown in
In a second example configuration, an interface between dilute and neat layers of a single molecular species can lead to a similar asymmetry in rates. One or more interfaces can be formed in a donor region of a device (e.g., a continuous region of one or more layers of donor material) and/or in an acceptor region of a device (e.g., a continuous region of one or more layers of acceptor material). To illustrate, referring to the schematic of
Although the use of electronic donor materials is described above, this is merely an illustrative example. In practice, this phenomenon is not limited only to the use of electron donor materials. In some cases, the same behavior could also be observed using dilute electron accepting materials.
Example guest donor materials include organic semiconductors such as phthalocyanines, subphthalocyanines, naphthalocyanines, rubrenes, indenes, linear acenes, metallocenes, squaraines, thiophenes, polythiophenes or polyphenylene-vinylenes among others.
Example wide energy gap host include organic semiconductors such as, for example, phenanthrolines, imidazoles, amines, carbazoles, triarylsilanes, polystyrenes, polyvinylalcohols, polyvinylcarbazoles, among others. Host materials are acceptable for use in either diluted donor layers or diluted acceptor layers, so long as the guest material's highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) levels are arranged with respect to the HOMO and LUMO levels of the host material so as to confine exciton diffusion to the guest material as described above. Consequently, for narrower gap host materials, similarly narrow gap hosts may also be used, as is the case with SubPc and boron subnaphthalocyanine chloride (SubNc) as host and guest.
In diluting acceptor materials, options could include, for example, fullerenes (e.g., C60 or C70), naphthalene derivatives, bathophenanthroline (Bphen), perylene derivatives, such as 3,4,9,10-perylenetetracarboxylic-bis-benzimidazole (PTCBI) or perylenetetracarboxylic dianhydride (PTCDA), fluorinated electron donors, or polymeric fullerene derivatives (PCBM).
In some implementations, the wide energy gap matrix material may also be absorbing and hence can serve as an additional contribution to the photocurrent. For example, the wide energy gap matrix material can be optically absorbing (e.g., such that it absorbs incident visible light). This absorbed energy in turn contributes to the device's photocurrent. This can be beneficial, for example, as it can enhance the efficiency of the device, while also maintaining the directed energy transfer and enhanced exciton diffusion properties provided by the exciton permeable interfaces.
Here, we present results demonstrating exciton gating and enhanced exciton transport for architectures exploiting both the energetic and site density asymmetries discussed above. In order to isolate the role of the interface in determining the overall efficiency of exciton transport, a Kinetic Monte Carlo (KMC) formalism was developed to solve the 1-D exciton diffusion equation across exciton permeable interfaces. The advantage of this stochastic solution is that the boundary condition for the permeable interface did not need to be known a priori, and was, instead, constructed by identifying the imbalance in exciton energy transfer rates at the interface. Other device related boundary conditions, such as exciton reflecting and dissociating, may also be easily incorporated as appropriate. Care was taken to ensure that the KMC solutions agree with analytical solutions for cases without permeable interfaces.
As discussed, energy-cascade OPVs derive an imbalance in energy transfer from differences in energy gap. In such a configuration, downhill and sometimes long-range energy transfer can take place from a larger energy-gap donor to a lower energy-gap donor as is the case for boron subphthalocyanine chloride (SubPc, Eg=2.0 eV) to boron subnapthalocyanine chloride (SubNc, Eg=1.8 eV). Förster-type energy transfer from SubPc to SubNc is often favorable due to their complementary photoluminescence and absorption spectra. Predictions for the Förster radius (R0) from SubPc to SubNc yielded R0=2.1 nm, whereas the reverse transfer was comparatively improbable with R0˜0 nm. Therefore, a perfect (or otherwise acceptable) imbalance was achieved leading to enhanced exciton diffusion efficiency (ηD) in both donor layers.
In an example implementation, energy-cascade OPVs were fabricated according to the layer structure 300 in
The KMC model for exciton diffusion in cascade structures incorporating exciton permeable interfaces allowed for the accurate prediction of the external quantum efficiency (ηEQE). As an example, the ηEQE was modeled for SubPc and SubNc at λ=590 nm and 700 nm, respectively, corresponding to regions of predominant absorption for each material, respectively (e.g., as shown in
The interface between dilute and neat layers of donor material may also form an exciton permeable interface due to an asymmetry in transfer rates. In some cases, such dilute donor OPVs have shown enhanced ηP relative to undiluted control devices. In these devices, dilute layers of the archetypical electron donating molecule SubPc (the molecular structure for SubPc 450 is shown in
In an example implementation, OPVs 400 were fabricated according to the layer structure 400 in
Similar to the energy-cascade OPVs these additional losses were expected and may reflect exciton quenching at the MoOx anode buffer layer and non-unity collection efficiency. Interestingly, ηD increased continuously upon dilution.
As described herein, for permeable interfaces formed between dilute and neat layers of material, the rate imbalance arises from an imbalance in molecular site density. While the aforementioned implementations uses UGH2 as an optically transparent host material, additional photocurrent can be generated if the host material is also optical absorbing, while still having an energy gap that is larger than the guest material. In this way, excitons generated on both the host and guest materials experience the permeable gating interface.
For example, SubNc can used as a guest material to integrate with a photoactive host of SubPc. When SubNc is diluted in SubPc, two donor exciton harvesting pathways exist in parallel. Similar to the case of dilute SubPc, excitons generated on SubNc diffuse along a pathway from SubNc molecules toward the donor-acceptor interface. The difference in energy-gap between SubNc and SubPc is much larger than the ambient thermal energy (e.g., approximately 25 meV). Thus, excitons generated on SubNc do not energy transfer to SubPc. In this way, SubPc acts analogously to UGH2 in the aforementioned example. A second pathway is also present for excitons that originate on SubPc; efficient Förster energy transfer from SubPc to SubNc occurs rapidly, and excitons may follow the same route to the interface as those originally generated on SubNc.
Overall, in this example, photogenerated excitons are quickly confined to molecules of SubNc, followed by short range exciton energy transfer toward the donor-acceptor interface where excitons are dissociated. Here, the host-guest donor layer is distinct from composite donor layers formed from multilayer stacks, as the photogenerated charges remain solely on the guest species (SubNc) during transport towards the anode.
Example systems incorporating a single permeable interface are described above. However, implementations also can include donor regions and/or acceptor regions having multiple exciton permeable interfaces. For example, a donor region can include three or more dilute donor layers (or two or more dilute donor layers and a neat donor layer), each of which is formed by diluting a different concentration of guest material in a wider band gap host material. Each interface between adjacent dilute donor layers (and between a dilute donor layer and a neat donor layer) may form an exciton permeable interface as disclosed herein. Likewise, an acceptor region can include three or more dilute acceptor layers (or two or more dilute acceptor layers and a neat acceptor layer), where the interface between adjacent dilute acceptor layers (and between a dilute acceptor layer and a neat acceptor layer) may form an exciton permeable interface as disclosed herein.
For instance, in some cases, inspection of the mean-squared displacement as a function of time can elucidate the connection between the number of permeable interfaces and the degree of anomalous diffusion. As an example, a generic system 500 having 16 1-nm-thick bins 502 was modeled, where the imbalance was derived from differences in molecular concentration. The first interface 504 was introduced by discretizing the system into two layers, one representing a very dilute layer (e.g. 1 wt. %) with LD=10 nm (506) and one representing a nearly undiluted layer (e.g. 99 wt. %) with LD=1 nm (508), depicted schematically in
To further inspect super-diffusion in these multiple interface systems, an example histogram of final exciton location for each of the structures is presented in
As the number of permeable interfaces increased, the relative difference in exciton density between adjacent bins decreased. This may have been due to smaller imbalances in energy transfer rates across the interface since the changes in concentration occur in finer steps as more interfaces are added. In the 16-layer system, where the rates changed continuously, there was a constant increase in exciton number density across the system. Coupled to the deeper penetration of excitons into this system was a concomitant increase in the ηT (e.g., as shown in
From the multiple example implementations presented above, it is clear that exciton permeable interfaces can play an impactful role in determining exciton transport in planar heterojunction OPVs. In fact, developing a better understanding of the phenomena that drive imbalance in energy transfer may serve to shift the paradigm from one that simply optimizes diffusion by enhancing LD or circumvents diffusion via the BHJ to one that deeply considers the properties of exciton permeable interfaces.
In the case of the energy-cascade OPVs modeled based on the donor pairing of SubPc and SubNc, variations in the energy-gap are able to increase the ηD for both constituent layers. Such a configuration is favorable in terms of exciton transport since the variation in energy-gap provides the ultimate exciton gate, as energy transfer back to the wider gap donor has a near-zero probability. A similar energetic asymmetry could also be realized using inorganic quantum dots (QDs), where the energy gap is tuned based on QD size via quantum confinement. Exciton transport in QD films is also diffusive, or even sub-diffusive owing to energetic disorder. To overcome this limit, layered structures with exciton permeable interfaces could be used to introduce a symmetry breaking imbalance in energy transfer, again achieving directed transport.
Energy cascade structures can, however, have an impact on other device parameters, notably the open-circuit-voltage (VOC) due to the resultant change in the molecular orbital energy landscape. Careful selection and alignment of molecular orbital energy levels allows for this limitation to be overcome, with energy-cascade OPVs having shown remarkable ηP. It should be noted that in the case of SubPc and SubNc, significant long-range Förster energy transfer can occur from SubPc to SubNc. While explicitly accounted for the in the simulations presented here, such is not the general case of any donor pairing. Excitons that move via the relatively short-range Dexter-type energy transfer often will only be able to transfer at the permeable interface, thereby reducing the relative ηD of the outer layer.
In dilute donor OPVs that incorporate SubPc in a wide energy gap host material, increases in LD only describe part of the overall increase in ηD. A significant contribution to the enhanced donor ηD can be attributed to the increasing imbalance in energy transfer from the dilute SubPc layer to the neat SubPc layer with dilution (e.g., as shown in
Overall, we have detailed the emergent properties of exciton permeable interfaces and their effect on the ηD in highly efficient OPVs. Combined with enhancements in the bulk LD, the further utilization of exciton permeable interfaces has the ability to fully revitalize interest in the planar heterojunction architecture for next generation OPVs. More broadly, this work demonstrates the utility of exciton permeable interfaces for directing exciton motion, and, in particular, the ability to move excitons to a desired location quickly (in less than the natural lifetime). The ability to overcome the diffusive limit is expected to impact the design of a broad range of organic optoelectronic devices where excitons play a mediating role in the conversion of light to charge and vice-versa.
The implementations described above can be implemented using a variety of techniques. Illustrative examples are described below.
Kinetic Monte Carlo modeling was used to generate simulations for the exciton density profiles ηEQE, ηA and ηD. Energy transfer rates for the bulk can were derived from a simple, nearest-neighbor interpretation of the exciton diffusivity, D=LD2τ−1=d2 k, where d is the discretization of the KMC model, or bin spacing, and k is the energy transfer rate input. Estimates for the molecular densities of each material were obtained from crystallographic information when available and from powder densities otherwise. The exciton generation rate, Q(x) were simulated using transfer matrix formalism of the incident optical field. The optical constants of each material were measured by variable angle spectroscopic ellipsometry. For the simulations of OPV devices, the MoOx anode buffer layer were approximated as a reflecting boundary.
Organic photovoltaic cells were fabricated on glass slides coated with a 150-nm-thick layer of indium-tin-oxide (ITO) having a sheet resistance of 15Ω/□. All substrates were cleaned with tergitol and solvents. Additionally, ITO substrates were exposed to a UV-ozone ambient for 10 minutes prior to the deposition of the active layers. Organic layers were deposited via vacuum thermal sublimation (<10−7 Torr) at a nominal rate of 0.2 nm/s. Devices were capped with a 100-nm-thick cathode layer of Al deposited at a nominal rate of 0.3 nm/s through a shadow mask defining an active area with a diameter of 1 mm. Layer thicknesses were initially optimized via transfer matrix simulations of the internal optical field.
External quantum efficiency testing was performed under illumination from a 300 W Xenon lamp coupled to a Cornerstone 130 ⅛ meter monochromator and chopped with a Stanford Research Systems SR540 optical chopper. Electrical characteristics can be measured using a Stanford Research Systems SR810 lock-in amplifier. Devices were also characterized under AM 1.5 G solar radiation, and the parameters can be extracted from current-voltage testing at an illumination of (100±5) mW/cm2.
In some implementations, the following strategy was employed to emulate an artificial energy-cascade organic photovoltaic cell (OPV) where no imbalance in energy transfer is present at the exciton permeable interface. In the actual energy cascade OPV (e.g., as shown in
In some cases, to simulate the artificial device, there must be no imbalance in energy transfer at the interface and the bulk LD for each layer must remain the same for both SubPc and SubNc. First, τ2 was adjusted to τ2=0.94 ns. As such, the bulk hopping rates were identical for each layer, but the LD for each layer remained unique. Second, R0,12 was set to R0,12=0 nm to ensure that there is no long range energy transfer occurring across the permeable interface. Both these considerations ensured the artificial device retains the bulk diffusive behavior of the real device while not incorporating the additional effects of the interfacial exciton gate created by the energy-gap variation at the permeable interface.
Photoluminescence (PL) quenching experiments were performed in order to confirm the optimum SubPc concentration for interlayer between the dilute donor and acceptor in a dilute donor OPV. To perform these measurements, the layer structures 800a and 810b found in
In order to fit the measured PL ratios, a Kinetic Monte Carlo (KMC) algorithm were used to solve the 1-D exciton diffusion equation. A transfer matrix formalism was used to determine the optical field and rate of exciton generation within the structure. Hopping rates within each layer were determined from measured values of LD as a function of concentration. The imbalance in energy transfer at the interfaces were captured by explicitly including the effects of both the imbalance in molecular site density and intermolecular separation. Care was taken to include the effect of a variable PL efficiency between the layers. The KMC modeling also allowed for the tabulation of the exciton diffusion efficiency (ηD) as a function of interlayer concentration. Example results of these measurements and corresponding simulations are found in
In an example implementation, good agreement was found between the measured and predicted PL ratios for all interlayer concentrations explored in this work. It was determined that the smallest PL ratios and largest ηD occur when then interlayer is most concentrated and includes a pure layer of SubPc, despite the fact that SubPc has a smaller exciton diffusion length (LD) than a majority of the other interlayer concentrations explored. This behavior can be rationalized only by considering the effects of the exciton permeable interface formed between the two donor layers.
It can be shown that the largest imbalances in energy transfer are achieved when the interlayer is most concentrated. Such a situation maximizes the difference in molecular site density and direct exciton transport towards the quenching interface. Such behavior confirms the selection of a neat SubPc donor layer nearest the donor-acceptor interface in dilute donor OPVs.
In general, this application discloses the use of exciton permeable interfaces that act as gates for excitons. These interfaces act as gates, as by design, the rates of forward and reverse exciton energy transfer are not equal. As such, the exciton may be funneled preferential in one direction. In implementations of the organic photovoltaic cells discussed above, excitons are funneled toward the dissociating interface for photoconversion. Implementations of these devices thus overcome the often undesired randomness of a normal diffusive process, in which the exciton has probability to hop away from the dissociating interface. In some implementations, the required asymmetry in transfer rates can be realized by engineering film composition. For example, an interface can be designed with a neat layer of donor material (SubPc) on the right side of the interface and a dilute layer of donor material (SubPc in UGH2) on the left side of the interface. As discussed above, the asymmetry here arises primarily from a difference in the number of available sites for hopping on either side of the interface as well as the distance to these sites. However, some implementations of this concept may not be limited to the use of a single interface. In some cases, multiple interfaces can be used, either in a donor region (e.g., adjacent one or more layers of donor material), in an acceptor region (e.g., adjacent to one or more layers of acceptance material), or in both donor and acceptor regions. For example,
A number of embodiments of the invention have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Accordingly, other embodiments are within the scope of the following claims.
This application claims the benefit of priority under 35 U.S.C. 119(e) to U.S. Application No. 62/062,387 filed Oct. 10, 2014.
This invention was made with government support under DMR-116566, DMR-1307066 and CBET 1067681 awarded by the National Science Foundation. The government has certain rights in the invention.
Number | Date | Country | |
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62062387 | Oct 2014 | US |