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1.
Small ; : e2402371, 2024 Apr 10.
Artículo en Inglés | MEDLINE | ID: mdl-38597692

RESUMEN

Quantum dot (QD) light-emitting diodes (QLEDs) are promising for next-generation displays, but suffer from carrier imbalance arising from lower hole injection compared to electron injection. A defect engineering strategy is reported to tackle transport limitations in nickel oxide-based inorganic hole-injection layers (HILs) and find that hole injection is able to enhance in high-performance InP QLEDs using the newly designed material. Through optoelectronic simulations, how the electronic properties of NiOx affect hole injection efficiency into an InP QD layer, finding that efficient hole injection depends on lowering the hole injection barrier and enhancing the acceptor density of NiOx is explored. Li doping and oxygen enriching are identified as effective strategies to control intrinsic and extrinsic defects in NiOx, thereby increasing acceptor density, as evidenced by density functional theory calculations and experimental validation. With fine-tuned inorganic HIL, InP QLEDs exhibit a luminance of 45 200 cd m-2 and an external quantum efficiency of 19.9%, surpassing previous inorganic HIL-based QLEDs. This study provides a path to designing inorganic materials for more efficient and sustainable lighting and display technologies.

2.
Nature ; 624(7991): 289-294, 2023 Dec.
Artículo en Inglés | MEDLINE | ID: mdl-37871614

RESUMEN

Inverted perovskite solar cells (PSCs) promise enhanced operating stability compared to their normal-structure counterparts1-3. To improve efficiency further, it is crucial to combine effective light management with low interfacial losses4,5. Here we develop a conformal self-assembled monolayer (SAM) as the hole-selective contact on light-managing textured substrates. Molecular dynamics simulations indicate that cluster formation during phosphonic acid adsorption leads to incomplete SAM coverage. We devise a co-adsorbent strategy that disassembles high-order clusters, thus homogenizing the distribution of phosphonic acid molecules, and thereby minimizing interfacial recombination and improving electronic structures. We report a laboratory-measured power conversion efficiency (PCE) of 25.3% and a certified quasi-steady-state PCE of 24.8% for inverted PSCs, with a photocurrent approaching 95% of the Shockley-Queisser maximum. An encapsulated device having a PCE of 24.6% at room temperature retains 95% of its peak performance when stressed at 65 °C and 50% relative humidity following more than 1,000 h of maximum power point tracking under 1 sun illumination. This represents one of the most stable PSCs subjected to accelerated ageing: achieved with a PCE surpassing 24%. The engineering of phosphonic acid adsorption on textured substrates offers a promising avenue for efficient and stable PSCs. It is also anticipated to benefit other optoelectronic devices that require light management.

3.
Nano Lett ; 23(10): 4298-4303, 2023 May 24.
Artículo en Inglés | MEDLINE | ID: mdl-37166106

RESUMEN

Solution-processed colloidal quantum dots (CQDs) are promising materials for photodetectors operating in the short-wavelength infrared region (SWIR). Devices typically rely on CQD-based hole transport layers (HTL), such as CQDs treated using 1,2-ethanedithiol. Herein, we find that these HTL materials exhibit low carrier mobility, limiting the photodiode response speed. We develop instead inverted (p-i-n) SWIR photodetectors operating at 1370 nm, employing NiOx as the HTL, ultimately enabling 4× shorter fall times in photodiodes (∼800 ns for EDT and ∼200 ns for NiOx). Optoelectronic simulations reveal that the high carrier mobility of NiOx enhances the electric field in the active layer, decreasing the overall transport time and increasing photodetector response time.

4.
Nature ; 618(7963): 74-79, 2023 Jun.
Artículo en Inglés | MEDLINE | ID: mdl-36977463

RESUMEN

The tunable bandgaps and facile fabrication of perovskites make them attractive for multi-junction photovoltaics1,2. However, light-induced phase segregation limits their efficiency and stability3-5: this occurs in wide-bandgap (>1.65 electron volts) iodide/bromide mixed perovskite absorbers, and becomes even more acute in the top cells of triple-junction solar photovoltaics that require a fully 2.0-electron-volt bandgap absorber2,6. Here we report that lattice distortion in iodide/bromide mixed perovskites is correlated with the suppression of phase segregation, generating an increased ion-migration energy barrier arising from the decreased average interatomic distance between the A-site cation and iodide. Using an approximately 2.0-electron-volt rubidium/caesium mixed-cation inorganic perovskite with large lattice distortion in the top subcell, we fabricated all-perovskite triple-junction solar cells and achieved an efficiency of 24.3 per cent (23.3 per cent certified quasi-steady-state efficiency) with an open-circuit voltage of 3.21 volts. This is, to our knowledge, the first reported certified efficiency for perovskite-based triple-junction solar cells. The triple-junction devices retain 80 per cent of their initial efficiency following 420 hours of operation at the maximum power point.

5.
J Am Chem Soc ; 145(11): 6428-6433, 2023 Mar 22.
Artículo en Inglés | MEDLINE | ID: mdl-36897963

RESUMEN

Indium phosphide (InP) quantum dots have enabled light-emitting diodes (LEDs) that are heavy-metal-free, narrow in emission linewidth, and physically flexible. However, ZnO/ZnMgO, the electron-transporting layer (ETL) in high-performance red InP/ZnSe/ZnS LEDs, suffers from high defect densities, quenches luminescence when deposited on InP, and induces performance degradation that arises due to trap migration from the ETL to the InP emitting layer. We posited that the formation of Zn2+ traps on the outer ZnS shell, combined with sulfur and oxygen vacancy migration between ZnO/ZnMgO and InP, may account for this issue. We synthesized therefore a bifunctional ETL (CNT2T, 3',3'″,3'″″-(1,3,5-triazine-2,4,6-triyl)tris(([1,1'-biphenyl]-3-carbonitrile)) designed to passivate Zn2+ traps locally and in situ and to prevent vacancy migration between layers: the backbone of the small molecule ETL contains a triazine electron-withdrawing unit to ensure sufficient electron mobility (6 × 10-4 cm2 V-1 s-1), and the star-shaped structure with multiple cyano groups provides effective passivation of the ZnS surface. We report as a result red InP LEDs having an EQE of 15% and a luminance of over 12,000 cd m-2; this represents a record among organic-ETL-based red InP LEDs.

6.
Adv Mater ; 35(8): e2209486, 2023 Feb.
Artículo en Inglés | MEDLINE | ID: mdl-36496257

RESUMEN

Semiconducting lead halide perovskite nanocrystals (PNCs) are regarded as promising candidates for next-generation optoelectronic devices due to their solution processability and outstanding optoelectronic properties. While the field of light-emitting diodes (LEDs) and photovoltaics (PVs), two prime examples of optoelectronic devices, has recently seen a multitude of efforts toward high-performance PNC-based devices, realizing both devices with high efficiencies and stabilities through a single PNC processing strategy has remained a challenge.  In this work, diphenylpropylammonium (DPAI) surface ligands, found through a judicious ab-initio-based ligand search, are shown to provide a solution to this problem. The universal PNC ink with DPAI ligands presented here, prepared through a solution-phase ligand-exchange process, simultaneously allows single-step processed LED and PV devices with peak electroluminescence external quantum efficiency of 17.00% and power conversion efficiency of 14.92% (stabilized output 14.00%), respectively. It is revealed that a careful design of the aromatic rings such as in DPAI is the decisive factor in bestowing such high performances, ease of solution processing, and improved phase stability up to 120 days. This work illustrates the power of ligand design in producing PNC ink formulations for high-throughput production of optoelectronic devices; it also paves a path for "dual-mode" devices with both PV and LED functionalities.

7.
J Am Chem Soc ; 144(45): 20923-20930, 2022 Nov 16.
Artículo en Inglés | MEDLINE | ID: mdl-36327099

RESUMEN

InP-based quantum dot (QD) light-emitting diodes (QLEDs) provide a heavy-metal-free route to size-tuned LEDs having high efficiency. The stability of QLEDs may be enhanced by replacing organic hole-injection layers (HILs) with inorganic layers. However, inorganic HILs reported to date suffer from inefficient hole injection, the result of their shallow work functions. Here, we investigate the tuning of the work function of nickel oxide (NiOx) HILs using self-assembled molecules (SAMs). Density functional theory simulations and near-edge X-ray absorption fine structure put a particular focus onto the molecular orientation of the SAMs in tuning the work function of the NiOx HIL. We find that orientation plays an even stronger role than does the underlying molecular dipole itself: SAMs having the strongest electron-withdrawing nitro group (NO2), despite having a high intrinsic dipole, show limited work function tuning, something we assign to their orientation parallel to the NiOx surface. We further find that the NO2 group─which delocalizes electrons over the molecule by resonance─induces a deep lowest unoccupied molecular orbital level that accepts electrons from QDs, producing luminescence quenching. In contrast, SAMs containing a trifluoromethyl group exhibit an angled orientation relative to the NiOx surface, better activating hole injection into the active layer without inducing luminescence quenching. We report an external quantum efficiency (EQE) of 18.8%─the highest EQE among inorganic HIL-based QLEDs (including Cd-based QDs)─in InP QLEDs employing inorganic HILs.

8.
Small ; 18(5): e2104933, 2022 02.
Artículo en Inglés | MEDLINE | ID: mdl-34846779

RESUMEN

π-Conjugated polyelectrolytes (CPEs) have been studied as interlayers on top of a separate hole transport layer (HTL) to improve the wetting, interfacial defect passivation, and crystal growth of perovskites. However, very few CPE-based HTLs have been reported without rational molecular design as ideal HTLs for perovskite solar cells (PeSCs). In this study, the authors synthesize a triphenylamine-based anionic CPE (TPAFS-TMA) as an HTL for p-i-n-type PeSCs. TPAFS-TMA has appropriate frontier molecular orbital (FMO) levels similar to those of the commonly used poly(bis(4-phenyl)-2,4,6-trimethylphenylamine) (PTAA) HTL. The ionic and semiconducting TPAFS-TMA shows high compatibility, high transmittance, appropriate FMO energy levels for hole extraction and electron blocking, as well as defect passivating properties, which are confirmed using various optical and electrical analyses. Thus, the PeSC with the TPAFS-TMA HTL exhibits the best power conversion efficiency (PCE) of 20.86%, which is better than that of the PTAA-based device (PCE of 19.97%). In addition, it exhibits negligible device-to-device variations in its photovoltaic performance, contrary to the device with PTAA. Finally, a large-area PeSC (1 cm2 ) and mini-module (3 cm2 ), showing PCEs of 19.46% and 18.41%, respectively, are successfully fabricated. The newly synthesized TPAFS-TMA may suggest its great potential as an HTL for large-area PeSCs.


Asunto(s)
Energía Solar , Compuestos de Calcio/química , Óxidos/química , Polielectrolitos , Titanio
9.
ACS Nano ; 14(10): 13246-13255, 2020 Oct 27.
Artículo en Inglés | MEDLINE | ID: mdl-32910640

RESUMEN

A series of poly(fluorene-co-phenylene)-based anionic conjugated polyelectrolytes (CPEs) are prepared with varying sizes of counterions (tetramethylammonium, tetraethylammonium, and tetrabutylammonium (TBA+)) and studied as a hole-transporting layer (HTL) for sky-blue-emissive perovskite light-emitting diodes (PeLEDs). Ionic CPE HTLs improve the wettability, compatibility, and nucleation of perovskite crystals at interfaces, enabling highly crystalline perovskite crystal growth with enhanced light-emitting properties. By incorporating the CPE HTLs containing bulky TBA+ counterions (MPS2-TBA) in place of PEDOT:PSS, the decreased phonon-electron coupling and increased exciton binding energy in perovskites are measured by temperature-dependent photoluminescence (PL) measurements. By increasing the size of counterions in CPE interlayers, the PL intensities and lifetimes of perovskite films increase. Through space-charge-limited current measurements, the lowest trap density is measured in the perovskite film on MPS2-TBA, emphasizing a critical role of larger counterions. Using density functional theory, MPS2-TBA is calculated to show the strongest adsorption affinity toward the interstitial defect of lead ions, explaining its pronounced interfacial defect passivation. The counterion size in CPE interlayers is interpreted as a main factor to determine the adsorption affinity onto perovskite, which determines the interacted area as noncovalent adsorption occurs. Finally, the sky-blue-emissive quasi-2D PeLED with MPS2-TBA shows the highest luminance efficiency (a peak EQE of 2.6% at 489 nm) and significantly improved spectral stability.

10.
Adv Mater ; 32(30): e2002333, 2020 Jul.
Artículo en Inglés | MEDLINE | ID: mdl-32567159

RESUMEN

A series of anionic conjugated polyelectrolytes (CPEs) is synthesized based on poly(fluorene-co-phenylene) by varying the side-chain ionic density from two to six per repeat units (MPS2-TMA, MPS4-TMA, and MPS6-TMA). The effect of MPS2, 4, 6-TMA as interlayers on top of a hole-extraction layer of poly(bis(4-phenyl)-2,4,6-trimethylphenylamine (PTAA) is investigated in inverted perovskite solar cells (PeSCs). Owing to the improved wettability of perovskites on hydrophobic PTAA with the CPEs, the PeSCs with CPE interlayers demonstrate a significantly enhanced device performance, with negligible device-to-device dependence relative to the reference PeSC without CPEs. By increasing the ionic density in the MPS-TMA interlayers, the wetting, interfacial defect passivation, and crystal growth of the perovskites are significantly improved without increasing the series resistance of the PeSCs. In particular, the open-circuit voltage increases from 1.06 V for the PeSC with MPS2-TMA to 1.11 V for the PeSC with MPS6-TMA. The trap densities of the PeSCs with MPS2,4,6-TMA are further analyzed using frequency-dependent capacitance measurements. Finally, a large-area (1 cm2 ) PeSC is successfully fabricated with MPS6-TMA, showing a power conversion efficiency of 18.38% with negligible hysteresis and a stable power output under light soaking for 60 s.

11.
ACS Appl Mater Interfaces ; 12(2): 2417-2423, 2020 Jan 15.
Artículo en Inglés | MEDLINE | ID: mdl-31856562

RESUMEN

Tin oxide (SnO2) is widely adopted as an electron transport layer in perovskite solar cells (PeSCs) because it has high electron mobility, excellent charge selective behavior owing to a large band gap of 3.76 eV, and low-temperature processibility. To achieve highly efficient SnO2-based PeSCs, it is necessary to control the oxygen vacancies in the SnO2 layer, since the electrical and optical properties vary depending on the oxidation state of Sn. This study demonstrates that the performance of PeSCs may be improved by using nitrogen-doped graphene oxide (NGO) as an oxidizing agent for SnO2. Since NGO changes the oxidation state of the Sn in SnO2 from Sn2+ to Sn4+, the oxygen vacancies in SnO2 can be reduced using NGO. Multiple devices are fabricated, and various techniques are used to assess their performance, including X-ray photoelectron spectroscopy, dark current analysis, and the dependence of the open-circuit voltage on light intensity. Compared with the average power conversion efficiency (PCE) of control devices, PeSCs with SnO2:NGO composite layers exhibit greater PCEs with less deviation. Therefore, the introduction of NGO in a SnO2 layer can be regarded as an effective method of controlling the oxidation state of SnO2 to improve the performance of PeSCs.

12.
ACS Appl Mater Interfaces ; 11(42): 39274-39282, 2019 Oct 23.
Artículo en Inglés | MEDLINE | ID: mdl-31573174

RESUMEN

Metal halide perovskites have been actively studied as promising materials in optoelectronic devices because of their superior optical and electrical properties and have also shown considerable potential for flexible devices because of their good mechanical properties. However, the large hole injection barrier and exciton quenching between the perovskite emitter and poly(3,4-ethylenedioxythiophene):poly-styrene sulfonate (PEDOT:PSS) can lead to the reduction in device efficiency. Here, a nonconductive fluorosurfactant, Zonyl FS-300 (Zonyl), is introduced into the PEDOT:PSS hole transport layer, which reduces the hole injection barrier and exciton quenching at the PEDOT:PSS/perovskite interface. Moreover, a flexible perovskite light-emitting diode with a polymer-silver nanowire composite electrode is demonstrated, showing a maximum current efficiency (CEmax) of 17.90 cd A-1, and this is maintained even after 1000 cycles of bending with a 2.5 mm bending radius.

13.
Nano Lett ; 19(6): 3707-3715, 2019 06 12.
Artículo en Inglés | MEDLINE | ID: mdl-31117753

RESUMEN

The mechanical flexibility of perovskite solar cells as well as high power conversion efficiency is attracting increasing attention. In addition to existing empirical approaches, such as cyclic bending tests, in this study we report the tensile properties of the perovskite materials themselves. Measuring the tensile properties of free-standing perovskite materials is critical because (1) tensile properties represent the realistic mechanical properties of the film-type perovskite layer in the solar cells including the effects of various defects, and (2) deformation behavior of the perovskite layer at any deformed state of the solar cells can be analyzed using solid mechanics with the tensile properties as input. Critical bending radius of MAPbI3-based flexible solar cells is found to be between 0.5 and 1.0 mm by the decrease in power conversion efficiency during cyclic bending deformation. This finding agrees well with the critical bending radius of 0.66 mm determined based on the elastic deformation limit of 1.17% for MAPbI3 found by in situ tensile testing. Scanning electron microscopy observations and hole-nanoindentation tests suggest that the formation of coarse cracks in the perovskite layers is the primary cause of the decrease in power conversion efficiency observed in flexible perovskite solar cells.

14.
ACS Appl Mater Interfaces ; 11(23): 21069-21077, 2019 Jun 12.
Artículo en Inglés | MEDLINE | ID: mdl-31094197

RESUMEN

A novel flexible transparent electrode (TE) having a trilayer-stacked geometry and high optoelectronic performance and operational stability was fabricated by the spin coating method. The trilayer was composed of an ultrathin graphene (Gr) film sandwiched between a transparent and colorless polyimide (TCPI) layer and a methanesulfonic acid (MSA)-treated poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) layer containing dimethylsulfoxide and Zonyl fluorosurfactant (designated as MSA-PDZ film). The introduction of solution-processable TCPI enabled the direct formation of high-quality graphene on organic surfaces with a clean interface. Stable doping of graphene with the MSA-PDZ film enabled tuning of the inherent work function and optoelectronic properties of the PEDOT:PSS films, leading to a high figure of merit of ∼70 in the as-fabricated TEs. Particularly, from multivariate and repetitive harsh environmental tests ( T = -50 to 90 °C, over 90 RH%), the TCPI/Gr heterostructure exhibited excellent tolerance to mechanical and thermal stresses and gas barrier properties that protected the MSA-PDZ film from exposure to moisture. Owing to the synergetic effect from the TCPI/Gr/MSA-PDZ anode structure, the TCPI/Gr/MSA-PDZ-based polymer light-emitting diodes showed highly improved current and power efficiencies with maxima as high as 20.84 cd/A and 22.92 lm/W, respectively (comparable to those of indium tin oxide based PLEDs), in addition to much enhanced mechanical flexibility.

15.
Nano Lett ; 19(2): 971-976, 2019 02 13.
Artículo en Inglés | MEDLINE | ID: mdl-30608699

RESUMEN

Organic-inorganic hybrid perovskites have been investigated extensively for use in perovskite-based solar cells and light-emitting diodes (LEDs) because of their excellent electrical and optical properties. Although the flexibility of perovskite LEDs has been studied through empirical methods such as cyclic bending tests, the flexibility of the perovskite layer has not been investigated systemically. Here, flexible and semitransparent perovskite LEDs are fabricated: a PEDOT:PSS anode and Ag nanowire cathode allow for flexible and semitransparent devices, while the use of a conjugated polyelectrolyte as an interfacial layer reduces the electron injection barrier between the cathode and the electron transport layer (SPW-111), resulting in enhanced device efficiency. Cyclic bending tests performed on the electrodes and in situ hole-nanoindentation tests performed on the constituent materials suggest that mechanical failure occurs in the perovskite MAPbBr3 layer during cyclic bending, leading to a decrease in the luminance. Tensile properties of the MAPbBr3 layer explain the critical bending radius ( rb) of the perovskite LEDs on the order of 1 mm.

16.
Adv Mater ; 31(6): e1805554, 2019 Feb.
Artículo en Inglés | MEDLINE | ID: mdl-30549300

RESUMEN

The addition of chemical additives is considered as a promising approach for obtaining high-quality perovskite films under mild conditions, which is essential for both the efficiency and the stability of organic-inorganic hybrid perovskite solar cells (PeSCs). Although such additive engineering yields high-quality films, the inherent insulating property of the chemical additives prevents the efficient transport and extraction of charge carriers, thereby limiting the applicability of this approach. Here, it is shown that organic conjugated molecules having rhodanine moieties (i.e., SA-1 and SA-2) can be used as semiconducting chemical additives that simultaneously yield large-sized perovskite grains and improve the charge extraction. Using this strategy, a high power conversion efficiency of 20.3% as well as significantly improved long-term stability under humid air conditions is achieved. It is believed that this approach can provide a new pathway to designing chemical additives for further improving the efficiency and stability of PeSCs.

17.
Materials (Basel) ; 11(11)2018 Nov 05.
Artículo en Inglés | MEDLINE | ID: mdl-30400607

RESUMEN

Herein, a novel strategy to fabricate haze films employing liquid crystal (LC) technology for photovoltaic (PV) applications is reported. We fabricated a high optical haze film composed of low-molecular LCs and polymer and applied the film to improve the energy conversion efficiency of PV module. The technique utilized to fabricate our haze film is based on spontaneous polymerization-induced phase separation between LCs and polymers. With optimized fabrication conditions, the haze film exhibited an optical haze value over 95% at 550 nm. By simply attaching our haze film onto the front surface of a silicon-based PV module, an overall average enhancement of 2.8% in power conversion efficiency was achieved in comparison with a PV module without our haze film.

18.
ACS Nano ; 12(6): 5826-5833, 2018 Jun 26.
Artículo en Inglés | MEDLINE | ID: mdl-29787241

RESUMEN

Perovskite-based optoelectronic devices have been rapidly developing in the past 5 years. Since the first report, the external quantum efficiency (EQE) of perovskite light-emitting diodes (PeLEDs) has increased rapidly through the control of morphology and structure from 0.1% to more than 11%. Here, we report the use of various conjugated polyelectrolytes (CPEs) as the hole injection layer in PeLEDs. In particular, we find that poly[2,6-(4,4-bis-potassium butanylsulfonate)-4 H-cyclopenta-[2,1- b;3,4- b']-dithiophene)] (PCPDT-K) transfers holes effectively, blocks electron transport from the perovskite to the underlying ITO layer, and reduces luminescence quenching at the perovskite/PCPDT-K interface. Our optimized PeLEDs with PCPDT-K show enhanced EQE by a factor of approximately 4 compared to control PeLEDs with PEDOT:PSS, reaching EQE values of 5.66%, and exhibit improved device stability.

19.
ACS Nano ; 12(4): 3417-3423, 2018 04 24.
Artículo en Inglés | MEDLINE | ID: mdl-29561134

RESUMEN

Organic-inorganic hybrid perovskites are emerging as promising emitting materials due to their narrow full-width at half-maximum emissions, color tunability, and high photoluminescence quantum yields (PLQYs). However, the thermal generation of free charges at room temperature results in a low radiative recombination rate and an excitation-intensity-dependent PLQY, which is associated with the trap density. Here, we report perovskite films composed of uniform nanosized single crystals (average diameter = 31.7 nm) produced by introducing bulky amine ligands and performing the growth at a lower temperature. By effectively controlling the crystal growth, we maximized the radiative bimolecular recombination yield by reducing the trap density and spatially confining the charges. Finally, highly bright and efficient green emissive perovskite light-emitting diodes that do not suffer from electroluminescence blinking were achieved with a luminance of up to 55 400 cd m-2, current efficiency of 55.2 cd A-1, and external quantum efficiency of 12.1%.

20.
Adv Mater ; 30(14): e1706034, 2018 Apr.
Artículo en Inglés | MEDLINE | ID: mdl-29450928

RESUMEN

Conjugated polyelectrolytes (CPEs) with π-delocalized main backbones and ionic pendant groups are intensively studied as interfacial layers for efficient polymer-based optoelectronic devices (POEDs) because they facilitate facile control of charge injection/extraction barriers. Here, a simple and effective method of performing precise interfacial energy level adjustment is presented by employing CPEs with different thicknesses and various ion densities under electric poling to realize efficient charge injection/extraction of POEDs. The effects of the CPE ion densities and electric (positive or negative) poling on the energy level tuning process are investigated by measuring the open-circuit voltages and current densities of devices with the structure indium tin oxide/zinc oxide/CPE/organic active layer/molybdenum oxide/gold while changing the CPE film thickness. The performances of inverted polymer light-emitting diodes and inverted polymer solar cells are remarkably improved by precisely controlling the interfacial energy level matching using optimum CPE conditions.

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