A dye-sensitized photo-supercapacitor based on PProDOT-Et2 thick films

A photo-rechargeable supercapacitor (photo-supercapacitor, or PSC) is studied using a N3-dye adsorbed TiO₂ photoelectrode and PProDOT-Et₂ poly(3,3-diethyl-3,4-dihydro-2H-thieno-[3,4-b][1,4]dioxepine) polymer films as supercapacitor materials for electron storage. The PSC device, comprising a dye-sensitized solar cell (DSSC) and a supercapacitor (SC), can store the photo-to-electric energy. The PProDOT-Et₂ films are potentiostatically electropolymerized to form thick films (ca. 0.5 mm) with a specific capacitance of ca. 6.5 F cm⁻². A symmetrical (p/p) supercapacitor, with PProDOT-Et₂ coated on both electrodes, is also characterized before fabricating the three-electrode PSC. The PSC is tested under light illumination of 100 mW cm⁻², and attaining a photocharged voltage of 0.75 V and a discharged energy density of 21.3 μWh cm⁻².     

Columnar rutile TiO2 based dye-sensitized solar cells by radio-frequency magnetron sputtering

Columnar-structured rutile TiO₂ film with a thickness of 1.4 μm is prepared using the radio-frequency (RF) magnetron sputtering technique, for application in dye-sensitized solar cells (DSSCs). Pure rutile TiO₂ films are fabricated by controlling the substrate temperature during sputtering and using a substrate with a rough surface morphology. Successive substrate heating to 623 K induces the growth of a rutile TiO₂ film that has a specific direction in the (1 1 0) plane, which results in a decrease in the average grain size. This causes in an increase of dye uptake and thereby contributes to enhancement of the photocurrent in the DSSC.     

On the photophysical and electrochemical studies of dye-sensitized solar cells with the new dye CYC-B1

In this study, the photoelectrochemical characteristics of a ruthenium photosensitizer with an alkyl bithiophene group, designated as CYC-B1, are studied. The effect of mesoporous TiO₂ film thickness on the photovoltaic performance of CYC-B1 and N3 dye-sensitized solar cells was investigated. The performance of the dye-sensitized nanocrystalline TiO₂ solar cells (DSSC) fabricated using CYC-B1 dye-anchored TiO₂ photoelectrode showed a convincing enhancement in cell efficiency when the TiO₂ film thickness was increased from 3 μm (eff.=5.41%) to 6 μm (eff.=7.19%). The efficiency of the CYC-B1-sensitized DSSC was maximum at 6 μm of the TiO₂ film thickness, reached its limiting value and remained constant up to 53 μm, although a similar trend was also observed for N3 dye-sensitized DSSC, however, the maximum efficiency achieved was only at 27 μm thickness (eff.=6.75%). As expected, the photocurrent density generated in the DSSC modified by CYC-B1 dye is larger than that from N3 dye. The effect of guanidinium thiocyanate (GuSCN) (additive) addition to the electrolyte on the photovoltaic performance of DSSCs based on CYC-B1 was also investigated. Furthermore, the electrochemical impedance spectroscopy (EIS) technique and photo-transient laser method have been employed to analyze the charge transfer resistances (R_ct) and the lifetime of the injected electrons on the TiO₂ containing different thicknesses.     

High efficiency flexible dye-sensitized solar cells by multiple electrophoretic depositions

A multiple electrophoretic deposition (EPD) of binder-free TiO₂ photoanode has been developed to successfully fill the crack occurring after air-drying on the first EPD-TiO₂ film surface. With the slow 2nd EPD, high quality TiO₂ thin films are acquired on flexible ITO/PEN substrates at room temperature and the device efficiency of the dye-sensitized solar cell achieved 5.54% with a high fill factor of 0.721. Electrochemical impedance spectroscopy measurements analyze the great enhancement of the photovoltaic performance through multiple EPD. The electron diffusion coefficient improved by about 1 order of magnitude in crack-less multiple-EPD TiO₂ films. With the scattering layer, the device reveals a high conversion efficiency of up to 6.63% under AM 1.5 G one sun irradiation, having a short circuit current density, open circuit voltage, and filling factor of 12.06 mA cm⁻², 0.763 V and 0.72, respectively.     

Thickness effect of RF sputtered TiO2 passivating layer on the performance of dye-sensitized solar cells

We report on the characteristics of a TiO₂ passivating layer grown by radio frequency (RF) magnetron sputtering on F-doped SnO₂ (FTO) electrodes as a function of its thickness. The optical transparency, surface roughness and passivation properties of the TiO₂ layer passivating the FTO electrode depend on the thickness of the TiO₂ passivating layer. In addition, it was found that the power conversion efficiency of the dye-sensitized solar cells (DSSCs) is critically dependent on the thickness of RF sputtered TiO₂ layer inserted between FTO electrode and nanoporous TiO₂ layer. The DSSC fabricated on 50 nm thick TiO₂ passivating FTO electrode showed the maximum power conversion efficiency of 4.42% due to effective prevention of the electron transfer to electrolyte. This indicates that the thickness optimization of the TiO₂ passivating layer is one of the important parameter to obtain high performance DSSCs.     

Fabrication of multilayer TiO2 thin films for dye-sensitized solar cells with high conversion efficiency by electrophoresis deposition

This research coats a commercial TiO₂ nanoparticle Degussa P25 with good roundness and size uniformity on an indium tin oxide (ITO) glass substrate and to be photoelectrical electrode by electrophoresis deposition. It combined with dye N719, electrolyte I^-/ and counter-electrode of Pt layer to produce dye-sensitized solar cells (DSSCs). Through the electrophoretic technique, a multilayer film of an appropriate thickness is deposited in the suspension containing TiO₂ nanoparticles and isopropanol. In this process, electric current, voltage, and the number of deposition cycles are well controlled to obtain a single TiO₂ film of around 3.3 μm thick. Stacking is then performed to obtain a multilayer-typed TiO₂ film of around 12 μm thick. As the sintering temperature reaches 400 °C, the prepared multilayer TiO₂ film with a good compactness can increase the dye adsorption capability of the thin film and enhance its adsorption percentage. In addition, the heat treatment will transfer a portion of the rutile crystalline into the anatase crystalline, resulting in better material properties for DSSCs application. DSSCs produced are exposed to metal halide lamp and their energy conversion efficiency is measured. The I-V curve of the produced DSSCs shows that it has an excellent energy conversion efficiency of 6.9%.     

Mechanical flexibility of transparent PEDOT:PSS electrodes prepared by gravure printing for flexible organic solar cells

The mechanical flexibility of transparent poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) films printed onto a flexible PET substrate using a gravure printing method was investigated using a lab-made bending test system. Gravure-printed PEDOT:PSS electrodes with a sheet resistance of 359 Ω/square and a transparency of 88.92% showed outstanding flexibility in several types of flexibility tests, including outer/inner bending, twisting and stretching. Notably, the PEDOT:PSS electrode had a constant resistance change (ΔR/R₀) within an outer and inner bending radius of 10 mm. In addition the stretched PEDOT:PSS electrode showed a fairly constant resistance change (ΔR/R₀) up to 4%, which is more stable than the resistance change of conventional amorphous ITO electrode. The twisting test revealed that the resistance of the PEDOT:PSS electrode began to increase at an angle of 36° due to delamination of the film from the PET substrate. Despite the high sheet resistance of the PEDOT:PSS electrode the flexible organic solar cells fabricated on the PEDOT:PSS electrode showed a power conversion efficiency of ∼2% (FF: 44.9%, V_o: 0.495 V and J_sc: 9.1 mA/cm²), indicating the possibility of using gravure printed PEDOT:PSS as a flexible and transparent electrode for printing-based flexible organic solar cells.     

Low-temperature oxygen plasma treatment of TiO2 film for enhanced performance of dye-sensitized solar cells

The effects of low-temperature O₂ plasma treatment of a TiO₂ film are studied with the objective of improving the performance of dye-sensitized solar cells (DSSCs). X-ray photoelectron spectra (XPS) reveal that the ratio of titanium dioxide to titanium sub-oxides is increased in the O₂ plasma-treated TiO₂ film, compared with that of the untreated TiO₂ film. This increase suggests that the oxygen vacancies in the film are effectively reduced. The near-edge X-ray absorption fine structure (NEXAFS) spectra results agree with the XPS result. It is proposed that there is a correlation between the shifts of the peaks in the NEXAFS spectra and the adsorption of N719 dye on the TiO₂ particles. A DSSC having an O₂ plasma-treated, 4 μm thick TiO₂ film electrode renders a short-circuit photocurrent of 7.59 mA cm⁻², compared with 6.53 mA cm⁻² for a reference cell with an untreated TiO₂ electrode of the same thickness. As a result of these changes, the solar-to-electricity conversion efficiency of the O₂ plasma-treated cell is found to be 4.0% as compared with 3.5% for the untreated cell. This improvement in the performance is rationalized on the basis of increased N719 dye adsorption on to the TiO₂, due to the reduction in the number of oxygen vacancies caused by the oxygen plasma treatment.     

Using modified poly(3,4-ethylene dioxythiophene): Poly(styrene sulfonate) film as a counter electrode in dye-sensitized solar cells

Dye-sensitized solar cells (DSSCs), assembling with nano-crystalline TiO₂ adsorbed cis-Ru(dcb)₂(NCS)₂ dye (known as N3) using polar solvent-treated poly(3,4-ethylene dioxythiophene): poly(styrene sulfonate) (PEDOT:PSS) coating on a conductive glass (fluorine-doped tin oxide, FTO) as a counter electrode, were studied. The conductivity of a bare PEDOT:PSS film was only 2±0.05 S/cm. However, the conductivities of PEDOT:PSS films treated with dimethyl sulfoxide (DMSO), N,N-dimethyl acetamide (DMAc), N,N-dimethyl formamide (DMF), and dichloromethane (DMC) reached 85±15, 45±10, 36±7, and 20±6 S/cm, respectively. In addition, carbon blacks (0.02, 0.1, 0.5, 1.0, 2.0 wt% with respect to PEDOT:PSS aqueous solution) were added into the DMSO-treated PEDOT:PSS solution (denoted as DMSO-PEDOT:PSS) to enhance the conductivity. Atomic force microscopy (AFM) images of PEDOT:PSS and various DMSO-PEDOT:PSS films coated on the FTO glasses were examined. The topographical images reveal that the increased surface roughness is responsible for the enhanced electrochemical property of the DMSO-PEDOT:PSS films. AC impedance technique was also employed to analyze the kinetics at the electrolyte/counter electrode interface. The DSSC using carbon black (0.1 wt%)-modified DMSO-PEDOT:PSS conductive coating as a counter electrode reached a cell efficiency of 5.81% under 100 mW/cm². This efficiency is higher than a DSSC using Pt as a counter electrode (5.66%).     

Hybrid inverted organic photovoltaic cells based on nanoporous TiO2 films and organic small molecules

Solar cells based on nanoporous TiO₂ films with an inverted structure of indium tin oxide (ITO)/TiO₂/copper phthalocyanine (CuPc):fullerene (C₆₀)/CuPc/poly(3,4-oxyethyleneoxythiophene):poly(styrene sulfonate) (PEDOT:PSS)/Au were fabricated. The best overall photovoltaic performance undergoing a series of device optimization was achieved with the device of ITO/dense TiO₂ (30 nm)/nanoporous TiO₂ (130 nm)/C₆₀:CuPc (1:6 weight) (20 nm)/CuPc (20 nm)/PEDOT:PSS (50 nm)/Au (30 nm). The device using the nanoporous TiO₂ films has better photovoltaic properties compared to those using dense TiO₂ films. Higher photovoltaic performances were obtained by introducing a coevaporated layer of C₆₀:CuPc between TiO₂ and CuPc. The stability of inverted structure was better than that of the normal device, which gives a promising way for fabrication of solar cells with improved stability.     

Effects of tetrabutoxytitanium on photoelectrochemical properties of plastic-based TiO2 film electrodes for flexible dye-sensitized solar cells

The flexible DSSCs based on conducting plastic substrates are fabricated using electrodes made of tetrabutoxytitanium (TBOT) mixed with P25 TiO₂ nanoparticles at low temperature. To investigate the effects of TBOT on the flexible dye-sensitized solar cells, electrochemical impedance spectroscopy (EIS) is performed in the dark and under illumination conditions. Resistances for electron transport through TiO₂, charge-transfer resistance related to the TiO₂/redox electrolytes interface recombination, electron transport time and electron lifetime are quantified under different weight ratios of TBOT/P25. Additionally, the photovoltaic characteristics I-V curves and incident photon to current conversion efficiencies (IPCE) of flexible anodes made of different weight ratios of TBOT/P25 are obtained as well. It is found that the electrode under weight ratio 0.17 has the smallest inherent resistance, longest electron transport time and electron lifetime, lowest recombination rate and best performance with conversion efficiency 3.94%. These results indicate that after the weight ratios of TBOT/P25 is optimized, TBOT could enhance the interconnection between the TiO₂ particles, improve the conductivity of the electrode and decrease the charge recombination. Above results demonstrate that adding TBOT to TiO₂ is an easy and efficient method to improve the performance of the flexible DSSC fabricated at low temperature.     

Influences of different TiO2 morphologies and solvents on the photovoltaic performance of dye-sensitized solar cells

The effects of TiO₂ photoelectrode's surface morphology and different solvents on the photovoltaic performance of dye-sensitized solar cells (DSSCs) were studied. By successive coating of TiO₂ suspension, composed of low and high molecular weight poly(ethylene)glycol (PEG) as a binder, double layered TiO₂ photoelectrodes with four different structures were obtained. Among the DSSCs with different TiO₂ electrodes, DSSC with P2P1 electrode (P2 and P1 correspond to PEG molecular weights of 20,000 and 200,000, respectively) showed higher performance under identical film thickness at a constant irradiation of 100 mW cm⁻², which may be correlated with large pore size and high surface area of the corresponding TiO₂ electrode. This was confirmed by electrochemical impedance spectroscopy (EIS) analysis of the DSSC and the transient photovoltage measurement of electrons in the TiO₂ electrode. Among the different solvents investigated here, the DSSC containing acetonitrile showed high conversion efficiency and the order of performance of the DSSCs with different solvents were AN > MPN > PC > GBL > DMA > DMF > DMSO. Better correlation was observed between the donor number of solvents and photoelectrochemical parameters of the DSSCs containing different solvents rather than the measured viscosity and dielectric constant of solvents. The reasons for the low performance of the DSSCs containing DMA, DMSO and DMF, respectively, were due to the negative shift of TiO₂ conduction band and the desorption of dye molecules from the TiO₂ photoelectrode by those solvents.     

A simple method to prepare uniform-size nanoparticle TiO2 electrodes for dye-sensitized solar cells

Nanoparticle TiO₂ electrodes are fabricated using an improved electrostatic spray coating (ESC) method which is more simple, low cost and well reproducible comparing with the conventional method of preparing electrode for dye-sensitized solar cells (DSSC) by introducing monoethanolamine (MEA) into precursor solution. It is surprised to find that high transparency of films and good adhesion between film and substrate achieve and that particles size can be easily controlled by adjusting the proportion of MEA. The relationship between particles size and proportion of MEA added is presented in our work. After samples with various particle sizes are applied in DSSC, an increase of open-circuit voltage (V_oc) from 620 mV to 765 mV is observed with the increase of particle size from 8 nm to 48 nm. Associated with photoluminescence results, we ascribe the change of V_oc to the different dominative states of films: surface defects and oxygen vacancies in 8 nm films, oxygen vacancy defects in 25 nm films and higher crystal quality with little of both defects in 48 nm films. In addition, different thickness films with optimized proportion of MEA is applied in DSSC, an overall light to electricity conversion efficiency (η) of 2.91% is obtained with a thickness of 2.0 μm.     

Synthesis of TiO2 submicro-rings and their application in dye-sensitized solar cell

In this paper, novel TiO₂ submicro-rings were synthesized via potentiostatic anodization of titanium powder coated on transparent conducting oxide glass. The TiO₂ submicro-rings film was characterized by SEM, XPS and 3D optical profiling. Accordingly, a possible growth mechanism of submicro-rings was discussed. The TiO₂ submicro-rings based dye-sensitized solar cell (DSSC) with the film thickness of ca. 3.1 μm was assembled and a conversion efficiency of 1.36% was achieved under AM 1.5 illumination. The photoelectron transport properties of TiO₂ submicro-rings based DSSC were also discussed according to the electron impedance spectroscopy.     

A high-performance counter electrode based on poly(3,4-alkylenedioxythiophene) for dye-sensitized solar cells

A poly(3,3-diethyl-3,4-dihydro-2H-thieno-[3,4-b][1,4]dioxepine) (PProDOT-Et₂) counter electrode prepared by electrochemical polymerization on a fluorine-doped tin oxide (FTO) glass substrate was incorporated in a platinum-free dye-sensitized solar cell (DSSC). The surface roughness and I⁻/I₃⁻ redox reaction behaviors based on PProDOT-Et₂, poly(3,4-propylenedioxythiophene) (PProDOT), poly(3,4-ethylenedioxythiophene) (PEDOT), and sputtered-Pt electrodes were characterized, and their performances as counter electrodes in DSSCs were compared. Cells fabricated with a PProDOT-Et₂ counter electrode showed a higher conversion efficiency of 7.88% compared to cells fabricated with PEDOT (3.93%), PProDOT (7.08%), and sputtered-Pt (7.77%) electrodes. This enhancement was attributed to increases in the effective surface area and good catalytic properties for I₃⁻ reduction. In terms of the film thickness effect, the fill factor was strongly dependent on the deposition charge capacity of the PProDOT-Et₂ layer, but the aggregation of PProDOT-Et₂ in thicker layers (>80 mC cm⁻²) resulted in decreases in J_SC and the cell conversion efficiency. The charge transfer resistances (R_ct1) of the PProDOT-Et₂ counter electrodes had the lowest value of ∼18 Ω at a deposition charge capacity of 40 mC cm⁻². These results indicate that films with high conductivity, high active surface area, and good catalytic properties for I₃⁻ reduction can potentially be used as the counter electrode in a high-performance DSSC.     

Fabrication of nanostructured titania on flexible substrate by electrochemical anodization

Titanium films were deposited on ITO (indium tin oxide)-coated PEN (polyethylene naphthalate) and flexible clay substrates by ion beam sputter deposition method. The surface morphology of the deposited films was smooth on PEN and rough on clay substrates. The titanium film deposited on Clay-mo (98% montmorillonite) substrate was anodized in ethylene glycol + 2 vol% H₂O + 0.3 wt% NH₄F solution, and the titanium films deposited on Clay-st (99% stevensite) substrate was anodized in 2-propanol + 16 vol% H₂O + 0.14 M NH₄F solution. Then nanohole-structured titania (TiO₂) films were firstly and successfully fabricated on the flexible transparent clay substrates. The nanohole structures of TiO₂ on both clay substrates were similar to those on PEN and glass substrates. The TiO₂ nanohole structure was almost maintained after annealing at 450 °C for 4 h in air. The optical transmittance of the nanohole-structured TiO₂ films on Clay-st increased from 26% to 54% at 800 nm in wavelength after annealing at 450 °C for 1 h in air.     

Preparation of flexible conductive composite electrode film of PEDOT:PSS/Aramid nanofibers via vacuum-assisted filtration and acid post-treatment for efficient solid-state supercapacitor

A highly conductive and flexible composite film of Poly (3,4-ethylenedioxythiophene):polystyrene sulfonate and aramid nanofiber (PEDOT:PSS/ANFs) is prepared by vacuum-assisted filtration and post-treated by acid. The composite displays excellent mechanical integrity under bending together with flexibility, properties being attributed to the strong attachment of PEDOT:PSS onto the surface of the ANFs via hydrogen bonding and the ANF structure, respectively. The conductivity of the prepared composite is progressively enhanced by the post-treatment using sulfuric acids (1 M H₂SO₄ and 1.5 M H₂SO₄), reaching 20–25 times higher than that of untreated film. This enhancement is traced to the removal of the insulating PSS group together with an analyzable change in crystallization of the PEDOT:PSS component. However, excessive use of acid treatment is seen to reduce the mechanical strength, and, thus, ultimate loss of conductivity after frequent bending (up to 1000 times), only having 59% conductivity retention with high concentration acid treatment (1.5 M H₂SO₄) compared to a high conductivity retention of 95% with 1.0 M H₂SO_4. Adopting the relatively weaker acid enables a balance to be reached between these crucial factors of electrical conductivity versus mechanical integrity. The prepared film of PEDOT: PSS/ANFs treated by acid as an electrode of supercapacitor shows good electrochemical performances, including good volumetric specific capacitance (83.5 F/cm³ with 1.0 M H₂SO₄ and 75 F/cm³ with 1.5 M H₂SO₄ at 0.5 A/cm^?3), cycle stability and capacitance retention of 83.3% and 87.5% after 2000 cycles, respectively. Furthermore, a solid flexible supercapacitor is finally assembled by the post-treatment of relatively low concentration acid with 1.0 M H₂SO_4. The configured supercapacitor displays excellent volumetric energy density of 23.44 mW h/cm² (power density of 399.95 mW/cm²) at a very wide operating potential window of 0–1.6 V and cycle stability. Therefore, it is quite feasible method to fabricate a highly conductive and flexible composite film using PEDOT:PSS and ANFs by vacuum filtration and acid post-treatment, which expects to be a promising flexible composite electrode material applied in the preparation of energy storage devices.     

Characteristics of triphenylamine-based dyes with multiple acceptors in application of dye-sensitized solar cells

We report the synthesis and photophysical/electrochemical properties of triphenylamine (TPA)-based multiple electron acceptor dyes (TPAR1, TPAR2, and TPAR3) as well as their applications in dye-sensitized solar cells (DSSCs). In these dyes, the TPA group and the rhodanine-3-acetic acid play the role of the basic electron donor unit and the electron acceptor, respectively. It was found that introduction of two rhodanine-3-acetic acid groups into the TPA unit (TPAR2) exhibited better photovoltaic performance due to the increase with a red shift and broadening of the absorption spectrum. The monolayer of these TPA-based dyes was adsorbed on the surface of nanocrystalline TiO₂ mesoporous electrode with the thickness of ∼6 μm, polyethylene oxide (PEO) used as the matrix of gel electrolyte, and 4-nm thick Pt used as a counter-electrode. Photovoltaic device can be realized in a single quasi-solid-state DSSC. TPAR2-based gel DSSC had an open circuit voltage and short circuit current density of about 541 and 10.7 mA cm⁻², respectively, at 1-sun.     

Cubic titanium dioxide photoanode for dye-sensitized solar cells

Following from the recently evolved concept of significantly improving the photovoltaic efficiency in dye-sensitized solar cells (DSSCs) by reducing the loss of electrons on the spherical surface of titanium dioxide, this study examines the synthesis of cubic TiO₂ with a special morphology to overcome this electron loss and investigates its application to DSSCs. Cubic TiO₂ is synthesized by an advanced rapid hydrothermal method, with the addition of an amine species additive. Transmission electron microscopy (TEM) images confirm the cubic shape of the TiO₂ particles with a diameter less than 5-10 nm. Using N719 dye under illumination with 100 mW cm⁻² simulated sunlight, the application of cubic TiO₂ to DSSCs affords an energy conversion efficiency of approximately 9.77% (4.0-μm thick TiO₂ film), which is considerably enhanced compared with that achieved using a commercial, spherical TiO₂. Electrostatic force microscopy (EFM) and impedance analyses reveal that the electrons are transferred more rapidly to the surface of a cubic TiO₂ film than on a spherical TiO₂ film.     

Patternable solution process for fabrication of flexible polymer solar cells using PDMS

PH 500, a highly conducting poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate) (PEDOT:PSS), is a typical conducting polymer anode material used in organic electric devices. However, it has the disadvantages of low conductivity and poor surface roughness and requires a patterning method for the electrode through including the laser and plasma. In this paper, therefore, the conducting polymer ink for a transparent anode was formulated by adding dimethyl sulfoxide (DMSO) and BYK-333 as the surfactant to enhance the conductivity and surface roughness. The conducting polymer anode was patterned through the application of a new patterning method that used polydimethylsiloxane (PDMS) on a flexible substrate. In addition, a photoactive layer was formed by applying the new patterning method to the conventional brush painting method in which patterning had previously been impossible. The resulting material was compared with the device fabricated by the spin coating method. The fabricated flexible polymer solar cells (PSCs) exhibited short-circuit current density (J_sc), open-circuit voltage (V_oc), fill factor (FF) and power conversion efficiency (PCE) values of 4.2 mA/cm², 0.878 V, 26.5% and 0.98%, respectively, which represented an efficiency improvement of 38% over those fabricated by the spin coating method. Meanwhile, the J_sc value was increased when the series resistance (R_s) decreased to 150 Ω cm².