Improved Hole Injection in Hybrid Light‐Emitting Transistors Incorporating Lithium and Copper(II) Poly(Styrene Sulfonate)

Light‐emitting transistors (LETs) are optoelectronic devices that perform switching and light‐emitting functions in a single device. Hybrid LETS (HLETs) using inorganic metal oxide semiconductors as the transport layer with organic emissive layers and hole‐injection layers (HILs) combine the excellent switching performance of metal oxides with the flexibility and tunability of organic semiconductors. However, the efficiency of n‐HLETs typically suffers from unbalanced electron and hole injection. To overcome this issue, two hybrid polyelectrolytes—lithium poly(styrene sulfonate) (Li:PSS) and copper(II) poly(styrene sulfonate) (Cu:PSS)—are investigated as HILs in HLETs. HLETs employing Cu:PSS interlayers exhibit significantly enhanced brightness values of up to 4.89 × 103 cd m−2 and an external quantum efficiency (EQE) of 0.45%, compared to HLETs without HIL (no emission) and pristine poly(3,4‐ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) (2.17 × 102 cd m−2 with an EQE of 0.01%). To understand how the HILs influence the performance, ultraviolet photoelectron spectroscopy (UPS) analysis and photoluminescence (PL) quenching studies are performed, which reveal improved energy band structure and reduced quenching using metal:PSS HILs. This work provides useful information about the function that polyelectrolyte HILs perform in HLET devices which may be exploited to develop new materials and applied in other types of optoelectronic devices.


Introduction
0][11][12][13][14][15] Despite the advantages of HLETs, ntype HLETs, which employ symmetric source (S) and drain (D) electrodes (composed of the same type of metal), are severely limited by localized emission regions beneath the drain electrode or even no emission due to the imbalance between electrons (majority carrier) and hole (minority carrier) injection.In particular, for n-channel HLETs, which employ high-mobility n-type metal oxide transport layers such as ZnO, In 2 O 3 , or indium-gallium-zinc oxide (IGZO), relatively low hole injection into the emissive layer often limits the performance of these devices.However, only a few studies have focused on hole-injection layers (HILs) in hybrid and organic LETs.He et al. reported the highest external quantum efficiency (EQE) to date of 13.2% in a quantum dot LET with efficiency comparable to LEDs using poly(9-vinlycarbazole) (PVK) material as an HIL in 2022. [16]Song et al. demonstrated improvement of EQE in organic LETs from 0.46% (a control device without an interfacial layer) to 4.7% at a brightness of 4620 cd m −2 by interfacial modification by inserting a combination of the p-type dopant 1,4,5,8,9,11-hexa-azatriphenylene hexacarbonitrile (HAT-CN) and N,N′-di(naphthalene-1-yl)-N,N′-diphenylbenzidine (NPB) between a hole-transporting pentacene layer and the emissive layer in 2016. [17]olybdenum oxide (MoO x ) and poly(3,4ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) are among the most effective and commonly used inorganic and organic HILs, respectively.MoO x provides many advantages in optoelectronic devices due to its high transmittance (≥ 85%) and suitable work function (; 6.7 eV in vacuo and 5.3 eV in ambient air). [18,19]However, this material usually requires high-temperature thermal evaporation to deposit, which can lead to thermal damage of organic active layers. [20,21]Meanwhile, PE-DOT:PSS is a well-known solution processible hole-transporting material with a  of 5.0-5.6 eV.However, its hygroscopic and acidic natures cause device performance to deteriorate and result in unstable performance.24] Recently, it has been reported that a novel class of solutionprocessible hybrid polyelectrolytes, which contain an anionic PSS backbone and metal cations Li + and Cu 2+ (referred to as Li:PSS and Cu:PSS), have been introduced as HILs in organic and perovskite solar cell devices.27][28][29] Metal:PSS polyelectrolytes feature outstanding solubility in polar solvents such as water or methanol and additionally offer pH neutrality relative to PEDOT:PSS.These attributes lead to easy processing on organic and hybrid devices.However, such metal:PSS polyelectrolytes have not yet been thoroughly investigated in field-effect transistors or LETs.
Herein, we have investigated the electrical and optical characteristics of HLETs incorporating two kinds of metal:PSS polyelectrolyte (Li:PSS and Cu:PSS) as single-component (S) layers as well as mixtures of these materials with PEDOT:PSS as HILs to improve the hole-injection current n-type HLETs.[27][28] We investigated the influence of these different interlayers on the band structure and performance of HLET devices and found that employing Cu:PSS M resulted in significantly enhanced brightness of up to 4.89 × 10 3 cd m −2 , with an EQE of up to 0.45%, which was a dramatic improvement compared to HLETs without no HIL (no emission was observed) and pristine PEDOT:PSS (2.17 × 10 2 cd m −2 with an EQE of 0.01%).To understand how the hybrid polyelectrolyte HILs influenced the charge injection and recombination in ntype HLET devices, we carried out ultraviolet photoelectron spectroscopy (UPS) analysis and photoluminescence (PL) quenching studies.

Results and Discussion
The configuration of HLET devices used in this study and the chemical structures of two metal:PSS polyelectrolytes (Li:PSS and Cu:PSS) are presented in Figure 1a,b.All devices were fabricated on p-doped Si substrates with 100 nm thick SiO 2 dielectric layers on top, which served as gate electrodes.Zinc oxynitride (ZnON) was used as the electron transport material due to its exceptional electron mobility (μ e > 120 cm 2 V −1 s −1 ) and optical properties including high transmittance (>87%) with an optical bandgap energy (E g ) of 3.17 eV. [3]The films were formed by patterning through a shadow mask using a sputtering process.The fluorescent poly(p-phenylenevinylene) derivative, Super Yellow (SY) was spin-coated on the patterned ZnON films as the emissive layer.A variety of solution-processible Li:PSS and Cu:PSS HILs were introduced with conditions including single component (S), additive (A), and mixture (M), as described above, with variable amounts of PEDOT:PSS in order to optimize hole injection from the D electrode to the emissive layer.Metal:PSS A contains small amount of PEDOT:PSS solution while Metal:PSS M is composed of a 3:7 ratio of solutions, as described above.The thickness of all HILs was estimated through X-ray photoelectron spectroscopy (XPS) data and the Beer-Lambert's law.The thicknesses of Li:PSS S, A, and M layers on SY film were 2.0, 7.3, and 40.4 nm, respectively.Those of Cu:PSS S, A, and M layers were 1.0, 6.3, and 7.3 nm, respectively.The thicknesses are summarized in Table S3 (Supporting Information).The thickness of PEDOT:PSS layer was 43.0 nm.The Ag metal with a  value of 4.60 eV was used for the S-D electrodes.Figure 1c shows a schematic diagram illustrating the operating mechanism of HLETs along with an energy-level diagram, where the energy levels of all materials were taken from the literature except for those of metal:PSS HILs, which were experimentally obtained by UPS. [11]Under positive gate bias, electrons, which are the majority carriers, are injected from the S electrode through the emissive layer (SY) into the ZnON layer.Upon increasing the gate potential, electrons accumulate in the ZnON layer at the dielectric interface due to the electric field effect.The electrons drift across the ZnON channel layer toward the D electrode under positive S-D bias.Near the drain electrode, they recombine with holes (minority carriers) injected from the D electrode in the thin SY layer.Ideally, electrons and holes recombine in the channel area between the S-D electrodes, allowing light to escape.In the case of symmetric Ag S-D electrodes, electrons are injected and transported effectively through the ZnON layer; however, holes tend to be injected at a lower rate, only near the D electrode for ntype LETs resulting in unbalanced charge-carrier injection and transport through the channel, imbalanced carrier recombination and suboptimal light emission.Therefore, we expected that introducing an appropriate HIL could significantly reduce the Ф h from the D electrode to the highest occupied molecular orbital (HOMO) level of the emissive layer, resulting in more balanced charge-carrier recombination and light emission.
The effect of HILs on the energy band structure can help understand how the HILs affect carrier transport and recombination in devices; the energy levels of all metal:PSS HILs were investigated using UPS.The  of PEDOT:PSS was measured to be 5.01 eV.Li:PSS and Cu:PSS have different trends in  depending on the amount of PEDOT:PSS mixed with in S, A, and M compositions (see Figures S1 and S2 and Table S1 in the Supporting Information).Interestingly, the  value of Li:PSS decreased from 4.82 to 4.74 eV with increasing PEDOT:PSS ratio (from Li:PSS S to Li:PSS M), while  of Cu:PSS slightly increased from 4.91 (Cu:PSS S) to 4.97 eV (Cu:PSS M).
Figure 2 shows the electrical and optical transfer characteristics of HLETs without and with various Li:PSS and Cu:PSS HILs (S, A, and M compositions).A summary of the performance of HLETs is included in Table 1.The μ e , on/off ratio (I on/off ), and threshold voltage (V th ) were calculated from the electrical transfer characteristics of the HLETs.Other parameters, including brightness and turn-on voltage (V on ), were obtained from the optical transfer characteristics of HLETs.Corresponding output curves and EQE spectra are reported in Figures S4 and S5 (Supporting Information).The EQE, also referred to as  ext , is defined as the ratio of the number of photons emitted from the device (n photon ) to the number of electrons injected into the device (n electron ) per second as shown in Equation ( 1) The device without (w/o) HIL showed the highest on current (≈8 × 10 −3 A) compared with other devices (≈3 × 10 −3 A) and exhibited the highest apparent μ e of 9.78 cm 2 V −1 s −1 with no light emission, as shown in Figure 2a,c.Upon introducing HILs, all devices showed light emission with different emission intensities depending on which HIL was used, and the apparent values of μ e decreased slightly to 4-6 cm 2 V −1 s −1 in all cases.This indicates that electron injection from the Ag S electrode to ZnON transport layer was decreased due to the electron-blocking effect of the HILs, while improved balance of electron-hole injection resulted in more efficient carrier recombination.
The HLET using PEDOT:PSS exhibited a low brightness of 2.17 × 10 2 cd m −2 with a μ e of 6.26 cm 2 V −1 s −1 (EQE = 1.52 × 10 −2 %) and the highest V on among all of the emitting devices (23.15 V), as shown in Figure 2b,d.The device with Li:PSS S exhibited a notably increased brightness of 1.76 × 10 3 cd m −2 (1.05 × 10 −1 %) and reduced V on (10.23 V).In the case of Cu:PSS S, the device showed the highest brightness of any singlecomponent layer at 2.62 × 10 3 cd m −2 (1.68 × 10 −1 % EQE) with a V on of 15.01 V. Upon mixing PEDOT:PSS with Li:PSS (Li:PSS A and L:PSS M), the brightness values gradually decreased (to 6.45 × 10 2 and 3.69 × 10 2 cd m −2 , respectively, similar to    To understand the influence of hybrid polyelectrolyte HILs on the charge injection in n-type HLET devices, we investigated the energy band structure of the SY emissive layer and various HILs through UPS analysis.All devices exhibited outstanding electron transport characteristics owing to the high electron mobility of ZnON, despite the electron-injection barrier (Ф e ) from ZnON to SY emitter (0.5 eV).This Ф e from ZnON to SY was the same for all devices and was generally lower than Ф h ; therefore, we will focus on understanding differences in Ф h as effects that underlie differences in device characteristics.Schematic energy-level diagrams of SY films, and Li:PSS and Cu:PSS HILs for different PEODT:PSS ratios (S, A, and M) and PEDOT:PSS are shown in Figure 3.All UPS spectra of the SY films and various HILs are included in Figures S1-S3 (Supporting Information).Here, E vac is the vacuum level and E F is the Fermi level.Ф h , which quantifies the energy barrier to hole injection, can be calculated from the difference in the energy of the  of Ag (4.60 eV) and the HOMO level of SY, as measured by UPS.A HOMO energy of 5.45 eV was obtained for pristine SY, and the lowest unoccupied molcular orbital (LUMO) level (3.15 eV) was estimated from the difference of the HOMO and E g of SY (2.30 eV), as shown in Figure S3 and Table S1 (Supporting Information).A Ф h value of 0.75 eV was observed, as shown in Figure 3a.We considered the interfacial dipole (Δ) created by ionic functionalities of Li:PSS, Cu:PSS, and PEDOT:PSS in more detail.Among the HILs, PEDOT:PSS forms a relatively strong interfacial dipole of 0.41 between the emissive layer and S-D electrodes, leading to efficient hole injection; it results in the lowest Ф h of 0.44 eV, as shown in Figure 3e.The Cu:PSS HILs form interfacial dipoles of 0.31, 0.35, and 0.37 (Figure 3f-h) between the emissive layer and S-D electrodes for S, A, and M compositions, respectively, showing that addition of PEDOT:PSS did not strongly affect the vacuum energy of Cu:PSS.In contrast, Li:PSS HILs exhibited a gradual reduction in E vac from 0.22 to 0.14 eV as a function of increasing PEDOT:PSS content, as shown in Figure 3b-d.We can infer that the Li + or Cu 2+ cations of Li:PSS and Cu:PSS, respectively, cause different shifts in the vacuum level.Additionally, the ability of Cu 2+ to reversibly accept electrons from the SY emissive layer (to form Cu 1+ ) can mediate hole transfer and support interfacial p-doping of the SY layer better than Li:PSS.Although PEDOT:PSS forms a proper interfacial dipole (Δ = 0.41) it yields considerably lower Ф h than the other HILs (below 0.37); however, the observed brightness of PEDOT:PSS devices was relatively poor (2.17 × 10 2 cd m −2 ) due to the low transmittance and exciton quenching as shown in Figure 4.Among the Li:PSS HILs, pristine Li:PSS (Li:PSS S) exhibited the lowest Ф h (0.63 eV) leading to efficient hole injection.Upon increasing PEDOT:PSS ratio (Li:PSS A and M), Ф h values were gradually increased to 0.66 and 0.71 eV, respectively, consistent with the observed decrease in brightness and luminous efficiency of the HLETs (Figure 3b-d).Cu:PSS S showed a lower Ф h of 0.54 eV compared to Li:PSS S (0.63 eV), the brightness of this device was comparable or slightly greater than Li:PSS S. Upon adding a small amount of PEDOT:PSS (Cu:PSS A), Ф h values were slightly decreased to 0.50 eV, and SY with Cu:PSS M yielded a similar Ф h (0.48 eV), as shown in Figure 3f-h.
In addition to affecting hole injection, interlayers may have electron-blocking effect, which may balance electron and hole currents, trap electrons in the emissive layer, and improve light emission.In order to probe the effect of the interlayers on electron transport, electron-only devices were fabricated without an SY layer (Si/SiO 2 /ZnON/metal:PSS/Ag).These data are included in Figure S6 (Supporting Information).We observed a decrease in current in devices in the "on" state and a decrease in the ap-parent electron mobility from 22.7 cm 2 V −2 s −1 for devices with no interlayer to 13.9 or 8.58 cm 2 V −2 s −1 for devices with Li:PSS or Cu:PSS HILs, respectively.This suggests that the HILs have an electron-blocking effect, consistent with the high LUMO energies of the materials, which serves to confine electrons in the emissive layer.Additionally, to compare the HILs to a benchmark p-type interlayer, we prepared devices using thermally evaporate MoO x in place of the metal:PSS HILs.These data are included in Figure S7 (Supporting Information).These devices showed light emission with relatively good performance including an EQE of 0.12%, suggesting that MoO x and metal:PSS polyelectrolytes perform similar functions as HILs.
To gain insight into the charge-recombination processes in the SY emissive layer when processed with various HILs, we investigated the transmittance of HILs and PL quenching of SY films, as shown in Figure 4.The transmittance of PEDOT:PSS layer was significantly lower than the other HIL, showing 96-98% transmittance throughout the visible spectrum while the metal:PSSbased HILs showed over 99% transmittance over the same range.The Li:PSS S layer showed the highest transmittance close to 100% across the visible region (Figure 4a).Upon increasing the PEDOT:PSS ratio, the transmittance gradually decreased.In the case of Cu:PSS, the highly transparent properties were observed despite the small amount of PEDOT:PSS addition (Cu:PSS A), as shown in Figure 4b.Although the 96-98% transmittance of PEDOT:PSS might seem to result in a negligible loss, light emitted in LET devices is poorly outcoupled compared to other device types such as organic LEDs and may be trapped and reflected multiple times between the D electrode and substrate before escaping near the edge of the D electrode.Therefore, apparently small parasitic absorption in the transmittance of an HIL may cause greater decreases in light intensity for light escaping an LET device than during a transmittance measurement.The PL spectra of SY without and with HILs are shown in Figure 4c,d.Commission internationale de l'èclairage (CIE) color coordinates were calculated for the fluorescence spectra and compared to electroluminescence (EL) spectra, as shown in Figure S8 (Supporting Information), revealing nearly identical color coordinates for all combinations of SY and HILs in both PL and EL.The spectrum of the SY film with PEDOT:PSS reveals the greatest amount of PL quenching, indicating an increase in nonradiative recombination.In detail, exciton-polariton quenching effects could cause a reduction of PL in SY films.Excitons generated in the emissive layer can undergo energy transfer or charge transfer to charge carriers (polaritons) in the highly doped PEDOT:PSS, or other polyelectrolytes, leading to exciton quenching. [30,31]Furthermore, EL in these devices is generated by electron-hole recombination near the SY/HIL interface; therefore, interface quenching effects observed in photoluminescence experiments with 40 nm thick SY films may underestimate the extent to which in EL is quenched, which may be why the EQE of PEDOT:PSS devices is relatively lower than that would be expected based on the relative PL quenching alone. [32]Li:PSS S exhibited slightly reduced PL intensity upon increasing the PEDOT:PSS ratio.In the case of Cu:PSS, similar PL quenching was observed regardless of the amount of PEDOT:PSS.We attributed differences in the PL quenching of SY films with Li:PSS and Cu:PSS, respectively, as a function of PEDOT:PSS ratios to the different abilities of the films to form interfacial dipoles, depending the cation (Li + or Cu 2+ ).The improved passivation toward exciton quenching observed with the Cu 2+ cation relative to the Li + cation can be attributed to the higher interfacial dipole.In addition to steady-state PL quenching experiments, we performed transient PL quenching experiments to quantify the effect of different interlayers on PL lifetimes ().These data are included in Figures S16 and S17 (Supporting Information).Compared to the  of SY alone (1.61 ns), the Cu:PSS and Li:PSS interlayers did not cause a dramatic decrease in PL lifetime (with measured  values in the range of 1.54-1.71ns).However, out of all of the samples, PE-DOT:PSS showed the largest decrease in  (1.46 ns), consistent with the steady-state PL quenching experiments.
Figure 5a compares the EL of optimized HLETs using Li:PSS and Cu:PSS HILs to the PL spectra of SY films.The EL spectra of HLETs with Li:PSS S and Cu:PSS M were slightly blueshifted compared to the corresponding PL spectra of SY films.Photographs of operating HLETs with all of the different metal:PSS materials and PEDOT:PSS HILs are shown in Figure 5b.Interaction with Li or Cu ions can induce charge-transfer interactions with the emissive material (SY emitter).These interactions can influence the energy of electronic transitions, thereby affecting the emission color.Slightly orange-yellow-colored light emission was observed in the channel of HLETs using Li:PSS HILs, and greenish-yellow-colored emission was observed in HLETs with Cu:PSS HILs.However, the color changes observed in microscope images in Figure 5b, which are affected by the optics of the microscope and contrast settings of the camera, may not accurately reproduce the true color of light emission.When the emission spectra (Figure 5b) and CIE coordinates of each composition were more accurately measured using a radiometer, we found that they all fell within a narrow range of CIE coordinates; the corresponding CIE coordinates of HLETs are shown in Figure S8 (Supporting Information).

Conclusions
In summary, we have investigated the electrical and optical characteristics of HLETs using two types of metal:PSS polyelectrolytes (Li:PSS and Cu:PSS) and mixtures of these with variable amounts of PEDOT:PSS as HILs to improve the hole injection in n-type HLETs.Devices using Cu:PSS M achieved the best device performance.HLETs employing Cu:PSS M exhibited enhanced brightness of 4.89 × 10 3 cd m −2 with an EQE of 0.45%, much higher compared to HLETs without an HIL (no emission) or with pristine PEDOT:PSS (2.17 × 10 2 cd m −2 with an EQE of 0.01%).Through the analysis of UPS and PL quenching data, we have identified that Ф h is affected by p-doping at the SY/HIL junction and the formation of an interfacial dipole at the interface by the ionic functionalities of HILs as the reasons for the improved performance in the polyelectrolyte HILs.This study provides useful information about the role of polyelectrolyte HILs in HLETs, which may be exploited to understand and improve HLET performance through the incorporation of ionic materials and to design new interfacial materials for other optoelectronic devices as well.

Experimental Section
Preparation of HIL Solutions: To fabricate the HILs, commercial PE-DOT:PSS (Heraeus Clevios P VP AI 4083) solutions were used.Freshly synthesized Li:PSS and Cu:PSS materials were prepared according to previously reported methods. [25,28]Li:PSS and Cu:PSS were dissolved in deionized water with concentrations of 0.5 and 0.15 mg mL −1 , respectively (Li:PSS S and Cu:PSS S).These concentrations were found to be optimal in previous work.Additive solutions (Li:PSS A and Cu:PSS A) were prepared by adding PEDOT:PSS (Clevios PVP Al 4083) to Li:PSS solutions in a volume ratio of 1:100, respectively.Mixed solutions (Li:PSS M and Cu:PSS M) with PEDOT:PSS were both prepared in a ratio of 7:3, respectively.
HLET Fabrication and Characterization: p-doped silicon substrates with thermally grown silicon oxide (SiO 2 ) layers (100 nm thick) were used for all devices.ZnON films (40 nm thick) with channel patterns were used as the electron-transport layers; these were deposited via a reactive magnetron sputter system using the Zn metal as a target material in a mixture of argon (Ar), oxygen (O 2 ), and nitrogen (N 2 ) reactive gases.The assputtered ZnON films were annealed at 300 °C for an hour in an ambient atmosphere.A 6 mg mL −1 solution of SY (PDY-132, M n (average molecular number) > 400 000 and M w (average mouclular weight) >1300 000), Merck) dissolved in toluene was spin-coated onto the patterned ZnON films at 2000 rpm for 60 s and then annealed on a hot plate at 180 °C for 20 min in a N 2 -filled glove box.PEDOT:PSS films were formed by spin coating at 4000 rpm for 30 s and then annealed at 140 °C for 10 min in the air.The other Metal:PSS solutions were spin-coated at 2000 rpm for 30 s and annealed at 120 °C for 10 min in the air.Finally, 60 nm thick Ag source and drain contacts were deposited by thermal evaporation at a pressure of 10 −6 Torr using a shadow mask.The ratio of channel length (L) and width (W) was 0.05.All HLET devices were electrically characterized using a Keithley 4200-SCS parametric analyzer in a N 2 atmosphere.The emission of the HLETs was acquired as photocurrent using a Hamamatsu H10720 series photomultiplier tube (PMT) calibrated using a reference light source to obtain accurate brightness values.Brightness and EQE calculation method are included in the Supporting Information in detail.EL and PL of HLETs were measured via an Ocean Optics USB 4000 VIS-NIR coupled with an optical fiber.Transmittance measurements were conducted using a Cary 5000 UV-vis spectrometer (Agilent Technologies).

Figure 1 .
Figure 1.Schematic diagrams.a) Device configuration of HLETs.b) Chemical structures of the two metal:PSS materials (Cu:PSS and Li:PSS).c) The working mechanism along with an energy-level diagram of HLETs with Metal:PSS HILs with variable PEDOT:PSS ratios (single component (S), additive (A), and mixture (M), respectively).

Figure 2 .
Figure 2. Electrical and optical transfer characteristics of a,b) HLETs without and with Li:PSS and c,d) Cu:PSS as a function of PEDOT:PSS ratio (Metal:PSS single component (S), additive (A), and mixture (M) and PE-DOT:PSS).b,d) The brightness characteristics of the device without an HIL, which exhibited no light emission, were not included in plots.

Figure 3 .
Figure 3. Schematic energy-level diagram of the interface at a) pristine SY and Ag electrode, e) PEDOT:PSS, b-d) Li:PSS HILs, and f-h) Cu:PSS HILs as a function of PEDOT:PSS ratio (single component (S), additive (A), and mixture (M), respectively) between SY and Ag electrodes.

Figure 4 .
Figure 4. a,b) Transmittance and c,d) PL quenching data of SY films without and with Metal:PSS HILs: single-component (S), additive (A), and mixture (M) and PEDOT:PSS HILs.

Figure 5 .
Figure 5. a) EL and PL spectra of SY and SY with Li:PSS single component (S) and Cu:PSS mixture (M).b) Photographs of operating HLETs.

Table 1 .
Summary of performances of HLETs: S, A, and M are single component, additive, and mixture, respectively.