Eliminating the Imbalanced Mobility Bottlenecks via Reshaping Internal Potential Distribution in Organic Photovoltaics

Abstract The imbalanced carrier mobility remains a bottleneck for performance breakthrough in even those organic solar cells (OSCs) with recorded power conversion efficiencies (PCEs). Herein, a counter electrode doping strategy is proposed to reshape the internal potential distribution, which targets to extract the low mobility carriers at far end. Device simulations reveal that the key of this strategy is to partially dope the active layer with a certain depth, therefore it strengthens the electric field for low mobility carriers near counter electrode region while avoids zeroing the electric field near collection electrode region. Taking advantage of these, PCE enhancements are obtained from 15.4% to 16.2% and from 16.9% to 18.0%, respectively, via cathode p‐doping and anode n‐doping. Extending its application from opaque to semitransparent devices, the PCE of dilute cell rises from 10.5% to 12.1%, with a high light utilization efficiency (LUE) of 3.5%. The findings provide practical solutions to the core device physical problem in OSCs.

Semitransparent device fabrication.PM6:BTP-eC9 (16 mg/ml, D/A = 1:3) were dissolved in CF solvent and stirring on a hot plate at 50 °C.After that, the blend solutions were spin-coated on ZnO to obtain similar film thickness of 75 nm ± 2 nm.
Then a 10 nm MoO 3 layer was deposited on the active layer.For the semi-transparent organic solar cell, ultrathin Ag and 35 nm MoO3 replaced the 100 nm Ag.The 15 nm   Ag was deposited at a rate of 2 Å•s -1 and the 35 nm MoO 3 was deposited at a rate of where N n and N p are n-and p-type concentrations of ionized dopants, respectively, e is the elementary charge, p and n are the concentrations of free holes and electrons, is the relative dielectric constant, o is the vacuum permittivity, and x is the spatial coordinate.In organic semiconductor, the concentration of ionized uncompensated dopants can reach 10 24 m -3 .Since ion current is neglective, the electron current, hole current, and continuity equations are the same as the non-doping model at quasi-steady state: where is the thermal voltage, μ h and μ p are the electron and hole mobility, and V is the electric potential.The charge-generation and recombination processes are described by the current continuity equations for electrons and holes.G is the generation rate of bound electron-hole pairs, P(E) is the probability of bound electron-hole pair dissociation.The current densities of electrons J n and holes J p are presented as a sum of drift and diffusion current densities.The total current density through the active layer is a sum of the electron and hole current densities J = J n + J p , as shown in Supplementary Figure S1.
DFT and TD-DFT calculation.We apply density functional theory (DFT) and time-dependent density functional theory (TD-DFT) to study the interaction among an oligomer of PTQ10 with two repeating units, Y6, water and BCF.All DFT and TD-DFT calculations in this work were performed using the Gaussian 16 package. [1] a first step, the gas-phase ground state geometry of the molecules were determined using the ωB97XD [2] functional, which is capable of capturing short-and long-range interactions, along with the base set 6-31G (d,p). [3,4] e then used the same functional and base set to perform all the remaining DFT calculations.
In order to evaluate the intensity of the interaction between the BCF(OH 2 ) adduct with the dimer of PTQ10 or with the Y6, we optimized the complex formed by the three molecules.We started with a initial configuration were the water molecule is located between the BCF and the polymer or the acceptor.In the case of Y6, two different initial configurations were tested, one with the BCF located near the Y6 edge an another one with the BCF positioned near the central groups of the acceptor.After running the optimization of the complex, a vibrational analysis was performed for the resulting configuration of the system.The Gibss free energy of the complex ∆G c ) was then estimated directly from this DFT calculation.We use the same procedure to estimate the Gibss free energy of the isolated molecules ∆G .The variation of the Gibss free energy due to the formation of the BCF(OH 2 )/oligomer or BCF(OH 2 )/Y6 complexes was estimated by the difference between ∆G c and the sum of the ∆G's of the isolated molecules.
GIWAXS characterization.GIWAXS measurements were performed at beamline 7.3.3 [5]at the Advanced Light Source.Samples were prepared on Si substrates using identical blend solutions as those used in devices.The 10 keV X-ray beam was incident at a grazing angle of 0.11°-0.15°,selected to maximize the scattering intensity from the samples.The scattered x-rays were detected using a Dectris Pilatus 2M photon counting detector.
Calculating the SCLC mobility.where 0 is the permittivity of vacuum, r is the relative permittivity of the active layer and it is assumed to be 3.5 here.
Flory-Huggins interaction parameter.The polymer solvent interaction parameter, which reflects the change in the interaction energy during the mixing of polymer molecules with the solvent, is expressed as χ.From the derivation of the thermodynamic theory of polymer solution, it is known that the value of polymer solvent interaction parameter χ can be used as a semi-quantitative criterion for the superiority of solvent.If χ is greater than 0.5, the polymer generally cannot be dissolved; if χ is less than 0.5, the polymer can be dissolved, and the smaller it is, the better the solvency ability of the solvent.Therefore, the value of χ can be used as a basis to determine whether the polymer and solvent system are mutually soluble.We first build the polymer 3D model, and then import it into HSPiP software to calculate the polymer-solvent interaction parameters.
Other measurements.TM-AFM images were scanned by Bruker INNOVA.The J-V curves were performed in the N 2 -filled glovebox under AM 1.5G (100 mW cm −2 ) using an AAA solar simulator (SS-F5-3A, Enli Technology Co., Ltd.) calibrated with a standard photovoltaic cell equipped with KG5 filter.The EQE curves were measured by Solar Cell Spectral Response Measurement System QE-R3018 (Enli Technology Co., Ltd.) with calibrated light intensity by a standard Si photovoltaic cell.
The transmittance was obtained on a Shimadzu UV-3600 Plus Spectrophotometer.
For the semitransparent devices, the reference is air.The EQE spectrum was obtained by using the corrected Si standard detector (S1337-1010Br).ESR spectra were tested on Bruker Biospin A300-9.5/12.TOF-SIMS were tested on ION-TOF M6.
AVT.The AVT value was calculated according to the average value of transmittance of semitransparent devices based on photonic response of the human eye.The wavelength range is usually adopted by 380-760nm, and the specific calculation formula is

∫
where is the wavelength, T is the transmission, is the normalized photopic spectral response of the eye, and S is the solar photon flux (AM1.5G).
Color coordinates.The color coordinates (x, y, z) of semi-transparent devices were calculated according to the transmission spectra based on chromaticity diagram of the CIE 1931xy.The color coordinates were calculated by the formulas The definition of color includes chromaticity (u, v) and luminous intensity L (the "brightness" of the light source and the "luminosity" of the physical object).When illuminated with a reference or transmitted source, a color sample (i) will exhibit color differences consisting of chromaticity differences ( and ) and luminance differences ( .Since the shape of T determines the extent to which a transmitted source can maintain the color rendering of AM1.5G, the geometric distance between the point of the transmitted source and the point of the reference AM1.5G in the chromaticity coordinate system accounts for the chromaticity difference.There were eight standard test color samples used as the basis for these chromaticity and luminance differences, and these chromaticity and luminance differences are averaged to calculate the CRI: The above calculation done by IES TM-30-18 Advanced Calculation Tool.
The IES TM-30-18 method.R f is a measure of average color fidelity and is calculated by determining the difference in CAM02-UCS coordinates for each CES at the test and reference light sources and then determining the arithmetic mean of these color differences.This average should be scaled by a factor of 6.73 and subtracted from 100: R f 100 6.73 Then, the scale should be adjusted so that the minimum R f value is 0 to avoid generating negative numbers.Rescaling to the final R f value should be accomplished using the following method: R f 10ln exp R f 10 1 The fidelity value for each of the 99 CES may be calculated using the same method as for R f .
To calculate the remaining specified measures, the 99 CES are divided in 6 groups.The above calculation done by IES TM-30-18 Advanced Calculation Tool.S1.                             a The parameters are obtained from 10 independent devices.a The parameters are obtained from 5 independent devices.

Figure S2 .
Figure S2.Simulated JV characteristics of (a) p-doping at cathode and (b) at anode.The hole mobility is μ h = 1×10 -4 cm 2 /Vs, electron mobility is μ e = 1×10 -3 cm 2 /Vs with different doping depth.Doping density is 2 ×10 17 cm -3 .from red line to black line, the doping depth increases at a step of 10nm.The hole-density-dependent mobility follows Gaussian disordering theory: μ p = μ o,p (1 + α n p /N site ) 0.50 , where n p is hole density, μ o,p is limiting hole mobility at low density (1×10 4 cm 2 /Vs), α is hole-density coefficient, and N site is transport site density.For parameter values, see caption of TableS1.

Figure S9 .
Figure S9.Hole-only and electron-only charge transport curves of the control and cathode p-doped PTQ10:Y6 devices

Figure S17 .
Figure S17.Evolution of photovoltaic parameters under dark aging condition for up to 1000 h storage of: (a) cathode p-doped and undoped devices, (b) anode n-doped and undoped devices.

Figure S18 .
Figure S18.MPP stability test of unencapsulated OSCs based on (a) undoped and

Figure S20 .
Figure S20.Thickness of thin films without/with PS layer measured by the step profiler.

Figure S21 .
Figure S21.Hole-only and electron-only charge transport curves of the control and anode n-doped PM6:BTP-eC9 device.

Figure S22 .
Figure S22.(a) H atom, which came out of the n-dopant, interacting with the sulfur atom of the BTP-eC9 and (b) H atom interacting with the carbon atom of the N-DMBI itself.(c) N-DMBI molecule.

Figure S25 .
Figure S25.Hole-only and electron-only charge transport curves of the control and anode n-doped semitransparent devices.

Figure S26 .
Figure S26.J-V curves of the undoped and n-doped devices based on different Y-series acceptors with a device area of 4 mm 2 .

Figure S30 .
Figure S30.Color coordinates of white point and optimal semitransparent devices.

Figure S31 .
Figure S31.Gamut Index vs. Fidelity Index.The range in possible R g values increases as R f decreases.The gray shaded area indicates the approximate region of combinations that are not possible for nominally white light sources.
The CIE 1960 UCS diagram is a graph of u and v values.The iso-temperature is a constant color temperature line for a blackbody radiator and can be drawn on this 1960 UCS diagram.The CCT of the test source can be obtained by projecting the calculated chromaticity coordinate values (u t , v t ) onto this UCS diagram.the temperature corresponding to the blackbody radiator closest to the chromaticity coordinate (u t , v t ) is determined as the CCT.
where X, Y, Z are tristimulus values, λ) is the spectral power distribution (SPD) of the transmission spectra of semi-transparent devices and ̅ , ̅ , ̅ are color-matching functions.CCT and CRI.
The boundaries are established by dividing the plane of CAM02-UCS into 16 sections following a radical pattern, with each encompassing 22.5 ∘ .R g is a measure of the area spanned by the average a , b coordinates of the CES in each hue-angle bin, a test,j , b test,j and a ref,j , b ref,j .The coordinate is discarded, so that the a test,j , b test,j and a ref,j , b ref,j coordinates each form a polygon.Rg is calculated as 100 times the ratio of the area of the two polygons ( t and r ,

Table S4 .
Flory-Huggins interaction parameters between donor/acceptor and different solvents.

Table S5 .
Device parameters of cathode p-doped PTQ10:Y6 devices with different dopant concentration.a

Table S6 .
The π-π stacking peak positions and coherence lengths from GIWAXS patterns for undoped and cathode p-doped PTQ10 film and PTQ10:Y6 blended film.Position and FWHM are available through multi-peak fitting and d-spacing, CLs can be calculated by Scherrer Equation.

Table S8 .
Bond length variation of n-dopant N-DMBI during interaction with molecule BTP-eC9.

Table S14 .
Detailed parameter on state-of-the-art ST-OSC devices reported in the literature.