Inter‐ and Intra‐Device Variation and Correlation of Hyperfine Interactions in Micron‐Scale Organic Light‐Emitting Diodes

The spin‐dependent properties of opto‐electronic devices, such as sensors, displays, and photovoltaics, are a key contributor to performance metrics such as sensitivity and efficiency. As these devices are pushed to smaller scales, an understanding of how the microscopic variations in their spin‐dependent properties impact the macroscopic scale is becoming increasingly important. In this study, the hyperfine interactions of charge carriers are investigated within a series of co‐polymer thin‐film organic light‐emitting diodes (OLEDs), with each set of devices having a different physical size. Using spatially resolved measurements, significant variation in hyperfine interactions within microscopic thin‐film OLEDs is found. The domain size of spatially correlated hyperfine regions is characterized within these devices, finding characteristic scales of several microns. Finally, multiple device averaged magneto‐electroluminescence (MEL) responses from arrays of identical devices are simultaneously measured, to probe the influence of microscopic variation on the macroscopic hyperfine properties. It is found that smaller devices typically display a smaller device‐averaged hyperfine interaction. These findings shed light on the importance of spin dynamics in optoelectronic devices and provide insights for improving their performance.


Introduction
The spin of charge carriers plays a central role in modern electronics.In organic semiconductor based optoelectonics, studying DOI: 10.1002/adsr.202300087 the spin-dependent properties of charge carriers has enabled the next generation of organic light-emitting diodes (OLEDs), [1,2] solar cells, [3] and spin-based sensors. [4,5]Organic semiconductors offer a cost effective platform for these technologies, with techniques such as solution processing allowing for manufacturing at an industrial scale. [6]Combining industry-scale manufacturability and tunability via synthetic chemistry [7][8][9] these materials offer the possibility of introducing low-cost, high performance, spin based optoelectronics into the consumer market.
Many of these applications call for miniaturization, which requires a thorough understanding of how microscopic variation of spin-dependent properties influences the device's averaged properties.In particular, hyperfine interactions play a large role in the spin-dependent processes of organic semiconductors due to an abundance of hydrogen nuclei [10] in combination with typically low spin-orbit coupling [11,12] and relatively long spin lifetimes. [13,14]The linewidth of magnetic resonance spectra is influenced by hyperfine interactions, playing a central role in the sensitivity of organic spin-based magnetic field sensors. [15]Traditionally, hyperfine interactions in organic devices have been studied at the macroscopic level by measuring magnetic field effects [16,17] or via optically/electrically detected magnetic resonance. [7,12,18]Recently, spatially resolved magneto-electroluminescence (MEL) [19] has been developed as a technique to probe the microscopic variation and underlying structure of hyperfine interactions.
In this paper, we apply both spatially resolved MEL and deviceaveraged measurements on a series of microscopic devices.Our aim is to understand if the microscopic variation seen in bulk devices persists with device miniaturization and how this influences the device averaged properties of micro-scale devices.The structure of this paper is as follows; First, we measure the intradevice variation of hyperfine interactions of individual microscopic devices with various physical sizes to test the persistence of hyperfine variation.Following this we characterize the spatial correlation of hyperfine regions, quantifying domain sizes.Finally, we simultaneously measure device averaged MEL of many, fixed-size devices and use these measurements to test how the macroscopic hyperfine properties of OLEDs is influenced by their physical size.

Concept
We use OLEDs made from a well studied, stable, active material with a vertical architecture.Using electron-beam lithography, we pattern a substrate of glass/indium tin-oxide (ITO)/Al 2 O 3 , resulting in arrays of fixed radius cavities in the insulating Al 2 O 3 . [20]ext, we spin coat layers onto the patterned substrate, before evaporating an aluminium electrode, resulting in an OLED being deposited inside each cavity with the layer stack-up ITO (120nm)/PEDOT:PSS (50nm)/SY-PPV active layer (100nm)/LiF (0.9nm)/Al (100nm).Importantly, the devices of each array are all fabricated at once on a single substrate, allowing the fabrication process to be controlled across each array.Examples of these arrays are displayed in Figure 1a), with a higher magnification image of single devices from our arrays imaged in Figure 1b).For further fabrication details refer to the Experimental Section and Section S1 (Supporting Information).
Due to the large magnitude of magnetic field effects in organic devices, [21] we choose to use MEL as a probe for the hyperfine interactions within these devices.This allows for a high signal-to-noise ratio, even when imaging at sub-micron resolution.The relationship between the MEL response and the underlying hyperfine interactions is drawn from the polaron-pair model, the key features of which are shown in Figure 1c).Polaron pairs are weakly bound electron-hole pairs, held together by their electrostatic attraction. [22]In this weakly bound state the polaron pairs form configurations of predominantly singlet-like (PP s ) and triplet-like (PP t ) character.During their evolution from polaron pair to exciton, each constituent of the pair will experience an effective local hyperfine field, with hyperfine mediated spin-mixing driven by the difference in the local fields experienced by each polaron. [23]These pairs evolve to form tightly bound excitons, which eventually undergo radiative recombination, with singletlike pairs undergoing this process faster than their triplet-like counterparts. [24]The degree of hyperfine mediated spin-mixing between the singlet-triplet subspaces therefore influences the electroluminescence (EL) of the device.Application of an external field alters the field experienced by each polaron in the pair, resulting in an effective field B eff = B local + B external .As the magnitude of the external field is increased, the influence of the local fields is minimized, resulting in a suppression of hyperfine mediated spin-mixing and a corresponding change in EL.By sweeping the applied field, the relative magnitude of the local fields can be inferred by studying the MEL lineshape.
The key elements of the experimental apparatus that we used to measure MEL are shown in Figure 1d).We sweep an applied field via an electromagnet while driving the OLED arrays with a constant current source.An objective and camera allow the resulting MEL response to be captured with spatial resolution.For spatially resolved MEL measurements we use a 20X magnification objective, allowing for MEL curves to be recorded inside individual devices from our OLED arrays.Swapping the objective to a 5X magnification counter-part allows for multiple devices from our arrays to be simultaneously measured.As commonly done in literature, we fit the resulting MEL lineshape to a Lorentzian curve, [25] , where A and B hf are both fitting parameters referred to as the MEL amplitude and the MEL width, respectively.The MEL amplitude is commonly attributed to competition between spin-mixing and recombination rates. [26]The MEL width is related to the overall spin-mixing rates and has been experimentally shown to be related to the hyperfine field strengths. [16]For further experimental and data-processing details refer to the Experimental Section.

Spatial Variation of Hyperfine Properties
We first employ spatially resolved MEL investigate the microscopic variation of hyperfine interactions within our OLEDs using single devices of fixed radii ranging from 40 to 5 μm.We drive the devices at a current density of 13.32 mAcm −2 while imaging their electroluminescence over a magnetic field range from 0 to 50 mT, with a spatial resolution of approximately 760 nm 2 .Fitting the MEL curves for each data point within the device produces the maps in Figure 2a-d (i) and 2a-d (iv) for the B hf and A fitting parameters respectively.The domain size and statistical correlation of these regions is discussed further in the following results section.
Columns ii) and iii) of Figure 2 show histograms of the MEL fitting parameters for each device radius with variatiability (Variability(X) = X full-width − half − maxima /X mean ) for each distribution as an annotation.Consistent with a previous result on bulk devices, we measure an average variability in B hf exceeding 20% in the 40 μm device with reduced variability in the corresponding MEL amplitude (A). [19]We see persistent spatial variation in the two smaller devices, with the 5μm device showing 16 % varation in B hf and 5% in A.
As these distributions appear to be non-normally distributed, we use Levene's test [27] to test the significance of the difference in variance between the distributions.The results indicate that there is a statistically significant difference in variance of our tested OLEDs at a 95% level of confidence with the exception of the distributions in the 10 and 5 μm devices.We do not observe a monotonic trend for either fitting parameter, however we see that the two smaller devices both have a reduced variation when compared to the two larger ones.A full table of Levene's test statisctics can be found in the Tables S1-S4 (Supporting Information).

Spatial Auto-Correlation of Hyperfine Properties
Next, we quantify the domain size of the spatially correlated hyperfine interactions observed in Figure 2. First, we re-normalize the B hf and A maps in terms of the number of standard deviations from the ensemble mean.Examples of the renormalized maps for the 10 and 5 μm radius devices are seen in Figure 3a,b.
We use Moran's I as a statistical measure for the degree of spatial auto-correlation,  r (see methods for calculation steps).We calculate  r for a range of lag distances spanning from 0 to 20 μm for both fitting parameters B hf and A. The resulting spatial auto-correlation plots corresponding to B hf and A are shown in Figure 3c,d, respectively.We use 95% confidence intervals as a threshold for the statistical significance of spatial autocorrelation between points separated by a lag distance.Our results for the 40 μm device is consistent with measurements on bulk SY-PPV devices showing statistically significant spatial auto-correlation up to 9 μm lag distances for both A and B hf , tending toward zero at long distances. [19]However, for the smaller devices the characteristic correlation length is altered; We find similar behavior for the 20 and 10 μm devices, with correlation lengths of 3.5 μm before trending toward zero.For the 5 μm device the B hf parameter auto-correlation decays more rapidly than in the A case, with a positive correlation for points at 2.5 μm radius and 3.5 μm for B hf and A. Interestingly at large lag distances the correlation in both parameters inverts, leading to a significant negative correlation.

Device Averaged Hyperfine Properties
Finally, we use device averaged MEL to investigate how the microscopic hyperfine variation influences the macroscopic device properties.Our OLED arrays form an ideal test bed for these measurements as all devices are fabricated and measured simultaneously, under identical conditions.Figure 4a shows two example device-averaged MEL curves with different widths and magnitudes.The inset displays the 20 μm OLED array these curves are drawn from with the regions averaged over labelled (i) and (ii).
We use OLED arrays with devices ranging from 40 to 2.5 μm in radius.Figure 4b,c show histograms of the fitting parameters B hf and A, respectively for each array.We perform a series of statistical tests on these datasets (full analysis results are displayed in the Tables S5-S8, Supporting Information); To test the difference in population means between each array without assuming equal variance we perform a Kruskal-Wallis H-test, [28] indicating a significant difference in the means of Figure 4b,c at a 95% level of confidence.To test the relationship between device properties and scale we perform pair-wise one-tailed t-test for both fitting parameters.For the MEL amplitudes, we find that in all cases when comparing larger radius devices to the smaller radius population, the smaller devices have a larger MEL amplitude at a 95% level of confidence.Here, we have the largest difference comparing the 2.5 μm array average A of 5.0 ± 0.1 % to the average of 3.1 ± 0.1 % in the 40 μm case.In the case of the MEL width our analysis shows a statistically significant decrease (again at a 95% level of confidence) in the MEL width (B hf ) with decreasing device radius, with the exception of the two larger radii arrays which do not have a significant difference in their mean B hf .Here, the mean MEL widths vary from 4.5 ± 0.1 mT in the 40 μm array to 3.9 ± 0.1 mT in the 2.5 μm devices.

Conclusion
Using spatially resolved magneto-electroluminescence, we have measured persisting variation and spatial auto-correlation of hyperfine properties with device miniaturization.We measure hyperfine domain sizes of several microns, occuring on much larger scales than would typically be expected, with polarons generally considered to be delocalized over a small number of molecular units and having low mobility. [29]The observed spatial variation and domain structures could impact miniaturised spin-based organic sensors, [4,30] as microscopic hyperfine variation within thin-film sensors would reduce the uniformity of a device's magnetic field sensitivity.By measuring the bulk MEL response of multiple arrays, each containing fixed radii OLEDs we have found statistically significant changes in the hyperfine properties with device scale.Our analysis supports that hyperfine induced spin-mixing is reduced with device scale, which may play a further role in optimization of organic magnetic field sensing [4,5] and improving measurements of novel physics within these devices under strong microwave coupling. [14,31]inally, our work highlights the importance of spatially resolved measurements in understanding variations in spindependent properties of disordered systems.With the emergence of several thin-film molecular materials that have optically [32,33] and electrically [29] addressable molecular spins understanding the spin properties of these materials is increasingly important.Device-averaged measurements may be blind to any spatial variation or spatially-correlative behavior, which is especially important within disordered materials.We anticipate that further understanding of the spatially resolved variations will be key in the next wave of solution processable organic spintronics.

Experimental Section
Device Fabrication: First, a substrate of glass/indium tin-oxide (ITO)/Al 2 O 3 was prepared and electron-beam lithography was used to pattern arrays of cavities into the Al 2 O 3 . [20]Then layers were spin-coated onto the patterned substrate, before evaporating an aluminium electrode, resulting in an OLED being deposited inside each cavity with the layer stackup ITO (120nm)/PEDOT:PSS (50nm)/SY-PPV active layer (100nm)/LiF (0.9nm)/Al (100nm).By controlling the dimensions of the pattern etched into the Al 2 O 3 it was possible to repeatably fabricate arrays of devices with regular spacing and fixed radii.For further details refer to the Supporting Information provided.
Experimental Setup: The OLEDs was mounted between an electromagnet (Lake Shore EH4-HVA) while driving the thin-film devices through a constant current source (Keysight B2901A).The applied magnetic field ranged from 0 to 50 mT and was controlled using a hall-probe (Lake Shore HST-S3) paired with a feedback controller (Lake Shore DSP 475), allowing for a stable field to be selected during each point in the magnetic field sweep.The devices were imaged under either 20X (20X Mitutoyo Plan Apo) or 5X (5X Mitutoyo Plan Apo) magnification infinity corrected lens in combination with a tube lens (ThorLabs ITL200).Data was captured using a high well depth CMOS camera (QHY 268M).
Data Processing: The data was measured as a series of images with a zero-field baseline matching for every field value measured.For spatially resolved measurements, the Circle Hough Transform was used to detect the center of the device, a detected circle is outlined in Figure 1a.The detected of each field value was used as the origin, this ensured that any movement while sweeping the applied field was cancelled (Using the change in the detected circle position less than 1 μm movement was estimated during the sweep).Before creating a MEL curve for each position in the device binning was used to average neighboring pixels so that the spatial resolution ≈ 760 nm was above the lateral resolution of our imaging system of 700 nm (the spatially resolved MEL results are repeated with a ≈ 950 nm in Section S4, Supporting Information).To prevent outliers the goodness of fit (R 2 ) was used, at a threshold of R 2 > 0.85.Due to a low number of data points and a poor signal-to-noise ratio (R 2 < 0.5) the 2.5 μm single device measurements were excluded from the spatially resolved MEL results.For device averaged measurements, regions surrounding each device in the array were averaged, with an example grid shown in Figure 4, producing a single MEL curve for each individual device.
Statistical Analysis: Population statistics: Statistical analysis was performed using the stats package from SciPy. [34]To test the significance of the change in variation between the spatial variation of tested OLEDs, SciPy's implementation of Levene's test was used.This test was chosen as it is robust to non-normally distributed populations.This test was applied to all four devices simultaneously and evaluate the result at a 95% level of confidence.To analyze the device averaged properties, a series of tests was applied.First, Levene's test [27] was used to check for equal variation between the array statistics.As this test indicates the variance of each OLED array is non-equal, a Kruskal-Wallis H-test [28] was used to evaluate the statistical significance of the difference in population means between each array.To narrow down the the population means follow, pair-wise one-tailed t-tests were applied to the arrays, checking if one population mean was greater than the other with statistical significance.All results were evaluated at a 95% level of confidence and tables containing test results can be found in Tables S1-S8 (Supporting Information).
Spatial Auto-Correlation: For each device, Moran's I was used as a statistical measure of correlation between two spatially separated regions.This calculates an expected index value ( r ) for pairs of regions separated by a lag distance r.Calculating this index value as a function of lag distance allows the characteristic length of spatial auto-correlation to be estimated.The index was calculated as where Λ,  ij are normalization constants,  ij is the deviation of the point (i, j), the sum over points (m, n) is over all points in the OLED, and the sum over points (k, l) is over all points within a lag distance r ± r from the point (m, n).

Figure 1 .
Figure 1.Device images, polaron-pair process, experimental setup.a) The 40 and 10 μm radius OLED arrays imaged under 5X magnification (scale bar: 40 μm).b) Single OLEDs with 20 and 5 μm radius under 20X magnification.For scaling the 5 μm device has the background zero-padded such that the number of pixels are equal in both images.c) A schematic of the polaron pair model used to relate measurements to the hyperfine interactions.d) The key components of the experimental setup.

Figure 2 .
Figure 2. Spatial variation in hyperfine properties.Each row corresponds to measurements for a single device of radius a) 40 μm, b) 20 μm, c) 10 μm, d) 5 μm.With columns corresponding to i) Spatial variation maps for the B hf fitting parameter.ii) Histograms for the B hf fiting parameter within each OLED.iii) Histograms for the MEL amplitude within each OLED.Annotations in the histograms of ii) and iii) display the variation in the corresponding fit parameter.iv) MEL amplitude spatial variation map for each device.

Figure 3 .
Figure 3. Spatial auto-correlation of hyperfine properties.a, b) Fitting parameter deviation maps for B hf and A, respectively.These maps are plotted for both the 10 and 5 μm devices.c, d) Correlograms for the B hf and A fitting parameters, respectivley.

Figure 4 .
Figure 4. Reproducibility of Hyperfine Properties a) MEL curves for the selected devices (i) and (ii) of the 20 μm OLED array showing variation in MEL amplitude and width (The devices and corresponding array is displayed in the inset).Histograms showing the statistics of B hf b) and amplitude (A) c) fitting parameters for OLED arrays with device sizes ranging from 40 to 2.5 μm.