A Universal Urbach Rule for Disordered Organic Semiconductors
Christina Kaiser, Oskar J. Sandberg, Nasim Zarrabi, Wei Li, Paul Meredith, Ardalan Armin
AA Universal Urbach Rule for Disordered Organic Semiconductors
Christina Kaiser, Oskar J. Sandberg * , Nasim Zarrabi, Wei Li, Paul Meredith, Ardalan Armin * Sustainable Advanced Materials (SΓͺr-SAM), Department of Physics, Swansea University, Singleton Park, Swansea SA2 8PP, United Kingdom * Email: [email protected]; [email protected]
Abstract
In crystalline semiconductors, the sharpness of the absorption spectrum onset is characterized by temperature-dependent Urbach energies. These energies quantify the static, structural disorder causing localized exponential tail states, and the dynamic disorder due to electron-phonon scattering. The applicability of this exponential-tail model to molecular and amorphous solids has long been debated. Nonetheless, exponential fittings are routinely applied to the analysis of the sub-gap absorption of organic semiconductors alongside Gaussian-like spectral line-shapes predicted by non-adiabatic Marcus theory. Herein, we elucidate the sub-gap spectral line-shapes of organic semiconductors and their blends by temperature-dependent quantum efficiency measurements in photovoltaic structures. We find that the Urbach energy associated with singlet excitons universally equals the thermal energy regardless of static disorder. These observations are consistent with absorption spectra obtained from a convolution of Gaussian density of excitonic states weighted by a Boltzmann factor. A generalized Marcus charge transfer model is presented that explains the absorption spectral line-shape of disordered molecular matrices, and we also provide a simple strategy to determine the excitonic disorder energy. Our findings elaborate the true meaning of the dynamic Urbach energy in molecular solids and deliver a way of relating the photo-physics to static disorder, crucial for optimizing molecular electronic devices such as organic solar cells. ntroduction
Recently, research on organic solar cells has seen significant progress through the development of non-fullerene electron acceptors (or NFAs), in particular delivering increases in single-junction efficiencies from 13.1 to 17.3 % between 2018 to 2020.
This has revived ambitions to ultimately achieve industrial scale low-cost photovoltaics with low embodied manufacturing energy. While chemists have been productively synthesising new materials, understanding of the opto-electronic properties lags behind β particularly in relation as to why these new n-type organic semiconductors are so effective at photogeneration with low voltage losses. A particular area of intense interest is light absorption and how it is related to molecular dipole moments and their energetic disorder. Of course, this is also a very relevant question for the fundamental solid state physics of molecular and disordered semiconductors. In general, semiconductors tend to absorb light at photon energies below the bandgap (sub-gap absorption) depending on the energetic disorder. In the case of inorganic semiconductors, the absorption coefficient often displays an exponential tail below the bands. These so-called Urbach tails increase their broadening with temperature π . The sub-gap absorption coefficient generally follows the expression πΌ(πΈ, π) β exp (
πΈβπΈ on (π)πΈ U (π) ) , (1) where πΈ is the photon energy and πΈ on is the energy onset of the tail correlated to the bandgap energy. πΈ U is the Urbach energy and it can vary between 10 to 100 meV depending on the semiconductor. β In banded semiconductors, the Urbach energy is believed to be related to the energetic disorder via πΈ U (π) = π D (π) + π S . Here, π D (π) is a temperature-dependent dynamical disorder term related the thermal occupation of phonon states, while π S is a temperature-independent term associated with structural or static disorder. In this regard, π S is the standard deviation of the distribution of localized states (induced by structural disorder) below the band edges. However, a unifying theory describing the density of states and their absorption leading to Urbach tails for materials of different chemical bonding and morphology is still lacking. In amorphous (disordered) semiconductors, the definition of a clear bandgap edge is often difficult due to large π S inducing sub-gap broadening. Organic semiconductors, which are excitonic and partially amorphous, display even more complex sub-gap features including intermolecular hybrid charge transfer (CT) states in technologically-relevant blends of electron donors and acceptors (analogous to p-and-n-type semiconductors respectively) , excitonic features and trap states . CT and trap states give rise to light absorption with Gaussian sub-gap spectral line-shapes in accordance with non-adiabatic Marcus theory. The associated CT energy is often seen as an effective bandgap found to correlate with the open-circuit voltage. With the recent rise of non-fullerene electron-accepting semiconductors with small energetic offset relative to donors , the lack of CT state sub-gap spectral features in donor-acceptor blends has led to the increased usage of Urbach energies to understand disorder and sub-gap photo-physics. As a rule of thumb, it has been assumed that low Urbach energies are indicative of lower π S and hence expected to result in higher performance such as reduced charge recombination and higher charge carrier mobilities in a photovoltaic device. β Due to the complex and often convoluted spectral features in sub-gap light absorption of organic semiconductors, Urbach energy carries significant ambiguity. Moreover, a long-standing debate β on the distribution of density of states (DOS) defining π S in organic semiconductors has been revived: does the DOS follow a Gaussian or an exponential distribution? With no doubt, the origin of π S is of great importance for the classification nd future development of organic semiconductors and their electro-optical properties. However, it has remained unclear how this important figure-of-merit relates to the Urbach energy. In this work, we show that the exciton sub-gap absorption in organic semiconductors is generally characterized by Urbach tails with characteristic energies equivalent to the thermal energy ππ as demonstrated by temperature-dependent EQE measurements. However, these Urbach tails are often convoluted with Gaussian line-shapes induced by trap states and/or CT states, resulting in erroneous, energy-dependent, Urbach energies larger than ππ. A simple model, combining the Gaussian distributed DOS with a Boltzmann factor for the absorption rate, is shown to reproduce the absorption profiles and to give an estimate for π S . Results
The spectral line-shape of the absorption coefficient and the EQE in the sub-gap tail ( πΌπ βͺ 1 ) are generally related via a modified Beer-Lambert law,
EQE = πΜπΌπ , where π is the thickness of the active layer and πΜ is an energy-dependent correction factor accounting for optical interference. Since πΜ is often assumed to be close to 1 for typical active thicknesses from 100 to 150 nm, EQE measurements have been used in the past to determine the Urbach energy, the EQE in this case following the spectral shape of πΌ . A previous lack of sensitivity in the EQE measurements has led to speculative assumptions about the spectral range of trap state absorptions, exponential tails and associated Urbach energies in organic semiconductors. By choosing a small fitting range exponential fits can be forced on to EQE spectra resulting in rather arbitrary Urbach energies, dependent on the spectral range of the fitting. More insight is gained from the apparent Urbach energy ( πΈ Uapp ) here defined as: πΈ Uapp (πΈ) = [π ln(EQE)ππΈ ] β1 (2) For a true exponential tail of the form eq. 1, πΈ Uapp is constant in the sub-gap spectral region and given by πΈ U (π) under the assumption of negligible optical interference effects. Figure 1 shows the EQE and πΈ Uapp for a wide range of organic semiconductor donor-acceptor (DA) blends. The material systems studied here can be generally grouped according to the DA energy offset or, in other words, by the difference between the CT state energy πΈ CT and the optical gap of singlet excitons πΈ SE , as illustrated in Figure 1. Large offset systems, such as PCDTBT:PC BM, BQR:PC BM and PBDB-T:PC BM, show three distinct spectral ranges for energies below the gap: (i) mid-gap trap state absorption at energies below 1.2 eV, (ii) CT state absorption in the mid-range ( ~ β These features are consistent with Marcus charge-transfer between states that are distributed in accordance with a Gaussian density of sub-gap states. The associated absorption coefficients are πΌ CT (πΈ) = π(πΈ, πΈ CT , π CT , π CT ) and πΌ t (πΈ) = π(πΈ, πΈ t , π t , π t ) for CT and mid-gap state absorption, respectively, where π(πΈ, πΈ π , π π , π π ) = π π πΈ β1 (4ππ π ππ) β12 exp (β (πΈ π + π π β πΈ) π ππ ). (3) Figure 1 | EQE and π¬ πππ©π© for organic BHJs with different energetic offsets between the HOMO energy levels of donor and acceptor.
From Gaussian fits in the spectral range of charge transfer state and trap state absorption, the charge transfer energy ( πΈ CT ) and trap energy ( πΈ t ) are extracted where possible. For low-energy offset materials, such as PM6:Y6, PM6:ITIC and PBDB-T:EH-IDTBR, the EQE tail has the form π πΈ/ππ and πΈ Uapp roughly equals ππ in the spectral range that is dominated by the absorption of the acceptor. For large-offset material systems, such as BQR:PC BM, PBDB-T:PC BM and PCDTBT:PC BM, πΈ Uapp shows a CT /(πΈ CT + π CT β πΈ) dependence in the spectral range of CT absorption. Here, π π is a prefactor that depends on the oscillator strength and number density of states, whereas πΈ π and π π are the energy and reorganization energy of the states, respectively, both being generally dependent of the width of the Gaussian DOS (see Supplementary Information ). The fit parameters obtained for this work are summarized in
Table S1.
As highlighted by the black solid line in Figure 1, πΈ Uapp in the spectral range of CT absorption is strongly energy-dependent and closely follows πΈ Uapp β2πππ CT (πΈ CT + π CT β πΈ)β as expected from eq. 3. At higher energies corresponding to sub-gap SE absorption, πΈ Uapp has a narrow parabolic shape with a sharp minimum at roughly 40 - 50 meV for the large offset blends. The EQE and πΈ Uapp of blends with a smaller offset between πΈ CT and πΈ SE (PTB7-Th:ITIC, PBDB-T:ITIC and PBDB-T:IT-4F) are shown in the middle panel of Figure 1. In this case, the Gaussian CT state line-hape is barely recognizable, and the SE absorption tail of the acceptor is visible over a wider spectral range. While πΈ Uapp retains its parabolic shape in the SE absorption regime, because of the wider range, the minimum value of πΈ Uapp is significantly reduced to values close to ππ . Finally, the EQE and πΈ Uapp of blends in low-offset systems (PM6:Y6, PM6:ITIC and PBDB-T:EH-IDTBR) are shown in the right panel of Figure 1. Such systems are characterized by similar energies for the highest occupied molecular orbital (HOMO) of the donor and the HOMO of the acceptor as illustrated in Figure 1. In these blends, the CT state absorption can no longer be discerned from the EQE spectra. Instead, the SE absorption remains dominant down to the energy range of mid-gap state excitation. In this limit, the πΈ Uapp in the SE-dominated range finally saturates and reaches a broad plateau where πΈ Uapp β ππ . The above experimental observation for low-offset D-NFA systems (where πΈ CT β πΈ SE ) suggests that intramolecular sup-gap absorption may generally follow πΌ β exp(πΈ ππβ ), but that its spectroscopic observation is obstructed by CT absorption in systems with larger offsets. To further clarify this, systems where one absorbing species dominates the sub-gap EQE spectrum were investigated and the data shown in Figure 2 . In the case of neat PC BM (Figure 2a), a narrow spectral range where πΈ Uapp β ππ can be identified. The spectral range is limited by trap-state absorption at low energies, while at high energies poor exciton dissociation severely reduces the EQE. However, the range can be increased by adding 0.1 mol% of the wide-gap donor m-MTDATA, resulting in enhanced exciton dissociation (we note that in this case the fullerene acceptor is the narrower gap component). Since m-MTDATA:PC BM is characterized by a low πΈ CT , the singlet exciton tail from PC BM can be clearly distinguished from CT states as shown in Figure 2a. By further increasing the donor content, the CT state absorption increases and the parabolic shape of πΈ Uapp emerges. This explains the parabolic shapes, seen for systems where πΈ CT βͺ πΈ SE in Figure 1, which appear when the SE absorption regime with πΈ Uapp β ππ becomes convoluted with CT state absorption. This is further supported by results for neat NFA devices comprising ITIC and IT-4F active layers, respectively, with the SE tail of the acceptor again following an inverse slope of ππ , as shown in Figure 2b. Figure 2 | EQE tail dominated by neat material absorption. a,
The inverse slope of the logarithm of the EQE for a series of m-MTDATA sensitized PC BM solar cells. The widest energy range over which πΈ Uapp equals ππ is observed for 0.1 mol% m-MTDATA in PC BM due to improved exciton dissociation in comparison to neat PC BM. BHJ examples for which the EQE tail is partially dominated by b, the neat donor absorption or by c, the neat acceptor absorption hence showing πΈ Uapp β ππ in some parts of the spectrum. EQE spectra of PTTBAI:PC BM and PBTQ(OD):PC BM are taken from reference 27. To check if πΈ Uapp β ππ is also true for donor materials has proven more challenging, since the neat donor absorption is often convoluted with deep trap-state absorption, effectively increasing πΈ Uapp above ππ as shown for PBDB-T in Figure 2c, where πΈ Uapp β
30 meV. This problem can be circumvented by using narrow-gap polymer donors such as PBTQ(OD) or PTTBAI, which show strongly redshifted EQE spectra when blended with PC BM as previously reported. As shown in Figure 2c, πΈ Uapp is around 22 meV in this case. While deviations of the type πΈ Uapp > ππ +
10 meV are due to the presence of other absorbing species like CT states or deep trap states, small deviations of πΈ Uapp around ππ are likely caused by interference effects, i.e. non-constant πΜ , as shown previously. Interference effects arises from the spectral dependence of the optical constants of the different layers in the thin-film stack and generally vary with the thickness of the active layer. To demonstrate the presence of interference effects, we therefore fabricated PM6:ITIC devices and PM6:Y6 devices of different active layer thicknesses. Indeed, as illustrated in the
Figures S3 , πΈ Uapp shows a weak thickness dependence leading to deviations around ππ from + β πΈ Uapp is further corroborated by optical transfer-matrix simulations (see
Figure S4 in the
Supplementary Information ). o verify that the absorption coefficient tail of the excitons follows a Boltzmann factor, we performed π -dependent EQE measurements on PBDB-T:EH-IDTBR, PM6:Y6 and PM6:ITIC, and the neat materials IT-4F and Y6. Figure 3a shows the normalized EQE and the respective πΈ Uapp spectra of three representative systems: PBDB-T:EH-IDTBR, PM6:Y6 and IT-4F. The remaining material systems are provided in the
Supplementary Information . Depending on π, two different regimes can be distinguished in the sub-gap absorption tail: At high π, πΈ Uapp spectra show a π -dependent plateau only influenced by interference effects and the shift in the absorption onset. At low π, however, the πΈ Uapp spectra generally attain a parabolic shape suggesting that the SE tail becomes convoluted with CT and/or mid-gap states. The thermal activation of the excitonic absorption tail is then finally illustrated by plotting the local minimum of πΈ Uapp (denoted as min (πΈ Uapp ) in Figure 3b ) in the plateau region as a function of ππ for all systems studied. We see that min (πΈ Uapp ) at higher temperature is linear and equals ππ + constant, where the constant offset arises from interference effects. At lower π, min (πΈ Uapp ) eventually deviates from linearity, as the spectral shape is increasingly affected by other absorbing species. For example, the low-energy tail of the CT absorption may emerge at low π owing to its distinctly different π -dependence compared to SE. Moreover, the absorption of trap states is expected to play a role as well, while little is yet known about their spectral broadening as a function of π . For comparison, we also measured π -dependent EQE spectra of a commercial a-Si:H thin-film solar cell (EQE and πΈ Uapp spectra shown in
Figure S6 ). In banded semiconductors such as a-Si:H, the total energetic disorder is πΈ U (π) = π s + π D (π) , where π D (π) is often described by the Einstein solid model as the thermal occupation of phonon modes. In Figure 3b , two regimes can be distinguished for a-Si:H: the low temperature saturation of min (πΈ Uapp ) to πΈ U (0) =
38 meV and thermal activation at higher temperatures with an offset of roughly 16 meV from ππ, in agreement with previous reports. β In contrast, for the organic semiconductor systems in
Figure 3b , an extrapolation to
π = 0 results in π s β 0 , suggesting that the Urbach energy is not governed by static disorder in these systems. This raises the question why excitons in organic semiconductors follow a Boltzmann factor resulting in πΈ Uapp β ππ and what is the role of π s in shaping the πΈ Uapp spectra. Answering this question may be a key to understanding the light-matter interaction in these systems.
Figure 3 | Temperature dependent apparent Urbach energies. a,
Normalized sub-gap EQE and Urbach energy ( πΈ Uapp ) spectra of inverted PM6:Y6, PBDB-T:EH-IDTBR and neat IT-4F solar cells at different temperatures. Independent of temperature, πΈ Uapp spectra show a local minimum (solid markers) at a constant energy within the spectral range dominated by exciton absorption. b, Minimum πΈ Uapp as a function of ππ for all tested materials systems including a commercial a-Si:H thin-film solar cell. In the context of the Marcus formalism for non-adiabatic charge transfer (high-temperature limit), πΈ Uapp β ππ in the spectral range of SE absorption may be rationalized in terms of non-equal potential energy surfaces for the SE state and the ground state. By assuming a significantly more diffuse or delocalized SE state, compared to the (strongly localized) ground state, a much smaller reorganization energy is obtained for the SE excited state in comparison to the ground state. β In this limit, we expect πΌ SE (πΈ, πΈ SE ) β πΌ sat exp([πΈ β πΈ SE ] ππβ ) for πΈ < πΈ SE , where πΈ SE is the energy of the singlet state (see Supplementary Information ). Here, πΌ sat includes a dependence, however, the sub-gap spectral line-shape is dominated by the Boltzmann factor. For above-gap absorption, we assume πΌ SE (πΈ, πΈ SE ) β πΌ sat for πΈ > πΈ SE . We note that this simplification of πΌ SE (πΈ, πΈ SE ) essentially follows a Miller-Abrahams-type charge-transfer formalism, sometimes used to describe exciton migration , but more commonly used for charge transport in organic semiconductors. Accounting for a DOS given by π DOS (πΈ SE ) , the total absorption coefficient is of the form πΌ SE (πΈ) = β« πΌ SE (πΈ, πΈ SE )π DOS (πΈ SE )ππΈ SE . In the Supplementary Information , expressions for the associated absorption coefficient are derived for the cases of a Gaussian DOS and an exponential tail DOS. For the case of an exponential tail DOS with the width π , we obtain πΈ Uapp = π (see
Figure S7 ). This is indeed not what we observe in experiments. For a Gaussian DOS, in turn, we obtain an absorption coefficient of the form (πΈ)πΌ sat = exp (πΈ β πΈ
ππΈ,0 + π π 2 ππΈ,0 + π π 2 πππ π β2 )] + erf (πΈ β πΈ ππΈ,0 π π β2 ) + 1 (4) where π π is the standard deviation of the Gaussian DOS and πΈ SE,0 is the DOS centre, i.e. the mean exciton energy. For
πΈ βͺ πΈ
SE,0 , eq. 4 reduces to the exponential part and πΈ Uapp therefore equals ππ . For πΈ β₯ πΈ
SE,0 , the error functions (with π π β2 in the denominator) govern the spectral shape at the absorption edge as demonstrated in Figure S8 in the
Supplementary Information . The above model explains the observed πΈ Uapp = ππ but also presents a general absorption line-shape for organic excitons near their onset from which π π and πΈ SE,0 can be obtained. To further validate the model, we applied eq. (4) to π -dependent EQE spectra, as demonstrated in Figure 4b for neat Y6 and IT-4F. Using neat materials avoids the influences of CT states in the low-energy tail although trap states are always present at lower energies. Doing so, we obtain π π values of 47.0 Β± Β± Figure S10 in the
Supplementary Information ). More fittings on room temperature EQE spectra of other material systems are shown in the
Figure S11 in the
Supporting Information ). For blend systems, the full experimental sub-gap EQE can be reconstructed assuming πΌ(πΈ) =πΌ SE (πΈ) + πΌ CT (πΈ) + πΌ t (πΈ) constituting the exponentially decaying absorption coefficient according to eq. 4 and the sum of two Gaussian functions as per eq. 3 (CT states and deep trap states). In Figure 4b, we demonstrate the model for PBDB-T:PC BM using the parameters πΈ SE,0 = π π =
60 meV, and other Gaussian fit parameters summarized in
Table S1 in the
Supplementary Information . PBDB-T:PC BM belongs to the group of blends for which πΈ CT βͺ πΈ SE,0 with β(πΈ CT βπΈ SE,0 ) β πΈ Uapp , including the parabolic behaviour in the SE-dominated regime. On the other hand, by keeping all other parameters constant while increasing πΈ CT with respect to πΈ SE,0 , the emergence of the πΈ Uapp = ππ plateau at around 1.6 Β± πΌ(πΈ) based on the dominant disorder mechanism as illustrated in Figure 4c . The steepness close to the gap is determined by π s , causing a redshift of the effective energy gap and an overall broadening with increasing π s . Although πΈ Uapp of organic semiconductors does not represent π π at any energy, a positive correlation between πΈ Uapp and π s may be observed at energies close to the absorption onset. This is simulated for the two cases π π =
70 meV and π π =
100 meV as shown in
Figure S9 : For π s =
70 meV, πΈ Uapp reaches ππ at πΌ(πΈ) values 3 to 4 orders of magnitudes below πΌ sat , while this is 6 orders below πΌ sat for π π =
100 meV. For energies well-below the bandgap πΈ Uapp β ππ , which can be considered as the spectral range where π D dominates, i.e. π D (π) = ππ . In our model, the Boltzmann factor stems from the absorption rate that describes the occupation of vibrational modes, in accordance with Marcus theory in the limit of relatively low reorganization energies of the excited state. We note that the equality πΈ U (π) = π s + π D (π) fails in the case of organic semiconductors, because π s and π D (π) define the steepness of πΌ SE (πΈ) at different energies. Figure 4 | The sub-bandgap EQE as a function of temperature and charge transfer energy. a, Experimental (black lines) and simulated (green lines) sub-gap EQE spectra of IT-4F and Y6. b, The line-shape of the experimental EQE of PBDB-T:PC BM can be described by Gaussian fits corresponding to (i) CT state absorption, (ii) trap state absorption and (iii) the SE absorption coefficient in the spectral range of singlet absorption. In the experiment, πΈ Uapp is above ππ , since πΈ CT βͺ πΈ SE,0 . Increasing πΈ CT in the simulation ( πΈ CT β πΈ SE,0 ) results in πΈ Uapp β ππ between 1.5 to 1.7 eV. c, Schematic representation of the spectral regimes of πΈ Uapp dominated by: (i) static disorder close to the band edge, (ii) dynamic disorder where πΈ Uapp = ππ and (iii) trap state absorption well-below the gap. Finally, trap state absorption is typically observed 6 orders of magnitude below πΌ sat limiting the spectral range dominated by π D . From that and the simulations in Figure S9, we estimate that it is possible to observe πΈ Uapp β ππ only when π π <
100 meV. Other conditions that must be met are: (i) the neat phase absorption of one component is spectrally separated from the other neat phase absorption, as well as from the CT states and trap states; (ii) the dynamic range of the EQE (or πΌ ) measurement is sufficiently wide to measure photocurrent at wavelengths well below the absorption onset of the neat material; and (iii) optical cavity effects are not significant. Exponential sub-gap EQE spectra previously reported in literature for BHJs often do not fulfill these requirements, explaining reported Urbach energies much larger than ππ . Importantly, the πΈ Uapp spectra introduced here do not suffer from the short fitting ranges of previous of πΈ U measurements. In contrast, we have shown that an exponential distribution of tail states cannot explain the sub-gap spectral line-shape associated with singlet absorption, nor CT or trap state absorption in organic semiconductors. Conclusion
In summary, we find that for a large number of organic semiconductors, the sub-gap slope of the excitonic absorption coefficient equals the thermal energy ππ within the variations caused by the optical interference. While exponential absorption tails have been previously observed mainly in non-fullerene systems, we show that this property is universal for organic semiconductors and consistent with a Gaussian density of excitonic states undergoing Boltzmann-like thermally activated optical transitions. A theory for the Boltzmann factor representing π D is presented via the extended Marcus theory in which the excited state is more delocalised than the ground state. π S is shown to arise from he width of the Gaussian DOS and to broaden the absorption onset at energies close to the optical gap. Using our model for the sub-gap excitonic absorption tail, it is possible to discriminate spectral regimes dominated by π D and π S , as well as to reproduce the temperature dependence of absorption coefficient due to excitons. This modified view of the sub-gap absorption coefficient in disordered organic semiconductors clarifies a longstanding debate concerning the shape of the DOS and the relevance of an Urbach description in these important and intriguing materials. Methods
Solar cells were fabricated with either a conventional architecture ITO/PEDOT:PSS/active layer/Ca/Al or inverted architecture ITO/ZnO/active layer/MoO /Ag. All material acronyms are detailed in the Supplementary Information . For a conventional device architecture, 30 nm of PEDOT:PSS was spin-coated at 6000 rpm for 30 s onto precleaned ITO substrates and annealed at 155 Β°C for 15 minutes. For an inverted device architecture with 30 nm of ZnO, a solution of 200 mg of zinc acetate dihydrate in 2-methoxyethanol (2 ml) and ethanolamine (56 Β΅l) was prepared and stirred overnight under ambient conditions. The ZnO layer formed upon spin-coating the solution at 4000 rpm followed by thermal annealing at 200 Β°C for 60 minutes. The processing conditions of the individual active layers are discussed in the
Supplementary Information . For the EQE measurements, a homebuilt setup including a Perkin Elmer UV/VIS/NIR spectrometer (LAMBDA 950) as a source for monochromatic light was used. The light was chopped at 273 Hz and directed onto the device under test (DUT). The resulting photocurrent was amplified by a low noise current amplifier (FEMTO DLPCA-200) and measured with the Stanford SR860 lock-in amplifier. To decrease the noise floor of the setup, the DUT was mounted in an electrically shielded and temperature controlled Linkam sample stage. An integration time up to 1000 seconds was used for detecting wavelengths above 1500 nm. NISTβ calibrated silicon and GaAs photodiodes from Newport were used as a calibration reference. The temperature inside the Linkam sample stage was set to -
120 to 60 β°C by the Linkam T96 temperature controller in combination with an LNP96 liquid nitrogen pump. The commercial amorphous silicon thin film solar cell, used for temperature dependent EQE measurements, was manufactured by TRONY with the part number sc80125s-8.
Data Availability
The data that support the findings of this study are available from the corresponding author upon reasonable request
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This work was funded through the Welsh Governmentβs SΓͺr Cymru II Program βSustainable Advanced Materialsβ (Welsh European Funding Office β European Regional Development Fund). C.K . is recipient of a UKRI EPSRC Doctoral Training Program studentship. N.Z. is funded by a studentship through the SΓͺr Cymru II Program. P.M. is a SΓͺr Cymru II Research Chair and A.A. is a Rising Star Fellow also funded through the Welsh Governmentβs SΓͺr Cymru II βSustainable Advanced Materialsβ Program (European
Regional Development Fund, Welsh European Funding Office and Swansea University Strategic Initiative).
Author Contributions
AA and PM provided the overall leadership of the project. OJS and AA conceptualised the idea. CK and AA designed the experiments. CK performed most measurements, analysed the data, performed optical modelling and drafted the manuscript. OJS developed the theoretical model. CK, OJS and AA interpreted the data. NZ assisted with
EQE PV measurements. WL fabricated the devices. All co-authors contributed in the development of the manuscript which was initially drafted by CK. Additional information Supplementary Information