Refine
Year of publication
- 2019 (6) (remove)
Language
- English (6)
Is part of the Bibliography
- yes (6)
Keywords
- Cayley Graph (2)
- Collatz (2)
- Free Group (2)
- Reachability (2)
- Kelvin probe (1)
- lead halide perovskite films (1)
- surface band bending (1)
- surface photovoltage (1)
- surface states (1)
- ultraviolet photoelectron spectroscopy (1)
Institute
The Collatz conjecture is a number theoretical problem, which has puzzled countless researchers using myriad approaches. Presently, there are scarcely any methodologies to describe and treat the problem from the perspective of the Algebraic Theory of Automata. Such an approach is promising with respect to facilitating the comprehension of the Collatz sequence’s "mechanics". The systematic technique of a state machine is both simpler and can fully be described by the use of algebraic means.
The current gap in research forms the motivation behind the present contribution. The present authors are convinced that exploring the Collatz conjecture in an algebraic manner, relying on findings and fundamentals of Graph Theory and Automata Theory, will simplify the problem as a whole.
The Collatz conjecture is a number theoretical problem, which has puzzled countless researchers using myriad approaches. Presently, there are scarcely any methodologies to describe and treat the problem from the perspective of the Algebraic Theory of Automata. Such an approach is promising with respect to facilitating the comprehension of the Collatz sequences "mechanics". The systematic technique of a state machine is both simpler and can fully be described by the use of algebraic means.
The current gap in research forms the motivation behind the present contribution. The present authors are convinced that exploring the Collatz conjecture in an algebraic manner, relying on findings and fundamentals of Graph Theory and Automata Theory, will simplify the problem as a whole.
The tremendous success of metal-halide perovskites, especially in the field of photovoltaics, has triggered a substantial number of studies in understanding their optoelectronic properties. However, consensus regarding the electronic properties of these perovskites is lacking due to a huge scatter in the reported key parameters, such as work function (Φ) and valence band maximum (VBM) values. Here, we demonstrate that the surface photovoltage (SPV) is a key phenomenon occurring at the perovskite surfaces that feature a non-negligible density of surface states, which is more the rule than an exception for most materials under study. With ultraviolet photoelectron spectroscopy (UPS) and Kelvin probe, we evidence that even minute UV photon fluxes (500 times lower than that used in typical UPS experiments) are sufficient to induce SPV and shift the perovskite Φ and VBM by several 100 meV compared to dark. By combining UV and visible light, we establish flat band conditions (i.e., compensate the surface-state-induced surface band bending) at the surface of four important perovskites, and find that all are p-type in the bulk, despite a pronounced n-type surface character in the dark. The present findings highlight that SPV effects must be considered in all surface studies to fully understand perovskites’ photophysical properties.
Photovoltaic cells based on halide perovskites, possessing remarkably high power conversion efficiencies have been reported. To push the development of such devices further, a comprehensive and reliable understanding of their electronic properties is essential but presently not available. To provide a solid foundation for understanding the electronic properties of polycrystalline thin films, we employ single-crystal band structure data from angle-resolved photoemission measurements. For two prototypical perovskites (CH3NH3PbBr3 and CH3NH3PbI3), we reveal the band dispersion in two high-symmetry directions and identify the global valence band maxima. With these benchmark data, we construct "standard" photoemission spectra from polycrystalline thin film samples and resolve challenges discussed in the literature for determining the valence band onset with high reliability. Within the framework laid out here, the consistency of relating the energy level alignment in perovskite-based photovoltaic and optoelectronic devices with their functional parameters is substantially enhanced.
The incorporation of even small amounts of strontium (Sr) into lead-base hybrid quadruple cation perovskite solar cells results in a systematic increase of the open circuit voltage (V-oc) in pin-type perovskite solar cells. We demonstrate via absolute and transient photoluminescence (PL) experiments how the incorporation of Sr significantly reduces the non-radiative recombination losses in the neat perovskite layer. We show that Sr segregates at the perovskite surface, where it induces important changes of morphology and energetics. Notably, the Sr-enriched surface exhibits a wider band gap and a more n-type character, accompanied with significantly stronger surface band bending. As a result, we observe a significant increase of the quasi-Fermi level splitting in the neat perovskite by reduced surface recombination and more importantly, a strong reduction of losses attributed to non-radiative recombination at the interface to the C-60 electron-transporting layer. The resulting solar cells exhibited a V-oc of 1.18 V, which could be further improved to nearly 1.23 V through addition of a thin polymer interlayer, reducing the non-radiative voltage loss to only 110 meV. Our work shows that simply adding a small amount of Sr to the precursor solutions induces a beneficial surface modification in the perovskite, without requiring any post treatment, resulting in high efficiency solar cells with power conversion efficiency (PCE) up to 20.3%. Our results demonstrate very high V-oc values and efficiencies in Sr-containing quadruple cation perovskite pin-type solar cells and highlight the imperative importance of addressing and minimizing the recombination losses at the interface between perovskite and charge transporting layer.
Charge transport layers (CTLs) are key components of diffusion controlled perovskite solar cells, however, they can induce additional non-radiative recombination pathways which limit the open circuit voltage (V-OC) of the cell. In order to realize the full thermodynamic potential of the perovskite absorber, both the electron and hole transport layer (ETL/HTL) need to be as selective as possible. By measuring the photoluminescence yield of perovskite/CTL heterojunctions, we quantify the non-radiative interfacial recombination currents in pin- and nip-type cells including high efficiency devices (21.4%). Our study comprises a wide range of commonly used CTLs, including various hole-transporting polymers, spiro-OMeTAD, metal oxides and fullerenes. We find that all studied CTLs limit the V-OC by inducing an additional non-radiative recombination current that is in most cases substantially larger than the loss in the neat perovskite and that the least-selective interface sets the upper limit for the V-OC of the device. Importantly, the V-OC equals the internal quasi-Fermi level splitting (QFLS) in the absorber layer only in high efficiency cells, while in poor performing devices, the V-OC is substantially lower than the QFLS. Using ultraviolet photoelectron spectroscopy and differential charging capacitance experiments we show that this is due to an energy level mis-alignment at the p-interface. The findings are corroborated by rigorous device simulations which outline important considerations to maximize the V-OC. This work highlights that the challenge to suppress non-radiative recombination losses in perovskite cells on their way to the radiative limit lies in proper energy level alignment and in suppression of defect recombination at the interfaces.