Theoretical limits of multiple exciton generation and singlet fission tandem devices for solar water splitting.

Photoelectrochemical (PEC) water splitting is one of the most important approaches being investigated for solar fuel generation. In this study, we determine the maximum thermodynamic power conversion efficiencies (PCEs) of PEC water splitting two-bandgap tandem devices that produce multiple carriers per photon absorbed via Multiple Exciton Generation (MEG) or Singlet Fission (SF) and in the presence of solar concentration. Here, we employ a detailed balance thermodynamic analysis to determine the effects of top cell thickness, solar concentration, carrier multiplication, electrode overvoltage (VO), and water absorption on PEC power conversion efficiency for water splitting cells. We have found a maximum PEC power conversion efficiency of 62.9% in cells using two ideal tandem MEG absorbers with bandgaps of 0.3 and 1.2 eV at 1000-suns solar concentration and 0 overvoltage; the maximum PCE for two tandem SF absorbers under the same conditions is nearly the same at 59% with the same values for the absorption thresholds. A very interesting and important result was that, upon thinning the top cell, the range of viable bandgaps for both the top and bottom cells is extended by as much as 0.5-1 eV while still maintaining high maximum conversion efficiency (60-63%). The effects of imposing different solar concentrations from 1X to 1000X and having different tandem configurations of SF and MEG layers were also studied.

Synthesis and Spectroscopy of Silver-Doped PbSe Quantum Dots.

Electronic impurity doping of bulk semiconductors is an essential component of semiconductor science and technology. Yet there are only a handful of studies demonstrating control of electronic impurities in semiconductor nanocrystals. Here, we studied electronic impurity doping of colloidal PbSe quantum dots (QDs) using a postsynthetic cation exchange reaction in which Pb is exchanged for Ag. We found that varying the concentration of dopants exposed to the as-synthesized PbSe QDs controls the extent of exchange. The electronic impurity doped QDs exhibit the fundamental spectroscopic signatures associated with injecting a free charge carrier into a QD under equilibrium conditions, including a bleach of the first exciton transition and the appearance of a quantum-confined, low-energy intraband absorption feature. Photoelectron spectroscopy confirms that Ag acts as a p-type dopant for PbSe QDs and infrared spectroscopy is consistent with k·p calculations of the size-dependent intraband transition energy. We find that to bleach the first exciton transition by an average of 1 carrier per QD requires that approximately 10% of the Pb be replaced by Ag. We hypothesize that the majority of incorporated Ag remains at the QD surface and does not interact with the core electronic states of the QD. Instead, the excess Ag at the surface promotes the incorporation of <1% Ag into the QD core where it causes p-type doping behavior.

Quantum confined electron-phonon interaction in silicon nanocrystals.

We study the micro-Raman spectra of colloidal silicon nanocrystals as a function of size, excitation wavelength, and excitation intensity. We find that the longitudinal optical (LO) phonon spectrum is asymmetrically broadened toward the low energy side and exhibits a dip or antiresonance on the high-energy side, both characteristics of a Fano line shape. The broadening depends on both nanocrystal size and Raman excitation wavelength. We propose that the Fano line shape results from interference of the optical phonon response with a continuum of electronic states that become populated by intraband photoexcitation of carriers. The asymmetry exhibits progressive enhancement with decreasing particle size and with increasing excitation energy for a given particle size. We compare our observations with those reported for p- and n-doped bulk Si, where Fano interference has also been observed, but we find opposite wavelength dependence of the asymmetry for the bulk and nanocrystalline Si. Our results have important implications for potentially controlling carrier energy relaxation channels in strongly confined Si nanocrystals.

Synthesis and spectroscopy of PbSe fused quantum-dot dimers.

We report the synthesis and characterization of Pb-chalcogenide fused quantum-dot (QD) dimer structures. The resulting QD dimers range in length from 6 to 16 nm and are produced by oriented attachment of single QD monomers with diameters of 3.1-7.8 nm. QD monomers with diameters exceeding about 5 nm appear to have the greatest affinity for QD dimer formation and, therefore, gave the greatest yields of fused structures. We find a new absorption feature in the first exciton QD dimer spectra and assign this to a splitting of the 8-fold degenerate 1S-level. The dimer splitting increases from 50 to 140 meV with decrease of the QD-monomer size, and we present a mechanism that accounts for this splitting. We also demonstrate the possibility of fusing two QDs with different sizes into a heterostructure.

The role of chromophore coupling in singlet fission.

Certain organic materials can generate more than one electron-hole pair per absorbed photon, a property that could revolutionize the prospects for solar energy. This process, called singlet fission, is one possible "exciton multiplication" scheme that could be useful in a variety of photovoltaic device designs from dye-sensitized solar cells to solar cell bilayers to bulk heterojunctions. For such applications to be possible, however, singlet fission must occur with near perfect efficiency in compounds that also have other requisite properties such as strong visible light absorption and photostability. Many recent investigations of singlet fission have focused on crystalline polyacenes, which have been known for some time to undergo singlet fission. While these materials have promise, limitations in stability, cost, and performance may hinder practical application of polyacene solar cells, while their complex photophysics may limit our fundamental understanding of singlet fission in crystalline polyacenes. In this Account, we describe rationally designed singlet fission chromophores whose excited state dynamics should be fairly simple and whose coupling can be well controlled through the formation of covalent dimers, aggregates, or polycrystalline films. In principle, investigations of these chromophores should provide the clearest connection to theoretical concepts explaining how an excited state evolves from a singlet (S1) into two triplets (TT). Realizing the promise of efficient singlet fission rests with two tasks: (i) producing an ideal molecular energy level structure and (ii) inducing the correct type and strength of chromophore coupling. In this Account, we offer theoretical guidance for achieving (i) and consider more extensively recent results aimed at (ii). For (i), theoretical guidance suggests that, in addition to alternant hydrocarbons like tetracene and pentacene, biradicals (i.e., molecules with two independent radical centers) may also be used as the basis for designing chromophores with low-lying triplet states such that the energy relationship 2E(T1) ≤ E(S1) is satisfied. Although molecules that do not fulfill this condition can also exhibit singlet fission from a higher lying or vibrationally excited singlet state, fast relaxation processes will likely reduce the singlet fission yield and complicate determination of the singlet fission mechanism. For (ii), once an appropriate chromophore has been chosen, the task of coupling two or more of them together must be done carefully. We discuss three pathways by which a dimer could undergo singlet fission: (1) A direct route in which slipped cofacial stacking is favorable under certain conditions. Cofacial stacking is common in molecular crystals, and it is likely not a coincidence that recent reports of efficient singlet fission involve slipped-stacked molecules in polycrystalline thin films. (2) A mediated route in which S1 interacts with (TT) through a virtual radical cation/anion state, which may be important in some situations. (3) A two-step route (i.e., through a real charge transfer intermediate) which others have suggested theoretically. We present data on 1,3-diphenylisobenzofuran (DPIBF) dimers that are consistent with this pathway. Finally, we review potential solar photoconversion efficiency gains utilizing singlet fission in several contexts.

Third generation photovoltaics based on multiple exciton generation in quantum confined semiconductors.

Improving the primary photoconversion process in a photovoltaiccell by utilizing the excess energy that is otherwise lost as heat can lead to an increase in the overall power conversion efficiency (PCE). Semiconductor nanocrystals (NCs) with at least one dimension small enough to produce quantum confinement effects provide new ways of controlling energy flow not achievable in thin film or bulk semiconductors. Researchers have developed various strategies to incorporate these novel structures into suitable solar conversion systems. Some of these methods could increase the PCE past the Shockley-Queisser (SQ) limit of ∼33%, making them viable "third generation photovoltaic" (TGPV) cell architectures. Surpassing the SQ limit for single junction solar cells presents both a scientific and a technological challenge, and the use of semiconductor NCs to enhance the primary photoconversion process offers a promising potential solution. The NCs are synthesized via solution phase chemical reactions producing stable colloidal solutions, where the reaction conditions can be modified to produce a variety of shapes, compositions, and structures. The confinement of the semiconductor NC in one dimension produces quantum films, wells, or discs. Two-dimensional confinement leads to quantum wires or rods (QRs), and quantum dots (QDs) are three-dimensionally confined NCs. The process of multiple exciton generation (MEG) converts a high-energy photon into multiple electron-hole pairs. Although many studies have demonstrated that MEG is enhanced in QDs compared with bulk semiconductors, these studies have either used ultrafast spectroscopy to measure the photon-to-exciton quantum yields (QYs) or theoretical calculations. Implementing MEG in a working solar cell has been an ongoing challenge. In this Account, we discuss the status of MEG research and strategies towards implementing MEG in working solar cells. Recently we showed an external quantum efficiency for photocurrent of greater than 100% (reaching 114%) at ∼4Eg in a PbSe QD solar cell. The internal quantum efficiency reached 130%. These results compare favorably with ultrafast transient spectroscopic measurements. Thus, we have shown that one of the tenets of the SQ limit, that photons only produce one electron-hole pair at the electrodes of a solar cell, can be overcome. Further challenges include increasing the MEG efficiency and improving the QD device structure and operation.

Size and composition dependent multiple exciton generation efficiency in PbS, PbSe, and PbS(x)Se(1-x) alloyed quantum dots.

Using ultrafast transient absorption and time-resolved photoluminescence spectroscopies, we studied multiple exciton generation (MEG) in quantum dots (QDs) consisting of either PbSe, PbS, or a PbSxSe1-x alloy for various QD diameters with corresponding bandgaps (Eg) ranging from 0.6 to 1 eV. For each QD sample, we determine the MEG efficiency, ηMEG, defined in terms of the electron-hole pair creation energy (εeh) such that ηMEG = Eg/εeh. In previous reports, we found that ηMEG is about two times greater in PbSe QDs compared to bulk PbSe, however, little could be said about the QD-size dependence of MEG. In this study, we find for both PbS and PbSxSe1-x alloyed QDs that ηMEG decreases lineally with increasing QD diameter within the strong confinement regime. When the QD radius is normalized by a material-dependent characteristic radius, defined as the radius at which the electron-hole Coulomb and confinement energies are equivalent, PbSe, PbS, and PbSxSe1-x exhibit similar MEG behaviors. Our results suggest that MEG increases with quantum confinement, and we discuss the interplay between a size-dependent MEG rate versus hot exciton cooling.

Comparison of carrier multiplication yields in PbS and PbSe nanocrystals: the role of competing energy-loss processes.

Infrared band gap semiconductor nanocrystals are promising materials for exploring generation III photovoltaic concepts that rely on carrier multiplication or multiple exciton generation, the process in which a single high-energy photon generates more than one electron-hole pair. In this work, we present measurements of carrier multiplication yields and biexciton lifetimes for a large selection of PbS nanocrystals and compare these results to the well-studied PbSe nanocrystals. The similar bulk properties of PbS and PbSe make this an important comparison for discerning the pertinent properties that determine efficient carrier multiplication. We observe that PbS and PbSe have very similar biexciton lifetimes as a function of confinement energy. Together with the similar bulk properties, this suggests that the rates of multiexciton generation, which is the inverse of Auger recombination, are also similar. The carrier multiplication yields in PbS nanocrystals, however, are strikingly lower than those observed for PbSe nanocrystals. We suggest that this implies the rate of competing processes, such as phonon emission, is higher in PbS nanocrystals than in PbSe nanocrystals. Indeed, our estimations for phonon emission mediated by the polar Fröhlich-type interaction indicate that the corresponding energy-loss rate is approximately twice as large in PbS than in PbSe.

Quantum dot size dependent J-V characteristics in heterojunction ZnO/PbS quantum dot solar cells.

The current-voltage (J-V) characteristics of ZnO/PbS quantum dot (QD) solar cells show a QD size-dependent behavior resulting from a Schottky junction that forms at the back metal electrode opposing the desirable diode formed between the ZnO and PbS QD layers. We study a QD size-dependent roll-over effect that refers to the saturation of photocurrent in forward bias and crossover effect which occurs when the light and dark J-V curves intersect. We model the J-V characteristics with a main diode formed between the n-type ZnO nanocrystal (NC) layer and p-type PbS QD layer in series with a leaky Schottky-diode formed between PbS QD layer and metal contact. We show how the characteristics of the two diodes depend on QD size, metal work function, and PbS QD layer thickness, and we discuss how the presence of the back diode complicates finding an optimal layer thickness. Finally, we present Kelvin probe measurements to determine the Fermi level of the QD layers and discuss band alignment, Fermi-level pinning, and the V(oc) within these devices.

n-Type transition metal oxide as a hole extraction layer in PbS quantum dot solar cells.

The n-type transition metal oxides (TMO) consisting of molybdenum oxide (MoO(x)) and vanadium oxide (V(2)O(x)) are used as an efficient hole extraction layer (HEL) in heterojunction ZnO/PbS quantum dot solar cells (QDSC). A 4.4% NREL-certified device based on the MoO(x) HEL is reported with Al as the back contact material, representing a more than 65% efficiency improvement compared with the case of Au contacting the PbS quantum dot (QD) layer directly. We find the acting mechanism of the hole extraction layer to be a dipole formed at the MoO(x) and PbS interface enhancing band bending to allow efficient hole extraction from the valence band of the PbS layer by MoO(x). The carrier transport to the metal anode is likely enhanced through shallow gap states in the MoO(x) layer.

Anomalous independence of multiple exciton generation on different group IV-VI quantum dot architectures.

Multiple exciton generation (MEG) in PbSe quantum dots (QDs), PbSe(x)S(1-x) alloy QDs, PbSe/PbS core/shell QDs, and PbSe/PbSe(y)S(1-y) core/alloy-shell QDs was studied with time-resolved optical pump and probe spectroscopy. The optical absorption exhibits a red-shift upon the introduction of a shell around a PbSe core, which increases with the thickness of the shell. According to electronic structure calculations this can be attributed to charge delocalization into the shell. Remarkably, the measured quantum yield of MEG, the hot exciton cooling rate, and the Auger recombination rate of biexcitons are similar for pure PbSe QDs and core/shell QDs with the same core size and varying shell thickness. The higher density of states in the alloy and core/shell QDs provide a faster exciton cooling channel that likely competes with the fast MEG process due to a higher biexciton density of states. Calculations reveal only a minor asymmetric delocalization of holes and electrons over the entire core/shell volume, which may partially explain why the Auger recombination rate does not depend on the presence of a shell.

Nanoscience and nanostructures for photovoltaics and solar fuels.

Quantum confinement of electronic particles (negative electrons and positive holes) in nanocrystals produces unique optical and electronic properties that have the potential to enhance the power conversion efficiency of solar cells for photovoltaic and solar fuels production at lower cost. These approaches and applications are labeled third generation solar photon conversion. Prominent among these unique properties is the efficient formation of more than one electron-hole pair (called excitons in nanocrystals) from a single absorbed photon. In isolated nanocrystals that have three-dimensional confinement of charge carriers (quantum dots) or two-dimensional confinement (quantum wires and rods) this process is termed multiple exciton generation. This Perspective presents a summary of our present understanding of the science of optoelectronic properties of nanocrystals and a prognosis for and review of the technological status of nanocrystals and nanostructures for third generation photovoltaic cells and solar fuels production.

Comparing multiple exciton generation in quantum dots to impact ionization in bulk semiconductors: implications for enhancement of solar energy conversion.

Multiple exciton generation (MEG) in quantum dots (QDs) and impact ionization (II) in bulk semiconductors are processes that describe producing more than one electron-hole pair per absorbed photon. We derive expressions for the proper way to compare MEG in QDs with II in bulk semiconductors and argue that there are important differences in the photophysics between bulk semiconductors and QDs. Our analysis demonstrates that the fundamental unit of energy required to produce each electron-hole pair in a given QD is the band gap energy. We find that the efficiency of the multiplication process increases by at least 2 in PbSe QDs compared to bulk PbSe, while the competition between cooling and multiplication favors multiplication by a factor of 3 in QDs. We also demonstrate that power conversion efficiencies in QD solar cells exhibiting MEG can greatly exceed conversion efficiencies of their bulk counterparts, especially if the MEG threshold energy can be reduced toward twice the QD band gap energy, which requires a further increase in the MEG efficiency. Finally, we discuss the research challenges associated with achieving the maximum benefit of MEG in solar energy conversion since we show the threshold and efficiency are mathematically related.

High triplet yield from singlet fission in a thin film of 1,3-diphenylisobenzofuran.

Direct observation of triplet absorption and ground-state depletion upon pulsed excitation of a polycrystalline thin solid film of 1,3-diphenylisobenzofuran at 77 K revealed a 200 ± 30% triplet yield, which was attributed to singlet fission.

Toward designed singlet fission: electronic states and photophysics of 1,3-diphenylisobenzofuran.

Single crystal molecular structure and solution photophysical properties are reported for 1,3-diphenylisobenzofuran (1), of interest as a model compound in studies of singlet fission. For the ground state of 1 and of its radical cation (1(+*)) and anion (1(-*)), we report the UV-visible absorption spectra, and for neutral 1, also the magnetic circular dichroism (MCD) and the decomposition of the absorption spectrum into purely polarized components, deduced from fluorescence polarization. These results were used to identify a series of singlet excited states. For the first excited singlet and triplet states of 1, the transient visible absorption spectra, S(1) --> S(x) and sensitized T(1) --> T(x), and single exponential lifetimes, tau(F) = approximately 5.3 ns and tau(T) = approximately 200 micros, are reported. The spectra and lifetimes of S(1) --> S(0) fluorescence and sensitized T(1) --> T(x) absorption of 1 were obtained in a series of solvents, as was the fluorescence quantum yield, Phi(F) = 0.95-0.99. No phosphorescence has been detected. The first triplet excitation energy of solid 1 (11,400 cm(-1)) was obtained by electron energy loss spectroscopy, in agreement with previously reported solution values. The fluorescence excitation spectrum suggests an onset of a nonradiative channel at approximately 37,000 cm(-1). Excitation energies and relative transition intensities are in agreement with those of ab initio (CC2) calculations after an empirical 3000 cm(-1) adjustment of the initial state energy to correct differentially for a better quality description of the initial relative to the terminal state of an absorption transition. The interpretation of the MCD spectrum used the semiempirical PPP method, whose results for the S(0) --> S(x) spectrum require no empirical adjustment and are otherwise nearly identical with the CC2 results in all respects including the detailed nature of the electronic excitation. The ground state geometry of 1 was also calculated by the MP2, B3LYP, and CAS methods. The calculations provided a prediction of changes of molecular geometry upon excitation or ionization and permitted an interpretation of the spectra in terms of molecular orbitals involved. Computations suggest that 1 can exist as two nearly isoenergetic conformers of C(2) or C(s) symmetry. Linear dichroism measurements in stretched polyethylene provide evidence for their existence and show that they orient to different degrees, permitting a separation of their spectra in the region of the purely polarized first absorption band. Their excitation energies are nearly identical, but the Franck-Condon envelopes of their first transition differ to a surprising degree.

Designing Janus Ligand Shells on PbS Quantum Dots using Ligand-Ligand Cooperativity.

We present a combined experimental and theoretical study of ligand-ligand cooperativity during X-type carboxylate-to-carboxylate ligand exchange reactions on PbS quantum dot surfaces. We find that the ligand dipole moment (varied through changing the substituents on the benzene ring of cinnamic acid derivatives) impacts the ligand-exchange isotherms; in particular, ligands with large electron withdrawing character result in a sharper transition from an oleate-dominated ligand shell to a cinnamate-dominated ligand shell. We developed a two-dimensional lattice model to simulate the ligand-exchange isotherms that accounts for the difference in ligand binding energy as well as ligand-ligand cooperativity. Our model shows that ligands with larger ligand-ligand coupling energy exhibit sharper isotherms indicating an order-disorder phase transition. Finally, we developed an anisotropic Janus ligand shell by taking advantage of the ligand-ligand cooperative ligand exchanges. We monitored the Janus ligand shell using 19F nuclear magnetic resonance, showing that when the ligand-ligand coupling energy falls within the order region of the phase diagram, Janus ligand shells can be constructed.

Structural, optical, and electrical properties of PbSe nanocrystal solids treated thermally or with simple amines.

We describe the structural, optical, and electrical properties of films of spin-cast, oleate-capped PbSe nanocrystals that are treated thermally or chemically in solutions of hydrazine, methylamine, or pyridine to produce electronically coupled nanocrystal solids. Postdeposition heat treatments trigger nanocrystal sintering at approximately 200 degrees C, before a substantial fraction of the oleate capping group evaporates or pyrolyzes. The sintered nanocrystal films have a large hole density and are highly conductive. Most of the amine treatments preserve the size of the nanocrystals and remove much of the oleate, decreasing the separation between nanocrystals and yielding conductive films. X-ray scattering, X-ray photoelectron and optical spectroscopy, electron microscopy, and field-effect transistor electrical measurements are used to compare the impact of these chemical treatments. We find that the concentration of amines adsorbed to the NC films is very low in all cases. Treatments in hydrazine in acetonitrile remove only 2-7% of the oleate yet result in high-mobility n-type transistors. In contrast, ethanol-based hydrazine treatments remove 85-90% of the original oleate load. Treatments in pure ethanol strip 20% of the oleate and create conductive p-type transistors. Methylamine- and pyridine-treated films are also p-type. These chemically treated films oxidize rapidly in air to yield, after short air exposures, highly conductive p-type nanocrystal solids. Our results aid in the rational development of solar cells based on colloidal nanocrystal films.

Optical Absorbance Enhancement in PbS QD/Cinnamate Ligand Complexes.

We studied the optical absorption enhancement in colloidal suspensions of PbS quantum dots (QD) upon ligand exchange from oleate to a series of cinnamate ligands. By combining experiments and ab initio simulations, we elucidate physical parameters that govern the optical absorption enhancement. We find that, within the cinnamate/PbS QD system, the optical absorption enhancement scales linearly with the electronic gap of the ligand, indicating that the ligand/QD coupling occurs equally efficient between the QD and ligand HOMO and their respective LUMO levels. Disruption of the conjugation that connects the aromatic ring and its substituents to the QD core causes a reduction of the electronic coupling. Our results further support the notion that the ligand/QD complex should be considered as a distinct chemical system with emergent behavior rather than a QD core with ligands whose sole purpose is to passivate surface dangling bonds and prevent agglomeration.

Enhanced Multiple Exciton Generation in PbS|CdS Janus-like Heterostructured Nanocrystals.

Generating multiple excitons by a single high-energy photon is a promising third-generation solar energy conversion strategy. We demonstrate that multiple exciton generation (MEG) in PbS|CdS Janus-like heteronanostructures is enhanced over that of single-component and core/shell nanocrystal architectures, with an onset close to two times the PbS band gap. We attribute the enhanced MEG to the asymmetric nature of the heteronanostructure that results in an increase in the effective Coulomb interaction that drives MEG and a reduction of the competing hot exciton cooling rate. Slowed cooling occurs through effective trapping of hot-holes by a manifold of valence band interfacial states having both PbS and CdS character, as evidenced by photoluminescence studies and ab initio calculations. Using transient photocurrent spectroscopy, we find that the MEG characteristics of the individual nanostructures are maintained in conductive arrays and demonstrate that these quasi-spherical PbS|CdS nanocrystals can be incorporated as the main absorber layer in functional solid-state solar cell architectures. Finally, based upon our analysis, we provide design rules for the next generation of engineered nanocrystals to further improve the MEG characteristics.