Cooling and Auger recombination of charges in PbSe nanorods: crossover from cubic to bimolecular decay

Charge Transfer from Quantum-Confined 0D, 1D, and 2D Nanocrystals

The properties of colloidal quantum-confined semiconductor nanocrystals (NCs), including zero-dimensional (0D) quantum dots, 1D nanorods, 2D nanoplatelets, and their heterostructures, can be tuned through their size, dimensionality, and material composition. In their photovoltaic and photocatalytic applications, a key step is to generate spatially separated and long-lived electrons and holes by interfacial charge transfer. These charge transfer properties have been extensively studied recently, which is the subject of this Review. The Review starts with a summary of the electronic structure and optical properties of 0D-2D nanocrystals, followed by the advances in wave function engineering, a novel way to control the spatial distribution of electrons and holes, through their size, dimension, and composition. It discusses the dependence of NC charge transfer on various parameters and the development of the Auger-assisted charge transfer model. Recent advances in understanding multiple exciton generation, decay, and dissociation are also discussed, with an emphasis on multiple carrier transfer. Finally, the applications of nanocrystal-based systems for photocatalysis are reviewed, focusing on the photodriven charge separation and recombination processes that dictate the function and performance of these materials. The Review ends with a summary and outlook of key remaining challenges and promising future directions in the field.

Electronic Structure and Excited State Dynamics of Cadmium Chalcogenide Nanorods

The cylindrical quasi-one-dimensional shape of colloidal semiconductor nanorods (NRs) gives them unique electronic structure and optical properties. In addition to the band gap tunability common to nanocrystals, NRs have polarized light absorption and emission and high molar absorptivities. NR-shaped heterostructures feature control of electron and hole locations as well as light emission energy and efficiency. We comprehensively review the electronic structure and optical properties of Cd-chalcogenide NRs and NR heterostructures (e.g., CdSe/CdS dot-in-rods, CdSe/ZnS rod-in-rods), which have been widely investigated over the last two decades due in part to promising optoelectronic applications. We start by describing methods for synthesizing these colloidal NRs. We then detail the electronic structure of single-component and heterostructure NRs and follow with a discussion of light absorption and emission in these materials. Next, we describe the excited state dynamics of these NRs, including carrier cooling, carrier and exciton migration, radiative and nonradiative recombination, multiexciton generation and dynamics, and processes that involve trapped carriers. Finally, we describe charge transfer from photoexcited NRs and connect the dynamics of these processes with light-driven chemistry. We end with an outlook that highlights some of the outstanding questions about the excited state properties of Cd-chalcogenide NRs.

Using Interaction of Nano Dipoles to Control the Growth of Nanorods

Charged facets of a nanocrystal can form an intrinsic nanometer-size electric dipole. When the spacing between these nano dipoles is adjusted, the dipolar interaction energy is tuned from a fraction to a multiple of the thermal energy. Consequently, the one-dimensional oriented attachment can be switched on or off, as is the growth of nanorods. This kinetically controlled growth is achieved at relatively low reaction temperatures while the thermodynamically controlled growth dominates at higher temperatures. The synthesized PbSe nanorods are branchless, exhibiting a single-exponential photoluminescence decay trace with an e-folding lifetime of 1.3 μs and a photoluminescence quantum yield of 35%.

Electron-Hole Correlations Govern Auger Recombination in Nanostructures

The fast nonradiative decay of multiexcitonic states via Auger recombination is a fundamental process affecting a variety of applications based on semiconductor nanostructures. From a theoretical perspective, the description of Auger recombination in confined semiconductor nanostructures is a challenging task due to the large number of valence electrons and exponentially growing number of excited excitonic and biexcitonic states that are coupled by the Coulomb interaction. These challenges have restricted the treatment of Auger recombination to simple, noninteracting electron-hole models. Herein we present a novel approach for calculating Auger recombination lifetimes in confined nanostructures having thousands to tens of thousands of electrons, explicitly including electron-hole interactions. We demonstrate that the inclusion of electron-hole correlations are imperative to capture the correct scaling of the Auger recombination lifetime with the size and shape of the nanostructure. In addition, correlation effects are required to obtain quantitatively accurate lifetimes even for systems smaller than the exciton Bohr radius. Neglecting such correlations can result in lifetimes that are two orders of magnitude too long. We establish the utility of the new approach for CdSe quantum dots of varying sizes and for CdSe nanorods of varying diameters and lengths. Our new approach is the first theoretical method to postdict the experimentally known "universal volume scaling law" for quantum dots and makes novel predictions for the scaling of the Auger recombination lifetimes in nanorods.

Charge Carrier Dynamics in Photocatalytic Hybrid Semiconductor-Metal Nanorods: Crossover from Auger Recombination to Charge Transfer

Hybrid semiconductor-metal nanoparticles (HNPs) manifest unique, synergistic electronic and optical properties as a result of combining semiconductor and metal physics via a controlled interface. These structures can exhibit spatial charge separation across the semiconductor-metal junction upon light absorption, enabling their use as photocatalysts. The combination of the photocatalytic activity of the metal domain with the ability to generate and accommodate multiple excitons in the semiconducting domain can lead to improved photocatalytic performance because injecting multiple charge carriers into the active catalytic sites can increase the quantum yield. Herein, we show a significant metal domain size dependence of the charge carrier dynamics as well as the photocatalytic hydrogen generation efficiencies under nonlinear excitation conditions. An understanding of this size dependence allows one to control the charge carrier dynamics following the absorption of light. Using a model hybrid semiconductor-metal CdS-Au nanorod system and combining transient absorption and hydrogen evolution kinetics, we reveal faster and more efficient charge separation and transfer under multiexciton excitation conditions for large metal domains compared to small ones. Theoretical modeling uncovers a competition between the kinetics of Auger recombination and charge separation. A crossover in the dominant process from Auger recombination to charge separation as the metal domain size increases allows for effective multiexciton dissociation and harvesting in large metal domain HNPs. This was also found to lead to relative improvement of their photocatalytic activity under nonlinear excitation conditions.

Efficient Carrier Multiplication in Colloidal Silicon Nanorods

Auger recombination lifetimes, absorption cross sections, and the quantum yields of carrier multiplication (CM), or multiexciton generation (MEG), were determined for solvent-dispersed silicon (Si) nanorods using transient absorption spectroscopy (TAS). Nanorods with an average diameter of 7.5 nm and aspect ratios of 6.1, 19.3, and 33.2 were examined. Colloidal Si nanocrystals of similar diameters were also studied for comparison. The nanocrystals and nanorods were passivated with organic ligands by hydrosilylation to prevent surface oxidation and limit the effects of surface trapping of photoexcited carriers. All samples used in the study exhibited relatively efficient photoluminescence. The Auger lifetimes increased with nanorod length, and the nanorods exhibited higher CM quantum yield and efficiency than the nanocrystals with a similar band gap energy E_g. Beyond a critical length, the CM quantum yield decreases. Nanorods with the aspect ratio of 19.3 had the highest CM quantum yield of 1.6 ± 0.2 at 2.9E_g, which corresponded to a multiexciton yield that was twice as high as observed for the spherical nanocrystals.

Broadband Cooling Spectra of Hot Electrons and Holes in PbSe Quantum Dots

Understanding cooling of hot charge carriers in semiconductor quantum dots (QDs) is of fundamental interest and useful to enhance the performance of QDs in photovoltaics. We study electron and hole cooling dynamics in PbSe QDs up to high energies where carrier multiplication occurs. We characterize distinct cooling steps of hot electrons and holes and build up a broadband cooling spectrum for both charge carriers. Cooling of electrons is slower than of holes. At energies near the band gap we find cooling times between successive electronic energy levels in the order of 0.5 ps. We argue that here the large spacing between successive electronic energy levels requires cooling to occur by energy transfer to vibrational modes of ligand molecules or phonon modes associated with the QD surface. At high excess energy the energy loss rate of electrons is 1-5 eV/ps and exceeds 8 eV/ps for holes. Here charge carrier cooling can be understood in terms of emission of LO phonons with a higher density-of-states in the valence band than the conduction band. The complete mapping of the broadband cooling spectrum for both charge carriers in PbSe QDs is a big step toward understanding and controlling the cooling of hot charge carriers in colloidal QDs.

Spectroscopic and Device Aspects of Nanocrystal Quantum Dots

The field of nanocrystal quantum dots (QDs) is already more than 30 years old, and yet continuing interest in these structures is driven by both the fascinating physics emerging from strong quantum confinement of electronic excitations, as well as a large number of prospective applications that could benefit from the tunable properties and amenability toward solution-based processing of these materials. The focus of this review is on recent advances in nanocrystal research related to applications of QD materials in lasing, light-emitting diodes (LEDs), and solar energy conversion. A specific underlying theme is innovative concepts for tuning the properties of QDs beyond what is possible via traditional size manipulation, particularly through heterostructuring. Examples of such advanced control of nanocrystal functionalities include the following: interface engineering for suppressing Auger recombination in the context of QD LEDs and lasers; Stokes-shift engineering for applications in large-area luminescent solar concentrators; and control of intraband relaxation for enhanced carrier multiplication in advanced QD photovoltaics. We examine the considerable recent progress on these multiple fronts of nanocrystal research, which has resulted in the first commercialized QD technologies. These successes explain the continuing appeal of this field to a broad community of scientists and engineers, which in turn ensures even more exciting results to come from future exploration of this fascinating class of materials.

Hole Cooling Is Much Faster than Electron Cooling in PbSe Quantum Dots

In semiconductor quantum dots (QDs), charge carrier cooling is in direct competition with processes such as carrier multiplication or hot charge extraction that may improve the light conversion efficiency of photovoltaic devices. Understanding charge carrier cooling is therefore of great interest. We investigate high-energy optical transitions in PbSe QDs using hyperspectral transient absorption spectroscopy. We observe bleaching of optical transitions involving higher valence and conduction bands upon band edge excitation. The kinetics of rise of the bleach of these transitions after a pump laser pulse allow us to monitor, for the first time, cooling of hot electrons and hot holes separately. Our results show that holes cool significantly faster than electrons in PbSe QDs. This is in contrast to the common assumption that electrons and holes behave similarly in Pb chalcogenide QDs and has important implications for the utilization of hot charge carriers in photovoltaic devices.

Multiple-exciton generation in lead selenide nanorod solar cells with external quantum efficiencies exceeding 120

Multiple-exciton generation—a process in which multiple charge-carrier pairs are generated from a single optical excitation—is a promising way to improve the photocurrent in photovoltaic devices and offers the potential to break the Shockley–Queisser limit. One-dimensional nanostructures, for example nanorods, have been shown spectroscopically to display increased multiple exciton generation efficiencies compared with their zero-dimensional analogues. Here we present solar cells fabricated from PbSe nanorods of three different bandgaps. All three devices showed external quantum efficiencies exceeding 100% and we report a maximum external quantum efficiency of 122% for cells consisting of the smallest bandgap nanorods. We estimate internal quantum efficiencies to exceed 150% at relatively low energies compared with other multiple exciton generation systems, and this demonstrates the potential for substantial improvements in device performance due to multiple exciton generation.

One-dimensional nanostructures have been shown to increase multiple-exciton generation, offering a pathway to breaking the Shockley–Queisser limit. Here, Davis et al. have fabricated working photovoltaic devices based on high-quality PbSe nanorods and a maximum external quantum efficiency of 122 % was demonstrated.

Synthesis and Optical Properties of PbSe Nanorods with Controlled Diameter and Length

The synthesis of PbSe nanorods with low branching (<1%), high aspect ratios (up to ∼16), and controlled lengths and diameters was demonstrated via the removal of water and oleic acid from the synthesis precursors. It was determined that the proper combination of reaction time and temperature allows for the control of PbSe nanorod length and diameter and therefore control over their electronic states, as probed through absorbance and photoluminescence measurements. Similar to PbSe nanowires, nanorods display higher Stokes shifts than for spherical nanocrystals due to intrananorod diameter fluctuations.

Facile synthesis of ultra-small PbSe nanorods for photovoltaic application

Nanocrystal array solar cells based on lead chalcogenide quantum dots (QDs) have recently achieved a high power conversion efficiency of over 8%. The device performance is expected to further increase by using 1-dimensional nanorods (NRs), due to their improved carrier transport over zero-dimensional quantum dots. However, previously reported PbSe NRs have not been used in solar cells mainly because of their large diameters, resulting in a small bandgap unsuitable for photovoltaic application. In this work, we have demonstrated a new method for synthesizing monodisperse ultra-small PbSe NRs with the diameter approaching 2 nm (Eg > 1.2 eV), which can be attributed to the use of diphenylphosphine (DPP) and trans-2-octenoic acid (t-2-OA). The introduction of trace DPP can greatly lower the reaction temperature, leading to reduced diameters for the obtained PbSe NRs as well as largely increased yield. The use of short-chain t-2-OA together with oleic acid as capping ligands results in high monomer reactivity, fast nucleus diffusion and high growth rate, which realize the anisotropic growth of ultra-small PbSe NRs at low reaction temperatures. The PbSe NRs show n-type properties and high electron mobility as measured using field-effect transistors. The PbSe NRs with narrow diameters also demonstrate a suitable bandgap for photovoltaic application. They are used for the first time in solar cells and their improved efficiency is demonstrated when used together with QDs.

Highly efficient carrier multiplication in PbS nanosheets

Semiconductor nanocrystals are promising for use in cheap and highly efficient solar cells. A high efficiency can be achieved by carrier multiplication (CM), which yields multiple electron-hole pairs for a single absorbed photon. Lead chalcogenide nanocrystals are of specific interest, since their band gap can be tuned to be optimal to exploit CM in solar cells. Interestingly, for a given photon energy CM is more efficient in bulk PbS and PbSe, which has been attributed to the higher density of states. Unfortunately, these bulk materials are not useful for solar cells due to their low band gap. Here we demonstrate that two-dimensional PbS nanosheets combine the band gap of a confined system with the high CM efficiency of bulk. Interestingly, in thin PbS nanosheets virtually the entire excess photon energy above the CM threshold is used for CM, in contrast to quantum dots, nanorods and bulk lead chalcogenide materials.

Anisotropic absorption in PbSe nanorods

We present absorption anisotropy measurements in PbSe nanostructures. This is accomplished via a new means of measuring absorption anisotropy in randomly oriented solution ensembles of nanostructures via pump-probe spectroscopy, which exploits the polarization memory effect. We observe isotropic absorption in nanocrystals and anisotropic absorption in nanorods, which increases upon elongation from aspect ratio 1 to 4 and is constant for longer nanorods. The measured volume-normalized absorption cross section is 1.8 ± 0.3 times larger for parallel pump and probe polarizations in randomly oriented nanorods as compared to nanocrystals. We show that this enhancement would be larger than an order of magnitude for aligned nanorods. Despite being in the strong quantum confinement regime, the aspect ratio dependence of the absorption anisotropy in PbSe nanorods is described classically by the effects of dielectric contrast on an anisotropic nanostructure. These results imply that the dielectric constant of the surrounding medium can be used to influence the optoelectronic properties of nanorods, including polarized absorption and emission, phonon modes, multiple exciton generation efficiency, and Auger recombination rate.