Nanophotonics 2018; 7(1): 111–126 Review article Heather Goodwin, Tom C. Jellicoe, Nathaniel J.L.K. Davis and Marcus L. Böhm* Multiple exciton generation in quantum dot-based solar cells https://doi.org/10.1515/nanoph-2017-0034 efficiency (PCE) of these devices is fundamentally limited Received March 3, 2017; revised June 30, 2017; accepted July 5, 2017 to around 33% [2, 3]. Means of overcoming this limit, com- bined with advancements in device manufacturing pro- Abstract: Multiple exciton generation (MEG) in quantum- cesses, can progress solar energy technologies towards confined semiconductors is the process by which multiple meeting the growing energy demands of the future. bound charge-carrier pairs are generated after absorption The fundamental principles of PVs are based upon of a single high-energy photon. Such charge-carrier mul- the concept of a reversible Carnot heat engine. As such, tiplication effects have been highlighted as particularly thermodynamics dictates a maximum efficiency limit beneficial for solar cells where they have the potential to of 87% for the conversion of solar energy into electri- increase the photocurrent significantly. Indeed, recent cal current [4]. This theoretical performance limit could research efforts have proved that more than one charge- only be approached in a device architecture where a carrier pair per incident solar photon can be extracted large number of sub-cells (each optimised for a small in photovoltaic devices incorporating quantum-confined section of the solar spectrum) were to be combined in a semiconductors. While these proof-of-concept applica- PV stack and illuminated under intense light concentra- tions underline the potential of MEG in solar cells, the tion [5]. In reality, most PV devices employ only a single impact of the carrier multiplication effect on the device cell using one absorbing semiconductor, which collects performance remains rather low. This review covers sunlight under non-concentrated conditions. This non- recent advancements in the understanding and applica- ideal solar cell environment introduces two dominant tion of MEG as a photocurrent-enhancing mechanism in loss mechanisms: first, non-absorption of photons with quantum dot-based photovoltaics. energy less than the semiconductor band gap and sec- Keywords: multiple exciton generation; quantum dots; ondly, rapid cooling of carriers with energy in excess of solar cells. the band gap where a portion of the initial photon energy is lost to heat [6]. As a consequence, the ultimate device performance is reduced dramatically from that of an ideal Carnot heat engine. 1 Introduction In their seminal work, Shockley and Queisser quan- tified the apparent loss processes in a detailed balance Optimised, large-scale manufacturing processes for the model [3]. They expressed the resulting impact on the fabrication of photovoltaic devices (PVs) have promoted maximum achievable solar cell efficiency limit in their solar cell technologies to the verge of becoming the cheap- band gap-dependent Shockley-Queisser model (SQ limit; est form of energy (4–6 cent/kWh expected by 2025) [1]. see Figure 1A). While PVs based on materials such as silicon continue to As light is absorbed in the active layer of a solar pass economic milestones due to reduced fabrication costs cell, excited bound charge-carrier pairs (i.e. excitons) and increased market penetration, the power conversion are generated. Before these can be extracted through an external circuit they often encounter loss processes that *Corresponding author: Marcus L. Böhm, Cavendish Laboratory, reduce the efficiency of the solar cell. In the SQ limit, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, incomplete light trapping or angle restrictions account UK, e-mail: [email protected] for up to 20% of all energy losses. It is, however, mainly Heather Goodwin and Nathaniel J.L.K. Davis: Cavendish Laboratory, incomplete absorption and rapid carrier cooling that set University of Cambridge, Cambridge CB3 0HE, UK Tom C. Jellicoe: Cavendish Laboratory, University of Cambridge, the SQ limit for single junction solar cells to maximum Cambridge CB3 0HE, UK; and Particle Works, Part of Blacktrace PCE of 33.7% for a semiconductor of Eg≈1.3 eV (see Holdings Ltd., Unit 3, Anglian Business Park, Royston SG8 5TW, UK Figure 1A) [6]. Open Access. © 2017 Marcus L. Böhm et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution- NonCommercial-NoDerivatives 4.0 License. 112 H. Goodwin et al.: MEG in quantum dot-based solar cells Figure 1: Shockley-Queisser limit: loss processes and potential efficiency enhancement by MEG. (A) Breakdown of the different loss processes leading to the band gap-dependent Shockley-Queisser limit for single junction solar cells (out, dark blue). <Eg (light blue) and cool (green) represent the energy losses due to incomplete absorption and rapid cooling of hot carriers, respectively, angle (orange) and emission (dark red) are entropic losses associated with angle restriction and incomplete light trapping, respectively, and Carnot (light red) expresses the thermodynamic efficiency limit. (B) Theoretical enhancement of the Shockley-Queisser limit for single junction solar cells due to MEG where the parameter P relates the rates for MEG (kMEG) and hot carrier thermalisation ktherm through the expression P = kMEG/ktherm. Part B has been adapted from [7]. Among the most promising concepts to supress loss phenomena are termed singlet exciton fission [17–19] and processes associated with incomplete absorption are multiple exciton generation (MEG) [7, 20, 21], respectively. photon up-conversion mechanisms where low energy It has been calculated that such CM mechanisms can raise photons below the band gap are recovered for solar the maximum efficiency of single-junction PVs from about cell operation [8, 9]. As this concept, however, is not 33% to almost 44% (see Figure 1B) [22]. within the main focus of this article, we refer the inter- Several materials and material combinations have ested reader to other reviews addressing the topic in the been suggested to exploit CM effects in solar cells. Singlet literature [10]. exciton fission materials in combination with suitable The most widely employed approach to reduce charge acceptors and QD-based solar cells have both been losses from rapid cooling is through multi-junction PV shown to produce external quantum efficiencies (EQEs) devices. These use multiple (usually two or three) semi- beyond 100% in a PV device [23–28]. While these proof- conductors of different band gaps to best match the solar of-concept studies show that CM effects can increase the spectrum [11, 12]. Multi-junction cells have produced PV photocurrent of a solar cell, PCEs in both types of device efficiencies far beyond the SQ limit for single junction remain low. For MEG in particular, recent spectroscopic solar cells (to date 42% under un-concentrated AM 1.5 G findings suggest a combination of high MEG threshold conditions), but their high fabrication cost still renders energies and photon energy-dependent MEG efficiency large-scale deployment challenging [12]. Another (i.e. MEG efficiency increases slowly after the threshold concept to minimise losses due to hot carrier cooling is energy rather than as a step function) as the predomi- the rapid extraction of the initial hot carriers. While this nant reasons for the modest contribution to PV power phenomenon has been theorised to produce superior conversion [29, 30]. photovoltages, convincing, experimental evidence for There are several comprehensive review articles sum- the effect’s benefit in a solar cell environment has not marising the current understanding of the MEG mecha- been produced yet. nism itself provided in the literature [29, 31, 32]. In this Carrier multiplication (CM) effects, where the energy review, we will only briefly discuss mechanistic details of a high-energy photon is distributed among multiple and will focus mainly on recent progress towards an effi- carrier pairs with lower energy, present another concept cient integration of MEG in operational solar cells. After a capable of reducing carrier-cooling losses [13–16]. Here, brief introduction to the process in its nanoscale environ- additional charges are produced from energy that would ment, we will proceed to discussing the underlying device otherwise have been lost as heat. Such processes have physics of recently reported QD-based solar cells that been demonstrated to occur efficiently in organic semi- demonstrate a contribution from MEG to the photocurrent. conductors and inorganic quantum dots (QDs), where the We will finally provide some material and device-related H. Goodwin et al.: MEG in quantum dot-based solar cells 113 suggestions to increase the impact of MEG in future PVs 2.2 Enhancing CM in QDs that may enable device performance beyond the SQ limit. A different scenario is presented when the semiconduc- tor is confined to the nanoscale where quantum confine- 2 Theoretical considerations for ment effects can reduce the aforementioned material restrictions for the generation of additional charge-carrier promoting MEG in PV devices pairs [29, 40]. Quantum confinement effects emerge when the generated excitons are restricted to smaller spatial 2.1 CM in inorganic bulk semiconductors volumes than they would occupy in the parental bulk material. The natural spatial range over which the exci- Upon absorption in bulk semiconductors, solar photons tonic wavefunction spreads is described by the material- with energy greater than the material band gap Eg gener- dependent Bohr exciton radius. In the quantum confined ate excited charge-carrier pairs that possess kinetic energy regime, generation of more than one exciton from a single equal to hν–Eg. They typically dissipate their extra kinetic high energy photon is termed MEG to underline the con- energy to lattice vibrations on ultra-fast timescales (pico- fined, quasi-excitonic (i.e. non-correlated) character of to sub-pico second regime [33, 34]) as they cool to the band generated charge carriers [41].