Spin-exchange carrier multiplication in manganese-doped colloidal quantum dots

Carrier multiplication is a process whereby a kinetic energy of a carrier relaxes via generation of additional electron–hole pairs (excitons). This effect has been extensively studied in the context of advanced photoconversion as it could boost the yield of generated excitons. Carrier multiplication is driven by carrier–carrier interactions that lead to excitation of a valence-band electron to the conduction band. Normally, the rate of phonon-assisted relaxation exceeds that of Coulombic collisions, which limits the carrier multiplication yield. Here we show that this limitation can be overcome by exploiting not ‘direct’ but ‘spin-exchange’ Coulomb interactions in manganese-doped core/shell PbSe/CdSe quantum dots. In these structures, carrier multiplication occurs via two spin-exchange steps. First, an exciton generated in the CdSe shell is rapidly transferred to a Mn dopant. Then, the excited Mn ion undergoes spin-flip relaxation via a spin-conserving pathway, which creates two excitons in the PbSe core. Due to the extremely fast, subpicosecond timescales of spin-exchange interactions, the Mn-doped quantum dots exhibit an up-to-threefold enhancement of the multiexciton yield versus the undoped samples, which points towards the considerable potential of spin-exchange carrier multiplication in advanced photoconversion.


Supplementary Section 1. Implications of Spin-Exchange Carrier Multiplication for Photovoltaics
The highest power conversion efficiency (PCE, hPCE) of a photovoltaic (PV) cell in the case of fully optimized carrier multiplication (CM) is 44.4% versus 33.7% reachable without CM. 1-3 To evaluate the PCE enhancement due to CM observed in the present experiments, we introduce quantity dPCE = (hPCE,CM − hPCE)/hPCE. In the case of 'ideal' CM, the CM onset corresponds to two bandgaps (Eg), and each increment in a photon energy of Eg above the threshold leads to a 100% increase in a quantum efficiency of photon-to-exciton conversion. In this 'ideal' situation, dPCE = 0.32 or 32%.
In principle, CM can affect the PCE via both a photocurrent and a photovoltage. 2,3 The changes in the photovoltage are expected to occur due to the increased carrier generation rate and the influence of nonradiative Auger recombination. 3 However, in the case of practically accessible multiexciton yields (hXX ≤ 100%), the generated voltage is virtually unmodified by the CM process. 3 Further, the presence of CM is expected to decrease an optimal bandgap (Eg,opt) and thus the generated photovoltage compared to a no-CM case. In the case of moderate CM yields, though, the effect of CM on Eg,opt is weak. In particular, if hXX is limited by 100%, Eg,opt is ~1 eV (see ref 2 , the "M2 quantum yield model"), that is, is close to that of standard Si PVs. Importantly, as discussed later in this section, Eg, of ~1 eV is also near a bandgap which corresponds to minimal energy losses during the SE-CM process in Mn-doped quantum dots (QDs).
Based on the above considerations, we do not expect a considerable effect of CM on the photovoltage either due to the CM-induced increase in the carrier generation rate or an excessive 3 photovoltage drop due to the reduced Eg,opt. Thus, the PCE enhancement occurs primarily due to the increased photocurrent. In this case, dPCE can be expressed as follows: where is the photon frequency, is the total incident solar flux density, $ ( ) is its spectral distribution, and ∆ $ is the flux density enhancement due to CM. The computed value of dPCE likely underestimates the actual PCE enhancement as the utilized '' ( ) neglects the contribution from ordinary CM at energies between 2Eg (1.66 eV) and EMn,T1 (2.1 eV), and further assumes a gradual (linear) growth of hXX at hv > E Mn,T1. However, even this lower bound of dPCE is quite impressive, as it is approximately a quarter of the maximal theoretical enhancement attainable with CM.
Next, we consider the model situation when the multiexciton yield of spin-exchange (SE) CM is described by a step-like dependence for which hXX is 1 at energies above EMn,T1 and 0 below it (black dashed line in Supplementary Fig. 8). To maximize the photovoltage and still allow for SE-4 CM, the PbSe core bandgap should be around EMn,T1/2, that is, Eg ≈ 1.05 eV. For these parameters, dPCE = 18%, which is more than a half of the maximal PCE improvement allowed by CM.
One potential complication for practical applications of Mn-doped PbSe/CdSe QDs studied in the present work is a large potential barrier for extraction of holes that are localized within the PbSe core. It is likely a lesser problem in solution-based photochemistry where holes need to traverse across a single, fairly thin CdSe layer. However, it might complicate applications in PVs that require long-range hole transport. This problem can, potentially, be overcome using, for example, 'inverted' CdSe/PdSe structures wherein holes are localized in the shell region while electrons are still delocalized across both the core and the shell.
To further optimize SE-CM for applications in solar photoconversion, one can, in principle, explore magnetic dopants other than Mn. One such possibility is Co 2+ ions. As Mn ions, these dopants enter II-VI and IV-VI semiconductors as isovalent substitutional impurities that exhibit a comparable strength of exchange coupling. 4 However, a potential advantage of Co 2+ dopants is that the energy of their spin-flip transition (ECo ≈ 1.7 eV; ref. 5 ) is appreciably lower than that of Mn, making them better suited for applications in solar energy conversion.