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Letter 2
Excitonic Effects in Emerging Photovoltaic Materials: A Case Study in CuO Stefan Thomas Omelchenko, Yulia Tolstova, Harry A Atwater, and Nathan S. Lewis ACS Energy Lett., Just Accepted Manuscript • DOI: 10.1021/acsenergylett.6b00704 • Publication Date (Web): 19 Jan 2017 Downloaded from http://pubs.acs.org on January 24, 2017
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ACS Energy Letters
Excitonic Effects in Emerging Photovoltaic Materials: A Case Study in Cu2O Stefan T. Omelchenko†§, Yulia Tolstova†, Harry A. Atwater†§||, Nathan S. Lewis*‡§||⊥ †
Division of Engineering and Applied Sciences, California Institute of Technology, Pasadena,
CA 91125 ‡
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena,
CA 91125 §
The Joint Center for Artificial Photosynthesis, California Institute of Technology, Pasadena, CA
91125 ||
Kavli Nanoscience Institute, California Institute of Technology, Pasadena, CA 91125
⊥
Beckman Institute, California Institute of Technology, Pasadena, CA 91125
Corresponding Author *E-mail:
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Excitonic effects account for a fundamental photoconversion and charge transport mechanism in Cu2O, hence the universally adopted “free carrier” model substantially underestimates the photovoltaic efficiency for such devices. The quasi-equilibrium branching ratio between excitons and free carriers in Cu2O indicates that up to 28% of photogenerated carriers during photovoltaic operation are excitons. These large exciton densities were directly observed in photoluminescence and spectral response measurements. The results of a devicephysics simulation using a model that includes excitonic effects agree well with experimentally measured current-voltage characteristics of Cu2O-based photovoltaics. In the case of Cu2O, the “free carrier” model underestimates the efficiency of a Cu2O solar cell by as much as 2 absolute percent at room temperature.
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Materials that can act as the top cell in a dual-junction architecture with traditional solar cells like silicon (Si), cadmium telluride (CdTe), and copper indium gallium diselenide (CIGS) could potentially reduce the levelized cost of electricity by producing increased photovoltaic efficiencies.1 Novel materials could also provide optionality for ultrathin, flexible photovoltaic technologies.1-4 The performance of photovoltaics is generally evaluated using the “free carrier” (FC) device model, in which the negatively charged electron and positively charged hole are treated as independent, non-interacting particles. However, substantial interactions between charge carriers can lead to the formation of excitons, comprising a coulombically bound state between a photo-excited electron in the conduction band and a hole in the valence band. For Si, CdTe, and GaAs, the interaction between the electron and hole is weak, with exciton binding energies of 15, 10 and 4 meV, respectively.5-7 Excitonic binding energies less than the thermal energy at room temperature (25.6 meV) allow for facile dissociation of photogenerated excitons into free electrons and holes at room temperature. Even in these devices, the role of excitons may be important in certain device configurations.8-10 Many emerging photovoltaic materials, however, exhibit large exciton binding energies (>> ݇ ܶ, see Table 1), so appreciable exciton densities are present at room temperature. For example, cuprous oxide (Cu2O), a promising candidate material for the top cell in a tandem solar cell with Si, has an exciton binding energy (Ex) of 151 meV.11 Cu2O has been the subject of intense investigation of the Bose-Einstein condensation phenomenon, which requires extremely large exciton densities (~1018 cm-3).12-15 Additionally, these large exciton densities lead to excitonic charge transport in Cu/Cu2O Schottky junctions even at room temperature.16-18
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Table 1. Exciton binding energies (Ex) and dielectric constants for established and emerging photovoltaic materials. The exciton binding energy scales with the inverse square of the dielectric constant.
Material
Ex
ࣕ
[meV] GaAs
4.2 7
12.9 7
Si
15.0 5
11.9
CdTe
10.0 6
11.0 20
ZnO
60 21
8.6 22
Cu2O
150 23
7.0 24
m-WS2
710 25
20 26
m-MoS2
910 – 1100 27-28
2526
19
We demonstrate herein that excitons play a fundamental role in the photovoltaic operation of Cu2O and that the FC model consequently underestimates the potential photovoltaic device efficiency of Cu2O. Specifically, the Saha-Langmuir equation, which governs ionization events, has been used to calculate the branching ratio at quasi-equilibrium between free electrons and holes and excitons as a function of temperature and total-excitation density. The exciton densities have been investigated experimentally under visible illumination by examination of a free exciton peak in the photoluminescence spectrum of Cu2O at room temperature.
The
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photovoltaic device performance has also been evaluated by comparing traditional FC device physics models to models that include levels of excitonic transport that are consistent with both theoretical and experimental results. When an exciton is created by absorption of a photon, the exciton diffuses to the device junction, where a strong electric field ionizes the exciton into a free electron and hole that are subsequently collected as current. The extent of the excitonic effects in a photovoltaic device is therefore governed during solar cell operating conditions by the branching ratio between free carriers and excitons. At thermodynamic equilibrium, free carriers coexist with excitons, and the two species exchange at an identical rate. The concentration of free electrons and holes (neh) and the concentration of excitons (nx) depends on the exciton binding energy (Ex), which determines the time before excitons dissociate into free carriers, as well as the total excitation density (N), which governs the probability of a free electron and free hole interacting to form an exciton. In Cu2O, the exciton Bohr radius is 1.1 nm, implying that exciton-exciton interactions occur only for exceedingly large exciton densities, >1020 cm-3. This process can, therefore, be neglected during normal photovoltaic operation under 1-100 Sun illumination intensities.29 Under such conditions, the interchange between the charge-neutral exciton and its ionized state, a free electron and hole, can be modeled in accord with the ionization of an ideal gas. The ratio between the free carrier concentration and the total excitation density (= ݔ
ே
) is thus
determined by the Saha equation:
௫మ
ଵି௫
ଵ
= ேቀ
ଶగఓಳ ଷ/ଶ మ
ቁ
݁
ಶ ି ೣ
ೖಳ
(1)
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where µ is the effective mass of the exciton (3.0 m0 in Cu2O), h is Planck’s constant, kB is Boltzmann’s constant and T is the absolute temperature.30-32 Equation (1) shows that the fraction of free carriers (x) increases with temperature, as the thermal energy approaches Ex and a larger number of excitons thus dissociate into free carriers. The fraction of excitons also increases with increasing excitation density, because the probability of free electron and holes binding into excitons also increases. Figure 1 shows the calculated free electron and hole fractions in Cu2O as a function of the total excitation density, as T is varied from room temperature to 40 K. The shaded region labeled “PV Regime” refers to the total, steady-state generated excitation density in Cu2O (where an excitation can be either an exciton or free carriers) under standard photovoltaic operating conditions. The absorbed solar flux was estimated by integrating the absorption in Cu2O over the standard Air Mass (AM) 1.5 solar spectrum. The ground-state exciton is split by the spin exchange into a spin singlet “paraexciton” state and a spin triplet “orthoexciton” state, with the orthoexciton lying 12 meV higher than the paraexciton.33-34 The inversion symmetry of the Cu2O crystal makes the paraexciton transition dipole- and quadrupole forbidden, and the orthoexciton dipole-forbidden. This characteristic leads to long exciton lifetimes for both the paraexciton and orthoexciton. The small energetic splitting between the ortho- and paraexcitons causes fast exchange (on the picosecond timescale) between the two states. Consequently, for temperatures relevant to photovoltaic operation, the ortho- and paraexciton lifetimes are mutually similar, and the “excitonic” lifetime is given by the fastest radiative decay. The paraexciton lifetime has been measured to be as large as 14 µs – 10 ms.12,
35-36
However, at room
temperature, the orthoexciton lifetime has been measured to be 350 ns.37-38 We have thus conservatively estimated the lifetime as 100 ns to 10 µs, which yields a steady-state excitation
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density between 1015 and 1017 cm-3.
Hence, at the excitation densities expected during
photovoltaic cell operation, excitons represent a substantial fraction, greater than 20%, of the total excitation density in Cu2O. In the high exciton lifetime limit, the branching ratio is as high as 0.27 at T = 300 K, and at lower temperatures, excitons become the dominant charge-carrier population.
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300K 240K
60
200K
PV Regime
160K 120K
40
80K 40K
20 0 13 10
1015
1017 N / cm- 3
1019
1021
Figure 1. The fraction of free electrons and holes relative to the total excitation density ቀ= ݔ
ே
ቁ in Cu2O. The upper limit of the branching ratio between excitons and free electrons
and holes during photovoltaic operation is 27.7%, suggesting that substantial exciton densities should be present during typical device operating conditions.
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At low temperature (4 K), cuprous oxide exhibits a peak in its photoluminescence (PL) spectrum due to the recombination of the free orthoexciton at 610 nm as well as several phonon-assisted exciton luminescence peaks at slightly lower energies.12,
39-42
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temperature the peak redshifts and thermally broadens, becoming convoluted with the ߁ 12 phonon-assisted peak, which is only separated by 13.6 meV from the exciton peak.37, 42 Figure 2a shows the photoluminescence spectra of the orthoexciton peak in our Cu2O samples for a selection of optical excitation wavelengths at T = 300 K. The orthoexciton peak was observed for all excitation energies below the Cu2O electronic band edge (2.1 eV, 590 nm).
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Figure 2. Experimental evidence of excitons in Cu2O. a) Photoluminescence spectra of the free exciton peak in Cu2O at room temperature under different visible light excitation. The free exciton peak is observed for all excitations above the Cu2O band gap. b) Spectral response of a polycrystalline Cu2O /Zn(O,S) solar cell. The red dashed line indicates the Cu2O electronic band gap beyond which, in the shaded region, are wavelengths for which only excitons can exist.
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Cu2O-based photovoltaics were fabricated on a Cu2O wafer grown by thermal oxidation of copper foil with a sputtered Zn(O,S) window layer, and an indium tin oxide (ITO) top contact and a Au back contact.43 Figure 2b shows the spectral response of a typical Cu2O /Zn(O,S) cell. The external quantum yield approached zero at 650 nm, which is consistent with the 1.91 eV optical band edge in Cu2O. However, the quantum yield was substantial in the region between the Cu2O electronic band gap (2.1 eV, 591 nm) and the Cu2O optical band gap (1.91 eV, 650 nm). In this region, absorption of a photon generates an exciton, so the current collection below 2.1 eV must be attributed solely to excitonic transport.13,
40
A similar spectral response
characteristic has been observed in high-quality Cu/Cu2O Schottky diodes with the current collection in the exciton region explained by exciton diffusion to the Schottky junction followed by ionization of the exciton into an electron and hole by the strong electric field in the depletion region.18, 44 The current in the excitonic region accounts for 9.3% of the short-circuit current density of the Cu2O/Zn(O,S) cells. Although this value is less than the ~27% predicted by the branching ratio, the 9.3% value does not account for excitonic transport in the region having excitation energies greater than 2.1 eV, where the PL data indicate that excitons are also generated. Aside from direct generation through bandgap absorption of a photon, excitons may also form via free carrier relaxation processes, such as when “hot” carriers that arise from aboveband-gap photon absorption thermally relax to the band edge. These free carrier cooling mechanisms may further contribute to excitonic transport in the region in which excitation energies are > 2.1 eV. The presence of substantial external quantum yield in our Cu2O/Zn(O,S) solar cells even at the low light intensities (
