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Solar & Alternative Energy

Nanocrystals generating >1 electron per photon may lead to increased solar cell efficiency

Optimizing a recently discovered quantum dot effect that gets multiple electrons from photons could make a critical difference in photovoltaics.
10 August 2006, SPIE Newsroom. DOI: 10.1117/2.1200606.0229

Unabated use of fossil fuels continues to drive our atmospheric concentration of CO2 toward unacceptable levels. Development of tremendous quantities of carbon-free energy would circumvent the potentially disastrous problems associated with this human-generated climate change. Sunlight represents a carbon-free source of renewable energy capable of far exceeding global power demands. The sun's radiative power at Earth's surface provides almost as much energy in one hour as the total energy consumed on Earth in one year.1 However, to generate economically competitive solar-based electricity and/or fuels, photovoltaic (PV) cells need to be both much less expensive than they are now and significantly more efficient than the ∼11–14% sunlight-to-electricity conversion efficiency achieved by conventional silicon-based cells.

In a conventional semiconductor PV solar cell, absorption of a photon boosts an electron from one of the non-conducting levels (called the valence band) to a conducting level within the so-called conduction band where the electron contributes to an electrical current. The ‘gap’ of unallowed energies between the valence and conduction bands is referred to as the bandgap, and the minimum energy required to elevate an electron across the gap is called the bandgap energy. For a photon to be absorbed by the semiconductor, its energy must equal or exceed the bandgap energy (the semiconductor is transparent to photons with energy below the bandgap energy). Typically, when the absorbed photon energy exceeds the bandgap energy, the resulting energetic electron quickly collides with atoms in the semiconductor, converting some of the electronic energy into heat as it relaxes down toward the lowest energy conduction band state.2 To efficiently generate electricity, a PV cell should generate as little heat as possible; therefore, one central goal is to maximize electrical power and minimize heating.

Solar cells based on ‘bulk’ (i.e., relatively large) semiconductor crystals yield just one electron per absorbed photon. For very high photon energies, nearly absent from sunlight, another process can occur in which the highly energetic electron itself frees a second electron from the valence band. This process, known in bulk semiconductors as impact ionization, occurs with such low efficiency in conventional solar cells that the effect on conversion efficiency is inconsequential. Contrast that with extremely small semiconductor crystals—generally less than 10 nanometers (nm) in diameter—called semiconductor nanocrystals (NCs) or quantum dots. With crystals of this size, a photon having more than twice the bandgap energy of the NC can produce two electrons within the conduction band. Photons with more than three times the bandgap energy can each produce three conduction electrons.3

In this case, some of the photoexcited electron's energy, which would normally end up as heat, instead generates one or more additional conduction electrons in a process analogous to impact ionization. (When an electron is photoexcited into the conduction band, the positively charged counterpart left behind in the valence band is called a hole; together, the pair consisting of the conduction band electron and the valence band hole is referred to as an exciton.) Because the process occurs in NCs with such high efficiency, we call it multiple exciton generation (MEG). The MEG effect represents an opportunity to significantly enhance the conversion efficiency of solar cells.

As in bulk semiconductor crystals, each photon absorbed by an NC generates (in the absence of MEG) one exciton. Studies have shown that when two or more excitons are confined within a single NC, they interact strongly and undergo Auger recombination, in which one electron and one hole recombine and transfer the electronic energy (approximately equal to one bandgap energy) to the remaining exciton. Auger recombination dominates the charge carrier dynamics for NCs with an initial population of two or more excitons.4 This observed strong exciton-exciton interaction suggested the possibility that the reverse of the Auger recombination process might also be enhanced in NCs.5 As mentioned above, in the inverse Auger process, an energetic electron generates a second electron-hole pair. When the MEG effect occurs in semiconductor NCs, it is detected by observation of the strong Auger recombination of multiple excitons produced following absorption of a high-energy photon.

Using time-resolved laser spectroscopy with sub-100 femtosecond resolution, we have studied the process of MEG in three different types of colloidal semiconductor nanocrystals (PbSe, PbS, and PbTe) in the range of 3–6nm in diameter, as shown in Figures 1(a) and (b), and 2. The samples consist of a very large number of individual NCs suspended colloidally in an organic solvent. These samples are highly fluorescent, and they exhibit quantized optical transitions that show up as structure within the linear absorption spectrum. When an exciton populates the lowest allowed state (the first exciton level, at an energy equal to the effective bandgap of the NC), the absorption at that photon energy decreases due to population state filling. We use transient absorption (also known as pump-probe) spectroscopy to measure the time-dependence of the average exciton population for the NCs in the sample. By varying the delay between an exciting laser pulse with photon energies greater than the bandgap and a probe pulse tuned to the first exciton energy, we trace out the population dynamics. Using a low pump pulse intensity to avoid absorption of multiple photons per NC, we vary the pump photon energy and measure the resulting exciton population.

Figure 1. (a) The graph of radius and shape (black circles for spherical particles, red squares for cube-shaped particles) of PbTe NCs versus the NC effective bandgap energy shows the effect of quantum confinement on the effective bandgap energy as a function of size. The sphere to cube transition for PbTe occurs at a radius of ∼ 4.7nm. The bars represent standard deviations of samples, and the ‘radius’ of a cubic NC is one-half the length of the nanocube. (b) This high-resolution transmission electron micrograph shows spherical PbTe NCs in a hexagonal close-packing configuration. These NCs exhibit a lowest-energy excitonic transition at 1534nm, an average radius of 2.7nm, and a standard deviation of 8%. (TEM image credit: A.G. Norman, National Renewable Energy Laboratory)

Figure 2. The graph describes multiple exciton generation quantum yield versus photon energy (photon energy is expressed here as a multiple of the semiconductor NC effective bandgap) for samples of PbTe, PbS, and three different sizes of PbSe NCs. The solid lines are guides to the eye, not formal fits to the data. The number of photons absorbed per NC is held constant by adjusting the excitation pulse intensity as the photon energy is tuned. The average per-NC excitation level is given by the product of the pump pulse fluence (jp, photons per cm2 per pulse) and the NC absorption cross-section (σa, in units of cm2) at the pump wavelength, < Neh >= jpσa.

In these types of NCs, a single exciton survives for about 1μs. However, a two-exciton state survives for only ∼0.1ns (depending on NC size) due to Auger recombination.5 Therefore, Auger recombination of multiple excitons shows up in the time-dependent exciton population as a fast decay component at early times. Once all multiple-exciton states have undergone the relatively fast Auger decay process, the signal consists only of those NCs with one exciton remaining.

The MEG process was first reported in 2004 by Schaller and Klimov,6 who found that PbSe NCs showed an increased quantum yield (QY) for photon energies above 3 times the NC bandgap and a maximum QY of 2.18 excitons per absorbed photon. Our studies show that we begin to generate more than one exciton per absorbed photon when the energy exceeds twice the bandgap energy. We measure a QY of 300% for 5.4nm diameter PbSe NCs (see Figure 2) at an incident photon energy of 4 times the bandgap, and we observe similarly high MEG efficiencies in NCs of PbS and PbTe.3,7 A recent report from Schaller and colleagues shows production of a remarkable seven excitons per photon for large PbSe NCs.8

Such highly efficient production of multiple excitons from absorption of a single photon suggests the presence of a process unique to semiconductor quantum dots. We have developed a model for efficient MEG based on a coherent superposition of single- and multiple-exciton states, coupled through the Coulomb interaction. An initial high-energy exciton, created upon absorption of a photon, can couple coherently with nearly energy-degenerate multiple-exciton states to form a coherent superposition. This superposition dephases due to interactions with phonons, and the dephasing process determines the yield of the multiple exciton generation process. Symmetric states, such as the 2Ph-2Pe,, are understood to interact less strongly with polar optical phonons, and therefore may dephase more slowly than asymmetric states such as the 1S-2P states; rapid dephasing of a multiple exciton state results in a quantum yield of more than one exciton per absorbed photon (refer to Figure 3).

Figure 3. We have developed a model for efficient multiple exciton generation (MEG) based on a coherent superposition of single- and multiple-exciton states, coupled through the Coulomb interaction. Not all electron and hole states are shown in this diagram; VC is the Coulomb coupling strength, 1Se and 1Sh are the lowest s-like electron and hole states, 2Pe and 2Ph are the second p-like electron and hole states, and τ is the dephasing time. The initial high-energy 2Ph-2Pe exciton created at 3 times the bandgap can couple with nearly energy-degenerate states as long as coherence lasts. The coherent superposition dephases due to interactions with phonons, and the dephasing process determines the yield of the multiple exciton generation process. Symmetric states, such as 2Ph-2Pe, are expected to interact less strongly with polar optical phonons, and therefore may dephase more slowly than asymmetric states; rapid dephasing of the multiple exciton states corresponds to enhanced MEG quantum yield.

Modeling done at the National Renewable Energy Lab shows that MEG can enhance the theoretically realizable conversion efficiency for a single-junction (single-layer) PV cell from about 32 to 45%, but that greater than 90% of the enhancement comes from generation of two excitons for each photon at or above twice the bandgap. Achieving higher-efficiency solar cells based on MEG will require optimizing the MEG process and efficiently collecting photocurrent from multiple excitons on a timescale faster than they naturally recombine via the Auger process. By learning more about the MEG process and ways to harvest the charge from multiple excitons, we hope to demonstrate the benefits of solar cells that utilize MEG, called MEG-active (MEGA) cells.

RJE, MCB, JCJ, JEM, KPK, KAG, JL, MCH, OIM, and AJN were supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences. AS and ALE were supported by the Office of Naval Research and the Photovoltaics Program of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy.

Randy Ellingson, Arthur Nozik, Matthew Beard. Justin Johnson, James Murphy, Kelly Knutson, Katherine Gerth, Josph Luther, Mark Hanna, and Olga Micic
Center for Chemical and Biological Sciences, National Renewable Energy Laboratory
Golden, CO
Randy Ellingson is a senior scientist at the National Renewable Energy Laboratory in Golden, CO. His research focuses on understanding charge carrier interactions in colloidal semiconductor quantum dots and single-walled carbon nanotubes to enhance solar energy conversion. In addition, he recently co-chaired the Symposium on Physical Chemistry of Interfaces and Nanomaterials IV during the 2005 SPIE Optical Sciences Conference in San Diego, California.
Andrew Shabaev, Alexander Efros
Naval Research Laboratory
Washington, DC

1. N. S. Lewis, G. Crabtree,
Basic Research Needs for Solar Energy Utilization, Report on Basic Energy Sciences Workshop on Solar Utilization,
2. A. J. Nozik, Exciton multiplication and relaxation dynamics in quantum dots: applications to ultrahigh-efficiency solar photon conversion,
Inorg. Chem.,
Vol: 44, pp. 6893-6899, 2005. doi:10.1021/ic0508425