solar cell A solar cell, also known as a photovoltaic cell (PV cell), is an electronic device that converts the energy of light directly into electricity by means of the photovoltaic effect.

research, carrier multiplication is the phenomenon wherein the absorption of a single

photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that can ...

leads to the excitation of multiple electrons from the valence band to conduction band. In the theory of a conventional solar cell, each photon is only able to excite one electron across the

band gap In solid-state physics and solid-state chemistry, a band gap, also called a bandgap or energy gap, is an energy range in a solid where no electronic states exist. In graphs of the electronic band structure of solids, the band gap refers to t ...

of the

semiconductor A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ...

, and any excess energy in that photon is dissipated as heat. In a material with carrier multiplication, high-energy photons excite on average more than one electron across the band gap, and so in principle the solar cell can produce more useful work. In quantum dot solar cells, the excited electron in the conduction band interacts with the hole it leaves behind in the valence band, and this composite uncharged object is known as an

exciton An exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic Coulomb's law, Coulomb force resulting from their opposite charges. It is an electrically neutral quasiparticle regarded as ...

. The carrier multiplication effect in a dot can be understood as creating multiple excitons, and is called multiple exciton generation (MEG). MEG may considerably increase the

energy conversion efficiency Energy conversion efficiency (''η'') is the ratio between the useful output of an energy conversion machine and the input, in energy terms. The input, as well as the useful output may be chemical, electric power, mechanical work, light (radi ...

of nanocrystal-based solar cells, though extracting the energy may be difficult because of the short lifetimes of the multiexcitons. The quantum mechanical origin of MEG is still under debate and several possibilities have been suggested: *1) Impact ionization: light excites a high-energy exciton (X) which decays irreversibly into a quasi-continuum of multiexciton (multi-X) states available at this energy. The model requires only the

density of states In condensed matter physics, the density of states (DOS) of a system describes the number of allowed modes or quantum state, states per unit energy range. The density of states is defined as where N(E)\delta E is the number of states in the syste ...

of multiexcitons being very high, while the Coulomb coupling between X and multi-X can be quite small. *2) Coherent superposition of single and multiexciton states: the very first suggested model but oversimplified (high density of states of multi-X is not taken into account). Light excites an X (which is not a true

eigenstate In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a prediction for the system re ...

of the system) which can then coherently convert to multi-X and back to X many times ( quantum beats). This process requires Coulomb coupling between them to be much stronger than the decay rate via

phonons A phonon is a collective excitation in a periodic, Elasticity (physics), elastic arrangement of atoms or molecules in condensed matter physics, condensed matter, specifically in solids and some liquids. In the context of optically trapped objects ...

(which is usually not the case). The excitation will finally decay via phonons to a lower energy X or multi-X, depending on which of the decays is faster. *3) Multiexciton formation through a virtual exciton state. Light directly excites the

of the system (in this case, a coherent mixture of X and multi-X). The term "virtual" relates here to a pure X, because it is not a true eigenstate of the system (same for model 2). All of the above models can be described by the same mathematical model (

density matrix In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed on physical systems. It is a generalization of the state vectors or wavefunctions: while th ...

) which can behave differently depending on the set of initial parameters (coupling strength between the X and multi-X, density of states, decay rates). MEG was first observed in 2004 using colloidal PbSe quantum dots and later was found in quantum dots of other compositions including PbS, PbTe, CdS, CdSe, InAs, Si, and InP. However, many early studies in colloidal quantum dots significantly overestimated the MEG effect due to undetected photocharging, an issue later identified and resolved by vigorously stirring colloidal samples. Multiple exciton generation was first demonstrated in a functioning solar cell in 2011, also using colloidal PbSe quantum dots. Multiple exciton generation was also detected in semiconducting single-walled carbon nanotubes (SWNTs) upon absorption of single photons. For (6,5) SWNTs, absorption of single photons with energies corresponding to three times the SWNT energy gap results in an exciton generation efficiency of 130% per photon. The multiple exciton generation threshold in SWNTs can be close to the limit defined by energy conservation.

Graphene Graphene () is a carbon allotrope consisting of a Single-layer materials, single layer of atoms arranged in a hexagonal lattice, honeycomb planar nanostructure. The name "graphene" is derived from "graphite" and the suffix -ene, indicating ...

, which is closely related to nanotubes, is another material in which multiple exciton generation has been observed. Double-exciton generation has additionally been observed in organic pentacene derivatives through singlet exciton fission with extremely high

quantum efficiency The term quantum efficiency (QE) may apply to incident photon to converted electron (IPCE) ratio of a photosensitive device, or it may refer to the TMR effect of a magnetic tunnel junction. This article deals with the term as a measurement of ...

References

{{Reflist Quantum electronics