Effect of electronic structure on carrier multiplication efficiency: Comparative study of PbSe and CdSe nanocrystals

Schaller, Richard D.; Petruska, Melissa A.; Klimov, Victor I.

doi:10.1063/1.2142092

Cited by 270 publications

(299 citation statements)

References 15 publications

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“…The two approaches predict similar trends for the CM FoM as a function of photon energy in most of the materials considered (with some quantitative differences at the boundaries of the energy region of interest), except in the case of InAs, where TCA predicts a more marked size dependence, in contrast with experiment 15 . On the other hand our calculations predict a clear size dependence for CdSe NCs, in contrast with TCA and experiment 5 .…”

Section: Methodscontrasting

confidence: 99%

“…Unfortunately, despite experimental confirmation of CM in a wide range of materials [3][4][5][6][7] , CM-based solar cells are still far from yielding multiplication factors even close to 2 (i.e., the best recorded internal quantum efficiencies are still far from 200%) 8,9 . What is more, the mechanism behind CM itself is still unclear and many aspects of it remain controversial.…”

Section: Introductionmentioning

confidence: 99%

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Origins of improved carrier multiplication efficiency in elongated semiconductor nanostructures

Sills

Califano

2015

Phys. Chem. Chem. Phys.

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Nanorod solar cells have been attracting a lot of attention recently, as they have been shown to exhibit a lower carrier multiplication onset and a higher quantum efficiency than quantum dots with similar bandgaps. The underpinning theory for this phenomenon is not yet completely understood, and is still the subject of ongoing study. Here we conduct a theoretical investigation into CM efficiency in elongated semiconductor nanostructures with square cross section made of different materials (GaAs, GaSb, InAs, InP, InSb, CdSe, Ge, Si and PbSe), using a single-band effective mass model. Following Luo, Franceschetti and Zunger we adopt the CM figure of merit (the ratio between biexciton and single-exciton density of states) as a measure of CM efficiency and investigate its dependence on the aspect ratio for both (a) constant cross section (i.e. varying the volume) and (b) constant volume (i.e., varying the cross section), by decoupling electronic structure effects from surface-related effects, increased absorption and Coulomb coupling effects. The results show that in both (a) and (b) cases elongation causes an increase in both single-and bi-exciton density of states, with the latter, however, growing much faster with increasing energy. This leads to the availability of more bi-exciton states than single-exciton states for photon energies just above the bi-exciton ground state and therefore suggests a higher probability of CM at these energies for elongated structures. Our results therefore show that the origin of the observed decrease of the CM threshold in elongated structures can be attributed purely to electronic structure effects, paving the way to the implementation of CM-efficiency-boosting strategies in nanostructures based on the lowering of the CM onset.

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Section: Methodscontrasting

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Origins of improved carrier multiplication efficiency in elongated semiconductor nanostructures

Sills

Califano

2015

Phys. Chem. Chem. Phys.

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“…For example, in PbSe and PbS NQDs, it is close to 3E g , 1,5,8 while it is ∼2.5E g in CdSe NQDs. 3 These observations can be understood by taking into account the fact that, in addition to energy conservation, the CM process in NQDs is also governed by selection rules that determine the magnitudes of the matrix elements of the electron-photon interaction and carrier-carrier Coulomb coupling.…”

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confidence: 99%

Carrier Multiplication in InAs Nanocrystal Quantum Dots with an Onset Defined by the Energy Conservation Limit

2007

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Carrier multiplication (CM) is a process in which absorption of a single photon produces not just one but multiple electron−hole pairs (excitons). This effect is a potential enabler of next-generation, high-efficiency photovoltaic and photocatalytic systems. On the basis of energy conservation, the minimal photon energy required to activate CM is two energy gaps (2E g ). Here, we analyze CM onsets for nanocrystal quantum dots (NQDs) based upon combined requirements imposed by optical selection rules and energy conservation and conclude that materials with a significant difference between electron and hole effective masses such as III−V semiconductors should exhibit a CM threshold near the apparent 2E g limit. Further, we discuss the possibility of achieving sub-2E g CM thresholds through strong exciton−exciton attraction, which is feasible in NQDs. We report experimental studies of exciton dynamics (Auger recombination, intraband relaxation, radiative recombination, multiexciton generation, and biexciton shift) in InAs NQDs and show that they exhibit a CM threshold near 2E g .Carrier Multiplication Thresholds in Bulk and Nanocrystalline Semiconductors. It has recently been established that carrier multiplication (CM), the production of multiple excitons following absorption of a single photon of sufficient energy, is efficient within the range of solar photon energies in semiconductor nanocrystal quantum dots (NQDs). [1][2][3][4][5][6][7][8][9] This finding is important because CM can potentially provide increased power conversion efficiency in low-cost, singlejunction photovoltaics via an enhanced photocurrent. 10,11 To obtain optimum photovoltaic power conversion efficiency using a single semiconductor material with energy gap E g , it is desirable that the CM onset energy is minimal and that the CM efficiency above the onset is as large as is allowed by energy conservation.According to energy conservation, the apparent minimal photon energy that is required to activate CM (pω CM ) is simply 2E g . However, the CM thresholds observed in bulk materials are significantly larger than this value. 12,13 In bulk semiconductors, the generally accepted mechanism for multiexciton generation is impact ionization in which a highenergy electron (or a hole) transfers its energy to a valenceband electron that is excited across the energy gap. 14 The CM threshold in this case is determined not only by conservation of energy but also by conservation of translational momentum, which increases the threshold above 2E g . For example, using a free-particle approximation 15,16 and applying both energy and momentum conservation laws, one can obtain that the CM threshold is approximately 4E g (Figure 1a).In NQDs, translational momentum conservation is relaxed. Therefore, one might expect that the CM threshold could reach the 2E g limit as defined by energy conservation. However, available experimental data indicate that pω CM is still greater than twice the energy gap in such materials. For example, in PbSe and PbS NQDs, it ...

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“…band-gap independent [4,5,11,12]. However, several recent studies have questioned the efficiency of CM in NCs, in particular for CdSe [13] and InAs [14].…”

mentioning

confidence: 99%

Distribution of Multiexciton Generation Rates in CdSe and InAs Nanocrystals

2008

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The distribution of rates of carrier multiplication (CM) following photon absorption is calculated for semiconductor nanocrystals (NCs). The NC electronic structure is described using a screened pseudopotential method known to give reliable description of NC excitons. The rates of biexciton generation are calculated using Fermi's golden rule with all relevant Coulomb matrix elements, taking into account proper selection rules. In CdSe and InAs NCs we find a broad distribution biexciton generation rates depending strongly on the exciton energy and size of the NC. The process becomes inefficient for NC exceeding 3 nm in diameter in the photon energy range of 2-3 times the band gap. PACS numbers: 78.67.Bf, 71.35.-y.Carrier multiplication is a process where several excitons are generated upon the absorption of a single photon in semiconductors [1]. Strict selection rules and competing processes in the bulk allow observation of CM only at energies larger than 5 times the band gap ( The theory of CM in bulk is based on the concept of impact ionization [15], by which the photon first creates an exciton, composed of the negative electron and positive hole, each having an effective mass depending on the band structure of the crystal. The lighter particle of the pair takes most of the kinetic energy and eventually looses part of this energy by creating additional charge carriers. For NCs, several theoretical approaches for describing CM have been proposed [4,6,[16][17][18][19]. Efros, Nozik and their co-workers [4,16] developed a time-dependent density matrix formalism taking into account the populations and coherences of single exciton coupled to a single biexciton state. Using this model, in conjunction with an effective mass theory, they developed a theory of impact ionization obtaining expression for the ratio of exciton to biexciton populations at steady states, which depend on the decay rate of the charged particle in the exciton into a trion. This approach treats a single trion neglecting the fact that the charged particle decays into a dense manifold of trions. Under such circumstance a rate approach might be more appropriate, describing the decay as an incoherent impact ionization process [17], similar to the treatment of the process in bulk.

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Effect of electronic structure on carrier multiplication efficiency: Comparative study of PbSe and CdSe nanocrystals

Cited by 270 publications

References 15 publications

Origins of improved carrier multiplication efficiency in elongated semiconductor nanostructures

Origins of improved carrier multiplication efficiency in elongated semiconductor nanostructures

Carrier Multiplication in InAs Nanocrystal Quantum Dots with an Onset Defined by the Energy Conservation Limit

Distribution of Multiexciton Generation Rates in CdSe and InAs Nanocrystals

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