Prospects of Colloidal Nanocrystals for Electronic - Computer Science

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432 Chemical Reviews, 2010, Vol. 110, No. 1 Talapin et al. Figure 48. Schematics of the structure (top) and energy diagram (bottom) of a dye(nanocrystal)-sensitized solar cell (Grätzel cell). Following the absorption of photons by sensitizer, the photogenerated electrons are injected into nanostructured TiO2 and collected into external circuit. Subsequently, positively charged dye molecules or nanocrystals are electrochemically reduced by I - or Co 2+ ions in solution converted into I 3- or Co 3+ , respectively. These diffuse to the counter electrode (Pt) and were being electrochemically reduced to I - or Co 2+ , closing the photoelectrochemical circle. tor NCs very attractive in this regard. Other advantages include sharp absorption onset, large absorption coefficients, and robustness of inorganic materials. In NC-sensitized solar cells (NSSC), the role of NCs is to absorb light and to inject photogenerated electrons into nanostructured TiO2, while the holes are scavenged and transported to the opposite electrode by the redox couple. Such electron transfer is quite efficient and fast at the TiO2/CdSe interface. 395,515,394 Various semiconductor NCs including CdS, 516-518 InP, 519 InAs, 520 PbS, 521,522 and Bi2S3 523,524 were examined as sensitizing components. All of these NCs, with few exceptions, were grown directly at the surface TiO2 electrode with rather poor control over the materials properties and surface chemistry. NSSC demonstrated so far relatively low efficiencies: some of the best recently reported cells sensitized by CdSe NCs combined with Co(II)/Co(III) redox system demonstrated ∼1% power conversion efficiency. 463 It is anticipated that the use of well engineered near-infrared-active colloidal NCs (CdTe, CuInSe2, PbS, PbSe, InAs, etc.) could substantially improve the performance and commercial perspectives for NSSC. 7.3.5. Can Nanocrystal Solar Cell Beat the Shockley-Queisser Limit? The efficiency of a solar cell can be improved by increasing three parameters: open-circuit voltage, short-circuit current, and the fill factor. In 1961, Shockley and Queisser determined the maximum theoretical light conversion efficiency for conventional solar cells. Their analysis led to the conclusions that maximum η for a single junction solar cell under one sun (AM 1.5) illumination requires a semiconductor band gap of 1.4 eV and cannot exceed ∼31%, known as the Shockley-Queisser (S-Q) limit. 525 This limitation is also mostly applicable to hybrid solar cells with distributed heterojunctions and DSSCs. The most straightforward way to obtain higher power conversion efficiencies is to build a stack of several solar cells with different band gaps (so-called multijunction or tandem cell), which can harvest solar radiation more efficiently. 526 The stack of layers is arranged in such a way that the higher energy photons are absorbed by the first layer, while low energy infrared photons are harvested in the last layer. Theoretically, tandem solar cell with an infinite number of layers and with absorption profile perfectly matching the solar spectrum can reach 66% power conversion efficiency. Fabrication of multijunction cells requires multiple deposition steps and is very demanding to materials purity and structural perfection. It is hard to envision this technology to be used for mass production. Instead, multijunction cells made of III-V semiconductors are used for satellite, military, and other applications where efficiency per weight is more important than cost. To beat the S-Q limit in a single-junction device, some new ways to utilize the excessive energy of short-wavelength photons have to be introduced. These days, several interesting ideas for harvesting the energy of hot carriers before they thermalize are widely discussed in literature. We should emphasize that physical phenomena described below are known and well-documented; however, their applicability for boosting up efficiency of real solar cells, as of 2009, has not been experimentally demonstrated. Hot Carrier Solar Cell. Theoretically, a very high lightto-electricity conversion efficiency can be achieved by using a material with suppressed electron-phonon scattering. In 1982, Ross and Nozik proposed the model of a solar cell where generation of electron-hole pairs is not followed by thermalization of electrons to the bottom of the conduction band and holes to the top of the valence band. 527 In this model, electron-electron scattering within the conduction band creates Fermi distribution of the electrons, which have a higher temperature than the lattice temperature (same idea applies to holes in the valence band). If the extraction of carriers would occur without heat loss, the thermodynamically attainable power conversion efficiency can ultimately reach 66%. 527 Despite obvious attractiveness, this approach would be very difficult to implement using bulk semiconductors where the intraband cooling process is extremely fast, on the order of subpicoseconds to picoseconds (Figure 49a). At the same time, cooling of the hot carriers is expected to be much slower in semiconductor NCs. In semiconductor NCs, three-dimensional quantum confinement gives rise to discrete electronic density of states, which was predicted to significantly slow the intraband relaxation because of reduced availability of pairs of electronic states that satisfy energy conservation in phonon-assisted processes (the phononbottleneck effect) (Figure 49b). 528 The phonon bottleneck is expected to particularly affect relaxation dynamics in strongly confined NCs where the separation between energy levels can exceed several longitudinal-optical phonon energies, and, therefore, phonon-assisted carrier relaxation can occur only via multiphonon processes. The efficiency of phonon bottleneck in real NC systems has been debated for a long time because, in the case of colloidally grown CdSe NCs, 529 surprisingly fast cooling rates (hundreds of femtoseconds) were demonstrated for the 1Pto-1S intraband relaxation. This fast relaxation has been attributed to confinement-enhanced, electron-to-hole energy transfer. 530 In this mechanism, the excess energy of the
Colloidal Nanocrystals in Electronic Applications Chemical Reviews, 2010, Vol. 110, No. 1 433 Figure 49. Dynamics of hot carriers in semiconductor nanocrystals. (a) Photogeneration of hot carrier in bulk semiconductors is followed by the fast cooling (thermalization) due to transfer of excessive kinetic energy to lattice vibrations (phonons). (b) In nanocrystals, the phonon emission is considered to be strongly suppressed due to the large spacing between electronic energy levels (i.e., mismatch between the frequency of electronic transitions and phonon frequencies). (c) However, because of typically smaller electron effective mass and larger hole density of states (CdSe nanocrystals is an example), the fast Auger-like relaxation is possible. The excessive kinetic energy of holes is subsequently scattered on phonons. (d) Because of increased carrier-carrier interactions in nanocrystals, carrier multiplication is a highly probable mechanism of the hot carrier relaxation. (e) Auger recombination essentially is an opposite process to carrier multiplication. This process is responsible for a fast decay of multiple excitons generated by impact ionization. electron is transferred to a hole, which subsequently loses its energy via phonon emission because in contrast to a sparse spectrum of the electron states, the hole states form a dense, quasicontinuous spectrum even in very small CdSe NCs 531 (Figure 49c). In agreement with this mechanism, the cooling rate increases with decreasing the NC size due to stronger electron-hole Coulomb interactions in smaller dots, as shown for InP NCs. 532 It was observed that electron cooling can be slowed by surface trapping of the holes leading to partial decoupling of carriers. 533 Harbold et al. showed that relaxation is slower in PbSe NCs, 534 where Auger-like relaxation is improbable due to nearly equal effective masses and densities of states of holes and electrons. Still, the relaxation in the picoseconds range was observed, much shorter than that expected from the effect of “phonon bottleneck”. Fast cooling in lead chalcogenide NCs could occur through the intermediate trap states or through the resonant energy transfer to molecular vibrations. 533 Slowing the cooling rate is a complex problem that requires removal or suppression of multiple competing relaxation mechanisms. Very encouraging results were recently reported by Pandey and Guyot-Sionnest. 262 They demonstrated a remarkable increase of intraband relaxation time to >1 ns in CdSe NCs with specially designed epitaxial shells including a thin (1/2 of lattice constant) layer of ZnS, thick (up to 10 monolayers) layer of of ZnSe, followed by 1 monolayer of CdSe. Such shell structure allowed separation of electron and hole: electrons are confined within the CdSe core, while holes are localized in the outer CdSe monolayer capped with holetrapping alkanethiol ligands. The presence of CdSe outer layer and thiol surface ligands also prevents surface trapping of electrons. Not only the NC design but also the device fabrication is a highly challenging task for hot carrier solar cells. The separation and collection of carriers has to be faster than their thermalization. One suggested design of hot carrier cell implies the use of selective energy contacts, which collect and transmit carriers only with energies within the narrow range. 535 Carrier-Multiplication (Multiple Exciton Generation) is another phenomenon that has been proposed to boost the efficiency of NC-based photovoltaics. The effect of carrier multiplication (CM) implies utilization of the excessive energy of the photogenerated carriers via creation of more than one electron-hole pair per one absorbed high energy photon (Figure 49d). This phenomenon is well-known in bulk semiconductors as impact ionization. However, the efficiency of impact ionization in solar cells made of bulk semiconductors is very low and does not provide any considerable contribution to overall light conversion efficiency. The possibility of much more efficient carrier multiplication (CM) in semiconductor NCs has attracted significant attention after it was reported in 2004 by Schaller and Klimov for PbSe NCs. 536 In the following years, highly efficient CM has been reported by several groups for PbSe, 537 PbS, 538 CdSe, 539 InAs, 426,540 and Si NCs. 541 Impressive CM efficiencies have been reported both for colloidal solutions and for NC films. 541 At the same time, other researchers subject the efficiency of CM in semiconductor NCs to intense debate. For example, Nair and Bawendi studied CM using time-resolved photoluminescence and found no evidence of CM in CdSe and CdTe NCs, 542 while PbS and PbSe NCs showed low CM efficiencies of at most 25%. 543 To date, all reports published on CM in semiconductor NCs have been based on spectroscopic measurements, where CM efficiency was determined by analyzing the effects of the formation of multiple excitons on light. All of these spectroscopic measurements are nevertheless indirect methods of measuring CM. The most direct method for determining how many electron-hole pairs are created per absorbed photon is to count the electrons in the photocurrent measured in an external circuit. The most convincing confirmation of efficient CM would be a measurement of the external quantum efficiency above 100% with respect to the incident photon flux, which has not been observed so far. 507 Another serious difficulty for utilization of CM in photovoltaic devices is a very fast (∼100 ps) decay of the multiexciton state via Auger recombination (Figure 49e). To make use of the CM process, the multiexcitonic state should be separated by rapid extraction of individual carriers or excitons from the photoexcited NC. At this moment, strong disagreement within the research community on the efficiency of CM processes in NCs and NC solids does not allow us to evaluate its potential utility for photovoltaic applications.
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