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Volumn 78, Issue 12, 2008, Pages

Carrier multiplication yields in PbS and PbSe nanocrystals measured by transient photoluminescence

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EID: 54049087746     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.125325     Document Type: Article
Times cited : (208)

References (44)
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    • In the literature CM yields are often reported as an internal quantum efficiency (IQE), which is related to our yCM by IQE=100% (yCM +1).
    • In the literature CM yields are often reported as an internal quantum efficiency (IQE), which is related to our yCM by IQE=100% (yCM +1).
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    • As in our previous work (Ref.), we delay fitting of the 1.55 eV -excited decays by a time ∼ τBX /2 to minimize unwanted interference from higher MX tPL components in the determinations of aX and aBX.
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    • For example, we find τBX ≈58 ps and τBX ≈140 ps for EX0 =0.84 eV and EX0 =0.68 eV PbSe NCs, respectively, while Beard
    • For example, we find τBX ≈58 ps and τBX ≈140 ps for EX0 =0.84 eV and EX0 =0.68 eV PbSe NCs, respectively, while Beard (Ref.) have determined τBX =67 ps for EX0 =0.84 eV and Schaller et al.(Ref.) report τBX =149 ps for EX0 =0.64 eV.
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    • See EPAPS Document No. E-PRBMDO-76-R08732, the supplemental to our previous work on CdSe and CdTe NCs, for details on analysis of tPL decay curves. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html.
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    • The steep volume dependence | 〈 2e2h | VCoul | 1e1h 〉 | 2 ̄ ∝ V-4 might appear surprising at first. It should be kept in mind that this square matrix element is averaged over all 2e2h configurations of nearby energy. However, for 〈 2e2h | VCoul | 1e1h 〉 ≠0, conservation of momentum and spin must be satisfied and one of either the initial electron or hole must not change state. The proportion of final 2e2h states that violate these conditions and thus have 〈 2e2h | VCoul | 1e1h 〉 =0 increases with volume, ultimately resulting in a stronger volume scaling of | 〈 2e2h | VCoul | 1e1h 〉 | 2 ̄ than would be expected from averaging only the nonzero terms.
    • The steep volume dependence | 〈 2e2h | VCoul | 1e1h 〉 | 2 ̄ ∝ V-4 might appear surprising at first. It should be kept in mind that this square matrix element is averaged over all 2e2h configurations of nearby energy. However, for 〈 2e2h | VCoul | 1e1h 〉 ≠0, conservation of momentum and spin must be satisfied and one of either the initial electron or hole must not change state. The proportion of final 2e2h states that violate these conditions and thus have 〈 2e2h | VCoul | 1e1h 〉 =0 increases with volume, ultimately resulting in a stronger volume scaling of | 〈 2e2h | VCoul | 1e1h 〉 | 2 ̄ than would be expected from averaging only the nonzero terms.
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    • Excitonic effects can plausibly be neglected when considering the shape of the average DOS in NCs. The Bohr radius of PbSe and PbS are 46 and 18 nm, respectively, while the NCs used in this study have a diameter less than 8 nm, well within the strong-confinement limit. In addition, the dielectric constants of PbSe and PbS are quite large, at 23.6 and 17, respectively, further reducing the coulomb energy between carriers. This approximation of treating the charge carriers in PbX NCs as largely independent of each other has been previously used in the theoretical literature (Ref.).
    • Excitonic effects can plausibly be neglected when considering the shape of the average DOS in NCs. The Bohr radius of PbSe and PbS are 46 and 18 nm, respectively, while the NCs used in this study have a diameter less than 8 nm, well within the strong-confinement limit. In addition, the dielectric constants of PbSe and PbS are quite large, at 23.6 and 17, respectively, further reducing the coulomb energy between carriers. This approximation of treating the charge carriers in PbX NCs as largely independent of each other has been previously used in the theoretical literature (Ref.).
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