Dielectric function of colloidal lead chalcogenide quantum dots obtained by a Kramers-Krönig analysis of the absorbance spectrum

Abstract

We combined the Maxwell-Garnett effective medium theory with the Kramers-Krönig relations to obtain the complex dielectric function ⑀ of colloidal PbS, PbSe, and PbTe quantum dots ͑Qdots͒. The method allows extracting both real ͑⑀ R ͒ and imaginary ͑⑀ I ͒ parts of the dielectric function from the experimental absorption spectrum. This enables the quantification of the size-dependent oscillator strength of the optical transitions at different critical points in the Brillouin zone, strongly improving our understanding of quantum confinement effects in these materials. In addition, the static-limit sum rule yields the electronic dielectric constant from the ⑀ I spectrum. Interestingly, values for lead chalcogenide Qdots remain close to the bulk dielectric constant. To verify these trends, we determined the dielectric constant of thin lead chalcogenide layers by ab initio calculations, and the results agree with the experimental data.

Anomalous quantum confinement of the longitudinal optical phonon mode in PbSe quantum dots

“…On one hand, in our calculations, we use vacuum (with a dielectric constant of 1) in between the layers. On the other hand, the periodic stacking of PbSe slabs leads to an average macroscopic dielectric constant (in the perpendicular direction) between 4.1 (for the 6-layer slab) and 7.2 (for the 15-layer slab) 47 and thus to an effective dielectric environment which is probably not very far from the situation of a stacking of nanocrystals separated by layers of organic materials. Increasing the vacuum width between the slabs reduces the average dielectric constant but also reduces the effective charges such that the net influence of the vacuum width in our calculations is rather weak.…”

Lead sulphide nanocrystal photodetector technologies

“…Photodetectors have already displayed a reponsivity of ~10 9 AW -1 , a 3dB bandwidth of ~3 MHz, a wide dynamic range of ~150 dB, and a detectivity of ~10 13 Jones. Additionally, with a broadband multispectral (UV-Vis-IR) sensitivity they have significant potential to be utilized in many applications including visible, biomedical and hyperspectral imaging systems, spectroscopy, power meters, opto-couplers, food and pharmaceutical inspection, remote sensing and surveillance.…”

“…PbS NC based vertically stacked p-i-n like photodiodes have also been reported, displaying gain (EQE ~18700%) with a detectivity >10 13 Jones Fig. 2f.…”

Nonmonotonic Size Dependence in the Hole Mobility of Methoxide-Stabilized PbSe Quantum Dot Solids

“…4,12,25À27 We stress an important difference in the treatment of the dielectric environment between electric and optical problems: Whereas for electric particleÀparti-cle interactions the static dielectric constant, that is, the real part of the dielectric function at low frequencies has to be considered, for optical interactions, it is the complex dielectric function at optical frequencies that is most relevant. 28 Calculations have shown that a sizable amount of electronic coupling is necessary to overcome the charging energy inherent to QDS and explain the observed mobilities, but the magnitude varied between 10 meV and 8 μeV for the same system depending on the calculation. 3,9 Strong polarization effects can result from a mismatch of optical dielectric constants at the interface between nanoparticle and ligand; however previous studies have shown such effects to be significantly smaller than the observed shifts.…”