Effect of Quantum Confinement on the Dielectric Function of PbSe

Abstract

Monolayers of lead selenide nanocrystals of a few nanometers in height have been made by electrodeposition on a Au(111) substrate. These layers show a thickness-dependent dielectric function, which was determined using spectroscopic ellipsometry. The experimental results are compared with electronic structure calculations of the imaginary part of the dielectric function of PbSe nanocrystals. We demonstrate that the size-dependent variation of the dielectric function is affected by quantum confinement at well-identifiable points in the Brillouin zone, different from the position of the band-gap transition. DOI: 10.1103/PhysRevLett.92.026808 PACS numbers: 73.22.Dj, 73.63.-b Semiconductor nanocrystals with dimensions below 10 nm possess optical properties that depend strongly on the size and shape of the nanocrystals. This is due to confinement of the exciton wave function in the limited space of the nanocrystal [1]. In many cases, the sizedependent optical properties can be understood by considering the effects of quantum confinement on the band-gap transition, i.e., the electronic transition with lowest energy, and a few other closely related transitions [2]. However, quantum confinement will affect all electronic transitions throughout the entire Brillouin zone and, thus, decide the dielectric function of a semiconductor nanocrystal in a broad energy range. Despite the scientific and technological importance, only a few studies have been published in which the dielectric function of semiconductors nanocrystals is considered [3,4].Here, we present a study on the effects of quantum confinement on the dielectric function of PbSe nanocrystals in the energy range 1.5-4 eV. Bulk PbSe is a low band-gap semiconductor, with a band-gap transition of 0.26 eV at room temperature (at the L point of the Brillouin zone) and several other critical points (Van Hove singularities) at higher energy (at the L point and along the and directions). PbSe nanocrystals form an ideal case for this study: They can be electrodeposited on a gold substrate with good control over their size and shape [5], and the effects of quantum confinement are expected to be strong due to the low effective masses of the electrons and holes [6]. We studied the dielectric function ! of PbSe nanocrystals deposited on gold by spectroscopic ellipsometry. The dielectric function of the PbSe nanocrystals can be described by a sum of two Lorentz oscillators, as reported before for bulk PbSe [7]. This shape of the dielectric function is determined by an increase of the oscillator strength and the joint density of states near the Van Hove singularities along the directions and in the Brillouin zone [8]. We found that the resonance energies of these oscillators increase strongly relative to the bulk values when the nanocrystal height is less than 5 nm. This blueshift is accompanied by a change of the oscillator width and the oscillator strength. These results are compared with a tight-binding calculation of the dielectric function of an infinite PbSe sheet with v...

Size dependence of nanostructures: Impact of bond order deficiency

“…Fig. 39(b) compares the 3 nano-Si derived herein and other sophisticated calculations of nanosolid Si and the third-order dielectric susceptibility of Ag nanodots [605]. Although the dielectric susceptibility does not follow the BOLS prediction, it shows the suppressed trend.…”

“…Delerue et al [605] deposited PbSe nanocrystals of several nanometers in height on an Au(111) substrate and measured the thickness-dependent dielectric function. Compared with electronic structure calculations of the imaginary part of the dielectric function of PbSe nanocrystals they suggested that the size-dependent variation of the dielectric function is affected by quantum confinement at well-identifiable points in the Brillouin zone, instead of the bandegap transition.…”

Infrared Emitting HgTe Quantum Dots and Their Waveguide and Optoelectronic Devices

“…Their use of this modelling approach can be followed back to early work on thin (few nm) crystalline PbSe films [124] where it was used to interpret the appearance of film thickness dependent confinement related features in the dielectric function determined by spectroscopic ellipsometry. The same modelling methods were used to derive a comparison between the tight binding theoretical density of states and the density of states function derived from STM measurements on 3 and 7 nm diameter PbSe colloidal QDs [125].…”

Response Concerning “On the Interpretation of Colloidal Quantum Dot Absorption Spectra”

“…In the literature there is evidence that quantumconfinement effects play an important role throughout the entire Brillouin zone (up to 4 eV) and also influences the dielectric response (and thus n and k) in the high-energy region. [3,4] It will be interesting to see if the analysis of more …”

“…The analysis by Moreels and Hens shows that a satisfactory agreement in the high-energy region (E 2 in their Figure 3) is obtained by using the wavelengthdependent values for n and k from bulk PbSe. Whether or not the high-energy transitions in PbSe QDs are affected by quantum confinement, if n and k are identical to the bulk values of PbSe in this high-energy region, [3][4][5] and also how to correctly correct for local field effects, [6][7][8] remain important questions. In the literature there is evidence that quantumconfinement effects play an important role throughout the entire Brillouin zone (up to 4 eV) and also influences the dielectric response (and thus n and k) in the high-energy region.…”