A comparative study for colloidal quantum dot conduction bandstate calculations Page: 2 of 10
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Many high quality colloidal semiconductor quantum dots (QDs) [1, 2] of III-V, II-VI, and
IV-IV materials have been successfully synthesized by wet chemistry methods. One of the
most predominate features of these quantum dots is their size dependent photoluminescence
(PL) due to carrier quantum confinement [1, 2]. Many theoretical methods have been used
to study this quantum confinement effect. These include the effective mass approximation
(EMA) ; multi-band k-p method [4, 5]; empirical tight-binding method (TB) ; empirical
pseudopotential method (EPM) [7-10]; and ab initio local density approximation (LDA)
method [11, 12]. The results of the atomistic methods (TB, EPM, and ab initio method)
could be very close to each other. For example, if the TB bulk band structure is fitted to the
EPM band structure, their calculated QD band gaps are very similar. A recent calculation
also indicates that the EPM results are very close to the ab initio LDA results . On the
other hand, it is now believed that the simple EMA method often grossly overestimates the
quantum confinement effect. There have been comparative studies between the k-p results
and the EPM results for both colloidal quantum dots  and embedded quantum dots .
For colloidal quantum dots, it was found that their quantum confinements can be a few
hundred meV different, and the order of the valence band states can also be different .
While the valence band hole states have been studied extensively in previous comparative
studies [8, 13], here we will focus on the conduction band states. Not only the conduction
band states contribute more than 70-80% of the total exciton quantum confinement for most
semiconductor QDs, the relatively simple characteristics of the conduction band allows us
to conduct an in-depth investigation for the causes of the differences between the continuum
models and the atomistic model. There are several possible causes: (i) the inadequate
description of the bulk band structure in the continuum models [13, 14]; (ii) the neglect of
multi-bulk band coupling [7, 13] induced by the quantum dot geometry; and (iii) inadequate
boundary conditions of the continuum models [15, 16]. The purpose of this paper is to
conduct a controlled analysis of these causes. It will benefit the future development of
the continuum models, and will also provide physical insights about the origin of quantum
confinement effects. We will focus on the differences between the EMA method and the
EPM method. We will study the conduction band minimum (CBM) states, and Si, InAs,
InP and CdSe colloidal QDs, which have been calculated previously using EPM methods
and their results agree well with experiments [7-10].
The empirical pseudopotential method (EPM)  describes the single-particle states /Z
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Luo, Jun-Wei; Li, Shu-Shen; Xia, Jian-Bai & Wang, Lin-Wang. A comparative study for colloidal quantum dot conduction bandstate calculations, article, December 1, 2005; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc885234/m1/2/: accessed March 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.