A comparative study for colloidal quantum dot conduction bandstate calculations Page: 3 of 10
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and energies EZ in a Schrodinger's equation:
(-2V2 + V(r))OZ(r) = EZOZ(r), (1)
where the total potential V(r) = Ea,R va(r - R) is a direct sum of the screened pseudopo-
tential va of the atoms type a, both inside and on the surface of the QD. The bulk atomic
pseudopotentials are fitted to the experimental bulk band structure, and the surface pseu-
dopotentials are fitted to remove the band gap states. For InAs, however, instead of using
surface passivation atoms, an artificial large band gap barrier material is used to represent
the vacuum . Folded spectrum method (FSM)  is used to solve the band gap states
The EMA models are obtained by taking the effective mass parameters from the EPM
bulk band structures. For Si EMA, the inverse effective mass is taken as an average along
the three principle directions near the X point. After the effective mass is obtained, a
confinement potential Vt(r) will be used to represent a quantum dot. This potential is
zero inside the dot, and equals the electron affinity of the EPM in the vacuum barrier
region. Outside the QD, the electron is treated as having the same effective mass as inside
The FSM/EPM and EMA results for the InAs, InP, CdSe, and Si colloidal QDs are shown
in Fig.1(a), (b), (c), and (d) respectively. We can see that there is a large difference between
the EMA results and the EPM results. EMA results significantly overestimate the quantum
confinement effects. In the following, we will trace the sources of this overestimation.
One way to make a clean comparison to the EMA model without the complication of the
boundary condition is to add the same EMA Vt(r) to an extended bulk EPM potential
Vb(r)  in the EPM formalism:
(- V2 + V(r) + Vxt(r))Oi(r) = Eioz(r). (2)
This is a direct analogous to the EMA QD model. Unfortunately, a direct solution (e.g, using
the FSM) for the CBM state of Eq. (2) is usually impossible since Ve outside the QD is
larger than the bulk band gap, hence there is no QD band gap in Eq.(2). To yield a sensible
CBM solution from Eq.(2), we will use the linear combination of bulk band (LCBB) 
method. In the LCBB method, the quantum dot state OZ is expanded using bulk Bloch
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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/m1/3/: accessed March 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.