First Principle Calculations of Positron Annihilation in CdSe Quantum Dots

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First Principle Calculations of Positron
Annihilation in CdSeQuantum Dots
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B. Barbiellini, A. Bansil (Northeastern
University, Boston, MA 02115), P. Mijnarends
(Delft University of Technology,Delft, The
Netherlands), R. Saniz (UCB, Cochabamba,
Bolivia), P. Sterne (Lawrence Livermore
National Laboratory),M. Weber, K. Lynn
(Washington State University, Pullman WA 99164),
A. Denison (INEEL, Idaho Falls, ID 83415
andLawrence Livermore National Laboratory)
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Theory I
The Density Functional Theory (DFT) is
generalized to positron-electron systems by
including electron and positron density( The
ground-state value of any operator is a
functional of the electron and positron densities
and be calculated via the Hellmann-Feynman
theorem
Coupling constant
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Theory II
The Local Density Approximation (LDA) was the
first implementation. It provides an explicit
formula for the Exchange-Correlation Energy
The Generalized Gradient Approximation (GGA)
reduces the LDA electron-positron correlation.
The GGA is very successful for positron
lifetimes, energetics, and momentum
distributions of the annihilating pairs.
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Positron lifetime in bulk CdSe
An experimental lifetime of 275 ps was found in
agreement with the theoretical value of 279 ps
based on the DFT GGA. A highly accurate
description of the electron-positron correlation
effects is needed to find such a good agreement.
Such agreement indicates also that our bulk
sample is of good quality (without any
significant concentration of atomic point
defects).
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Positron state in a CdSe Qdot

• The state of the positron can be explained in
  terms of the positron Affinity (calculated by DFT
  GGA) between the Qdot and the matrix.
• Potential well is about 2 eV therefore positrons
  are trapped in the CdSe Qdots.
• Using an LMTO basis set we find that almost 80
  of the positron wave function is confined to the
  interstitial region between the atoms thus
  limiting the fraction that could extend beyond
  the quantum dot volume.

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MOMENTUM DENSITY I
DOS
The variation of the gap is proportional to the
variation of the momentum density smearing width
(Peter Friedel model).
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Momentum density II
Gap ZnSegtCdSegtCdTe
P (2pi/a)
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Mometum smearing width of -dn(p)/dp
Smearing width
P (2pi/a)
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Spectral functions
From the H atom to the H chain the
momentum cutoff gets shaper
Momentum density
Orbitals of the H chain
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Conclusion
The scheme based on measuring and calculating
positron lifetime and momentum distributions is a
reliable tool to analyze materials properties.
The study (Lifetime and Doppler profile) of bulk
CdSe gives credence to use the DFT GGA scheme.
The localized positron states at Qdots have also
been found well described by the DFT GGA
(Affinity). The Doppler profile shows a
smearing at the boundary of the Jones zone
proportional to the widening of the band gap that
may occur due to a reduction in the size of the
quantum dots.