First Principle Calculations of Positron Annihilation in CdSe

Quantum Dots

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 and

Lawrence Livermore National Laboratory)

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 calculatedvia the Hellmann-Feynman theorem:

: Coupling constant

Theory IIThe Local Density Approximation (LDA) was the first implementation. It provides an explicit formula forthe 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.

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).

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.

The variation of the gap is proportional to the variation of the momentum density smearing width (Peter & Friedel model).

DOS

MOMENTUM DENSITY I

Momentum density II

P (2pi/a)

Gap: ZnSe>CdSe>CdTe

Mometum smearing: width of -dn(p)/dp

P (2pi/a)

Smearing= width

From the H atom to theH chain: the momentumcutoff gets shaper

Spectral functions

Momentum density Orbitals of the H chain

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.