# NERSC Initiative for Scientific Exploration (NISE) 2011 Awards

## An Efficient Real-Space Approach to Calculating Auger Spectra

### Keith Gilmore, Lawrence Berkeley National Lab

**Associated NERSC Project: Understanding and controlling semiconductor nanocrystal surfaces (m1141)Principal Investigator: David Prendergast, Lawrence Berkeley National Lab**

NISE Award: | 800,000 Hours |

Award Date: | March 2011 |

At the Molecular Foundry we are members of an experimentally driven Grand Challenge project that seeks to understand how the surface environment of semiconductor nanoparticles influences their electronic and optical properties. Nanoparticles are routinely proposed for use in a wide variety of applications including photovoltaics, solid-state lighting, and bio-imaging. However, the behavior of these particles depends sensitively on their surface environments and this dependence has been insufficiently investigated. We are in the process of correlating various spectroscopic techniques – both experimental and computational – in order to better understand the influence of surface chemistry on the properties of nanoparticles.

Many varieties of x-ray spectroscopy exist and each type gives information about some aspect of the local electronic and chemical structure of a material. Auger spectroscopy interrogates the occupied valence states while x-ray absorption spectroscopy probes the unoccupied conduction levels. Combining these complementary data sets with structural information obtained from electron microscopy and numerical relaxation calculations will allow us to construct a whole picture of the influence of surface environment on the physical properties of nanoparticles.

We propose to develop a highly parallel code to efficiently evaluate Auger spectra using real-space techniques. While many electronic structure programs are based on plane-wave Fourier-space approaches, electronic excitations and decay processes are typically localized in space. In order to accurately describe a localized disturbance an unreasonably large number of plane waves must be used, making such approaches very inefficient. Real-space approaches solve this problem by allowing for a much smaller basis set.

An efficient real-space code for calculating static dielectric screening has already been developed by Eric Shirley of NIST [1]. As a previous postdoc of Dr. Shirley, the PI proxy Keith Gilmore is very familiar withthis code and has already extended it to the dynamic screening case, which will be necessary to capture Auger decay processes. Remaining code development includes constructing the electron self-energy from the dynamic screening and evaluating the direct and exchange coulomb matrix elements between the initial and final states. Both of these steps are routine and can be completed quickly. The resulting code will be folded into the OCEAN / Abinit-NBSE package described in the following section, and made publicly available.

Auger decay cross-sections will be calculated for both core-core-valence and core-valence-valence cases similarly to the method described in [2]. In each case, the initial state contains one hole while the final state contains two holes. Eigenstates and energies of the single-hole initial states will be determined within the GW method while the GW-based Bethe-Salpeter equation will be solved to find the two-hole final states.