1. Empirical Molecular Dynamics Simulations to Analyse Holographically Determined Mean Inner Potentials Kurt Scheerschmidt, Max Planck Institute of Microstructure Physics, Halle/Saale, Weinberg 2, Germany, schee@mpi-halle.de, http://mpi-halle.deschee@mpi-halle.dehttp://mpi-halle.de x y Si substrate Ge- Si CTEM: - two dimensional projection - dynamical diffraction complexity - strains and composition gradients - mean inner potential MIP GOAL: Determination of mean inner potentials (MIP) to analyze 3D (Si,Ge) nanostructures Applicability electronic / photonic devices Physical properties (confinement) Composition, structure, strain, morphology of (Si,Ge) nanostructures V0V0 Vacuum Phase shift t V 0 : Mean inner Coulomb potential t: Object thickness Object  e iAt = C -1 {e i  t }C EXPERIMENTAL: Electron Holography Electron hologramAmplitudeUnwrapped phase Si Ion milling Amplified phase image of (Si,Ge) QDs 10  amplified phase image Unwrapped phase profile Electron holography of (Si,Ge) islands Hologram amplitude phase unwrapped phase + = j i j i k +...... + j i k l dihedral,,,, torsion angles j i j i k distance Molecular Dynamics using Bond Order Potentials embedded bonds instead atoms – two-center orthogonal TB density matrix instead diagonalisation E tot = E rep + E prom + E band (k)    empirical s 2 p 2 ->sp 3 S H i a,j b Q i a,j b   hopping integrals BOmatrix Pettifor-Aoki = [E-H] -1 Slater-Koster ss s, sp s, pp p... Lanczos recursion & electronic hopping in closed loops SiGeQD MDrelaxed & simulated exit wave Amp Phase 21 a b c d Si.95Ge.05Si.75Ge.25Si.5Ge.5Si.25Ge.75Si.05Ge.95 potential scan potential average ab cd Si.5Ge.5 background histogram (counts/eV) & linescans (Vo in eV) -4eV MD using BOP : structure relaxations phononmodes via frozen lattice charge density Mean inner potential (MIP in eV) of (Si,Ge) compounds as function of the Ge concentration x for different scattering models: SCFfit = isolated atom approximation (Doyle-Turner) with atomic form factor of Si (5.828Å) and Ge (7.378Å). - DFTfit = linear fitted DFT data of Kruse & Schowalter UM106(2006)105, i.e. Si (12.57 V) and Ge (14.67 V). perfect/relaxed = scan of the bond order potential before (perfect) and after (relaxed, NpT conditions) annealing up to 400 K using classical molecular dynamics for vacuum super cells (small=sSC/extended=eSC) of 7nm/23nm box length (13x13x13, 10478atoms/ 41x41x41, 312666 atoms) half filled with (Si,Ge) of different Ge concentration x. Total energies including all attraction terms, i.e.  -,  -bonds, promotion, and negative repulsive energy. Static relaxation: i=sSC,NVE, ii=sSC,NpT, iii=eSC,NpT, iv=eSC,NVE final: v=eSC,NVE, vi=sSC,NVE, xi=sSC,weak-p, xii=sSC,weak-T 400K-dynamics: vii=eSC,NVE, viii=eSC,NpT, ix=sSC,NVE, x=sSC,NpT Sample A: h~ 66 nm Sample B: h ~ 130 nm Analysis via STEM & CTEM MD - BOP scattering potential V(r) DFT (in Ha) V(r) BOP (in eV) REFERENCES: C.L.Zheng, Thesis, HU-Berlin, 2010; K.Scheerschmidt, et.al., IMC17, Rio de Janeiro 2010, I8.4; C.L.Zheng, UM 2012, in prep.