Si substrate

1. Empirical Molecular Dynamics Simulations to Analyse Holographically Determined Mean Inner Potentials Si.95Ge.05 Si.75Ge.25 Si.5Ge.5 Si.25Ge.75 Si.05Ge.95 a b j i 2 1 j j potential scan Vacuum k Ge-Si j i y c k i x Si substrate V0 t Object i d j potential average SiGeQD MDrelaxed & simulated exit wave Vacuum Si.5Ge.5 background histogram (counts/eV) & linescans (Vo in eV) angles -4eV Phase shift distance l k V0: Mean inner Coulomb potential t: Object thickness a b Phase i Amp dihedral ,,,, torsion c d + + ...... + = Kurt Scheerschmidt, Max Planck Institute of Microstructure Physics, Halle/Saale, Weinberg 2, Germany, schee@mpi-halle.de, http://mpi-halle.de GOAL: Determination of mean inner potentials (MIP) to analyze 3D (Si,Ge) nanostructures MD using BOP: structure relaxations phononmodes via frozen lattice charge density Molecular Dynamics using Bond Order Potentials embedded bonds instead atoms – two-center orthogonal TB density matrix instead diagonalisation Composition, structure, strain, morphology of (Si,Ge) nanostructures Analysis via STEM & CTEM E tot = Erep + Eprom + Eband (k)  empirical s2p2->sp3SHia,jbQia,jb  Physical properties (confinement) hopping integrals BOmatrix Pettifor-Aoki = [E-H]-1 Slater-Koster sss, sps, ppp... Lanczos recursion & electronic hopping in closed loops V(r)BOP (in eV) V(r) DFT (in Ha) Applicability electronic / photonic devices • CTEM: • - two dimensional projection • - dynamical diffraction complexity • strains and composition gradients • mean inner potential MIP EXPERIMENTAL: Electron Holography y ~ eiAt = C-1{eigt}C MD - BOP scattering potential Electron holography of (Si,Ge) islands amplitude Si Ion milling Electron hologram Amplitude Unwrapped phase phase Amplified phase image of (Si,Ge) QDs unwrapped phase Hologram Sample A: h~ 66 nm 10  amplified phase image Unwrapped phase profile Sample B: h ~ 130 nm 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. s-, p-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 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.