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First-principles Study on Intrinsic Defects of Ge in Strained Condition O-4-PO31 1~6, July, 2007 Singapore International Conference on Materials For Advanced Technologies 2007 Jung-Hae Choi, Seung-Cheol Lee, and Kwang-Ryeol Lee Computational Science Center Future Fusion Technology Laboratory Korea Institute of Science and Technology email@example.com http://diamond.kist.re.kr/CSC
Science 309, 388 (2005). MOSFET scaling down Physical limitations on scaling-down of conventional Si/SiO2 semiconductors various researches on next generation devices Ge channel ??? High-k gate oxide strained Si & Many others
Ge film Ge film Si substrate graded SiGe Ge Si substrate Si 2 nm Ge as a channel materials • Higher mobility than Si • Application on high performance device Disadvantages Advantages • Unreliable oxide • Difficulties of growing single crystals & their high cost Strained ! Next generation MOS ?
Motivations • Understanding and controlling the defect structures in the strained condition are the fundamental steps in solid state reactions such as crystal growth, processing and operation of devices, which accompany diffusion. • Despite the rising importance of Ge and its similarities with Si, the intrinsic defects of Ge in strained condition are seldom characterized experimentally and theoretically. • The calculation on the defect formation in Ge is controversial in terms of defect formation energy, atomic configurations, etc. • Investigations of the strain effect on the vacancy formation was not performed yet.
Controversial results on the vacancy formation Depend on • Code • Exchange-correlation scheme - parametrization • Number of atoms • Cutoff energy • Convergence of Relaxation • K-point sampling • Symmetry constraints • Spin • ……. • …….
Purpose of this work ? ≠ Evstrained Evunstrained s < 0 Ge s < 0 Ge Si aGe = 5.66 Å aSi = 5.43 Å Unstrained Ge Strained Ge • First-principles calculations • the dependency of vacancy formation energy on the strain • only on neutral vacancy
Calculation condition using VASP • DFT scheme • Ecut = 300 eV • Exchange-correlation potential; LDA(CA) • Projector Augmented-Wave (PAW) potential • Brillouin zone sampling using Monkhorst-Pack technique • Ionic relaxation; Conjugate gradient method (force < 0.01 eV/Å) • Convergence = 10-5 eV • Spin-unrestricted calculations • Symmetry-off conditions • Gaussian smearing factor = 0.1 eV
Tests of exchange-correlation potential on Si & Ge PAW-LDA was selected !
Vacancy formation energy • Eqv ; vacancy formation energy • N ; number of atom • EqN ; total energy of N atom system • EqN-1 ; total energy of (N-1) atom system • q ; charge state of vacancy • me ; EF relative to the VBM Ev Eqv Perfect structure One vacancy
Vacancy formation energy • Decrease of the vacancy • formation energy of (~1.3 ev) • by the compressive planar strain • Easier formation of vacancies • Fast diffusion and intermixing in Ge epitaxial layer on Si ?? • Effect of supercell size due to vacancy-vacancy interactions ; 2x2x2 supercell is not large enough
up dn vac a d dn up c b y initial x z Atomic configuration of supercell with 1 vacancy Unstrained Ge; 2dNN = (2dNN-S =Dac=Dbd) ≒(2dNN-L =Dab=Dad=Dbc=Dcd) ~Td symmetry Strained Ge; (2dNN-S =Dac=Dbd) ≠(2dNN-L =Dab=Dad=Dbc=Dcd) D2d symmetry
2x2x2 2x2x2 3x3x3 4x4x4 4x4x4 z y x Supercell geometry strained unstrained 3x3x3 Not large enough
Comparison with previous reports Neutral vacancy in Ge in the unstrained condition ; Jahn-Teller distortion is negligiblysmall.
Effects on diffusion • Vacancy is much more important for self-diffusion in Ge than Si !! • Under the compressive planar strain, the role of vacancy in Ge is more dominant than in unstrained condition. > >
Summary • The formation energy and atomic configuration of neutral vacancy inGe under planar-strained condition was studied by the first-principles calculation. • We used large supercells (63-, 216-, 511-atoms) with non G-point calculations. • The formation energy of vacancy decreased drastically by the compressive planar strain. The easier formation of vacancies could induce the fast diffusion and intermixing in Ge epitaxial layer on Si. This calculations were performed on the KIST grand supercomputer. http://accms-4.kist.re.kr