First-principles Study on Intrinsic Defects of Ge in Strained Condition Jung-Hae Choi, Seung-Cheol Lee, and Kwang-Ryeol Lee Computational Science Center Future Fusion Technology Laboratory Korea Institute of Science and Technology 1~6, July, 2007 Singapore O-4-PO31 International Conference on Materials For Advanced Technologies 2007

MOSFET scaling down Science 309, 388 (2005). Physical limitations on scaling-down of conventional Si/SiO 2 semiconductors  various researches on next generation devices Physical limitations on scaling-down of conventional Si/SiO 2 semiconductors  various researches on next generation devices High-k gate oxide strained Si Ge channel ??? & Many others

Ge as a channel materials Higher mobility than Si  Application on high performance device Higher mobility than Si  Application on high performance device Unreliable oxide Difficulties of growing single crystals & their high cost Unreliable oxide Difficulties of growing single crystals & their high cost Disadvantages graded SiGe Ge film Si substrate Ge film Si substrate Advantages Ge Si 2 nm Next generation MOS ? Strained !

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 …….

Si Ge Unstrained Ge Purpose of this work First-principles calculations - the dependency of vacancy formation energy on the strain - only on neutral vacancy Strained Ge E v unstrained  < 0 a Ge = 5.66 Å a Si = 5.43 Å E v strained ≠ Ge ?

Calculation condition using VASP  DFT scheme  E cut = 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 = eV  Spin-unrestricted calculations  Symmetry-off conditions  Gaussian smearing factor = 0.1 eV supercell Number of atoms K-points 2x2x2646x6x6 3x3x32162x2x2 4x4x45122x2x2

Tests of exchange-correlation potential on Si & Ge a Si (Å)B Si (GPa)a Ge (Å)B Ge (GPa) (a Si -a Ge ) /a Ge PAW-LDA PAW-PBE US-LDA US-PW Experimental  PAW-LDA was selected !

Vacancy formation energy E q v ; vacancy formation energy N ; number of atom E q N ; total energy of N atom system E q N-1 ; total energy of (N-1) atom system q ; charge state of vacancy  e ; E F relative to the VBM E v E q v ; vacancy formation energy N ; number of atom E q N ; total energy of N atom system E q N-1 ; total energy of (N-1) atom system q ; charge state of vacancy  e ; E F relative to the VBM E v Perfect structure One vacancy EqvEqv

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 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

Atomic configuration of supercell with 1 vacancy x y z initial up dn a b c d vac Unstrained Ge; 2dNN = (2dNN-S =D ac =D bd ) ≒ (2dNN-L = D ab =D ad =D bc =D cd )  ~T d symmetry Strained Ge; (2dNN-S =D ac =D bd ) ≠(2dNN-L = D ab =D ad =D bc =D cd )  D 2d symmetry Unstrained Ge; 2dNN = (2dNN-S =D ac =D bd ) ≒ (2dNN-L = D ab =D ad =D bc =D cd )  ~T d symmetry Strained Ge; (2dNN-S =D ac =D bd ) ≠(2dNN-L = D ab =D ad =D bc =D cd )  D 2d symmetry

Supercell geometry 2x2x2 3x3x3 4x4x4 2x2x2 4x4x4 x y z unstrainedstrained supercellx=y=zdiagonalx=yzdiagonal 2x2x x3x x4x a Ge equil D v-v a Si equil a Ge relax D v-v unstrained strained Not large enough

Comparison with previous reports Number of atoms Brillouin zone sampling E f v (eV)D L /D s Jahn- Teller distortion Code This work5122x2x / VASP PRB 61 (2000) 128  only / Fritz- Haber J. Phys; Condens. Matter 17 (2005) 376cluster3.7/ AIMPO (LSDA) Neutral vacancy in Ge in the unstrained condition ; Jahn-Teller distortion is negligibly small.

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. 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. Neutral Vacancy formation energy Si unstrained Ge unstrained Ge strained E f v (eV) > >

Summary The formation energy and atomic configuration of neutral vacancy in Ge under planar-strained condition was studied by the first-principles calculation. We used large supercells (63-, 216-, 511-atoms) with non  -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.