Atomistic simulations of point defect diffusion in Si and SiGe
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1 Atomistic simulations of point defect diffusion in Si and SiGe P. Pochet, D. Caliste, K. Rushchanskii, F. Lançon & T. Deutsch CEA UJF INAC Institute for Nanoscience and Cryogenics Partially founded by the OSiGe_Sim project ANR-05-NANO-004 1
![Context and outline Diffusion in the microelectronic material 2.5 Z[nm] 2 Ge & PD diffusion Strain Charge state Dopant 1.5 1 0.](/docs-images/81/82655726/images/2-2.jpg "5 0 SiGe Cmos 2006 STMicroelectronics 0 10 20 30 X[nm] 40 50 SiGe QD 2006 CEA-Recherche Fondamentale The need of multi-scale for diffusion simulations!")
2 Context and outline Diffusion in the microelectronic material 2.5 Z[nm] 2 Ge & PD diffusion Strain Charge state Dopant SiGe Cmos 2006 STMicroelectronics X[nm] SiGe QD 2006 CEA-Recherche Fondamentale The need of multi-scale for diffusion simulations! Some insight of Ge diffusion in SiGe The case of Si vacancy diffusion Summary and outlooks 2
3 The multi-scale method for diffusion studies Phenomenological model Analysis Kinetic Kinetic Lattice Monte Carlo Equilibrium Coupling Migration Em Formation Ef ab initio calculation DFT (CPMD, SIESTA): 216 atoms simulation box, Γ or 2x2x2, only some typical configurations; NEB driver for saddle point calculation Coupling through models that reproduce the DFT energies for all possible configurations BKL-type KLMC simulations (resident time) 3
4 Diffusion in Siy-Ge1-y alloys (DFT step only) Vacancy and interstitial diffusion [Strohm etal. al.' ] Strohm et GeSi * Vacancy diffusion for y < 0.70 and T < ~ 1000 C [Faheyetetal.al.' ] Fahey Ge@Si * Dual diffusion for lower concentration DFT study of Ge diffusion in Si 4
5 The vacancy mechanisms Only one Ge in the Si box Formation energy Ef = 3.6 ev (216-2k) Migration path with a ring mechanism Jahn-Teller effect Ge Si pairing <Em> = 0.37 ev D. Caliste, P. Pochet, T. Deutsch, F. Lançon PRB 75, (2007) 5
6 The interstitial formation Mixed dumbbell d<110> 3.16 ev Hexagonal SiH 3.33 ev Hexagonal GeH 3.45 ev D. Caliste, P. Pochet, T. Deutsch, F. Lançon PRB 75, (2007) 6
7 The migration mechanism of the <110> dumbbell Second neighbor diffusion Through hexagonal interstitial D. Caliste, P. Pochet, T. Deutsch, F. Lançon PRB 75, (2007) 7
8 The interstitial migration mechanism d<110> --> GeH Em = 0.44 ev d<110> --> SiH Em = 0.37 ev GeH d<110> d<110> Direct migration of GeH : <Em> ~ 0.10 ev Back movement GeH --> d<110> : Kick-off scheme diffusion but with a dumbbell to hexagonal ratio is not << 1 <Em > = 0.44 ev Em = 0.15 ev! D. Caliste, P. Pochet, T. Deutsch, F. Lançon PRB 75, (2007) 8
9 The FFCD mechanism: an intrinsic mechanism ~ SW in C60 [Pandey, PRL 57, 2287 (1986) and Goedecker, PRL 88, (2002)] Low formation energy: Ef = 2.62 ev High migration energy: Em = 1.63 ev D. Caliste, P. Pochet, T. Deutsch, F. Lançon PRB 75, (2007) 9
10 Ge diffusion in Si (comparison with experiments) Direct use of ab initio value: 1 mediator only For FFCD Ea = 4.2 ev Saddle point unknown For interstitials Ea = 3.7 ev Ea = Ef + <Em> unknown For vacancies Ea = 4.0 ev Ea = Ef + <Em> 4.18 ev [Strohm et al. 2002] All mediators might contribute to diffusion as observed in experiments but the Ge diffusion activation energy is ~ 5 ev?! For complex diffusion mechanism, effective activation energies could be higher than the direct sum of individual one? Need of Monte Carlo step for correct physical average! D. Caliste, P. Pochet, T. Deutsch, F. Lançon PRB 75, (2007) 10
11 The case of Si vacancy An old but controversial story for migration energy... Watkins Em = 0.45 ev [MSS. Proc. 3, (2000)] direct measurement of Em Bracht et al. Em = 1.8 ev measurement of Ea Ranki et al. Em = 1.2 ev measurement of Ea [PRL 91, (2003)] [PRL 93, (2004)] Can we explain these scattered data from effective phenomena? 11
12 DFT step: vacancy formation energy Si pairing 3.52 ev (216-1k) 3.6 ev (Dannefaer 1986) In Si, DFT fit well with exp [D. Caliste PhD (2005); see also Wright (2006)] Only neutral vacancy! Jahn-Teller effect [G.GWatkins D Watkins1992]
13 NEB+DIIS 216-1k DFT step: vacancy migration energy 1V 2V 0.30 ev Exp: 0.45 ev [ Watkins '79 ] 1.19 ev Exp: 1.3 ev [ Watkins '65 ] 13
14 Coupling step: migration landscape D. Caliste and P. Pochet PRL (2006) 14
15 Monte Carlo step 2 vacancies and 0,1 à 18 M silicon atoms Einstein formula T = 1200 K Mean square displacement r2 (t) = 2 ddt Average on 20 trajectories --> D as function of T and Cv time (s) 15
16 Non-Arrhenius diffusion is predicted! --> DSi Em 10-7 at at diffusion regimes! 16
17 Step-like trajectory in intermediate temperature? Dissociated 1V x 2 2V Mean square displacement T = 1200 K Associated time (s) 17
18 Three temperature regime rationalization Concurrent diffusion in 1V or 2V 2V dissociation 1V migration (fast) 2V migration (slow) Analytical derivative gives a model for effective migration energy With fα and fβ being [0-1] bounded D. Caliste and P. Pochet PRL (2006) 18
19 Model vs MC simulations (high T) region I T < 200 K ~ équilibium Em = 0.45 ev > high T or low Cv 0.45 ev Watkins ' K e- irradiation Em = 1.8 ± 0,5 ev Bracht ' K Highly doped Em = 1.3 ev Ranki '04 low Cv <-- medium Cv <-- high Cv D. Caliste and P. Pochet PRL (2006) 19
20 Model vs MC simulations (low T) T < 200 K ~ équilibium Em = 0.45 ev Watkins ' K e- irradiation Em = 1.8 ± 0,5 ev K Highly doped Em = 1.3 ev Ranki '04 region III Bracht '03 < 850 K for Cv =10-7 at ev D. Caliste and P. Pochet PRL (2006) 20
21 Model vs MC simulations (intermediate T) T < 200 K ~ équilibium Em = 0.45 ev Watkins '79 region II K e- irradiation Em = 1.8 ± 0,5 ev K for Cv=10-7 at ev Bracht ' K Highly doped Em = 1.3 ev Ranki '04 D. Caliste and P. Pochet PRL (2006) 21
22 Experiment reconciliation T < 200 K ~ équilibium Em = 0.45 ev Em = 0.45 ev [ Watkins '79 ] K e- irradiation Em = 1.8 ± 0.5 ev Em = 2.1 ev K Highly doped Em = 1.3 ev Em = 1.25 ev [ Bracht '03 ] [ Ranki '04 ] D. Caliste and P. Pochet PRL (2006) 22
23 3 temperature regimes already observed in Si! Evolution of the He cavity radius as function of implantation T [M. L. David et al JAP (2003)] Intermediate T, slow diffusion 1V II Low T, slow diffusion 2V III Low T, fast diffusion 1V I Fast diffusion allows effusion; slow diffusion allows cavity formation. The slower the diffusion the bigger the mean cavity radius. D. Caliste and P. Pochet PRL (2006) 23
24 Summary In complex diffusion mechanism effective activation energies might be higher than the direct sum of individual one! Multi-scale simulation is a powerful tool for diffusion studies DFT step is not enough when concurrent mechanisms are involved. Coupling between DFT and KLMC is a good solution Effective mechanisms might explain simulation/experiment discrepancy Drawbacks: On lattice simulations Pre-calculated events database 24
25 Outlooks Strain effect:? Work in progress to go above our first analysis [K. Z. Rushchanskii, et al. APL 92, (2008)] Charge effect: Work in progress to develop an accurate ab initio scheme Growth on Ge QD on Si using ab initio and off-lattice on-the-fly KMC MUSCADE project founded [N. Mousseau et al. (2008)] Study of possible mechanisms of LID in SOG silicon (cf 4.3) 25
26 Acknowledgments Acknowledgment to all the OSiGe_Sim partners: P. Blaise and P. Rivallin (Leti) A. Pakfar and H. Jaouen (STmicroelectronics) P. Ganster, A. Saul and G. Treglia (CINAM) S. Fetah, A. Dkhissi, A. Upadhyay, A. Estève, G. Landa and M. Djafari-Rouhani (LAAS) Partially founded by the OSiGe_Sim project ANR-05-NANO-004 References: D. Caliste and P. Pochet PRL (2006) D. Caliste, P. Pochet, T. Deutsch and F. Lançon PRB 75, (2007) K. Z. Rushchanskii, P. Pochet and F. Lançon APL 92, (2008) 26
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