first-principles investigations on vacancy of ge in strained condition
DESCRIPTION
First-principles Investigations on Vacancy of Ge in Strained Condition. P7-19. 12~16, Sep., 2007 KIST, Korea. The 4 th Conference of the Asian Consortium on Computational Materials Science. Jung-Hae Choi , Seung-Cheol Lee , and Kwang-Ryeol Lee Computational Science Center - PowerPoint PPT PresentationTRANSCRIPT
First-principles Investigations on Vacancy of Ge
in Strained Condition
Jung-Hae Choi, Seung-Cheol Lee, and Kwang-Ryeol LeeComputational Science Center
Future Fusion Technology LaboratoryKorea Institute of Science and Technology
[email protected]://diamond.kist.re.kr/CSC
12~16, Sep., 2007KIST, Korea
P7-19
The 4th Conference of the Asian Consortium on Computational Materials Science
• Physical limitations on scaling-down of conventional Si/SiO2 semiconductors various researches on next generation devices
• Physical limitations on scaling-down of conventional Si/SiO2 semiconductors various researches on next generation devices
strained Si
MOSFET with new channel
Ge or strained Ge
Ge as a channel materials
• Higher mobility than Si
- 2X for e-, 4X for h.
Application on high performance device
• Higher mobility than Si
- 2X for e-, 4X for h.
Application on high performance device
• Unreliable oxide
• Low Eg leakage
• Difficulties of growing single crystals & their high cost
• Unreliable oxide
• Low Eg leakage
• Difficulties of growing single crystals & their high cost
DisadvantagesDisadvantages
graded SiGeGe film
Si substrate
Ge film
Si substrate
AdvantagesAdvantages
Ge
Si2 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
Evunstrained
< 0
< 0
aGe = 5.66 Å aSi = 5.43 Å
Evstrained≠
Ge
?
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
supercellNumber of atoms
K-points
2x2x2 64 6x6x6
3x3x3 216 2x2x2
4x4x4 512 2x2x2
Tests of exchange-correlation potential on Si & Ge
aSi (Å) BSi (GPa) aGe (Å) BGe (GPa)(aSi-aGe)
/aGe
PAW-LDA 5.402 97 5.646 72 -0.043
PAW-PBE 5.468 88 5.783 61 -0.054
US-LDA 5.389 95 5.625 71 -0.042
US-PW 5.456 88 5.759 60 -0.053
Experimental 5.43 99 5.66 75 -0.041
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
e ; EF relative to the VBM Ev
• 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
e ; EF relative to the VBM Ev
Perfect structure One vacancy
Eqv
Vacancy formation energy
0 100 200 300 400 500
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.02x2x2 3x3x3 4x4x4
E
fvac (
eV
)
Number of Atoms
unstrained strained difference
• 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 ??
• 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 ??
unstrained strained
Supercell
x=y=z diagonal x=y z diagonal
2x2x2 11.292 19.558 10.804 11.882 19.355
3x3x3 16.938 29.337 16.206 17.823 29.033
4x4x4 22.584 39.117 21.608 23.764 38.711
aGe equil Dv-v
aSi equil aGe relax Dv-v
Large supercell is required
Atomic configuration of supercell with 1 vacancy
x
y
z
0 100 200 300 400 5001.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
o
initial
4x4x43x3x32x2x2
Dis
tan
ce (
A)
Number of Atoms
2dNN-us 2dNN-st-L 2dNN-st-S 2dNN-L/S d1NN-us d1NN-st
initial
up
updn
dna
b c
d
vac
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
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
Vacancy formation energy vs. biaxial strain
Z-axis ; relaxed
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2 4x4x4 supercell
planar-strain (%)
Efva
c (e
V)
graded SiGeGe film
Si substrate
Ge film
Si substrateGe bulk
Comparison with previous reports
Number
of
atoms
Brillouin zone
samplingEf
v (eV) DL/Ds
Jahn-Teller
distortionCode
This work 512 2x2x2 2.123 3.15/3.12 1.006 VASP
PRB 61 (2000)
128 only 1.927 3.55/3.40 1.044Fritz-Haber
J. Phys; Condens. Matter 17
(2005)
376 cluster 3.7/3.3 1.12AIMPO
(LSDA)
Neutral vacancy in Ge in the unstrained condition; Jahn-Teller distortion is negligibly small.
v v I ID C D C D exp[ ]
f mo v v
v v vB
h hC D d
k T
exp[ ]
f mo I I
I I IB
h hC D d
k T
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 energySiunstrained Geunstrained Gestrained(4%)
Efv (eV) 3.763 2.123 0.776> >
Summary• The formation energy and atomic configuration of neutral
vacancy in Ge under biaxially-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.