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

choijh@kist.re.krhttp://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.