Investigation of Defects from DFT-II 15 April 2010;...

P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 15 April2010 Investigation of Defects from DFT-II

Investigation of Defects from DFT-II

15 April 2010; Ø186

2Convergence aspects for defect calculations

3Electronic Effect – I(Neutral GaP: P-vacancy)

Relative CPU time consumption

Example: First ionization energy of an atom

Defect Formation Energy

12Defect Formation Energy: H in GaN

13Point defects in GaN

14Defects transition level calculations: Semiconductor surfaces

Defects charge transition levels: InP(110)

16Charge-transition levels: The (+/0) level of VP at InP(110)

17Defects transition level calculations: Improved by many body effects

18GW calculations better for defects transition level prediction

19Defect Concentrations

22Positrons: To probe vacancies in semiconductors

23Vacancy clusters: Electron-irradiated Ge

24Vacancy clusters: Electron-irradiated Si

25Positron lifetime: Probe to Vacancy clusters

26Vacancy clusters in Si: Theoretical Study

27Vacancy clusters: Voids in GaAs

28Defects in ZnO

Oxygen vacancy in ZnO

Neutral vacancy (negative charge) attracts Zn atomsSurrounding Zn atoms are relaxed towards the vacancy site

Positively charged vacancy repels Zn atomsSurrounding Zn atoms are relaxed outwards (away from) the vacancy site

Charge present at the vacancy site affects neighboring atoms !!

Pure ZnO Neutral VO

Electron localization function (ELF) Analysis shows charge at the vacancy site

Charged VO+

Charged VO2+

VZn VZn‐

Zinc vacancy in ZnO

32Positron lifetime calculations

33Positron lifetimes in ZnO (Theory)

34Positron lifetimes in ZnO :new ideas about defects

35Positron lifetimes in ZnO:with H

36Defects in ZnO: with H

37Defects in ZnO: with H …

38Hydrogen in ZnO surfaces?

39Vibrational spectroscopy H/ZnO(10-10): HREELS

40Hydrogen on Zn(10-10): Electronic structure

42Water/ZnO(10-10)

43Neutral oxygen vacancy in α-quartz

44Bandgap shrinkage by C-doping in GaAs

45Why bandgap Shrinkage?

46Burstein-Moss effect-An opposite effect to Bangapshrinkage

47Deep level dopants in InP & GaAs

48Dopants and Defect in Semiconductors

49Structure of Defects and Dopants

50Diffusion of silicon interstitials

51From compact to extended defect structures

52Accuracy of Defect Energies

53Accuracy of Diffusion Barriers

Electronic Transition Levels of Dopants

55Electronic Transition Levels of Dopants

Doping in c-SiP-typeBoronacceptors

N-typePhosphorousdonors

+1 e -

Hydrogen in Silicon Systems

• Compensates both p-type and n-type doping• Passivates dangling bonds at surfaces and interfaces• Hydrogen related charge traps in MOSFETs• Participates in metastable defect formation in poly- and

amorphous silicon • Forms very mobile H2 molecules in bulk Si

• Forms large platelets used for cleaving silicon

For more details see reference below and references therein:C. Van de Walle and B. Tuttle, “Theory of hydrogen in silicon devices”IEEE Transactions on Electron Devices, vol. 47 pg. 1779 (2000)

Concentration of defects: H in Si

• Etot = total energy for bulk cell with Nsi silicon atoms and NH hydrogen atoms.

• μΗ , μSi = the chemical potential for hydrogen, Si • The charge q and the Fermi energy (EF).

ZPFHHSiSitotform

formformformform

kTGsites

EqENNqEqE

PVTSEGeNC form

+−−−=

+−== −

μμ)()(

Acceptor and Donor levels for atomic hydrogen in crystalline silicon

• Donor level is the Fermi Energy when:

• Calculate Eform for H at its local minima for each charge state q = +1,0,-1

• Calculate valence band maximum to compare charge states

)()( 01 =+= = qq formform EE

Convergence: Basis size• Plane waves are a complete basis so crank up the G

vectors until convergence is reached.

00.020.040.060.08

0.10.120.140.16

10 15 20 25 30 35 40

DE ( eV )

[ ])()()( SictotBCtotPW EHEE E −−=Δ +

EPW [Ryd.]

ΔE [e

Convergence: Supercell size

• Prevent defect-defect interactions. – Electronic localization of defect level as determined by

k-point integration– Steric relaxations: di-vancancy in silicon– Coulombic interaction of charged defects

For more details see reference below and references therein:1. C. Van de Walle and B. Tuttle, “Theory of hydrogen in silicon devices”IEEE Transactions on Electron Devices, vol. 47 pg. 1779 (2000) 2. http://cms.mpi.univie.ac.at/vasp/vasp/vasp.html

Convergence: k-point sampling

• Reciprocal space integration– For each supercell size, converge the number of

“special” k-points – Data for 8 atom supercell:

K points E per Si (eV) for c-Si

ΔΕ (eV) for H+

BC in c-Si2x2x2 5.8826 7.581

3x3x3 5.9549 7.514

4x4x4 5.9691 7.485

5x5x5 5.9705 7.484

Convergence data at Epw = 15 Ryd.

N atoms K points E per Si (eV) in c-Si

ΔΕ (eV) for H+

BC in c-Si8 5x5x5 5.9705 7.484

64 2x2x2 5.9693 7.311

64 3x3x3 5.9700 7.309

64 4x4x4 5.9711 7.308

216 2x2x2 5.9708 7.240

•N=64, Kpt=2x2x2 results converged to within 0.1 eV

Bandstructure of 64 atom supercell

1 2 3 4 5 6 7 8 9 10 11

VBMCBM

1 2 3 4 5 6 7 8 9 10 11

VBMDefectCBM

L Г X L Г X•Bulk bands retained even with defect in calculation

Bulk c-Si Bulk c-Si + H+BC

Results for H in c-Si

• H0 and H+1 at global minimum• H-1 at stationary point or saddle point

– Will lower its energy by moving to Td site

EFermi

0.5 eV 1.0 eV

For more info see: C. G. Van de Walle, “Hydrogen in crystalline semiconductors” Deep Centers I Semiconductors , Ed. by S. T. Pantelides, pg. 899 (1992).

Hydrogen in Silicon

E in eV E(0,-) E(+,0) E(+,-) U-corrExp. 0.51 0.92 0.72 -0.41LDA 0.46 1.07 0.77 -0.61

Solid = LDA, Dashed =LDA + rigid scissor shift

• H2 min. at T site • EB ~ 1.9 eV per H atom• 0.6 eV less than free space

• H2* along <111> direction• EB ~ 1.6 eV per H atom• H+ (BC) + H_(T)

H2 complexes in Silicon

• 5-fold Si defects are paramagnetic:• D center in a-Si & Pb center at Si-SiO2 interface

• EB ~ 2.45 eV per H for Si-H at Si-interstitials in c-Si• EB ~ 2.55 eV per H for Si-H at a 5-fold defect in a-Si

Si-H Bond Frustrated Bond

Passivation of a 5-fold Si defect

• Si dangling bonds paramagnetic• EB ~ 4.1 eV for H-SiH3

• EB ~ 3.6 eV for pre-existing isolated Sidb in c-Si• EB ~ 3.1 - 3.6 eV for pre-existing isolated Sidb in a-Si

Si 3sp3

H passivation of dangling bonds

Hydrogen in SiO2

• H0 favors open void• EB ~ 0.1 eV• Very little experimental info

on charge states• Defect is paramagnetic

• H2 free to rotate• EB ~ 2.3 eV per H atom

Binding Energy per H (eV)

0.0 1.0 2.0 3.0 4.0

H0 (free)&SiO2

H in c-Si

H2 in c-Si

H2* in c-Si

(Si-H H-Si) in a-Si

H2 (free)&SiO2

H at pre-existing isolated silicon dangling bond (db)

H at pre-existing “frustrated” Si bond

H at pre-existing db with Si-H in a cluster e.g. a Si vacancy

Energy of H in a-SiEB (eV)

Clustered Si-H

H at frustrated bonds

Isolated Si-H bonds

HEa~1.5 eV

Ed~.3 eV

B. Tuttle and J. B. Adams, “Ab initio study of H in amorphous silicon” Phys. Rev. B, vol. 57 pg. 12859 (1998).

Si-SiO2 Interface

M. Staedele, B. R. Tuttle and K. Hess, 'Tunneling through unltrathin SiO2 gate oxide from microscopic models', J. Appl.Phys. {\bf 89}, 348 (2001).

74Energy of H at Si(111)Energy of H at Si(111)--SiOSiO2 2 interfaceinterface

EB (eV)0.0

Isolated Si-H bonds

H in SiEB~2.6 eV

H in SiO2

75Band offset and defect levelsBand offset and defect levels

76Vacancy Formation Energy on Cu(111) surface (Vacancy Formation Energy on Cu(111) surface (eVeV))

77Binding Energy of Vacancies (Binding Energy of Vacancies (eVeV))

78DOS of Sn/Cu(111)DOS of Sn/Cu(111)

79AdatomsAdatoms in Cu(111)in Cu(111)

80Defects levels in Si on HfODefects levels in Si on HfO22

81Surface study of Surface study of ZnOZnO: TCO for Solar Cells & Model : TCO for Solar Cells & Model

catalyst for catalyst for MethonolMethonol synthesissynthesis

82NonpolarNonpolar Surfaces of Surfaces of ZnOZnO(10(10--10) surface10) surface

83Polar Surfaces of Polar Surfaces of ZnOZnO

85MgOMgO NanoNano--structuresstructures

86Why lowWhy low--coordinated sites are important?coordinated sites are important?

87Energy Mapping of Energy Mapping of MgOMgO surfacessurfaces

93Defects in disordered materialsDefects in disordered materials

Investigation of Defects from DFT-II 15 April 2010;...

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