defects in semiconductors and their optical...

Defects in Semiconductors and their opticalspectra

Michel Bockstedte, Andrea Marini, and Angel Rubio

Universidad del Paıs Vasco Universita’ di Roma Tor Vergata

Universitat Erlangen-Nurnberg

A Prespective

.

shallow deepdefects

+e−

D

-h+

A

V

D-VEV

EC

D A V D-V DV

I

Activation Diffusion

Key issues in physics of a semiconductor

I Understanding the nature of intrinsic defects

I Identifying the experimental defect centers with a defect model

A Prespective

.

shallow deepdefects

+e−

D

-h+

A

V

D-VEV

EC

D A V D-VVI

Key issues in physics of a semiconductor

I Understanding the nature of intrinsic defects

I Identifying the experimental defect centers with a defect model

Defect signatures

Si1

Si2 Si3 Si4

e−

VE

CE

ea

+++

_

VE

CE_ _

0

electron spin density ⇔ spin resonance techniques

defect levels ⇔ electrical characterization

optical excitations ⇔ photo luminescence,absorption experiments

defect vibrations ⇔ photo luminescence

Does the optical signature give access to the physics of the defect?

Defect signatures

Si1

Si2 Si3 Si4

e−

VE

CE

ea

+++

_

VE

CE_ _

0

I EI5 in 4H ↔ V+C,k

I Annealing of the EI5 signal


Defect signatures

Si1

Si2 Si3 Si4

e−

VE

CE

ea

+++

_

VE

CE_ _

0

Can we

I predict accurately level positions?

I determine excitation energies?

I disentangle complicated spectra?


Overview

Introduction

Theoretical Approach

Identified intrinsic centers in SiC and their models

Excited states of the carbon vacancy

Summary

Defect properties: the ground state

Defect ground state and DFT-L(S)DA

I FHI96SPIN/ABINIT: pseudopotentials and plane wave basis setI super cells: 216 atoms (3C-SiC) and 288 (128) atoms (4H-SiC)

Defect signatures of the electronic groundstate

I defect vibrational modesI hyperfine parameters

Hyperfine tensors

Si1

Si2 Si3 Si4

S

B

ISi1

HB = µB B←→g S +∑

ν

Iν←→A S + . . .

Ai j ∝∫

dVns(r)

(8π

3δ(r) +

3 xixj

r5− δi, j

r3

)

Defect properties: excited states and band gap problem

band gap and defect levels in DFT

EC

EV

EC

EV

DFT-LDA exact



EC

EV

EC

EV

shallow deep shallow deepDFT-LDA exact



EC

EV

EC

EV

shallow deep shallow deepDFT-LDA exact

Many particle approach: SELF

I quasi particle corrections based on the G0W0-approximation

εqpi = εLDA

i +1

Z0

⟨i |Σ− V LDA

XC |i⟩

I electron-hole interaction via the Bethe-Salpether-Equation∑c′,v ′

{(εc − εv ) δc,c′δv ,v ′ + Kcv ,c′v ′} Ac′v ′ = E Acv

Defect properties: technical parameters

DFT-LDA calculation

I softened Trouillier-Martins pseudopotentialsI Plane wave basis set: 30 RyI special k-point sets

GW-corrections:

I plasmon pole approximationI plane wave cut-off of χ0: 6 RyI conduction bands in χ0 (3C-SiC): 2000 (Ef + 40 eV)

BSE-spectra:

I Tamm-Dancoff approximationI static screeningI plane wave cut-off of Kernel: 4 Ry

Overview

Introduction




Summary

Intrinsic Defects and EPR-centers in SiC

c-ax

is

3C

A B C A

2.39 eVEgap

zinc blende

2H

A B

3.33 eV

wurzite

4H

A B C

3.27 eV

cubic

hexagonal

6H

A B C A

2.86 eV ∆Exp-LDAgap : 1.12 eV

∆QPgap : 0.95 eV

Si1

Si2

Si3 Si4

V+C↔ EI5/EI6

V−C↔ HEI1

Si

C

Si

VC-V0Si↔ P6/P7

CCI

C+sp↔ T5/EI1


c-ax

is

3C

A B C A

2.39 eVEgap

zinc blende

2H

A B

3.33 eV

wurzite

4H

A B C

3.27 eV

cubic

hexagonal

6H

A B C A


∆QPgap : 0.95 eV

C1

C2

C3 C4

V−Si

Si1

Si2

Si3 Si4

V+C↔ EI5/EI6

V−C↔ HEI1

Si

C

Si

VC-V0Si↔ P6/P7

CCI

C+sp↔ T5/EI1


c-ax

is

3C

A B C A

2.39 eVEgap

zinc blende

2H

A B

3.33 eV

wurzite

4H

A B C

3.27 eV

cubic

hexagonal

6H

A B C A


∆QPgap : 0.95 eV

CSi

Si4

Si2Si3 VC

VC-C−Si ↔ SI5

Si1

Si2

Si3 Si4

V+C↔ EI5/EI6

V−C↔ HEI1

Si

C

Si

VC-V0Si↔ P6/P7

CCI

C+sp↔ T5/EI1

Identification of the Carbon Vacancy in 4H SiC

Si1

Si2

Si3 Si4

cubic, C1h

Si2

Si4Si3

Si1

hexagonal, C3v

EPR experiments and tentative models

I VC: T5 center1 (3C) and EI5 center2 (4H)

I Si+C: EI6 center2 (4H)

Problems with the assignment

I T5 and EI5:

I conflicting HF-tensorsI T5: reassignment3 to VC-H2

I EI6:

I large central HF-tensor in conflict withextended states of Si+C

1 H Itoh et al. phys. stat. sol. (a) (1997) .2 N.T. Son et al., PRB 2001; PRL (2001).3 N.T. Son et al. MSF (2001).4 J. von Bardeleben et al. (2000); Bratus et al. Physica B (2001)

Identification of the Carbon Vacancy in 4H SiC

Si1

Si2

Si3 Si4

cubic, C1h

Si2

Si4Si3

Si1

hexagonal, C3v

Calculated and measured HF-tensors (MHz)

V+C cub. (DFT1) EI5 (EPR2)

Si1 197 114 122 181 125 125Si2 155 87 93 141 103 107Si3,4 161 103 109 141 103 107

V+C hex. (DFT1) EI6 (EPR2)

Si1 400 275 275 434 297 297Si2−4 43 22 20 59 39 39

1 M. Bockstedte, M. Heid, and O. Pankratov, PRB (2003); MSF (2002).2 N.T. Son et al., PRB 2001; T. Umeda et al., PRB (2004).3 Bratus et al. PRB (2003); T. Petrenko et al. Physica B (2001)

Tri-Carbon antisite and the carbon aggregationLocalized vibrational modes [meV]:1

Mode Sym. 3C 4H, cub. U-Center2

1 u 130 1302 g 149 154 1513 u 181 1824 g 249 255 247

1 Mattausch, Bockstedte, and Pankratov PRB (2004).

2 Evans et al. PRB (2002); Mattausch et. al. PRB (R) (2006).

Tri-Carbon antisite and the carbon aggregationLocalized vibrational modes [meV]:1

Mode Sym. 3C 4H, cub. U-Center2

1 u 130 1302 g 149 154 1513 u 181 1824 g 249 255 247

Carbon aggregation

CSi

spCspC

C( )Si3

spC

C( 2)SispC

spC

C( sp 2)

spC

C( sp)3

C( 2)Hex

1 Mattausch, Bockstedte, and Pankratov PRB (2004).

2 Evans et al. PRB (2002); Mattausch et. al. PRB (R) (2006).

Overview

Introduction




Summary

Photo-EPR of V+C and its interpretation

Son et al APL 2002

Si1

Si2

Si3 Si4

cubic, C1h

EC

EV

ea

a′aa

C3v C1h

δQ

E (δQ)

C3v


Son et al APL 2002

Si1

Si2

Si3 Si4

cubic, C1h

EC

EV

ea

a′aa

C3v C1h

δQ

E (δQ)

C3v

V +C


Son et al APL 2002

Si1

Si2

Si3 Si4

cubic, C1h

EC

EV

ea

a′aa

C3v C1h

δQ

E (δQ)

C3v

V +C

V 0C

Excitation of VC: DFT and quasiparticle corrections

EC

EV

ea

a′aa

C3v C1h

Experimental thresholds

I 1.47 eV: decrease of EI5I 1.80 eV: increase of EI5

V+C + e−(VB)→ V0

C V0C → V+

C + e−(CB)DFT-LDA GW DFT-LDA GW

3C 1.60 eV 1.85 eV 1.84 eV (0.56) 1.67 eV (0.72)4H,c 1.96 eV 2.01 eV (1.28)4H,h 1.73 eV 2.08 eV (1.21)

Ea

Ee EC

EV

3C LDA GWEe EV + 2.0 eV EV + 2.4 eVEa EV + 1.6 eV EV + 1.8 eV

δQ

E (δQ)

C3v

V +C

V 0C

Excitation of VC: DFT and quasiparticle corrections

EC

EV

ea

a′aa

C3v C1h

Experimental thresholds

I 1.47 eV: decrease of EI5I 1.80 eV: increase of EI5

V+C + e−(VB)→ V0

C V0C → V+

C + e−(CB)DFT-LDA GW DFT-LDA GW

3C 1.60 eV 1.85 eV 1.84 eV (0.56) 1.67 eV (0.72)4H,c 1.96 eV 2.01 eV (1.28)4H,h 1.73 eV 2.08 eV (1.21)

V+C → V2+

C + e−(CB) V2+C + e−(VB)→ V+

C

DFT-LDA DFT-LDA4H,c 1.88 eV (1.41) 2.01 eV

δQ

E (δQ)

C3v

V +C

V 0C

Excitation spectra of V+C and the electron-hole interaction

0 1 2 3ω (eV)

0

0.2

0.4

0.6

0.8

ε 2(ω)

BSE+GW @ RV

0

BSERPABSE+GW @ R

V+

BSERPA

EV->E

a @ R

V0

EV->E

a @ R

V+

CEEa

VE

VCR +

VCR 0

∆∼180 meV

meV∆∼60

C

C

C

C

V+C in 3C-SiC:

I electron-hole interaction depends on geometryI RV+

C: first peak arises from states well below EV

I RV0C: GW- and BSE-corrections cancel each other

Excitation of V+C : valence versus conduction band states

1 2 3ω (eV)

0

5

10

15

20

25

ε 2(ω)

Ea->E

C+E

e

EV

->Ea

all

1.5 2 2.5 3ω (eV)

0

0.5

1

ε 2(ω)

Ea

Ee EC

EV

V+C in 3C-SiC:

I e-levels remain resonant states after GW-correctionsI huge effect due to Ea → EC and Ea → Ee

I excitation of valence band electrons is a minor effect

⇒V+C → V2+

C + e−(CB) is the dominating process in 3C-SiC

What is the situation in 4H-SiC?

Overview

Introduction




Summary

Summary

Theoretical approach to defects in SiC

I Density functional theoryI GW and BSE towards excited statesI Microscopic analysis kinetic processesI Defect signatures as link to experiments

Intrinsic defects SiC

I Identification:I hyperfine tensors: vacancies and related centersI phonon replica: carbon interstitial complexes

I Quasiparticle levels via the GW-approximationI Analysis of optical spectra:

I excitonic effectsI calculated spectra to uncover the relevant transitions

Collaborations and Support

Lehrstuhl f. Theor. Festkorperphysik

I Prof. Dr. O. PankratovI A. MattauschI M. Heid

University of Erlangen-Nurnberg

I SiC-Research GroupI Dr. G. Pensl

Funding (DFG)

I SFB Mekos

I SiC-Forschergruppe

Collaborations/Support

I Dr. Adam GaliBudapest, Hungary

I Dr. N. T. Son,Linkoping, Schweden

I Prof. Dr. W. J. Choyke,Pittsburgh, USA

I Dr. M. E. Zvanut,Bermingham, USA

I Prof. Dr. J. Steeds,Bristol, UK

I Dr. H. BrachtMunster

defects in semiconductors and their optical...

Documents