vibrational lifetime of hydrogen-related defects in silicon ......vibrational lifetime of...

Vibrational Lifetime of Hydrogen-related

Defects in Silicon and Germanium

Norman Tolk

Department of Physics and AstronomyVanderbilt University, Nashville, TN

Supported by DOE and ONR

Collaborators

G. Lüpke and X. H. Zhang

The College of William and Mary, Williamsburg, VA

M. Budde, L. C. Feldman, and C. Parks Cheney

Vanderbilt University, Nashville, TN

M. Stavola and E Chen

Lehigh University, Bethlehem, PA

Motivation

Key Issues:

•Understanding the Mechanisms of Nonlinear Energy Deposition

into Local Vibrations by Intense Infrared Radiation,

•Its Influence on the Structural and Electronic Properties of the Material,

•Its Relaxation and Transfer Channels,

•and on Its Impact on Optimum Energy Use in Materials Processing.

Our Approach:

•Identifying the Energy Relaxation Channels,

•Determining the Lifetime of the Local Vibrational Modes,

•First Dynamical Studies of Hydrogen in Crystalline Silicon.

Motivation• Hydrogen is incorporated in semiconductors duringgrowth processes.

• It interacts with almost any lattice imperfection.

• H-related defect structures have been well characterized.

• Degradation of electronic devices

• Dynamical properties, such as the time-scalesand mechanisms for population and phase relaxation, are key to understanding energy incorporation anddissipation in these materials.

Scientific Issues

• How is the energy absorbed by the local vibrational modedistributed?

• What is the mechanism for phase relaxation?

Time-scalesChannels of decay (phonons or pseudo-localized modes)

Experiment: Measurements of temperature-dependent absorptionline shapes.

OutlineI. Hydrogen-related local vibrational modes (LVM’s) in

in silicon and germanium at low temperatures

• Positive-charge state of hydrogen at the bond-center site (HBC+)• Negative-charge state of hydrogen near the tetrahedral site (H-)

II. Absorption of light

• Fermi’s Golden Rule• Fourier Transform Infrared Spectroscopy (FTIR)

III. Vibrational Dynamics

• Energy Relaxation• Phase Relaxation

IV. Conclusions

Ideal Silicon Crystal

Hydrogen in Semiconductors

Pb

Experimental

10

0.020

0.015

0.005

0.010

Depth ( m)µ

�H c

once

ntra

tion

(at.

%

20 30 40

• Energies = 1.0 - 1.8 MeV• [H] = 0.02 at%• Temp = 80 K

Sample preparation

Characterization• In-situ FTIR • 5 - 160 K

Time-resolved spectroscopy• In-situ pump-probe spectroscopy• 5 - 160 K

Absorbance Spectrum (Si:H)

Wave Number (cm-1)500 1000 1500 2000 2500 3000

Abs

orba

nce

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2 + 3 phonon 3 phonon

1800 1900 2000 2100 2200

Si-H local vibrational modes

1800 1900 2000 2100 2200

• H2-doped Si• 2.5 MeV e-irradiation • Tmeas = 10 K

H2*

VH2

VH2

V2H2

H2*

IH2

Wave numbers (cm-1)

Local mode spectroscopy

0

1

2

E

Technological relevance

• Degradation of MOSFETs [1]• STM-induced H desorption from Si:H surfaces [2]• UV-induced SiGa-H depassivation in GaAs [3]

[1] J. W. Lyding et al, Appl. Phys. Lett. 68, 2526 (1996)[2] T.-C. Shen et al, Science 268, 1590 (1995)[3] J. Chevallier et al, Appl. Phys. Lett. 75, 112 (1999)

Giant H/D isotope effect↓

Vibrational heating model

Vibrational heating model

Truncated harmonic oscillator

N ~ 12

01

Dissociation rate:

B. N. J. Persson et al, Surf. Sci. 390, 45 (1997)E. T. Foley et al, Phys. Rev. Lett. 80, 1336 (1998)

11)(

)(−+ TfeI

feI

in

inR ∝N

Dissociation rate stronglydependent on vibrational lifetime

Sample preparation

Depth (microns)

0 10 20 30 40 500

4

8

12

16

20

CH

(ppm

)

• Ion implantation

• Multiple energies

• Implantation temp = 80 K

• Sample kept cold

TRIM simulation

Local Vibrational Modes

Bond-stretch

Bond-bend

1800 cm-1 < ω < 2250 cm-1

ω < 850 cm-1

• ω reflects microstructure

ω ~HM

k

Characteristics:

•

2000 cm-1 = 6 × 1013 Hz = 0.25 eV

Example: Si-H

• Light impurities

• Localised vibration

Bond-center hydrogen in silicon

HBC(+)

Case study: HBC(+) in Si

• Most fundamental H-related defect• Involved in H-reactions • Well characterized (exp + theory )• Very large absorption cross section

Wave number (cm-1)1980 1990 2000 2010 2020

Hydrogen in Crystalline Silicon

• Si-H stretch mode• Defect contains single Si-H bond

Wave Number (cm-1)1970 1990 2010 2030

1998 cm-1

Si:D

Si:HD

Si:H

1420 1440 1460 1480

1449 cm-1

Wave Number (cm-1)

Hydrogen-Decorated Defects in Si

1998 cm-1

H2*

H2*

VH2

Wave Number (cm-1)

r

r

Etot

0.44 eV0.25 eV

(1998 cm )-1

Bond-center Hydrogen

Transient bleaching spectroscopy

9%

91%

Sample/cryostat

Detector

Pump-probesetupLaser

Time delay

Thermal equilibrium

0

1

100%

0%

Bleached

0

1

50%

50%

Vibrational lifetime of HBC(+) stretch

0 10 200.0

0.2

0.4

0.6

0.8

1.0

0 10 20

-3

-2

-1

0

Time delay (ps) Time delay (ps)

Sb

Ln[S

b]

T1 = 7.8 ± 0.2 ps

Lifetime of Si-H stretch modes

HBC(+)

Si(111)/H:1×1

a-Si:H

ω (cm-1)

1998

2086

2000

T1 (ps)

7.8

1500

~15~100

Ref.

[2]

[4,5]

[1] M. Budde et al, Phys. Rev. Lett. 85, 1452 (2000)[2] P. Guyot-Sionnest et al, Phys. Rev. Lett. 64, 2156 (1990)[3] P. Guyot-Sionnest et al, J. Chem. Phys. 102, 4269 (1995)[4] Z. Xu et al, Journ. Non-Cryst. Solids 198-200, 11 (1996)[5] M. van der Voort et al, Phys. Rev. Lett. 84, 1236 (2000)

Si(100)/H:2×1 2099 >6000 [3]

[1]

Decay mechanism

• Radiative:• Electronic:

• Vibrational:

0 500 1000 1500 2000

Si-H

phonons

No, T1,IR~ 2 msNo, donor level of HBC

(+) is unoccupiedand > 0.25 eV from valence band Yes, but requires emission of ≥ 4 phonons

Wave number (cm-1)

Phonon Density of States in Silicon and Germanium

0 100 200 300 400 500 (cm-1)

0 67 133 200 267 330 (cm-1)Ref. [W. Webber, Phys. Rev. B 15, 4789 (1977).]

Temperature Dependence of the Lifetime of HBC

+ in Silicon Measured Using Transient Bleaching Spectroscopy

8

6

4

2

T1 (

ps)

140120100806040200

Temperature (K)

4 modes at 499.5 cm-1

3 modes at 150 cm -1

3 modes at 516 cm -1

2 modes at 114 cm -1

2 modes at 385 cm -1

2 modes at 500 cm -1

If HBC+ in Ge decays into the same

type of accepting vibrational modes as HBC

+ in Si,how many quanta are required?

Ge-related accepting modes: modes shifted down in

frequency by about a factor of ~0.6 (301 cm-1/522 cm -1)

as compared to the Si case.

H-related accepting mode:

you would not expect a large difference in the vibrational

frequency (4-8 %) of those modes in the Ge and Si cases.

Let’s Look at One Possibility

4 quanta of ~75 cm-1

5 quanta of ~300 cm-1

9 quanta required for decay

(compared to 6 required in the Si case.)

What else can we learn from the lifetime of HBC

+ in Ge?

If decay of HBC+ in Ge is similar to that of HBC

+

in Si, how come the an order of 9 versus 6 only gives an increase in lifetime by a factor of 2-3?

The anharmonic coupling term must be important in determining the lifetime.

HBC+ in Ge Lifetime: Conclusions

• HBC+ in Ge has a lifetime of 15-23 ps decays into phonons

and/or pseudo-localized modes.

• The order of decay is most likely not the minimum order (6) of decay that is energetically possible. The anharmonic coupling of the LVM to the accepting modes is an important parameter in determining the lifetime.

• Low-frequency modes are involved in the decay process. These modes could be Ge-related or could be a bendmode of HBC

+ in Ge.

What happens to the absorption peaks as the temperature is

increased??

1.0

0.8

0.6

0.4

0.2

0.0

1800179017801770

x4

x2

25 K

50 K

90 K

1.0

0.8

0.6

0.4

0.2

0.0

760750740730

x2

Abs=0.2∆

The H- and HBC+ absorption lines as a function of temperature

What causes the observed broadening, shift, and asymmetry

with increasing temperature?Let’s look at HBC

+ in Si for a moment. Is it energy relaxation? No

25

20

15

10

5

0

FW

HM

(cm

-1)

140120100806040200

Temperature (K)

Temp. Dep. WidthDifference

Lifetime Width

Is it phase relaxation? Yes!

• As T ↑, a low-frequency mode is populated.

• The low-frequency mode is anharmonically coupled to the LVM.

• As the low-frequency mode is populated, the frequency of the LVM is shifted due to the perturbation.

• At any instance, there are thermal fluctuations and the low-frequency mode may change its occupation number, causing the frequency to change. These thermal fluctuations cause the LVM frequency to be randomly modulated.

Energy Diagram for the LVM

|0, 0>

|1, 0>

0 K

|0, 1>

|1, 1>

70 K

In the |LVM> manifoldwhere the low-frequency mode

is not thermally populated.

In the |LVM, low-frequency mode> manifold where the low-frequency

mode is thermally populated.

Energy Diagram for the LVM and Low-Frequency Mode

0

)22( eLVM ωδωω ′++′h)( eLVM ωδωω ′++′h

LVMω ′h

eω ′h2eω ′h

|nLVM, ne>

δωωω 21+=′ ee

δωωω 21+=′ LVMLVM

E

τ

|1,2>|1,1>|1,0>

|0,2>|0,1>|0,0>

δω depends on the anharmonic terms and is a measure of the coupling strength.τ is the lifetime of the first excited state of the exchange mode.

Dephasing ModelsThree Dephasing Models Based on the Theory of Anderson:[P. W. Anderson, J. Phys. Soc. Jpn. 9, 316 (1954)]1) Model of Harris et al. is applied in the low-temperature limit,

It does not include degeneracy and cannot predict an asymmetricline shape.[C. B. Harris, R. M. Shelby, and P. A. Cornelius, Phys. Rev. Lett. 38, 1415 (1977)]

2) Model of Persson, et al. is applied in the weak-coupling limit,|δωτ|<<1 .[B. N. J. Persson and R. Ryberg, Phys. Rev. B 32, 3586 (1985)]

3) Extended Exchange Model includes degeneracy of the exchangemode and is applicable at all temperatures and for any value δωτ. It also accounts for the observed asymmetric line shape.

TkBe >>′ωh

Frequency Shift, ∆ω, and Broadening, ∆ΓT2*, of HBC

+ line at 1794 cm-1 in Ge

Data: ∆

Nondeg. Model: ____

Twofold Deg. Model: -----------

The data is nicely described by the modelfor 25-80 K.

0.01

0.1

1

10

∆ΓT 2*

(cm

-1)

0.060.040.020

1/T (K-1)

(d)

12

8

4

0

|∆ω

| (cm

-1)

150100500

T (K)

(a)12

8

4

0∆

ΓT 2* (cm

-1)

150100500

T (K)

(b)

0.01

0.1

1

10

|∆ω

| (cm

-1)

0.060.040.020

1/T (K-1)

(c)

Decay mechanism

][1 2

1

TfGT i

ii∑∝

Decay of LVM into “phonon” bath:

∑=j

jωω hh

( ) ∏∏==

−+=ii N

jBi

N

jBii TknTknTf

11

][1][][ ωω hh

0,1][ →→ TTfi

ω

ω1

ω2

ω3

ωNi

A. Nitzan et al, J. Chem. Phys. 60, 3929 (1974)

Bose-Einstein meanoccupation number

Temperature dependence

T (K) 0 25 50 75 100 125

0

2

4

6

8

10

T1

(ps)

Decay channel:

4 phonons at ~500 cm-1

3 modes at ~150 cm-1

+ 3 modes at ~500 cm-1

• HBC(+) stretch does not decay

by lowest-order channel

• 2 - 3 modes at ~150 cm-1

involved

Natural line shapeab

sorb

ance

0.00

0.05

0.10

0.15

0.20

1990 1998 2006wavenumber (cm )

1 10 100C (ppm)

0.0

0.5

1.0

1.5

2.0

Γ (c

m

)

Γ

-1

-1

H

0

inhom12

1Γ+=Γ

cTπT = 10 K

Time and frequency domain consistent

T (K)

0 20 40 60 80 100 120 140

T1

(ps)

0

2

4

6

8

10

Lifetime Temperature Dependence

0

4

8

12

16

0 20 40 60 80 100 120T (K)

Hom

ogen

ous

linew

idth

(cm

-1)

LifetimeDephasingTotal

Linewidth vs temperature

FWHM =1π

12T1

+1

T2

Ratio of ∆ω for H and D à No Isotopic Shift

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

0 20 40 60 80 100 120T (K)

SiH data from SiHD 121799SiD data from SiD 112999

∆ω

H/∆

ωD

Lower Limit for DBC+

Lifetime in Si (>6 ps)

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

1435 1440 1445 1450 1455 1460

WAVENUMBER (cm-1)

Interpretation

1998-cm-1 mode strongly coupled to

optical phonons?

Dynamical Processes

0.20

0.15

0.10

0.05

0.00

184018201800178017601740

Γ

ω

a

• Natural Lifetime• Inhomogeneous Broadening• Isotopic Broadening• Temperature-Dependent Shift,Broadening, and Asymmetry

+=Γ −

*21

1 2121

)(TTc

cmπ

Homogeneous Broadening:

T1: Energy Relaxation TimeT2

*: Pure Dephasing Time

What causes the linewidth of the absorption peak at low T??

• Inhomogeneous Broadening• Instrumental Resolution• Isotopic Broadening• Lifetime

isotopicin

cTcΓ+Γ+=

Γ=Γ hom

121

2 ππσ

* for Lorentzian lineshapes

Asymmetric Line Shape

].|))Re(|)2(())Im(((

))Im(((

|))Re(|)2(())Im(((|)Re(|)2(

[)(

211

2

211

2

11

1|0|

llLVM

lLVM

llLVM

l

Ta

TT

I

′−

′

′

′−

′

′−

>>→

++−−−−

−

++−−+

∝

λλωωλωω

λλωωλ

ω

Γ=Full Width Half Maximum=2*[(2T1)-1+|Re(λl´)|]ω =Center Frequency=ωLVM-Im(λl´)a=Asymmetry parameter

But how do we relate these anharmonic interactions and thermal fluctuations to the

absorption spectrum?

OK. Now we know how the frequency changes with the low-frequency occupation number.

What happens with time evolution of the system?

Let’s start with the Hamiltonian.22

2

2

0 21

21

iii i

QQ

H ω+∂∂

= ∑Where Qi is the normal mode coordinate for the mode i.The summation is taken over all the possible normal modes, whichincludes the phonon, HBC

+, and low-frequency normal modes. Themass is contained in the normal mode coordinate.

Ref. [P. W. Anderson, J. Phys. Soc. Jpn. 9, 316 (1954)].

∑=ml

me

lLVMmlanh QQCH

,,

Now let’s include the anharmonic term that couples the LVM to the low-frequency mode (or exchange mode):

where l+m>2.

)ˆˆ)(ˆˆ(4

,

,,

,

2

,

,,,

sksk

skee

skesk

skskeskexch

aaaa

QQH

rr

rr

r

rrr

h++=

=

∑

∑

++

ωωα

α

The low-frequency mode “exchanges” energy with the phonon bathwith changes in quantum number of ±1:

Where the phonon is represented by a vector k and branch index s.

∆ω and ∆Γ as a Function of Temperature for HBC

+ in Silicon

-3

-2.5

-2

-1.5

-1

-0.5

0

0 10 20 30 40 50 60 70 80

T (K)

∆ω

SiH data

1. order

2. order 0

1

2

3

4

5

6

0 10 20 30 40 50 60 70 80

T (K)

∆Γ

SiH data

1. order

2. order

The Fit Deviates at High Tà Two Exchange Modes Needed

0

5

10

15

20

25

0 25 50 75 100 125 150T (K)

∆Γ

SiH data

1. order

2. order

Results

l The activation energy for both SiH and SiD is ~113 cm-1

» no isotopic shift à the exchange mode cannot be the bending mode

l At higher temperatures there are two exchange modes for SiH» 112.7 cm-1 acoustic-like » 366 cm-1 optical-like

A Simple Three Atom Model

Mode

A2uA2uA1gEuEuEg

The exchange mode is assigned to a Si(Ge)-related twofold degenerate mode with either Eu or Egsymmetry.

HBC+ in Si(Ge) Phase Relaxation:

Conclusions

• The exchange mode for HBC+ in Si(Ge) is

assigned to a twofold degenerate, Si(Ge)-related PLM with frequency,ω′e=114 ± 2 (74±2) cm-1.

Summary of Ge Results• The lifetime of HBC

+ in Ge is in between 15 and 23 ps. Based on HBC

+ in Si, the HBC+ in Ge is not likely to decay

by a lowest-order, energy-conserving process.

•The exchange mode associated with HBC+ is assigned to a

Ge-related PLM with frequency, ω′e =75 cm-1.

•The lifetime of H- in Ge is ≥ 36 ps, where the anharmoniccoupling strength is found to be important in determining the lifetime.

• The exchange mode associated with H- is assigned to a Ge-related mode with frequency ω′e=77 cm-1.

ConclusionSummary:

•First Measurement of the Vibrational Lifetime of Hydrogen

in Crystalline Silicon,

•Strong Coupling between the HBC(+) Mode and Optical Phonons,

•Dephasing of the HBC(+) Mode due to elastic scattering with

130 cm-1 phonon or wagging mode,

1. 1. “Vibrational Lifetime of Bond-Center Hydrogen in Crystalline Silicon”, M. Budde, G.

Lupke, C. Parks Cheney, N. H. Tolk, and L. C. Feldman, Phys. Rev. Lett. 85, 1452 (2000).

2. 2. ”Local Vibrational Modes of Isolated hydrogen in Germanium”, M. Budde, B. Bech

Nielsen, C. Parks Cheney, N. H. Tolk, and L. C. Feldman, Phys. Rev. Lett. 85, 2965 (2000).

3. 3. “Vibrational dynamics of bond-center hydrogen in crystalline silicon”, M. Budde, C.

Parks Cheney, G. Lupke, N. H. Tolk, and L. C. Feldman, Phys. Rev. B 63, 195203 (2001).

4. 4. “Dynamics of Hydrogen-Related Local Vibrational Modes in Germanium”, C. Parks

Cheney, M. Budde, G. Lupke, L. C. Feldman, and N. H. Tolk, submitted to Phys. Rev. B.

CONCLUSIONS

How is the energy absorbed by the local vibrational mode distributed?

• The times-scale of energy dissipation is of the order of picoseconds

• Multi-quanta vibrational energy relaxation. It is still not known whether the accepting modes are phonons or pseudo-localized modes or a combination of both.

What is the mechanism for phase relaxation?

Anharmonic coupling to at least one thermally populated pseudo-localized mode. From the analysis, one gets

• the energy of the low-frequency mode

• lifetime of the low-frequency mode

Absorbance spectrum

1800 1900 2000 2100 2200

• H2-doped Si• 2.5-MeV e-irradiation • Tmeas = 10 K

H2*

VH2

VH2

V2H2

H2*

IH2

Wave numbers (cm-1)

Structural dependence

2055 2060 2065 2070 2075

H2*

T1 = 1.9 ps

V2H2

T1 > 110 ps

Wave numbers (cm-1)

Transient bleaching of V2H2

0 200 400 600 800

0.05

0.1

0.2

0.5

1

Time delay (ps)

Tran

sien

t ble

achi

ng (

arb.

uni

ts)

T1 = 340 ± 8 ps

2050 2060 2070 2080

Wave numbers (cm-1)

-5 0 5 10 15 200.0

0.2

0.4

0.6

0.8

1.0

Transient bleaching of H2*

Time delay (ps)

Tran

sien

t ble

achi

ng (

arb.

uni

ts)

Wave numbers (cm-1)2050 2060 2070 2080

T1 ~ 4 ps

Interstitial-type defects

H2*HBC

(+) IH2

ω (cm-1)

1998

T1 (ps)

7.8

ω (cm-1)

18382062

T1 (ps)

3.31.9

ω (cm-1)

19871990

T1 (ps)

1312

Vacancy-type defects

VH2 V2H2

ω (cm-1)

2072

T1 (ps)

350

ω (cm-1)

21222145

T1 (ps)

7750

Point-defect versionof Pb:H center at Si/SiO2

D/H lifetime comparison

2054 2058 2062 2066 2070

1492 1496 1500 1504 1508

2072.4 2072.6

1510.35 1510.55

D2*

V2H2T1(D) > T1(H) T1(D) <T1(H)

Wave numbers (cm-1)Wave numbers (cm-1)

H2*

D/H lifetime comparison

V2H2

2.64.6

0.792.50

1312

Defect

Si-H

Lifetime (ps) Ratio

Si-D D/H

IH2

H2*

VH2

HBC(+)

350

3.31.9

7750

7.8

85

1614

9474

> 6.4

1.221.21

0.24

1.221.48

Conclusion

• Lifetimes of Si-H/Si-D modes measured in

time and freq. domain

• Strong structural dependence

• T1(D) > T1(H), except H2* and V2H2

• Order of decay does not determine T1

• Decay mechanism poorly understood

• VmHn defects large T1 ⇒Pb:H centers at Si/SiO2 interface susceptible

to “hot electron” induced dissociation (?)