vibrational lifetime of hydrogen-related defects in silicon ......vibrational lifetime of...
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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
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 (?)