A New Model for {311} Defects Base on In-Situ Measurements
Mark E. Law, Dept. of ECE, University of Florida, Gainesville, FL, 32611-6130
Kevin S. Jones, Jing Hong Li, Dept. of MSE, University of Florida, Gainesville, FL, 32611-6130
Tel: (352) 392-6459, Fax: (352) 392-8381, Email: law@tec.ufl.edu
Introduction: {311} defects are important factor in transient
enhanced diffusion. This paper presents a new {311} model
and compares it extensively to experimental results. The
model has three new features. First, there is no energy
dependence on the size of the defect. Second, dissolution is
controlled by the release of interstitials from the defects, rather
than diffusion to the surface. Finally, the defects nucleate
heterogeneously on damage that occurs during the implant
process. In-Situ and post-anneal TEM measurements have
been used to validate the model.
In-Situ Defect Observations: In-Situ annealing in the TEM
allows individual defect behavior to be observed and
monitored. A 100keV Si 1014cm-2 implant was used to damage
a silicon wafer. These samples were then preannealed at
750°C for two hours in a conventional furnace. The samples
were then annealed in-situ in the TEM at a variety of
temperatures. Figure 1 shows the evolution at 0 and 15
minutes. In this time period, note that the defect in the lower
left has completely dissolved. The longer defects are not more
stable energetically than smaller defects. This work clearly
shows that longer defects can dissolve much faster than
shorter defects. Fundamental energetic analysis of the defects
has shown this previously1, and experimental confirmation is
now available.
Figure 2 shows the dissolution of nine different defects
from the {311} ensemble. These dissolution curves are fit
better by linear decay rates than exponential decay rates.
Linear decay fits are shown in figure 2, and the decay rates as
a function of initial defect size are extracted. Figure 3 shows
the extracted decay rates. There is not strong trend of decay
rate as a function of length, further supporting that longer
defects are not more stable than short defects. Results from
other temperatures also support this result, and will be
presented in the final version of the paper.
Model Description: The {311} model proposed here solves
for the total number of interstitials in the defects (C311) and the
total number of defects (D 311). Nucleation of the defects
occurs during the implant process. Initial distributions of
defects are from UT-Marlowe using the Kinchin-Pease
damage model. Vacancies and interstitials are allowed to
recombine and complex during the implant process.
Interstitials can form small interstitial clusters or submicroscopic {311} defects. This agrees with MD simulations
that show most of the damage cascade in small clusters after
implantation2. The small cluster energies are similar to those
used by Cowern.3 for his most stable defect. The proto 311’s
provide nucleation site for the growth of the {311} defects.
Capture and release of the {311} defects occurs only at
the end of the defects, and therefore is proportional to the
number of defects, D311. This provides two distinct results.
First, individual defects dissolve at a nearly constant rate,
since the dissolution is proportional only to the end size. The
length of the defect does not determine the dissolution rate.
This is similar to the in-situ result observed in Figure 3. The
model predicts a decay rate of 2.3nm/min at 770°C, within the
one standard deviation error bars in Figure 3. The second
interesting result is that the defect ensemble decays at a rate
that is dependent on size. The number of defects determines
the decay rate. Consider two ensembles with the same number
of interstitials, but with different sizes. The ensemble with the
smaller size has more defects than the one with the larger size,
and therefore will decay faster.
The {311} defect population decays at a rate that is
proportional to the interstitial loss rate and inversely
proportional to the size of the defect. For a given loss rate,
more defects will dissolve completely when the defects are
smaller than one they are larger. The equations for the
extended defects are summarized in Table 1.
Comparison to Data: Figure 4 shows the simulated result for
the decay of the defects and interstitials at 750°C as a function
of energy and time compared to the data of Saleh et. al 4. Good
fits are obtained for both the D311 and C311 populations. The
decay rates are within 20% error bars on the data for all
energies, and results from the size dependence of the decay
rate. The defects from the 20keV implant are smaller than
those from the 160keV implant, and that creates the change in
decay rates. The initial defect concentrations are also predicted
well, and this is difficult to obtain with a homogenous model,
since the nucleation is proportional to a power of the peak
damage concentration. Since the peak damage concentration
drops with energy, it is difficult to get an increase in the
number of defects with energy. Figure 5 shows the size of the
defects as a function of time and energy. Incresing size is
observed as a function of energy both experimentally and in
the model.
Figure 6 shows the width of the {311} defect layer
simulated and as measured by cross-sectional TEM5. Since
the interstitial loss rate is not surface diffusion limited, the
{311} layer does not decay only from the top down, in
agreement with the experimental result. Figure 7 shows the
plus factor for a 15minute 750°C anneal as a function of dose
along with measured data reported here for the first time. The
fit is within 20% counting error.
Conclusion: A model with several new features has been
introduced for {311} defects. The model is based on in-situ
TEM observations of the defect behavior, and is compared to a
large set of experimental data. For the first time, a model
accounts for both the width and energy dependence of the
{311} defects.
350
References:
1N. Cuendet, T. Halicioglu, and W. A. Tiller, Appl. Phys. Lett. 68 (1),
19-21 (1996).
2M.J. Cuturla, T.D. delaRubia, L.A. Marques et al, Phys Rev. B 54 (23),
(1) (2000).
5K. Moller, Kevin S. Jones, and Mark E. Law, Applied Physics Letters,
72 (20) (1998).
dC311 D311 CI  C311Eq 

dt
 311
dD311  D311 C311Eq D311

dt
 311
C311
dCSMIC CSMIC CI  CSMICE q 

dt
 SMIC
Table 1 – Model equations for the {311} model. The
SMIC equation time constant has energetics from Cowern 3.
SMIC’s have a dissolution energy of 3.7eV. The {311} time
constant is diffusion limited with a barrier height. The total
dissolution energy for the {311} is 3.77, close to the measured
energy of dissolution. The term D311/C311 in the second
equation is the inverse of the average size, and accounts for
smaller {311} defects disappearing faster than large ones.
250
Size (nm)
16683-95 (1996).
3N.E.B. Cowern, M. Jaraiz, F. Cristiano et al., International Electron
Devices Meeting, Washington, DC, 1999.
4H. Saleh, M.E. Law, Sushil Bharatan et al., Applied Physics Letters, 77
300
200
150
100
50
0
0
20
40
60
80
100
120
Time (minutes)
Figure 2 – Size of individual defects as a function of insitu anneal time. Best fits are linear decays. The slowest
decaying defect is about average size at time zero. Regression
factors are higher for most of these defects for a linear decay
as opposed to an exponential decay.
6
Decay Rate (nm/min)
5
4
3
2
1
0
50
Figure 1 – Left picture
is the start of the in-situ annealing. The right picture is after
15minutes at 770°C. The large defect in the lower left has
completely dissolved in 15 minutes. The left of the bright pair
in the center of the picture has shrunk in length by about a
factor of 2, while the neighboring defect has only changed
about 10% in size.
100
150
200
Defect Initial Size (nm)
250
300
Figure 3 – Decay rates of defects. Error bars are plus and
minus one standard deviation about the mean. The model
value at 770°C is 2.3nm/min, only about 20% higher than the
mean and well within the one standard deviation error bars.
-3
Concen tration of Defect and Trap ped Interstitials (cm )
10
14
2000
1013
1500
1012
11
Position (
)
10
20Kev
40Kev
80Kev
1000
500
1010
10
9
0
20
40
60
80
Time (min)
100
120
140
Figure 4 – Defect and Total Interstitial decay. The top three
curves are the dose of interstitials contained in the {311}
defects. The bottom curves are the total dose of defects. Data
are the symbols and the solid lines are simulated results.
Good fits are obtained both with the decay rate (slope) as well
as the plus factor (y-intercept).
0
0
60
80
100 120 140
Time (min)
Figure 6 – The position of the top and bottom of the {311}
defect layer as a function of time. The simulation and data
both show that the layer collapses from both sides.
1.2 10
14
1 10
14
8 10
13
6 10
13
20kev
Size (nm)
80
40
-2
{311} Interstitial Dose (cm )
100
20
40kev
60
40
4 10 13
2 10 13
20
0
4 10 13 6 10 13 8 10 13 1 10 14 1.2 10 141.4 10 141.6 10
0
0
20
40
60
Time (min)
80
100
Figure 5 – Size of the defects as a function of anneal time.
Symbols are the measured data and lines are the simulated
result. The defect size is nearly constant with time.
14
Implant Dos e (cm -2 )
Figure 7 – The number of interstitial s contained in {311}
defects after a 15minute, 750°C anneal. The symbols are data
and the line is the simulated result. Error bars are 20% of the
data value. The model slight over estimates the dependence of
interstitials on implant dose.