A New Model for 311 Defects Base on In-Situ Measurements

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

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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 (D311). 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 sub-microscopic {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. al4. 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.

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), 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 (1) (2000).

5K. Moller, Kevin S. Jones, and Mark E. Law, Applied Physics Letters, 72 (20) (1998).

Table 1 – Model equations for the {311} model. The SMIC equation time constant has energetics from Cowern3. 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.

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.

Figure 2 – Size of individual defects as a function of in-situ 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.

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.

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).

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.

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.

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.