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Calibrated and Predictive Simulation of Doping Profiles: Low Energy As, B and BF2 Ion Implantation
LETI (CEA-Grenoble) - 17, rue des Martyrs - 38054 Grenoble Cedex 09 - FRANCE
Introduction
This article will present an efficient and original methodology for global and predictive modeling of low energy Boron, BF2 and Arsenic ion implantation, in the suitable range for sub-100nm CMOS technology.
The International Technology Roadmap for Semiconductors (ed. 1999) underlines the need for development of analytical models for ion implantation simulations, supported by Monte Carlo code. These models become more and more complex, from the simple Gaussian approximations to the latest double Pearson-4 distributions [1], or Legendre polynomials fitting [2].
Leaving apart the domain of the sophisticated ion implantation models, we found that the value of the doping concentration itself could be directly expressed with a fair accuracy, as a function of the experimental conditions. The predictivity of this technique is insured by the use of Design Of Experiments (DoE) and Response Surface Methodology (RSM) [3][4].
This article will explain the methodology used and demonstrate how we can include it in ATHENA.
New Approach For Modeling Profiles
Usually, the simulation of as-implanted doping profiles is obtained through complex statistical or analytical functions, with parameters depending on the experimental conditions. The tuning of these parameters is not always obvious for achieving a good fit with experiments.
We have decided to express directly the concentration as a a function of
experimental conditions (dose, energy) with a polynomial. By using DoE to
choose the experimental implantation conditions (dose, energy), and RSM
for the modeling of the concentrations along the depth, we obtained a predictive
and calibrated modeling of the implantation profiles. Figure 1 illustrates
the principle of this technique, called Sampling CALibration of Profiles
(SCALP): for a given percentage of the total profile depth, one searches
a unique polynomial response function for describing the doping concentration,
for any combination of the process factors.
Figure 1: Illustration of the SCALP technique:
Each point of the graph (concentration, depth)
is calculated using a unique polynomial function,
which model the concentration as a function of
the total depth (here 45%) whatever the
experimental conditions are.
Experimental
The experiments were chosen using a 32 design in the aim of obtaining a quadratic modeling of the responses depth and log (concentration), as a function of the factors log(dose) and energy, see Table 1. The center of the design is replicated 3 times on different wafers to estimate the experimental dispersion.
| Factors | Energy | Dose As BF2 (at. cm ) |
Dose B (at. cm) |
Tilt (deg) | Twist (deg) |
|---|---|---|---|---|---|
| range | 3 to 10 | 3 10
to 10 |
1 10to
5 10 |
7 | 27 |
Table 1: Experimental ranges for As, BF2 and B.
The implantations were performed on 8" wafers, through a 2 nm screen oxide layer, with an EATON NV8200P implanter.
The analysis of these narrow profiles requires carrying out a specific measurement technique [5]: SIMS measurements were performed using a CAMECA IMS-5f with an effective impact energy and incidence angle of 1keV and 60? respectively, in order to reduce ion beam mixing and equilibration depths.
Results and Modelization
The empirical models of the concentrations and depth were generated with the software ECHIP [6]. For all the three dopants, the adjusted R2 were higher than 0.8 until 2/3 of the depth, as shown in Figure 2.
Figure 2: The values of the adjusted R_ higher
than 0.8 indicate the quality of the RSM,
particularly in the case of B and BF2
As an example the coefficients of the quadratic model for Boron and BF2 are given for some concentrations in Table 2. They allow the accurate reconstruction of all the profiles of the DoE, but also any interpolation within the experimental range. Furthermore the simulations are predictive within a 95% confidence interval. Inside this interval, in the case of boron, log(concentration) is predicted at +/-2% and depth at +/-10%. The excellent predictive capability of the models is evidenced in Figure 3 for Arsenic the prediction of the model is superimposed with test points, which have not been used to generate the model.
| Constant | log(d) | W | log(d)*W | log(d)? | W? | |
|---|---|---|---|---|---|---|
| Depth | 1.28E-01 | 3.60E-02 | 1.39E-02 | 3.15E-03 | -8.30E-03 | 2.52E-04 |
| C 0% | 1.86E+01 | 8.53E-01 | -1.14E-01 | -1.13E-02 | 1.47E-01 | 3.25E-02 |
| C 10% | 1.89E+01 | 9.70E-01 | -6.64E-02 | 8.27E-03 | 2.60E-02 | 2.65E-02 |
| C 20% | 1.89E+01 | 8.43E-01 | -2.20E-02 | 2.57E-02 | 3.46E-02 | 2.03E-02 |
| C 30% | 1.88E+01 | 6.87E-01 | 6.69E-03 | 2.67E-02 | 4.64E-02 | 1.60E-02 |
| C 40% | 1.85E+01 | 5.43E-01 | 1.48E-02 | 1.42E-02 | 8.26E-02 | 1.35E-02 |
| C 50% | 1.82E+01 | 4.41E-01 | 1.25E-02 | 5.42E-02 | 1.03E-01 | 1.20E-02 |
| 75% | 1.76E+01 | 3.27E-01 | 4.96E-03 | 2.06E-03 | 1.05E-01 | 8.71E-03 |
| Constant | log(d) | W | log(d)*W | log(d)? | W? | |
|---|---|---|---|---|---|---|
| Depth | 5.97E-02 | 1.99E-02 | 5.57E-03 | 1.07E-03 | -2.46E-03 | -1.01E-04 |
| C 0% | 2.01E+01 | 1.09E+00 | -4.90E-02 | -8.22E-03 | 4.38E-01 | -4.65E-03 |
| C 10% | 2.01E+01 | 8.13E-01 | 1.17E-02 | 3.50E-02 | -1.77E-01 | -1.47E-03 |
| C 20% | 1.94E+01 | 5.27E-01 | 2.86E-02 | 3.78E-02 | -6.34E-03 | 5.34E-03 |
| C 30% | 1.88E+01 | 2.87E-01 | 2.55E-02 | 2.58E-02 | 4.87E-02 | 3.16E-03 |
| C 40% | 1.84E+01 | 1.56E-01 | 2.96E-02 | 2.26E-02 | -2.20E-02 | 3.45E-04 |
| C 50% | 1.82E=01 | 1.00E-01 | 3.44-02 | 2.13E-02 | -9.18E-02 | -1.03E-03 |
| C 75% | 1.76E=01 | 3.86E-02 | 2.58E-02 | 4.65E-03 | -6.58E-02 | -2.04E-03 |
Table 2: Boron and BF2; centered variables; "d"=dose; "W"=energy.
Figure 3: Predictions of Arsenic test points versus SIMS and SVDP.
In Figure 4, we show the global improvement provided by SCALP over the whole As and B profile database, as compared to the simulations performed with the SIMS Verified Dual Pearson (SVDP) model of ATHENA [7]. The improvement is evaluated by the Root Mean Square Relative Error:
where yexpi and ysimi are respectively the ith experimental and simulated concentration values of a n points discretization of the profile.
Figure 4. Graph showing the global
improvement for As and B.
V. Application to ATHENA
The run-time environment for all SILVACO TCAD simulators,
DeckBuild, allows users to include any UNIX command inside
any simulator input file. The option uses the keyword SYSTEM before the
UNIX command. This feature authorizes users to include their own simulators
or other external routines inside DeckBuild. This is what
we did to use in ATHENA, the new method described above.
For example to call a program named 'SCALP' that reads dopant, dose and
energy as an input and create as an output a doping profile, we use the
syntax illustrated in Figure 5.
Figure 5: Illustration of the 'system' command
The external program 'SCALP' contains the polynomial model that describes
the concentration of the dopant as a function of the depth. Figure 6 is
an illustration of the profile obtained using SCALP, SVDP and compared
to SIMS.
Figure 6: Boron profile resulting from SCALP
and SVDP implantation in ATHENA
VI. Conclusion
We have developed an efficient technique for predictive
simulation of ion implantation. The methodology allows the calibration
of As, BF2 and B profiles, with the knowledge of a confidence interval,
for the low energy, high dose conditions of sub-100nm CMOS technology.
This new technique can be then applied into ATHENA.
References
- Al. F. Tash et al. - J. Elec. Soc. 136(3) 1989 - pp 810-814.
- G. Balamurugan et al. - IEDM'98 - pp 517-520.
- G.E.P. Box, N.R. Draper, John Wiley & sons, N.Y., 1987.
- G. Le Carval et al.- SISPAD'97 - pp 177-180.
- Ph. Holliger et al - Proc. of 13th An. Workshop on SIMS.
- ECHIP 6.4 user's guide.
