# Fast, Physical, Predictive and Calibrated Modeling of Ion Implantation

Introduction

Ion implantation has become a critical step for controlling ultra-shallow junctions, in sub-0.1mm CMOS technology. In a Research & Development environment, Technology Computer Aided Design (TCAD) is involved in the device optimization loop and requires efficient and predictive implantation modeling with frequent updating of the range of validity. For this purpose, semi-empirical models using statistical distributions are mainly chosen, because this kind of simulation is faster than the physically based Monte-Carlo (MC) approach. We propose a methodology which can be applied to ion implantation modeling with easy build-up, and which gives a predictive capability in the explored experimental domain. This calibration strategy will enhance the efficiency of analytical modeling by the combination the use of SIMS profile and the statistical qualities of Design of Experiments (DoE). Thus, only a few extra experiments are needed to extend the ion implantation simulation domain, in order to take into account the most advanced process conditions accurately. Our methodology is carried out for low energy B and As implantation, which is the case in practice for ultra-shallow junction engineering.

Calibration of Ion Implantation Modeling

The results provided by a TCAD simulator are a function of both the experimental conditions and of the parameters of the used model, parameters which may themselves depend on the experimental conditions. In the case of analytic simulation of ion implantation, the tuning of the parameters (for example the moments of the statistical distribution) is often necessary, because they incorporate the experimental uncertainties. On the contrary, for MC computations, parameters are purely physical, so do not need to be adjusted.

The problem of predictive calibration of TCAD simulators has been previously addressed and an original methodology has been proposed [1]. The main idea is that a simulation can be considered as calibrated not only if the set of model parameters is fitted to particular experiments, but also if the sensitivity of these parameters to the experimental process parameters, is determined. With this aim, the use of Design of Experiments (DoE) and Response Surface Modeling (RSM) permits the choice of the most significant experiments, to finally generate an empirical model for the parameters of the implantation model.

Nowadays, the parameters of the most advanced analytical ion implantation models, like the Dual-Pearson 4 (DP4) [2], are linearly interpolated in lookup tables to produce fast and accurate simulation.

However, these lookup tables suffer from several drawbacks:

(i) default values in TCAD software must be calibrated and extended over the whole interesting range, to make the modeling results closer to the specific experimental conditions of each fab, in particular the dose loss;

(ii) the global consistency of the table is not maintained when further parameter values are incorporated;

(iii) a great number of experiments is required to obtain discrete sets of model parameters that cover the experimental domain with a sufficient accuracy.

The advantages of RSM could then fulfill the requirements of predictive calibration of ion implantation analytical models.

Application to Advanced Analytical Models

We applied our strategy to the DP4 ion implantation modeling: we attempted to find a quadratic modeling of the parameters (Rp, DRp, skewness, kurtosis,...), of the DP4 models. To do that we have applied the following strategy:

- DoE on which SIMS profile will be extracted.

The domain of variation is shown on Table 1.

Factors | Energy | Dose As BF2 (at. cm) | Dose B (at. cm) | Tilt (deg) | Twist (deg) |

range | 3 to 10 | 3 10 to 10 | 1 10 to 5 10 | 7 | 27 |

Table 1: Experimental ranges for As, BF2 and B.

- Use of the SILVACO OPTIMIZER to extract moments of
DP4 from experimental SIMS profile (Figure 1 and 2).

- Modelisation (RSM) of the DP4 moments. We found that the RSM of these models parameters, as function of the experimental process condition are satisfactory. Indeed the adjusted R_ criterion value, which indicates the quality of the empirical models, is rarely below 0.8.

Figure 1. Input deck used for Dual Pearson 4
moments extraction.

Figure 2: View of the Optimizer windows during extraction procedure.

Results

As already explained in [4], we have used the ability
of * DeckBuild* to include any UNIX command inside any simulator
input file. This feature authorizes users to include their own external
routines inside

*. This is what we did in*

**DeckBuild***to specify the values of the moments of the SIMS Verified Dual Pearson (SVDP) mode. The external routine contains the polynomial model that describes the SVDP model parameter (Rp for example) as a function of the process parameters like dose and energy (see Figure 3.). Figure 4 and 5 are an illustration of the profile obtained using this methodology for respectively Arsenic and Boron, SIMS profile was superimposed for comparison purpose.*

**ATHENA**

Figure 3. Coefficients of the analytical model
for each SVDP model

parameter as a function of the process parameters.

Figure 4: Arsenic profile in TonyPlot before and

after calibration, comparison with SIMS profile.

Figure 5: Boron profile in Tonyplot before and after

calibration, comparison with SIMS profile.

In Figure 6, we show the global improvement over the
whole As and B profile database, as compared to the simulations performed
with the SVDP model of * ATHENA* [3]. 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 6: RMSRE for Arsenic and Boron which show the reduction after

calibration, of the difference between SIMS profile and simulation.

Influence on Device Characteristics

It is often recognized in the TCAD word that an accurate
simulation of electrical MOSFET characteristics is primarily due to a
good process simulation. This is illustrated as an example in the Figure
7 where we have made the same * ATLAS* simulation with two
different

*process simulation. One using the default value of the moments of the SVDP model and the other one using the calibrated one.*

**ATHENA**

Figure 7: Comparison of the use of calibrated
profiles on a device characteristic.

Conclusion

In this study, we have presented an original and efficient
methodology for global ion implantation modeling. The advantages of this
methodology are a lower number of experiments, confidence in the values
of the calibrated model parameters, and the rapid implementation of new
data within our process simulator * ATHENA*. However it is
of great importance to notice that the aim of this paper was to show a
calibration methodology and not necessary to give new parameters for the
SVDP implant model. Indeed it is not guaranty that replacing the default
values by the values obtained from this work will give better results
in all cases. The reason is that the confidence we have in the results
done in this work could not be maintained if we take the values "out
of their context". This is due to the high degree of dependency of
the way of doing calibration (DoE used, optimizer setup..), making measurements
and more important the Fab itself.

References

- G. Le Carval - SISPAD'97 - pp 177-180
- A. F. Tash - J. Electrochem. Soc. 136(3) 1989 - pp 810-814
- SILVACO International
*-***ATHENA**Use's Manual - SILVACO
*Simulation Standard May 2000*