Automated TCAD Calibration Procedure Using A Combination of VWF Automation and Production Tools

Introduction

Calibration is one of the major issues facing users and potential users of process and device simulation tools. The current generation of TCAD tools contain advanced and physically accurate models for most of the phenomena to be simulated. However, there are still many issues to be resolved in using the tools. A user's perspective on these issues can be found on page 4.

As new physical models are proposed, including deeper insight into the exact physical phenomena, often more and more fitting parameters are required. This is the case, for example, in the area of transient enhanced diffusion models.

At the basis of any physical model are a series of fitting parameters. These parameters have typically been fit to a model by a university or research institute, resulting in a best set of model parameters. The difficulties visible with this approach relate to the limited availability of measured data that may be used to fit to the model in order to cover all cases.

Some universities are to be commended in their strategic direction to generate controlled sets of measured data in an experimental matrix format such that models may be characterized over useful ranges of experimental space. These efforts should form the basis of a calibrated set of parameters used by simulators. However, this is not the end of the job. Many parameters are highly material or equipment dependent or relate to a set of physics that would be overly time-consuming to include in a given set of simulations for process design.

Perhaps in years to come, highly physical and rigorous atomic and quantum level simulations may result in us being able to determine many of these parameters from first principles, but realistically and practically speaking, this dream is a long way off. The current approach is to treat the major model parameters as fitting co-efficients to be tuned to match a set of measured data.

Adding complexity to the problem, measurement techniques are progressing at a rapid rate leading to more accurate and updated experimental data each year. Ideally the models should be re-fit to the latest measured data regularly.

 

An Automated Solution

It has become necessary to merge both physically simulated predictive response surface models with a limited set of onsite measured data. Today this is the only way of producing useful results over a range of experimental space.

Clearly what is now required in a TCAD framework is the ability to calibrate TCAD simulators to a limited and statistically useful set of measured data in an automated environment. A "Calibration Tool". This job should be performed routinely and ideally with a high degree of automation, such that eventually a user is simply monitoring progress.

A good approach for the calibration of physical models must require a mixture of intelligence and statistics. The end result of the calibration exercise must be useful, or predictive, and not limited to a single insular case or single set of results. The theme of VWF development has been moving towards this goal for several years. With each release another step towards this goal is accomplished.

An approach to calibration and a description of the VWF tools to do the job is presented in summary below and is illustrated in the flowchart (Figure 1).

 

Figure 1. Calibration Methodology Flow Chart

 

 

Objective

The objective is to use VWF to create a set of Response Surface Models (RSM) of the target parameters with respect to some process input parameters and some simulation model parameters. Examples might be Vt as a function of implant dose, diffusion and segregation model parameters, or oxide thickness as a function of diffusion recipe and oxidation model parameters.

The VWF calibration strategy starts with an ATHENA input file describing a process flow, followed by a DevEdit remeshing routine, and one or more ATLAS device tests. A powerful and flexible extraction syntax built into the user interface allows users to measure the final design parameters of interest and have these logged to the VWF database. Targets can be geometric process simulation results (eg. junction depth, layer thickness), 1D electrical results (Vt, sheet resistance) or complex functions of ATLAS results (eg fT, breakdown voltage).

Sensitivity Analysis

Next, a large number of potential calibration parameters are added to the process and device flow, directly into the input deck. These parameters are chosen as a result of the engineer's best guess of the physics involved. What the VWF provides is the large number of parameters that may be added such that an engineer is hardly limited in his choice. The first step is to study the relative statistical strength of the response of the chosen target parameters to both model parameters and optimizable process parameters. With perhaps 20 extra potential calibration parameters in place, a sensitivity analysis experiment may be run. This experimental run is set up automatically with the VWF database system and is most conveniently run on a multiprocessor machine or across a Local Area Network of workstations for optimum throughput. The VWF will assign the individual experiments across the available CPU's automatically and in parallel.

The VWF system displays the results (at this point stored in the underlying database) of the sensitivity analysis experiment automatically on a spreadsheet or in a report format hardcopy. The result is the generation of a future reference table of sorted, "most important" calibration parameters for a given process flow. Armed with this new information, an engineer may now tackle the calibration problem with more confidence. For example, they might now understand that the Poly reox process is critical to Vt or leakage; and that the Boron DIX.0 diffusion coefficient hardly makes any difference to the set of design parameters. Ideally engineers would understand the relationship of all physical models in their simulator to their device or circuit performance. However, in practice this form of statistical ordering is far more valuable.

Along side the list of most important calibration parameters, and in exactly the same manner, a list of most important processing parameters may also be generated.

The end result of this exercise is a list of both the most important physical process parameters and the most important calibration parameters.

The number of these parameters is technology and problem dependent and should further be limited by the amount of computer power available to a user.

 

Experimental Design

If the total number of parameters is less than around five, an orthogonal Design of Experiments (DOE) should be constructed. Either Partial Factorial or Box Behnken is the best selection depending upon whether a first or second order accuracy is required. A CPU power vs. accuracy trade off is the main consideration here. If the complete list of sensitive parameters exceeds five, a Latin HyperCube DOE would typically be a better choice, with around 1000 split runs for simulation.

A multi-dimensional DOE is built by defining split points on both physical process parameters and calibration model parameters, in a single VWF experiment. The VWF system is designed for exactly this purpose. The high performance database that underlies the system, allows the automatic construction of large split trees with hundreds of split branches.

At this point the VWF experiment is run. Most experiments aimed at calibration are highly. parallelized tasks that can be run efficiently on a network of computers or, better still, on an MP Unix Server.

 

Results Analysis

After all jobs are complete, an RSM can be created for this data set. The RSM is an analytical expression of the target values as functions of the process parameter and model parameters inputs.

Analysis of the RSM can be done in the VWF automation tools to ensure the analytical expression adequately fits the simulation results. From this point on optimization and calibration can be done using the analytical RSM equation rather than by re-running the simulators.

Simple point calibration to one set of measured data can be done in the VWF automation tools. However as already described, this approach is limited and cannot give simulators tuned to be predictive. More complete calibration to a set of measured data points must be done in the VWF Production Tools.

 

The TCAD Calibration Tool

The VWF Production Tools (version 2.5.0 or later) have the ability to import measured data points and display these together with RSM results. The initial condition of the calibration function requires an overlayed display of the measured and RSM data to be made. At this time the user chooses which parameters are to be varied to do the calibration. The user's choice is to set the process parameters to be fixed while the model parameters are allowed to vary. VWF will then apply statistical analysis to the comparison of measured data and analytical RSM equation. It varies the model parameters to produce the best fit it can to the measured data.

An example of a calibrated experiment is shown in Figures 2 & 3.

 

Figure 2. Production Tools are used to calibrate an
RSM from VWF to a range of measured data.

 

Figure 3. The control panel of the Calibration Tool allows
either automated optimizer fitting, interactive manual
control, or a combination of the two.

 

The oxide thickness from various high temperature dry oxidation recipes is displayed versus oxidation time with temperature variation also shown. Calibration using the VWF production tools has been done to vary the oxidation parameters to achieve a match.

 

Conclusion

A new Calibration Tool has been developed for TCAD model parameter calibration. This tool will be demonstrated at the IEDM conference.