Through many years of research and development, technology computer-aided design (TCAD) has matured to a stage where complex semiconductor processes and devices can be simulated with reasonable accuracy.  As we move into the deep-submicron technology era, we are facing many challenges as well as opportunities for the predictive TCAD approach to semiconductor technology development and ultra-small transistor design and optimization.

In this article, we first discuss some of the problems associated with the use of TCAD in technology development.  Then, we introduce some ideas about an alternative approach, namely, the multi-level TCAD synthesis approach, which is being carried out as a joint research project, Project DOUST: Design and Optimization of Ultra-Small Transistors, with Chartered Semiconductor Manufacturing, Ltd. (CSM).  It is hoped that the successful completion of the project will be a first step towards the establishment of a Virtual Fab Foundry (VFF) to provide TCAD services to technology developers, circuit designers, and device researchers.
 

THE MYTH OF TCAD PREDICTABILITY AND ACCURACY
 

This question has attracted as much attention and interests as confusion and frustration among semiconductor technology developers, TCAD tool vendors, and device researchers.  Predictive TCAD, as implied by its very nature, has set an “ultimate standard” but yet an “elusive goal” for modeling semiconductor technologies and devices.  The problem stems from the ambiguous definition of predictability and unrealistic expectations, since in many cases it is expected that a “match” of the TCAD-simulated I–V characteristic (through all process steps and device analyses) to the measured one can be obtained.  In fact, there is a great potential danger if a “perfect” match is obtained and it is claimed that the model is “accurately” calibrated without stating the conditions.
 

Definition of Predictability and Accuracy

In a sense, the answer lies in the question itself being asked.  By and large it depends on how much accuracy is required for the target variable to be predicted.

Metrology analogy.  A similar question is: “can we measure linewidths?”  The answer varies whether you mean 1-µm or 0.1-µm linewidth.

Physics analogy.  The well-known uncertainty principle states that one cannot make precise determination of both position and momentum (or energy and time) of an object simultaneously.  In analogy, the precision of a target to be predicted by TCAD depends on many (not one) variables.  “Absolute accuracy,” in general, does not make sense.

Mathematics analogy.  In the mathematical definition of the limit of a function f(x), for any arbitrarily small value of e > 0, one can always find a positive number d such that for all values of x satisfying 0 < |x – a| < d, | f(x) – A| < e, i.e.,  f(x) approaches A as x approaches a.  This is analogous to the fact that, no matter how accurate the TCAD result can match the measured data, we can always find a better model as we gain deeper understanding of the process/device physics.

Philosophical viewpoint.  From a philosophical point of view, the art of science is the constant search for the ultimate truth, which lies only beyond one’s imagination.  The history of mankind has been a history of breaking our own physical limits in approaching (instead of reaching) the ultimate truth through scientific and technological advancements.

The point is that an unambiguous definition of predictability must be associated with the required accuracy.  With these in mind, the answer to the question whether TCAD is predictive should be rephrased as:
 

Now, the real questions are:

• What is the right question?
• How to approximate the solution?
• How accurate will the answer be satisfactory?

Problems with TCAD Calibration

What are the problems?  Predictive TCAD obviously requires a very high degree of accuracy.  This is determined by its own nature and objective -- emulating a very complex phenomenon of a complete semiconductor processing and characterization process with physics-based models.  The problem often renders itself a formidable task because to predict a complex phenomenon, the physical models and the model parameters must be well understood and calibrated.

TCAD calibration refers to the process of selecting appropriate models and adjusting the model parameters so that the response of the physical model (assuming physically correct) can predict in a wider range (within a specified tolerance) the measured one the model represents.  This task itself creates a lot of problems.  First, there are simply too many variables to be adjusted, especially when a “full-loop” calibration (i.e., calibrating to the device electrical characteristics from the process variables) is performed.  Secondly, in some cases the physical models (required for the desired accuracy) are not well understood, or even not implemented.  Thirdly, for the measured data one is calibrating to (e.g., SIMS or I–V), there is bound to have experimental errors, some of which cannot be controlled or estimated.  Last, but not the least, if the goal is to predict a new technology which is being developed and is changing, TCAD calibration will be essentially a dynamic process.

Where do the problems come from?  Aside from the difficulties intrinsic to TCAD calibration, such as measurement errors and our physical understanding, some problems arise from the way we develop and use the models, which, in principle, can be avoided or minimized if the question is properly addressed.

TCAD users are facing two contradicting problems.  On one hand, they need more detailed (atomic-level) physical models to account for the increased complexity in problems for deep-submicron devices; on the other hand, they are already overwhelmed by an excessive selection of models and coefficients, and the burden of selecting and calibrating the models rests with the user.  The latter problem is partially due to the fact that the TCAD tools developed by the vendors are meant to be general tools with maximum user flexibility.  In fact, in many cases the coefficients for a given implemented model are not supposed to be adjusted arbitrarily; and probably a good portion of the implemented models in a simulator is completely irrelevant to the problem at hand.

Most software vendors claim that they are the leader in providing “solutions” to the problems in the respective area of their products.  But in fact what they provide are actually “tools,” and it is up to the users to find their own solutions using the tools.  This is not to blame the CAD tool vendors.  But from the user’s perspective, there is an increasing need to “get the job done, and fast,” rather than “tweaking coefficients for all days.”

How to solve the problems?  The key to the effective use of TCAD tools is to identify the specific objectives and make the best use of available resources to achieve the goals.  For example, if the problem is to predict or optimize a particular process step (e.g., implantation or diffusion), a calibrated 1-D process simulator may be sufficient.  If the objective is to study the performance of a sub-0.1-µm transistor, depending on the region of operation, existing device models may not be adequate and new (atomic-level) models must be developed.

For the most difficult task of full-loop calibration, the urgent need is to come up with a “standard” procedure and benchmarking.  However, so far there is no commonly agreed standard and, perhaps, there will never be one.  To develop a general framework and a systematic approach to the use of TCAD in aiding technology development and circuit design, it is important to understand the nature of TCAD and to make the best use of it.
 

TCAD Perspectives

Vendor’s perspective.  From the vendor’s perspective, TCAD tools are products that are supposed to cover a wide spectrum of applications, and should include the state-of-the-art physical models and numerical algorithms.  User interface, user friendliness, tool integration and support, etc., are of important concern. Commercial tool vendors and in-house tool developers also have different objectives and strategy in their software development.

User’s perspective.  From the user’s perspective, everyone has his/her own objectives.  Technology developers (process engineers) are more interested in getting the trends and trade-off in reducing split-lots.  Device physicists use TCAD to study the physical limits and to optimize device performance.  Circuit engineers expect a set of SPICE parameters for their design that can be made available before the design is fabricated.  Very often, engineers are working on a multi-target optimization problem in a multi-variable design space, which involves a lot of trade-off; whereas physicists are more interested in a specific physical mechanism.

Industrial vs. academic.  Applications of TCAD in industry and academia also have different perspectives.  Problems exist in the TCAD arena that new physical models from the research community often lag behind the technology in the industry; and software vendors are not in a co-development mode with technology developers.  Commercial tools with complex models and comprehensive data post-processing, although attractive to researchers to probe insights into the device physics, often complicate the problems for “non-expert” process engineers.
 

Trade-off in TCAD

There is a lot of trade-off in the development as well as use of TCAD software.  Some are general and some are specific.  Different concerns arise depending on who develops/uses the tool, when it is to be used, how it is to be used, and so on.

Flexibility vs. complexity.  Commercial TCAD tools are developed for the general public with maximum user flexibility, which increases the complexity of the tool (e.g., number of implemented models and coefficients).  However, the particular user, for the specific problem, may use only a subset of the available models.

Interactive vs. batch mode.  Commercial TCAD tools have excellent interactive user interface and comprehensive data post-processing.  The user can create his/her own design using the built-in design of experiment (DOE) or response surface modeling (RSM) facilities, and probe detailed device structure, profile, distribution of physical quantities at will.  However, he/she must be experienced in understanding the models to use these tools.  There are also times when it is advantageous to run the computer experiment in batch mode and use the “templates” to reduce the amount of repeated work.

Accuracy vs. speed.  Accuracy/speed trade-off is always a big concern in computer simulation.  It is specially so in TCAD since the accuracy and speed of a simulation are highly grid dependent.  In TCAD simulation, one has to make sure that the error associated with the grid must be smaller than the required accuracy for the target variable being simulated and, at the same time, a reasonable simulation time can be maintained.
 

Comparison with ECAD

In order to understand the nature of TCAD and make use of its features, it is helpful to make some comparisons with the electronic CAD (ECAD).

Skeptical or optimistic.  It has always been skeptical about TCAD, even among experts; but very few people question the use of ECAD tools in IC design.  In fact, it is hard to believe that one does not use ECAD tools to design IC’s.  This is largely due to the different expectations.  One never expects a “very accurate” transistor timing delay from a logic-level simulator, although the same device (to be fabricated) as the one for TCAD is simulated.

Statistical or deterministic.  The numerical results from TCAD always have statistical fluctuations, while ECAD (such as SPICE) is continuous and deterministic in nature.  This is because TCAD is based on the numerical solution of partial differential equations (PDE), which imitates more closely the behavior of the actual device, as opposed to ECAD which is based on macroscopic, analytic, logic, or closed-form equations.  This feature of TCAD, however, is not a fatal one, since computer experiments are, in principle, exactly reproducible (even for Monte Carlo device simulator).  The important thing is to know the source of fluctuation or error (physical or numerical), and to be able to quantify it.

Linkage.  Although TCAD and ECAD are quite different in terms of their features and level of abstraction, they become more closely linked as we go into the deep-submicron regime.  One area is electrical characterization in which SPICE circuit parameters can be extracted from TCAD-simulated I–V characteristics.  The other area is technology characterization in which interconnect delays can be modeled by TCAD and RC-delay models can be extracted for design-rule checking (DRC) and timing verification.
 

MULTI-LEVEL TCAD SYNTHESIS

There are many “right” questions to ask about predictive TCAD.  Some large projects, such as the Computational Prototyping for 21st Century Semiconductor Structures (hierarchical simulation from atoms to interconnect) at Stanford University and the Michigan Synthesis Tools for IC’s (process compilation and device synthesis) at the University of Michigan, are all addressing important, but different, problems in TCAD.

If we ask the question: “how to provide TCAD solutions for process/device engineers in aiding technology development?” we are facing all the problems discussed in the previous section, such as calibration and all kinds of perspectives and trade-off.

In this section, we propose one approach to the above question -- multi-level TCAD synthesis -- for getting “approximate” solutions with “satisfactory” accuracy.
 

Motivation

The motivation behind the idea of multi-level TCAD synthesis is based on the following general belief that T-C-A-D

• should not be “tweaking coefficients for all days,” but
• should be used for “testing concepts by analysis and design.”

If we look at what has happened in the ECAD and IC design community, sometimes it may help in setting the directions in using TCAD to aid technology development.

ASIC analogy.  In the IC design community, the semi-custom design approach (as opposed to full-custom design) for the application-specific integrated circuits (ASIC) has become popular, which uses gate array, standard cell, or programmable logic devices as building blocks that have been thoroughly studied or even partially implemented in silicon.  In analogy, we can develop “application-specific TCAD” (or AS-TCAD) for the specific device structures and processes (e.g., CMOS, SOI, DRAM, LDD) based on the generic TCAD tools.  This will help users to trade-off generalization/specialization and flexibility/complexity concerns, and to arrive at the solutions faster.

Multi-level simulation analogy.  In the circuit simulation community, especially for mixed-signal simulation, a hierarchy of simulation tools has been developed (e.g., gate-level, switch-level, timing, electrical, behavioral, table lookup) to trade-off speed and accuracy.  For TCAD, although being mainly a bottom-up analysis tool, it is also advantageous to adopt the notion of “multi-level TCAD” (or ML-TCAD) and come up with compact models (CM) for the devices and processes based on the TCAD results, similar to the idea of table lookup (e.g., TimeMill of EPIC).  The compact models can be formulated through empirical nonlinear regression of the TCAD data, which can be considered as a higher-level model that incorporates all the nonuniformities and nonlinearities of the original TCAD data.  This will help users to quickly examine trends in device/process parameters, to generate response surfaces and process boxes, and to perform multi-target optimization.

High-level synthesis analogy.  In the systems design community, it is simply too complex to design the whole system from bottom-up.  With the accumulation of design expertise and advancement in knowledge-based systems, high-level synthesis becomes the ultimate and powerful solution to systems design.  In general, synthesis means an ensemble of answers waiting for the right question.  In principle, a TCAD-Synthesis approach can be applied to the prediction and characterization of semiconductor technologies and devices as long as a “large” process/device-variable space can be covered.
 

Objectives, Scope, and Advantages

Objectives.  The primary objective of the proposed application-specific, multi-level TCAD synthesis approach is to construct a general “framework” for the design and optimization of ultra-small transistors for a given technology.  This framework will provide a link between the device performance parameters (“targets”) and the process variations (“variables”), and hence, a guide for process/device engineers in technology development and transistor optimization.  Other major objectives are listed below:

• The approach used in the construction of the database must be general and efficient so that it can be easily repeated/extended if a new process technology, a more accurately calibrated simulator, or a new physical model is given.
• The range of the database should cover all major design (process/device) variables such that design target parameters can be obtained by interpolation with adequate accuracy.
• Compact models for the major targets will be formulated using nonlinear regression based on the TCAD database.  These continuum, compact models include all the nonuniformities in chemical/electrical distributions and nonlinearities in carrier transport, and yet will be very efficient for use in creating design curves, process windows, and contour plots for the design targets.
• The target parameters, whenever possible, should be modeled/formulated as a “change” due to the variation of certain variables.  Then, presumably, the error associated with all other uncertainties will be canceled out, and the relative accuracy of the change in the target will give meaningful trends.
• The framework should be able to provide trends for transistor scaling, which is to be verified with the measurement of the nominal technology simulated, and to be used for predicting new technologies.  In other words, all the targets will be simulated/formulated as a function of the channel length.
• The framework should be able to provide a guide in multi-target optimization and process centering.  In other words, the objective is to trade-off different process/device alternatives for the optimization of all (not one) major device performance figures of merit.
• The framework should be able to quantify the error of the TCAD database from different sources (physical models, grid, etc.) with respect to the measured data, and the error of the compact models with respect to the TCAD data.

Advantages.  There are several advantages for the proposed synthesis approach over the full-loop calibration approach to technology development:

• If the constructed framework (database) and the approach in the compact-model formulation is general and has been automated, it can be relatively easily repeated if a new technology or physical model is given.
• Accuracy vs. speed can be traded-off by using the most complex models and dense grids for the construction of the database (since presumably it will be run only once), while the compact models would be extremely efficient to use with quantifiable accuracy with respect to the original TCAD database.
• The compact models, which are formulated based on the TCAD data, could in principle be extracted from the measured data if the same set of the measurement data as TCAD is available.  The compact models would also smooth out the fluctuations in the original TCAD data, and are definitive in nature.
• The approach makes use of the expertise of professional modeling efforts and provides a solution for non-expert engineers so that they can concentrate on the design optimization and trade-off and do not need to care about all the pitfalls in the modeling.  Eventually, this approach has the potential as a professional service to technology developers and device engineers.

Feasibility and Assumptions

The first question that comes in mind is whether this approach is feasible.  Basically, this is the question of emulating a real, complex phenomenon (deep-submicron transistor electrical characteristics due to process and structural variations) using an ideal, also complex model (process and device TCAD model).

Hypothesis.  If the “ideal” device covers large enough design-variable space, the behavior of the “real” device should fall somewhere in between, as long as the process/device physics is reasonably well understood.

Challenge.  It seems that there are simply too many (may be “infinite”) variables for the design space.  And it is difficult to determine how “large” the database is “enough” for accurately predicting the device performance.

Rebuttal.  It seems that we are limited by the computing resources to design such an “infinite” database, but if you ask the question “what you can do if computer speed and memory capacities were infinite?”  you will find that the real question is how we approach the problem and whether the effort is worth the investment.

Assumptions.  There are two major assumptions behind the whole idea of TCAD synthesis.  First, the physical (process and device) models implemented in the TCAD tools are valid in the region of the database to be constructed.  Secondly, the device performance (target parameters) can be predicted by interpolation of the TCAD data either through table lookup or compact model.  These two prerequisites call for proper use and careful treatment of the available models in the database construction as well as appropriate definition and formulation in the compact modeling.
 

Problem Specification and Approach

The following is a brief discussion on the main problems, considerations and approaches in the proposed TCAD synthesis.

Design specification: targets and variables.  The first step is to specify what are the target parameters and what are the design variables. Since our proposed TCAD-Synthesis is intended to be multi-level (ML-TCAD) and application-specific (AS-TCAD), the design specification will depend on the particular technology to be developed.  For example, if we are trying to predict a 0.18-µm CMOS technology based on the 0.25-µm technology for logic applications, a list of major targets and variables could be as follows:

• Targets: threshold voltage, saturation current, off-state leakage/punch-through current, subthreshold swing, transconductance, gate/junction capacitance, device lifetime, etc., as well as derived circuit parameters such as gate propagation delay, static power, noise margin, etc.
• Variables: channel length, gate oxide thickness, junction depth, channel doping profile, source/drain (2D) doping profile, supply voltage, etc., as well as all the major processing variables (diffusion/oxidation time and temperature, implant dose and energy, etc.) which influence the layer structures and profiles.

• All the target parameters should be extracted at one time in one or more experiments, if possible, and preferably be done in batch mode.
• The number of splits in one experiment and the number of experiments should be such that data storage and repeated simulations are minimized.
• All the DOE’s should be designed with different channel lengths as one level of split such that scaling of all the targets can be predicted.

Compact modeling.  Compact models are the essential part of the proposed multi-level TCAD synthesis approach, although table lookup can always be used as long as the database is constructed.  The philosophy behind the compact modeling is to come up with closed-form equations that represent the TCAD data with all the nonlinearities included and yet efficient to use.  The following is a brief guideline in formulating compact models:

• The approach is different from the analytic formulation starting from physical assumptions, since it is assumed that all the complex device physics has already been included in the TCAD data.  The formulation should be based on empirical nonlinear regression to curve-fit the TCAD data.
• It is still important to use physics-based equations whenever possible so that the functionality can represent the data in a wide range and different conditions.  It is important to manipulate the data to find a “global” functionality.  Usually, polynomial curve fitting will not always work.
• The parameters in a compact model should be unambiguously defined and should be easily extracted from the TCAD data.  The extraction procedure should be easily automated since it is expected that it will be repeated if a new set of data is given.
• It is preferable that the compact model includes as many variables as possible such that different target–variable dependencies can be easily evaluated.  However, there will be a trade-off in terms of the complexity in the formulation and extraction.
• Associated with each compact model, there should be an estimation of the relative error to the original TCAD data.  In this way, the accuracy of the compact model can be quantified.
• In principle, the same procedure for the compact-model formulation can be applied to the same set of data obtained from measurements, if available.

Potential Problems

Database range.  There are some anticipated problems with this synthesis approach.  The range of the variables for the database may be one problem.  Since in general extrapolation will not be reliable, the variable range should be large enough, but yet reasonable, for interpolation.  However, in some cases the conditions may be non-physical and the TCAD solutions may not converge.  For example, at the extreme conditions of short channel length and low channel doping, the device may be punched through so that the target electrical parameters will not be available.

Inverse modeling: multiple solution.  Another major difficulty is the “multiple solution” problem.  One example is the inverse modeling of reverse short-channel effect (RSCE) in which the pileup of the 2D channel doping profile is modeled to account for the observed increase in the threshold voltage at shorter channel lengths.  In principle, there are many (infinite) combinations of the 2D profiles that may give rise to the desired RSCE.  Another example is the compact model for the nonuniform doping profile (used in threshold voltage formulation).  If a nonuniform doping profile is characterized (defined) by some parameters (say, surface concentrate, peak concentration, and peak location) to be used in the compact model, there will be multiple profiles that satisfy the same set of parameters.
 

TOWARDS A VIRTUAL FAB FOUNDRY

Although commercial TCAD tools are developed with comprehensive models and interactive user interface, it is still a novelty for the general, non-expert, process/device engineers who need it most.  Borrowed from the concept of IC design houses and wafer fabs that provide “foundry services” to customers, the proposed multi-level TCAD synthesis approach can be a first step towards the establishment of a Virtual Fab Foundry that will provide TCAD modeling services to technology developers and device/circuit engineers.
 

Commercial Exploitation

There are many unique features of the proposed TCAD synthesis approach for commercial exploitation.

AS-TCAD tool development.  From the tool development point of view, what process engineers need are application-specific TCAD tools that can give them solutions and guidance.  Currently, TCAD environment (such as TMA WorkBench from Technology Modeling Associates and ATHENA/ATLAS from Silvaco) is developed by commercial vendors with highly user-friendly, interactive interface.  However, it is still up to the users to create their own experiments, which requires expertise in using TCAD tools.  The virtual fab foundry can be in such a position to develop AS-TCAD tools that generate specific target parameters for the user while hiding all the physical models and parameter extraction behind.  Even the background simulators can be from any vendors -- the user does not have to care about.  Graphical plotting can also be “standardized” for the specific type of plots to minimize the “flexibility” (or repeated work such as labeling) in generic tools so that the user can concentrate on getting the solutions.

Professional service.  From the professional service viewpoint, the complete TCAD database developed by the VFF, which builds in the dedicated modeling expertise and the state-of-the-art models and parameters, can be a valuable resource for technology developers.  Even for a non-calibrated TCAD database, the user can roughly know what he/she would get if he/she is to use the same simulator, same models, same grids, same processing and boundary conditions.  With the efforts in compact modeling, the compact models can be very useful and efficient design aids for the user.  All these development and services can be, in principle, applied to the notion of internet-based TCAD.
 

Potential Impact

Successful implementation of the virtual fab foundry based on the TCAD synthesis approach would have great potential impact to the chip design and fabrication industry.  Combining the expertise in the TCAD tool vendors, process and device modeling efforts, and a calibrated TCAD to a specific wafer fab, the virtual fab foundry will provide a guide to technology developers, a bridge between the wafer fab and the design house, and a dynamic solution to the future technologies and design methodologies.
 

SUMMARY

What has been discussed and proposed in this article is an alternative approach to the design and optimization of ultra-small transistors for the new deep-submicron technology development.  The central idea is to use the multi-level synthesis approach for application-specific problems in aiding new technology development.  The approach emphasizes on the multi-target optimization and speed/accuracy trade-off in providing trends with quantifiable accuracy for non-expert users.  It is not claimed that the proposed approach is better than other practices (such as full-loop calibration, hierarchical modeling, or process compilation), instead, the validity and relevance of the synthesis approach will be dependent upon simulator calibration and new physical models.  However, the proposed approach will be generic and dynamic, which can and must be adapted to new technologies as well as the accumulation of our knowledge.