Data processing: structural design – modeling – simulation – and em – Simulating electronic device or electrical system – Software program
Reexamination Certificate
1999-05-03
2002-04-30
Frejd, Russell W. (Department: 2123)
Data processing: structural design, modeling, simulation, and em
Simulating electronic device or electrical system
Software program
C703S002000, C703S013000, C700S030000, C700S031000
Reexamination Certificate
active
06381564
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to a method and system for providing optimal tuning for complex simulators.
2. Brief Description of the Prior Art
In the fabrication of semiconductor devices, there are many standard steps required to be performed to fabricate the completed device, such as, for example, doping, deposition, fabrication of the various metal and/or semiconductor layer and other steps. While the physical phenomena involved in many of these steps are well understood, this is not the case for all of the physical phenomena involved, some of the physical phenomena involved not being so well understood.
With the ever-increasing cost of manufacturing full-flow semiconductor devices, there is a great effort to reduce the number of semiconductor wafers used in developing new technologies, one such effort involving performance of process and device simulations to replace fabrication of the semiconductor wafers themselves. However, in order for this method to be useful, the simulations must accurately predict the actual results that would occur if the devices were to be manufactured and measured.
Furthermore, both the process and device simulators of the prior art have several deficiencies that result in poor predictive capability with the data being approximately 2.5 orders of magnitude below the simulation data, such results being clearly unacceptable for prediction purposes. As a result of this type of inaccuracy, simulation has been relegated to providing “trend” information that is used to aid in the design of experiments on real wafers instead of actually replacing fabrication of those wafers.
For this reason, complex simulators, such as semiconductor process and device simulators, often have to be “tuned” so that they can predict real-world data. The reasons for this are that many of the physical constants that the simulators use are not known exactly a priori and that the simulators often do not capture all of the physical phenomena involved. Tuning of these simulators requires determination of the correct values for the tunable parameters in the simulators such that the simulator can predict real-world data. Since each run of the simulator is expensive in terms of time and resources, the number of runs required to tune the simulators must be minimized. Additional problems arise from the presence of multiple objectives in the tuning (which gives rise to nonlinear objective functions). Known methodologies for tuning generally involve optimizing the tuning parameters by directly running the simulator (i.e., the simulator is in the optimization loop) The problems resulting from the prior art of the type described above are that the nonlinear objective functions lead to local minima, the expense of running simulations inhibits the use of global optimizers that can escape from local minima, advantage cannot be taken of job farming and multiple evaluations of the gradient are required (expensive for high dimensions).
“The most basic prior art system places the simulator in the loop along with the optimizer with the objective function being derived by operation on the output of the simulator and experimental data such as is shown in FIG.
1
. There is shown typical prior art simulating circuitry which is a closed loop containing an objective function device
1
, typically a summing amplifier, an optimizer
3
which is typically a gain stage and a simulators
5
which is an unknown circuit. The output of the simulator
5
and experimental data are both fed to the objective function device
1
which provides an error signal at its output, such as by sum squared difference or other appropriate well known procedure. This output is optimized by the optimizer
3
, in well known manner, and fed to the simulator
5
. The simulator
5
utilizes the output of the optimizer
3
in its circuit to provide the output which is fed to the object function device
1
. The output of the simulator is altered by altering one or more of the parameters measured therein when there is an error until the error is zero. The simulations require a great deal of time. Problems with this prior art system are that the operation is serial in nature, requires an unknown number of simulations which affect speed and the quality of the solution depends upon the starting point with the system, on occasion, not finding a solution at all. It follows that the prior art system is not very thorough and it is apparent that a system which will provide the same result on a more rapid basis is highly desirable.”
A further prior art system replaces both the simulator and the objective function with a response-surface model (RSM) and is shown in
FIG. 2
with optimization taking place as shown in FIG.
3
. This system is described in a paper of Gilles Le Carval et al. entitled
Methodology For Predictive Calibration of TCAD Simulators
, Proceedings of 1997 International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), pp. 177-180 (1997), sponsored by IEEE, the contents of which are incorporated herein by reference, wherein there is a proposal to obtain a set of calibrated model parameters for predictive simulations. This methodology associates Design of Experiments (DOE) with Response Surface Method (RSM) and also advanced concepts of statistical analysis: D-optimal filtering and Taguchi's method. It has the characteristics of insensitivity to process conditions, optimal use of existing experimental results, rigorous statistical analysis of the data and clever selection of the model parameters. A problem with this system is that the method attempts to model the objective function (based upon those outputs and the experimental data) instead of modeling the functions themselves. In order to calculate the error signal, the square root of the sum of the squares of the target value (a low frequency signal) of each response minus the measured value must be calculated, this providing a very complex (high frequency) result. The prior art has attempted to model this complex result directly. It follow that when this complex result is compared with the experimental data received, which is much less complex (low frequency), a great deal of data is lost with the concomitant results of such data loss. By combining the simulator and data into the RSM, statistical analysis of tuning is not possible as can be demonstrated since, in general, the amount of noise in the coefficients can not be determined by the prior art and especially by the system and method described by Carvel et al.
SUMMARY OF THE INVENTION
In accordance with the present invention, the error is made to be the objective function of the RSM of the inputs rather than having the error signal being the RSM of the inputs or parameters as in the Le Carval method described above. Therefore, the RSMs, which replace the simulator, are the inputs that are received from the simulator, thereby retaining the high frequency behavior much more accurately and making the system more extensible in that, if the experimental data is now changed, such as tuning to another set of data over the same region of parameters, the experimental data need merely be replaced with subsequent recalculation. Furthermore, the RSMs in accordance with the present invention are independent of the experimental data whereas the prior art RSMs are dependent upon the experimental data. Therefore, the prior art must rebuild its models with any change in experimental data. Accordingly, the system in accordance with the present is more accurate than are prior art systems and independent of experimental data. In addition, the methodology in accordance with the present invention has broader applicability due to modeling the low frequency outputs of the simulator rather than the high frequency objective function.
Briefly, there is provided a general coherent methodology for tuning simulators to experimental data. With this methodology, excellent matches between simulated and experimental data are achieved to within one percent. The initial phase
Burch Richard G.
Davis Joseph C.
Fernando Chenjing L.
Mozumder Purnendu K.
Rao Suraj
Brady III Wade James
Frejd Russell W.
Telecky , Jr. Frederick J.
Texas Instruments Incorporated
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