JPH04239976A - Parameter extracting system - Google Patents

Abstract

PURPOSE:To freely select a measurement data point and to extract a parameter which is appropriate to the sensitivity of the parameter without the necessity of special knowledge or experience as against an analysis type having the new parameter. CONSTITUTION:A sensitivity calculation part 2 calculates the sensitivity of the parameter as against respective data points, a high sensitivity area definition part 3 and a data block definition part 4 define data blocks divided by the boundary of a high sensitivity area at every parameter, a extraction parameter decision part 5 sequentially extract the value of the high sensitivity parameter which is extracted from the data block where there are high sensitivity parameters whose value is extracted and inputs them to a parameter pickup part 6.

Description

[Detailed description of the invention]

0001

[Industrial Field of Application] The present invention is applied to a parameter extraction system for automatically modeling numerical data obtained through measurements or the like using analytical formulas. The present invention particularly relates to a device model parameter extraction system necessary for circuit simulation of semiconductor devices.

0002

[Prior Art] Determining the parameter values of an analytical model formula so that measured data such as current-voltage characteristics of a transistor can be accurately represented by the analytical model formula is extremely important in order to increase the reliability of circuit simulation. It is a great technology.

FIG. 4 is a block diagram showing an example of such a conventional parameter extraction system, and FIG. 5 is a flowchart showing its operation. With the measured data 1 as input, the extraction parameter selection unit 17 determines the parameters to be extracted and the data area to be extracted (step S11), and the model formula calculation unit 18 calculates an analytical formula for each data point (step S12). ), the error evaluation section 19 compares the input measurement data with the calculated value using the analytical formula (step S
13) If the error between the two exceeds the allowable value, the parameter value changing unit 20 changes the value of the extracted parameter.
(Steps S14, S15) The processing of the model formula calculation unit 18→error evaluation unit 19→parameter value change unit 20 is performed until the error falls within the allowable value, and as a result, model parameter set 7 is obtained.

In FIG. 4, each process of the model formula calculation section 18, error evaluation section 19, and parameter value change section 20 is as follows.
It can be reduced to a multivariable optimization problem, and general mathematical methods exist. However, since there are usually about 10 to 20 parameters of a device model used in circuit simulation, for example, it is not practical to optimize all of these parameters at once. Generally, in multivariable optimization, as the number of extracted parameters increases,
Not only does it take a long time to calculate, but in many cases the optimization process does not converge or reaches a locally optimal solution.
The extracted parameter values tend to converge to meaningless values considering the physical background of the analytical formula.

Therefore, the extraction parameter selection section 17 in FIG.
In this, the parameters to be extracted and the data area are limited in advance, but the extraction parameter extraction unit 1
The processing required in step 7 is not limited to the input measurement data.
There is no general method because it depends on the properties of the analytical model formula. As a conventional technique, there is a method in which parameters are grouped in advance for a specific model formula, and areas of data points on which the parameters of each group can be considered to have a strong influence are programmed. (Ebrahim Kahaleri “An Interactive
Device characterization and
Model Development Systems,” International Conference on Computer Aided Design, EbrahimKha.
lily etal “An interactive
device characterization a
nd model development system
em” International conference
nce On Computer Aided Des
ign 1984, P149-151).

[0006]

[Problems to be Solved by the Invention] In the conventional parameter extraction system described above, the selection of extraction parameters and the extraction data area are programmed in advance, so the area of measured data points cannot be arbitrarily selected as the target area. There were drawbacks. In addition, in particular, model equations for semiconductor devices may need to be improved or changed due to rapid advances in process and device technology, but conventional programmed extraction parameter selection processing It has the disadvantage that it is difficult to respond flexibly to changes in the formula. In addition, even if we try to develop a new extraction parameter selection method that corresponds to a new model formula, it is important to know how to combine parameters that are correlated with each other and to determine the extraction data area, which requires extensive experience and The drawback was that it required deep knowledge.

An object of the present invention is to eliminate the above-mentioned drawbacks so that measurement data points can be freely selected, and model equations with new parameters can be applied without the need for special knowledge or experience. The object of the present invention is to provide a parameter extraction system that can extract parameters that match the sensitivity of the parameters.

[0008]

[Means for Solving the Problem] The present invention provides a parameter extraction system that applies selected parameters to an analytical formula, performs error evaluation, and extracts parameters whose error is within a specified value. For each data point in the point sequence, there is a sensitivity calculation unit that calculates the sensitivity of the parameter of the analytical formula that expresses the point sequence data as a rate of change in the parameter value, and a sensitivity calculation unit that calculates the independent variable area of the highly sensitive data point sequence for each parameter. a data block definition unit that associates a data block of a data point sequence divided by a boundary of a high sensitivity region of each parameter with a set of highly sensitive parameters within each data block; Starting from a data block with a small number of high-sensitivity parameters whose values have not yet been extracted, the values of unextracted high-sensitivity parameters are sequentially extracted using the data point sequence within the data block.
The apparatus is characterized by comprising an extraction parameter determination section that outputs an output to the parameter extraction section.

[0009]

[Operation] For each data point in the numerical data point sequence, the sensitivity of the parameter of the analytical formula that expresses the point sequence data is determined as the rate of change in the parameter value, and each parameter is determined as a highly sensitive data point sequence. Define a highly sensitive data point sequence independent variable region for each parameter. Then, by associating blocks of data point sequences divided by the boundaries of the high-sensitivity regions of each parameter with sets of high-sensitivity parameters within each data block, data with a small number of high-sensitivity parameters whose values have not yet been extracted is created. Values of unextracted high-sensitivity parameters are sequentially extracted from each block based on the data point sequence within the data block, and output to the parameter extraction section.

Therefore, for a given data point sequence,
Selection of extraction parameters and determination of extraction data area can be performed automatically, measurement data points can be freely selected, and analytical formulas with new parameters can be developed without the need for special experience or knowledge. It becomes possible to extract parameters that match the sensitivity of the parameters.

[0011]

Embodiments Hereinafter, embodiments of the present invention will be described with reference to the drawings.

FIG. 1 is a block diagram showing an embodiment of the present invention. This embodiment is a parameter extraction system equipped with a parameter extraction unit 6 that applies selected parameters to an analytical formula, performs error evaluation, extracts parameters whose error is within a specified value, and outputs a parameter set 7.

A feature of the present invention is that the measurement data 1 is input, and for each data point of the numerical data point sequence, the sensitivity of the parameter of the analytical formula expressing the point sequence data is calculated as the rate of change of the parameter value. A sensitivity calculation unit 2 to seek, a high sensitivity region definition unit 3 that defines an independent variable region of a highly sensitive data point sequence for each parameter, and a data block of a data point sequence divided by the boundary of the high sensitivity region of each parameter. and a data block definition unit 4 that associates a set of highly sensitive parameters within each data block, and a data block definition unit 4 that associates a set of highly sensitive parameters in each data block, and a data block definition unit 4 that associates each data block with a set of highly sensitive parameters in each data block. The extraction parameter determination section 5 extracts the values of unextracted high-sensitivity parameters and outputs them to the parameter extraction section 6.

Next, an embodiment of the present invention will be described with reference to the flowchart shown in FIG. With respect to the measurement data 1, the sensitivity calculation section 2 calculates the change in the calculated value of the analytical formula with respect to the change in the parameter value at each data point to obtain the sensitivity of the parameter (step S1), and the high sensitivity region determination section 3 In step S2, a region of data points whose sensitivity is equal to or higher than a certain value for each parameter is defined as a high-sensitivity region (step S2), and the data block definition unit 4 defines data points divided by the boundaries of the high-sensitivity region of each parameter. A column block and a set of high-sensitivity parameters within the block are determined (step S3), and the extraction parameter determination unit 5 determines the data block and parameters to be extracted next (step S4). In,
By executing parameter extraction by multivariable optimization (step S5) and repeating steps S4 and S5 until all parameter extraction is completed (step S
6), obtain parameter set 7.

In FIG. 1, the contents of the parameter extraction section 6 are the same as in the conventional example shown in FIG.

[0016] Below, the operation of the sensitivity calculation unit 2 to extraction parameter determination unit 5 will be explained as shown in FIGS. 3(a) to 3(d).
Please refer to for further details. As an example, consider a case where four parameters P1, P2, P3, and P4 of the analytical formula f are extracted from measurement data consisting of two-dimensional independent variables x1 and x2. Sensitivity calculation unit 2 in Figure 1
Then, the sensitivity Si of each data point is S1 = f(P1
+Δ1,P2,P3,P4) -f(P1,P2,P
3, P4 )/Δi, etc. here,
Δi represents a minute change to the parameter Pi.

Next, the high-sensitivity region determination unit 3 determines a data region in which the sensitivity Si is equal to or greater than a certain value for each parameter Pi. FIG. 3(a) shows an example of high-sensitivity regions determined in this way, and high-sensitivity regions 8 to 11 are shown.

Next, the data block definition unit 4 defines data areas delimited by the boundaries of each high sensitivity area 8 to 11;
The high-sensitivity parameters within that region are associated with each other. Figure 3 (
b) is the data block 12~ obtained in this way
16 and high sensitivity parameters within each data block.

Next, the extraction parameter determining section 5 selects the data block 12 as the data block with the least number of high-sensitivity parameters, and the parameter extracting section 6 determines the value of the parameter P4 within this data area. As a result, the relationship between each data block and the high sensitivity parameter is
The result will be as shown in Figure 3(c). Since parameter P4 has been determined, the number of high-sensitivity parameters in data blocks 13 to 16 is decreased one by one. In addition, Fig. 3(c) ~(
The shaded area in d) indicates the data block for which parameter extraction has been completed.

In the state shown in FIG. 3(c), data block 1
Since the high-sensitivity parameters are the minimum in data blocks 3 and 14, parameters P2 and P3 are extracted from these data blocks. This results in data block 15 as shown in Figure 3(d).
All parameters are determined by extracting parameter P1 in this region.

[0021] Through the above procedure, each parameter can be extracted only in a data area with higher sensitivity, and extraction can be performed in order of parameters that are least affected by other parameters.

[0022]

As explained above, the present invention automatically selects extraction parameters and determines the extraction data area for a given data point, so measurement data points can be freely selected. Furthermore, even for model formulas with new parameters, it is possible to extract parameters that match the sensitivity of the parameters without requiring special experience or knowledge.

[Brief explanation of the drawing]

FIG. 1 is a block configuration diagram showing one embodiment of the present invention.

FIG. 2 is a flowchart showing the operation.

FIG. 3 is an explanatory diagram showing an example of parameter extraction in this embodiment.

FIG. 4 is a block configuration diagram showing a conventional example.

FIG. 5 is a flowchart showing the operation.

[Explanation of symbols]

1 Measurement data 2 Sensitivity calculation section 3 High sensitivity area definition section 4 Data block definition section 5 Extraction parameter determination section 6 Parameter extraction section 7 Parameter set 8-11 High sensitivity area 12-16 Data block 17 Extraction parameter selection section 18 Model formula calculation section 19 Error evaluation section 20 Parameter value change section

Claims (1)

[Claims] [Claim 1] A parameter extraction system equipped with a parameter extraction unit that applies selected parameters to an analytical formula, performs error evaluation, and extracts parameters whose error is within a specified value. ,
a sensitivity calculation unit that calculates the sensitivity of a parameter of an analytical formula expressing the point sequence data as a rate of change in the parameter value; a high sensitivity region definition unit that defines an independent variable region of the highly sensitive data point sequence for each parameter; A data block definition part that associates a data block of a data point sequence divided by the boundary of a high sensitivity region of each parameter with a set of highly sensitive parameters in each data block, and a high sensitivity parameter whose value is not yet extracted. and an extraction parameter determination unit that sequentially extracts values of unextracted high-sensitivity parameters based on data point sequences in the data blocks starting from a data block with a small number of data blocks, and outputs the values to the parameter extraction unit. parameter extraction system.