CN1086039C - Method for defining processing-time target of estimated item - Google Patents
Method for defining processing-time target of estimated item Download PDFInfo
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- CN1086039C CN1086039C CN96101903A CN96101903A CN1086039C CN 1086039 C CN1086039 C CN 1086039C CN 96101903 A CN96101903 A CN 96101903A CN 96101903 A CN96101903 A CN 96101903A CN 1086039 C CN1086039 C CN 1086039C
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Abstract
The present invention relates to a method for determining a regression equation in order to design a production device, which comprises the following steps: data is input towards a computer; the data is utilized for determining the frequency distribution of batch processing time relevant to each batch; a plurality of groups of batch processing time is extracted form each frequency distribution by changing the extraction rate of data; the average processing time of each group of the batch processing time is calculated; a plurality of regression lines of the average batch processing time relevant to each batch are determined; the degree of each average batch processing time deviating from a corresponding value on each regression line; the deviation degree is utilized for selecting one regression line which is determined to represent the regression equation.
Description
The present invention relates to determine a kind of method of regression equation, this equation is very suitable for designing the process units of the numerous items in the batch that is used for processing different scales.Below in conjunction with IC (integrated circuit) manufacturing installation the present invention is discussed, but the present invention never is limited to this application.
As everyone knows, IC is included in the many microscopic regions on the wafer surface of transistor formed, diode etc.In planar technology, these zones are by the series of steps preparation, and each step is added to another floor in the selected district of wafer surface.Determine every layer form by the geometric scheme of representing circuit-design information, and be transferred on the wafer surface by the process that is called as photoetching.
Fig. 1 be a series of devices of being illustrated on the silicon wafer preparation IC (by A1, A2 ..., An ..., Az represents) synoptic diagram.Fig. 2 is that expression is processed the synoptic diagram of the mode of three wafers (a collection of) in proper order by the device An of for example Fig. 1.
Under the situation of making ASIC (application-specific integrated circuit), in order to satisfy client's various different requirements, each device of IC preparation section all is provided different batches usually.Scale in batches for example can be in one to tens scope.
The IC preparation facilities is made of various parts, and the situation of these parts is relevant with time factor, as wearing and tearing and aging.In addition, the IC preparation facilities is subjected to the influence of external disturbance such as ambient temperature variation, humidity etc.Therefore, change easily each different process time in batches.Yet the batch machining time is always by empirical estimating up to now, and therefore in order to design each IC preparation facilities, (quantitatively) estimation is unusual difficulties the different process times of scales in batches exactly.
Need no matter inside and outside interference is correctly estimated and processed in identical preparation facilities different process times in batches.
The purpose of this invention is to provide a kind of method of determining an index, this index can be estimated the different process times in batches that will process exactly in given preparation facilities.
One aspect of the present invention is a kind of method that adopts regression equation with the design process units, described process units is used for processing a plurality of projects of the batch of a plurality of different scales, described regression equation is estimated a plurality of process times of described a plurality of batches, said method comprising the steps of:
(a) measure process time of a plurality of batches of the described process units be used for described a plurality of batches;
(b) to computing machine input data, a plurality of process times of described data represented described a plurality of batches;
(c) utilize described data to determine the frequency distribution of the described batch machining time relevant with each described batch;
(d) by changing the data extract rate, extract many groups batch machining time from each frequency distribution;
(e) calculate the described average process time of organizing each group of batch machining times more;
(f) determine relevant with each batch average bulk many tropic of process time;
(g) determine that each average bulk departs from the degree of every analog value on the described tropic process time; With
(h) utilize described departure degree to select wherein described tropic, described selecteed wherein tropic is confirmed as described regression equation.
The features and advantages of the present invention will become by the description below in conjunction with accompanying drawing and be easier to understand, and part identical in the accompanying drawing represents with identical reference number, wherein:
Fig. 1 is the synoptic diagram of a series of IC preparation facilities of expression, and this figure has quoted at the beginning paragraph of instructions;
Fig. 2 is that expression is processed the synoptic diagram of the mode of three layer wafers by the device sequence of Fig. 1;
Fig. 3 is data (batch machining time) table that expression inputs to computing machine;
Fig. 4 is the process flow diagram that embodies the step of operating characteristics of the present invention;
Fig. 5 is the frequency distribution table of expression batch machining time;
Fig. 6 represents to correspond respectively to a plurality of frequency histograms of the frequency distribution of Fig. 5;
Fig. 7 is the table corresponding to the frequency distribution table of Fig. 5, and also represents to utilize the order of part batch machining time data in addition;
Fig. 8 represents to correspond respectively to histogrammic a plurality of frequency histograms of Fig. 5, and also represents to utilize the order of part batch machining time data in addition;
Every width of cloth figure among Fig. 9 to Figure 13 is illustrated in the data extract rate of discussing in the most preferred embodiment;
Figure 14 is the expression average bulk table of process time;
Figure 15 has listed many tropic (regression equation) of batch machining time;
Figure 16 lists the table that is in a plurality of batch machining times on the tropic shown in Figure 15; And
Figure 17 is the table that is used for finally determining regression equation (equation of the tropic).
Below with reference to Fig. 3-17 most preferred embodiment of the present invention is discussed.
Though describe the present invention by the process units (referring to Fig. 1 and 2) that the present invention is used for IC preparation order, the present invention never is limited to this application.
Only be for the content that exposes for simplicity, the number of supposing below the wafer batch gauge mould that will discuss is in one to five scope.Collected data, and before delivering to the computing machine (not shown), kept always in the expression batch machining time of given manufacturing installation.As an example, suppose that above-mentioned data are concentrated from device An (Fig. 1 and Fig. 2).For obtain being suitable for evaluating or design example as the information of device An, collected data a reasonable time section.
Prepare the example of the data of (collection) before having listed among Fig. 3.As shown in the figure, the sum of data (being batch machining time (the branch)) part of each batch scale 1-5 reaches 8,20,21,32 and 47 respectively.
Fig. 4 is the process flow diagram that embodies the step of operation of the present invention (being that data shown in Figure 3 are imported computing machine and are stored in operation later in the suitable storer) feature.
In Fig. 4,, utilize the data that are input to computing machine to determine five frequency distribution of the batch machining time relevant with each batch (scale in batches) in step 10.Determine that frequency distribution itself is well known in the art.Above-mentioned five frequency distribution are shown in Fig. 5 with the form of tabulation, and further illustrate with the represented as histograms of Fig. 6.
In step 12, extract many groups batch machining time (data division) from each frequency distribution (Fig. 5 and 6) by changing the data extract rate.In the present embodiment, by extraction ratio is changed to 20% downwards from 100% with 20% interval, extract data.
Describe the operation of step 12 in detail with reference to Fig. 7-13.
At first determine the highest frequency of five frequency distribution.Can clearly be seen that from Fig. 5 or Fig. 6 frequency 3,9,7,7 and 9 is respectively each maximal value of scale 1-5 in batches.In addition, the sum of the data division of each of definite relevant five frequency distribution (or directly determining) from the line data (Fig. 3) that is input to computing machine.The sum of data division and is represented on the right side of Fig. 6 as mentioned above.
After this, the order of the extraction frequency when determining to change the data extract rate.In order to carry out following calculating, extract highest frequency earlier.Then, two relatively more adjacent frequencies with highest frequency, and be elected to be second frequency to higher one and be added on the highest frequency.If above-mentioned two frequencies equate, then select the frequency of longer batch machining time.In addition, if a side of highest frequency presents " remainder according to ", then be assumed that an adjacent frequency near the frequency of highest frequency.This is applicable to that also the both sides of highest frequency all are the situations of empty (remainder certificate).
When determining the extraction order of two frequencies, these two frequencies are counted as one group (in other words, regard as if a frequency).Therefore, be appreciated that mentioned above principle is applicable to the extraction order of determining all the other frequencies.
In Fig. 7, expression each the data extract order of scale 1-5 in batches in the bracket.In addition, Fig. 7 is identical with Fig. 5.
It is illustrative that above-mentioned relevant regulations are selected the principle of the order of frequency, can change in order more suitably to extract data.For example, there are two same frequencys, therefrom selecting to select the frequency of shorter batch machining time under the situation of conduct frequency formerly.
In Fig. 8, also expression each the data extract order of scale 1-5 in batches.In addition, Fig. 8 is identical with Fig. 6.
Fig. 9-13 represents data extract rate 100%, 80%, 60%, 40% and 20% respectively.Shown in Fig. 9-13, the frequency of shaded bar is extracted or is used for calculating average bulk process time in step 14.
At first from suitable storer, extract or retrieval total data (i.e. 100% data extract), be coated with top shadow so in Fig. 9, will represent all bars of frequency.Average bulk is calculated as follows process time.The frequency of each extraction be multiply by the corresponding batch machining time.Then with the product addition of gained, and the sum that is extracted frequency is removed.As an example, under the situation of 100% data extract (scale is one in batches):
[(1×1)+(1×2)+(2×3)+(3×4)+(1×5)]/8＝3.25
The average bulk that data extract rate according to 100% (in batches scale 1-5) is calculated is listed in Figure 14 process time.
Get back to the data extract rate and be 80% situation (Figure 10).Be under one (1) the situation in the batch scale, the sum of data division (promptly 8) multiply by coefficient 0.8 (80%), so obtain product 6.4.The first frequency (being highest frequency (3)) that this product and grade is the highest compares, so that carry out addition (Fig. 7 and 8).Because this product is greater than first frequency, so this product further with by the numerical value that the frequency of second grade (promptly 2) and first frequency addition are obtained compares.Above-mentioned product (promptly 6.4) still greater than with (3+2=5).Like this, this product is also further with next and (3+2+1=6) compare.Under above situation, this product (promptly 6.4) is still greater than this and (promptly 6), then further make addition, obtain one new with (3+2+1+1=7).In this case and since product less than with, so the number of specified data part is 7, that it equals to mention just now and.By the summation, with above-mentioned product continuously with gained and compare, up to product less than last and.
Above-mentioned discussion is applicable to that also scale is the situation (Figure 10) of 2-5 in batches, and is applicable to also that further the data extract rate is 60%, 40% and 20% situation (Figure 11-13).
The average bulk of calculating is like this listed in Figure 14 process time.
In step 16, under situation, determine five tropic after this about each average bulk process time of as shown in figure 14 batch scale 1-5.Obtain five tropic like this and be shown in (a)-(e) part among Figure 15.In Figure 15, average bulk is drawn with stain in corresponding figure process time.The method of determining the tropic is well known in the art, and therefore the description to it is unnecessary, is omitted in order to simplify disclosed content spy.
Next in step 18, determine the batch machining time on each tropic of being in as shown in figure 16.Then as shown in figure 17, determine bias ratio, each bias ratio is represented average bulk process time of calculating and the deviation of the corresponding process time on the tropic.
By obtained bias ratio divided by the corresponding process time (Figure 16) on the tropic average process time (Figure 14), the merchant of gained subtracts 1 then.After this, determine to belong to the minimum and maximum value (Figure 17) among each the bias ratio of five data extraction ratios.Again with the absolute value addition of minimum and maximum value, determine minimum then and.In this example, data extract rate is 40% o'clock 0.32 minimum.Therefore, the regression equation (referring to Figure 15) of selecting data extract rate 40% is as being used for the regression equation of design apparatus An.
In above-mentioned discussion, the data extract rate is made as 100%, 80%, 60%, 40% and 20%.Yet, much less can determine the number of extraction ratio arbitrarily.
Should understand above-mentioned disclosed content and only represent a feasible embodiment of the present invention, the present invention based on notion be not limited to this.
Claims (4)
1. method that adopts regression equation with the design process units, described process units is used for processing a plurality of projects of the batch of a plurality of different scales, and described regression equation is estimated a plurality of process times of described a plurality of batches, said method comprising the steps of:
(a) measure process time of a plurality of batches of the described process units be used for described a plurality of batches;
(b) to computing machine input data, a plurality of process times of described data represented described a plurality of batches;
(c) utilize described data to determine the frequency distribution of the described batch machining time relevant with each described batch;
(d) by changing the data extract rate, extract many groups batch machining time from each frequency distribution;
(e) calculate the described average process time of organizing each group of batch machining times more;
(f) determine relevant with each batch average bulk many tropic of process time;
(g) determine that each average bulk departs from the degree of every analog value on the described tropic process time; With
(h) utilize described departure degree to select wherein described tropic, described selecteed wherein tropic is confirmed as described regression equation.
2. the method for claim 1 is characterized in that, step (c) comprising:
Determine described many group batch machining times from each described frequency distribution one is extracted grade; With
Change the data extract rate by a predetermined value.
3. the method for claim 1 is characterized in that, a minimum departure degree in the departure degree of determining in the described wherein tropic rendering step (g) of selecting in step (h).
4. the method for claim 1 is characterized in that, it is further comprising the steps of:
(i) design described device and process described a plurality of project according to described selected wherein tropic.
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN96101903A CN1086039C (en) | 1996-01-19 | 1996-01-19 | Method for defining processing-time target of estimated item |
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| CN96101903A CN1086039C (en) | 1996-01-19 | 1996-01-19 | Method for defining processing-time target of estimated item |
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| CN1155124A CN1155124A (en) | 1997-07-23 |
| CN1086039C true CN1086039C (en) | 2002-06-05 |
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Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0624847A1 (en) * | 1993-05-12 | 1994-11-17 | Laboratoires D'electronique Philips S.A.S. | Device and method to generate an approximating function |
| US5446681A (en) * | 1990-10-12 | 1995-08-29 | Exxon Research And Engineering Company | Method of estimating property and/or composition data of a test sample |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5446681A (en) * | 1990-10-12 | 1995-08-29 | Exxon Research And Engineering Company | Method of estimating property and/or composition data of a test sample |
| EP0624847A1 (en) * | 1993-05-12 | 1994-11-17 | Laboratoires D'electronique Philips S.A.S. | Device and method to generate an approximating function |
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