Classifications

• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01L—SEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
  • H01L22/00—Testing or measuring during manufacture or treatment; Reliability measurements, i.e. testing of parts without further processing to modify the parts as such; Structural arrangements therefor
  • H01L22/20—Sequence of activities consisting of a plurality of measurements, corrections, marking or sorting steps
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01J—ELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
  • H01J37/00—Discharge tubes with provision for introducing objects or material to be exposed to the discharge, e.g. for the purpose of examination or processing thereof
  • H01J37/32—Gas-filled discharge tubes
  • H01J37/32917—Plasma diagnostics
  • H01J37/32935—Monitoring and controlling tubes by information coming from the object and/or discharge
• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01L—SEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
  • H01L2924/00—Indexing scheme for arrangements or methods for connecting or disconnecting semiconductor or solid-state bodies as covered by H01L24/00
  • H01L2924/0001—Technical content checked by a classifier
  • H01L2924/0002—Not covered by any one of groups H01L24/00, H01L24/00 and H01L2224/00

Definitions

• the present invention relates to a method and a processing apparatus for predicting a processing result of an object to be processed such as a wafer to be processed in a semiconductor manufacturing apparatus or an apparatus state.
• a processing apparatus such as a plasma processing apparatus is widely used in a film forming step and an etching step of an object to be processed such as a semiconductor wafer and a glass substrate.
• Each processing apparatus has its own process characteristics for the object to be processed.
• an object to be processed for example, a semiconductor wafer
• an etching process using an individual processing apparatus, for example, a test wafer is prepared in advance, and the test wafer is periodically subjected to the etching process.
• the state of the processing equipment at each time is determined based on the processing results (eg, the amount of test wafer scraping).
• the method of judging the state of the processing equipment at each time on the basis of test wafers requires the production of many test wafers.
• many test wafers must be processed using the processing equipment, and each processing result must be measured. Therefore, much man-hours and time are not required for producing test wafers and measuring the processing results. Must not There was a problem.
• Japanese Patent Application Laid-Open No. 10-125660 proposes a process monitoring method for a plasma processing apparatus.
• This method uses a test wafer to create a model equation that correlates the electrical signal that reflects the plasma state with the plasma processing characteristics using a trial wafer, and then uses the model equation to detect the detected electrical signal obtained when the actual wafer is processed. To predict the plasma processing characteristics.
• this method is excellent in that it can predict the plasma processing characteristics, it performs high-precision prediction in actual wafer processing, which includes lot fluctuation over time and sudden changes in the state of application of high-frequency power. Is not enough, and further improvement is needed.
• the present invention has been made in view of the above-mentioned problems of the conventional technology, and a process characteristic prediction equation is obtained by collecting only a small number of operation data and process characteristic data obtained by processing a small number of samples. (Model) can be obtained, and then a processing result prediction method and processing device that can easily and accurately predict the process characteristics simply by applying the operation data when processing the object to be processed to the prediction formula. It is intended to provide.
• a processing apparatus such as a plasma processing apparatus.
• Collecting the operation data and the processing result data the step of performing a multivariate analysis based on the data group; and the correlation between the operation data and the processing result data through the multivariate analysis).
• a processing device such as a plasma processing device, for predicting a processing result based on the operation data and the processing result data in a process of processing the data one by one (for example, an etching process).
• the processing apparatus can be obtained by processing a small number of samples.
• the correlation between the operating data and the processing result data (for example, a prediction formula such as a regression formula) can be obtained by multivariate analysis. After that, the processing results of the object can be predicted simply and with high accuracy simply by applying the operating data when the object is processed to the correlation.
• the multivariate analysis is configured to perform multiple regression analysis, the multiple regression analysis makes it easy to obtain a regression equation that is the correlation between operating data and processing result data even for a large number of variable data. it can.
• the relational expression that is the correlation between the operation data and the processing result data can be easily obtained even for a large number of variable data.
• the operation data may include data of a temperature of a mounting table on which the object is mounted, and may further include data of a back gas pressure. Since the operation data easily affects the processing result data (there is a correlation) and includes the mounting table temperature data and the back gas pressure data, the accuracy of the processing result prediction can be improved.
• the operation data may include standard deviation data of the back gas pressure (for example, the back side gas pressure of He gas or the like), and the in-plane pressure difference of the object to be processed with the back gas pressure (for example, the center of the back gas, Data such as the pressure difference between three systems, middle and edge). Since the standard deviation of the back gas pressure indicates the stability of the back gas pressure, it is highly useful for predicting the in-plane uniformity of the amount of wafer W scraped as processing result data of the workpiece. Accuracy can also be improved. Further, the operation data may include at least data of the voltage of the high frequency power supply applied when processing the object to be processed, and may include at least data of the integrated operation time of the high frequency power supply.
• both the data of the voltage of the high frequency power supply and the data of the integration operation of the high frequency power supply may be included.
• These high-frequency power supply voltage data and high-frequency power supply integrated operation time data are highly useful especially for predicting the amount of wafer W scraping (eg, Etchingle net) as processing result data for the object to be processed. Accuracy can also be improved.
• the integrated operation time of the high frequency power supply may be reset to zero every time the maintenance of the processing chamber is performed.
• the integration time of the high-frequency power applied to the trace data for example, (1) the integration time of the application is set to zero each time maintenance such as jet cleaning is performed, so it is possible to obtain the integration time of the application for each wet cleaning cycle. it can.
• the processing result data is the processing amount data of the etching object including the shaving amount data of the processing object or the in-plane uniformity of the shaving amount data.
• the processing result of the target object related to the etching including the data of the shaving amount of the body or the data of the in-plane uniformity of the shaving amount may be used.
• FIG. 1 is a sectional view showing a processing apparatus according to a first embodiment to which a prediction method according to the present invention is applied.
• FIG. 2 is a block diagram showing an example of the multivariate analysis device according to the embodiment.
• FIG. 3 is a graph showing the temporal change of the upper electrode temperature obtained by the multivariate analyzer shown in FIG.
• FIG. 4 is a graph showing the change over time of the wall temperature of the processing chamber obtained by the multivariate analyzer shown in FIG.
• FIG. 5 is a graph showing the change over time of the lower electrode temperature obtained by the multivariate analyzer shown in FIG.
• FIG. 6 is a graph showing the change over time of the standard deviation of the He gas pressure obtained by the multivariate analyzer shown in FIG.
• Fig. 7 shows the voltage of the high-frequency power source obtained with the multivariate analyzer shown in Fig. 2. It is a graph which shows a temporal change.
• FIG. 4 is a graph showing the change over time of the wall temperature of the processing chamber obtained by the multivariate analyzer shown in FIG.
• FIG. 5 is a graph showing the change over time of the lower electrode temperature obtained by the multivariate analyzer shown in FIG.
• FIG. 6 is a graph showing the change over time of the standard
• FIG. 8 is a graph showing the change over time in the in-plane uniformity of the abrasion amount of the silicon oxide film of the wafer W obtained by the multivariate analyzer shown in FIG.
• FIG. 9 is a graph showing predicted values and measured values of the process characteristic data obtained by the multivariate analyzer using the operation data and the process characteristic data of FIGS.
• FIG. 10 is a graph showing a correlation between a predicted value and an actually measured value obtained by the same embodiment.
• FIG. 11 is a sectional view showing a processing apparatus according to a second embodiment to which the prediction method according to the present invention is applied.
• FIG. 12 is a block diagram showing an example of the multivariate analyzer according to the embodiment.
• FIG. 13 is a graph showing the relationship between the etching rate of the CVD oxide film on the wafer W and the number of processed wafers obtained by the multivariate analyzer shown in FIG.
• Fig. 14 (a) is a graph showing the predicted and measured values of the etching rate without pretreatment using optical data as the operation data.
• Fig. 14 (b) is the predicted and measured values.
• 6 is a graph showing the correlation of the above.
• Figure 15 (a) is a graph showing the predicted and measured values of the etching rate without pretreatment, using optical data and trace data as the operation data
• Figure 16 (a) is a graph showing the predicted and measured values of the etching rate without pre-processing, using trace data as the operation data.
• Figure 16 (b) is the predicted and measured values. It is a graph which shows the correlation of.
• Figure 17 (a) is a graph showing the predicted and measured values of the etching rate without pretreatment using VI probe data as the operation data, and
• Figure 17 (b) is the graph showing the predicted value and the measured value. This is a graph showing the correlation between the measured values.
• Figure 18 (a) is a graph showing the predicted and measured values of the etching rate when the optical data was used as the operating data and the pretreatment by OSC was performed, and
• Figure 18 (b) is the predicted value and the measured value. This is a graph showing the correlation between the measured values.
• Fig. 19 (a) is a graph showing the predicted and measured values of the etching rate when preprocessing by OSC is performed using optical data and trace data as operating data. Is a graph showing the correlation between predicted and measured values.
• Figure 20 (a) uses trace data as operating data
• the OCS Fig. 20 (b) is a graph showing the predicted value and the measured value of the etching rate when the pretreatment is performed by Fig. 20,
• Fig. 20 (b) is a graph showing the correlation between the predicted value and the measured value.
• Figure 21 (a) is a graph showing the predicted and measured values of the etching rate when pre-treatment with OcS was performed using the VI probe data as the operation data
• Figure 21 (b) is the predicted value.
• Figure 22 (a) is a graph showing the predicted and measured values of the etching rate when preprocessing by SNV is performed using optical data as the operation data.
• Figure 22 (b) is the predicted and measured values. This is a graph showing the correlation between the two.
• Fig. 23 (a) is a graph showing the predicted and measured values of the etching rate when preprocessing by SNV is performed using optical data and trace data as the operation data.
• Fig. 23 (b) is the graph showing the predicted values and the measured values. It is a graph which shows the correlation of a measured value.
• Figure 24 (a) is a graph showing the predicted and measured values of the etching rate when preprocessing by SNV was performed using trace data as the operating data.
• Figure 24 (b) shows the correlation between the predicted and measured values. It is a graph showing the relationship.
• Figure 25 (a) shows the predicted and actual measured etching rates in the case of pretreatment by SNV using VI probe data as operation data.
• Fig. 25 (b) is a graph showing the correlation between the predicted value and the measured value.
• Figure 26 (a) is a graph showing the predicted and measured values of the etching rate when the optical data was used as the operating data and the pretreatment was performed by MSC, and
• Figure 26 (b) is the predicted and measured values. This is a graph showing the correlation between values.
• Figure 27 (a) is a graph showing the predicted and measured values of the etching rate when preprocessing by MSC is performed using optical data and trace data as the operation data.
• Figure 27 (b) is the predicted and measured values. 6 is a graph showing the correlation between the two.
• Figure 28 (a) is a graph showing the predicted and measured values of the etching rate when preprocessing by MSC was performed using trace data as the operation data.
• Figure 28 (b) shows the correlation between the predicted and measured values. It is a graph showing the relationship.
• Fig. 29 (a) is a graph showing the predicted and measured values of the etching rate when pretreatment by MSC was performed using VI probe data as the operation data
• Fig. 29 (b) is a graph of the predicted and measured values.
• FIG. 30 is a table summarizing the prediction error PE from the experimental results in each of FIGS. 14 to 29 (a).
• Fig. 31 is a table summarizing the correlation coefficient R based on the experimental results in Figs. 14 to 29 (b).
• Figure 32 is a table summarizing the influence variables VIP on the prediction results for each type of data in the trace data.
• Figure 33 (a) is a graph showing the predicted and measured values of the etching rate when using data obtained by removing only the high-frequency voltage Vpp from the trace data
• Figure 33 (b) is the graph showing the predicted and measured values. It is a graph which shows the correlation of a value.
• Figure 34 (a) is a graph showing the predicted and measured values of the etching rate when using data obtained by removing only the integration time of high-frequency power from the trace data.
• Figure 34 (b) shows the predicted value.
• 6 is a graph showing a correlation between a value and an actually measured value.
• Figure 35 (a) is a graph showing the predicted and measured values of the etching rate when data excluding the high-frequency voltage Vpp and the high-frequency power application time from the trace data is used. ) Is a graph showing the correlation between the predicted value and the measured value.
• processing apparatus 10 a magnetron reactive etching apparatus (hereinafter, referred to as "processing apparatus 10") will be described as a plasma etching apparatus according to the first embodiment.
• this processing apparatus 10 is made of an aluminum processing chamber 1 and an ascending and descending aluminum supporting the lower electrode 2 disposed in the processing chamber 1 via an insulating material 2A.
• a shower head (hereinafter, also referred to as an “upper electrode” as necessary) which is disposed above the support 3 and supplies a process gas and also serves as an upper electrode.
• the upper part of the processing chamber 1 is formed as a small-diameter upper chamber 1A, and the lower part is formed as a large-diameter lower chamber 1B.
• the upper chamber 1A is surrounded by a dipole ring magnet 5.
• the dipole ring magnet 5 has a plurality of anisotropic segmented columnar magnets accommodated and arranged in a ring made of a ring-shaped magnetic material, and faces in one direction as a whole in the upper chamber 1A. Form a uniform horizontal magnetic field.
• An entrance for loading and unloading the wafer W is formed in the upper part of the lower chamber 1B, and a gate valve 6 is attached to this entrance.
• a high-frequency power source 7 is connected to the lower electrode 2 via a matching device 7A, and a high-frequency power of 13.56 MHz is applied from the high-frequency power source 7 to the lower electrode 2 to make the upper chamber 1A Thus, a vertical electric field is formed with the upper electrode 4.
• a matching device (not shown) for measuring the high frequency (RF) voltage V pp on the lower electrode 3 side (high frequency voltage output side) is provided in the matching device 7A.
• a power meter 7B is connected to the matching device 7A and the lower electrode 2 side (high-frequency power output side).
• the high frequency power P from the high frequency power supply 7 is measured by the power meter 7B.
• a magnetron discharge is generated by the electric field from the high-frequency power supply 7 and the horizontal magnetic field by the dipole ring magnet 5 via the process gas, and a plasma of the process gas supplied into the upper chamber 1A is generated.
• An electrostatic chuck 8 is arranged on the upper surface of the lower electrode 2, and a DC power supply 9 is connected to an electrode plate 8 A of the electrostatic chuck 8. Therefore, the wafer W is electrostatically attracted by the electrostatic chuck 8 by applying a high voltage to the electrode plate 8A from the DC power supply 9 under a high vacuum.
• a focus ring 10a is arranged on the outer periphery of the lower electrode 2, and the plasma generated in the upper chamber 1A is collected on the wafer W.
• An exhaust ring 11 attached to an upper portion of the support 3 is disposed below the focus ring 1 O a.
• a plurality of holes are formed in the exhaust ring 11 at regular intervals in the circumferential direction over the entire circumference, and the gas in the upper chamber 1A is exhausted to the lower chamber 1B through these holes.
• the support 3 can be moved up and down between the upper chamber 1A and the lower chamber 1B via the ball screw mechanism 12 and the bellows 13.
• the lower electrode 2 descends to the lower chamber 1 B via the support 3, opens the gate valve 6, and opens the wafer via a transfer mechanism (not shown).
• W is supplied onto the lower electrode 2.
• a refrigerant flow path 3 A connected to the refrigerant pipe 14 is formed inside the support 3, and the refrigerant is circulated in the refrigerant flow path 3 A via the refrigerant pipe 14.
• the wafer W is adjusted to a predetermined temperature.
• the support 3, the insulating material 2A, the lower electrode 2, and the electrostatic chuck 8 are each provided with a gas passage 3B, and the gas introduction mechanism 15 is connected to the electrostatic chuck 8 via a gas pipe 15A.
• He gas is supplied to the gap between the wafers W as a pack side gas at a predetermined pressure to increase the thermal conductivity between the electrostatic chuck 8 and the wafer W via the He gas.
• the backside gas pressure is detected by a pressure sensor (not shown), and the detected value is displayed on a pressure gauge 15B.
• 16 is a bellows cover.
• a gas inlet 4 A is formed on the upper surface of the shower head 4, and a process gas supply system 18 is connected to the gas inlet 4 A via a pipe 17.
• the process gas supply system 18 has a C 4 F 8 gas supply source 18 A, an O 2 gas supply source 18 D, and an Ar gas supply source 18 G.
• gas supply sources 18 A, 18 D, 18 G are connected via valves 18 B, 18 E, 18 H and the mass flow controller 18 C, 18 F, 18 I, respectively.
• Each gas is supplied to the shower head 4 at a specified flow rate, and is adjusted inside as a mixed gas with a specified mixture ratio.
• a plurality of holes 4B are uniformly arranged on the lower surface of the shower head 4 over the entire surface, and the mixed gas is supplied from the shower head 4 into the upper chamber 1A through the holes 4B.
• 1C is an exhaust pipe
• 19 is an exhaust system consisting of a vacuum pump and the like connected to the exhaust pipe 1C. For example, as shown in FIG.
• a multivariate analyzer 50 for statistically processing the processing result data, and an input / output device 60 for inputting the processing result data and outputting information such as analysis results are provided.
• the processing unit 10 multivariately analyzes the operation data and the processing result data via the multivariate analysis unit 50 to obtain a correlation between the two, and then, if necessary, transmits information such as the analysis result to the input / output unit 60. Output from.
• the multivariate analyzer 50 includes an operation data storage unit 51, a processing result data storage unit 52, a multivariate analysis program storage unit 53, a multivariate analysis processing unit 54, and a multivariate analysis unit 54.
• An analysis result storage unit 55 is provided.
• the operation data storage section 51 constitutes means for storing operation data
• the processing result data storage section 52 constitutes means for storing processing result data.
• the multivariate analysis processor 54 constitutes means for determining the correlation (eg, prediction formula, regression formula) between the operation data and the processing result data, and means for predicting the processing result based on the correlation.
• the multivariate analysis result storage unit 55 constitutes means for storing the correlation obtained by the multivariate analysis processing unit 54.
• the multivariate analysis device 50 may be constituted by, for example, a microphone port processor that operates based on a program from the multivariate analysis program storage unit 53.
• the operation data storage unit 51, the processing result data storage unit 52, and the multivariate analysis result storage unit 55 may each be constituted by a recording means such as a memory, or may be provided in a recording means such as a hard disk. Each memory area may be provided.
• the multivariate analyzer 50 stores the respective data in the operation data storage unit 51 and the processing result data storage unit 52 by inputting the operation data and the process characteristic data.
• the program of the variable analysis program storage unit 53 is taken out to the multivariate analysis processing unit 54, and the multivariate analysis processing unit 54 performs multivariate analysis of the operation data and process characteristic data.
• the operation data refers to detection data obtained from each of a plurality of measuring instruments attached to the processing apparatus 10 when processing the wafer W
• the processing result data refers to a wafer obtained as a result of processing the wafer W.
• the operation data is measured intermittently during the processing of the wafer W, and the processing result data is measured as necessary after the processing of the wafer. These measurement results are stored in the respective storage units 51 and 52.
• the correlation between the operation data and the processing result data is determined, it is preferable to use data that easily affects the processing result as the operation data.
• the operating data includes the temperatures at a plurality of locations in the processing chamber 1, the pressure of the backside gas, and the electrical data of the processing apparatus 10.
• the processing characteristic data of the processing result data includes, for example, the amount of abrasion of the silicon oxide film of the wafer W having the silicon oxide film on the surface or the etching including the in-plane uniformity of the abrasion amount. Data to be used.
• the apparatus state data data indicating the apparatus state including the deposited film thickness of by-products in the processing chamber 1 and the consumption of parts such as the focus ring 10a can be used.
• the process characteristic data of the processing result data is used, and among them, the in-plane uniformity of the wafer W abrasion amount is used.
• the temperature of the shower head 4, which is the upper electrode, the temperature of the inner wall surface of the processing chamber 1, and the temperature of the lower electrode 2 are used as the temperature inside the processing chamber 1. In particular, the effect of the temperature of the lower electrode 2 is great.
• These temperatures can be measured via a conventionally known temperature sensor (not shown) such as a thermocouple disposed at each site. More specifically, as the temperature in the processing chamber 1, the average temperature during processing of a single wafer in each of the above-described portions is used.
• the pressure in the processing chamber 1 for example, the pressure of the process gas in the processing chamber 1 or the pressure of a backside gas such as He gas can be used. In the first embodiment, the pressure in the processing chamber 1 is used as the pressure in the processing chamber 1. Gas pressure.
• the electrical data of the processing device 10 for example, a fundamental wave, a harmonic voltage, a current, a phase, an impedance, and the like of the high-frequency power applied from the high-frequency power source 7 can be used.
• a high-frequency voltage (RF voltage) Vpp on the output side of the matching device 7A measured by a measuring device (not shown) in the matching device 7A is used.
• High frequency voltage V pp is an example For example, as shown in Fig.
• the in-plane uniformity of the abrasion amount of the silicon oxide film on the wafer W used as the process characteristic data can be determined by measuring the thickness of the silicon oxide film at 13 points on the surface of the wafer W before and after processing, for example. Data showing the in-plane uniformity obtained from the variation in the difference between them is used. For in-plane uniformity, use the value obtained from (maximum value-minimum value of measured values) Z (average value of 2X measured values).
• the multivariate analysis device 50 uses the following types of operation data as explanatory variables (explanatory variables) and process characteristic data as explained variables (object variables, objective variables).
• the relational expression (predictive expression such as regression equation, model) is obtained using a multivariate analysis program.
• X means the matrix of the explanatory variables
• Y means the matrix of the dependent variables.
• B is a regression matrix consisting of the explanatory variables (weights)
• E is a residual matrix.
• This PLS method can obtain the relational expression between X and Y if there are a large number of explanatory variables and a large number of explanatory variables in each of the matrices X and Y, but only a small number of measured values. Moreover, it is a relational expression obtained with few actual measurements, Is also a feature of the PLS method in that it is highly stable and reliable.
• the multivariate analysis program storage unit 53 stores a program for the PLS method.
• the multivariate analysis processing unit 54 processes the operation data and the process characteristic data according to the program procedure, obtains the above equation (1), and obtains the multivariate result.
• the analysis result storage unit 55 stores it.
• the process characteristics can be predicted by applying the operating data to the matrix X as an explanatory variable. Moreover, the predicted value becomes highly reliable.
• the i-th principal component corresponding to the i-th eigenvalue relative to X T Y matrix is represented by ti.
• the matrix X is expressed by the following formula using the score t of the i-th principal component and the vector P i
• the matrix Y is expressed by the following formula using the score t of the i-th principal component and the vector c; 3 expressed by the formula.
• X i + 1 and Y i + are the residual matrices of X and Y
• X ⁇ is the transposed matrix of matrix X.
• the exponent ⁇ means the transposed matrix.
• the PLS method used in the first embodiment is In this method, multiple eigenvalues and their respective eigenvectors when equations (1) and (3) are correlated are calculated with a small amount of computation.
• the convergence of the residual matrix X i + 1 to the stopping condition or zero is fast, and the residual matrix converges to the stopping condition or zero by repeating the calculation about 10 times.
• the residual matrix converges to a stopping condition or zero by repeating the calculation four to five times.
• the first main component of X T Y matrix using the maximum eigenvalue and its specific base-vector obtained by the calculation process And find the maximum correlation between the X and Y matrices.
• the operation of the processing apparatus 10 will be described together with an embodiment of the method of the present invention.
• the above equation (1) for predicting process characteristics is obtained by multivariate analysis, and then a predetermined wafer W is processed.
• the process characteristics at that time can be predicted by applying the operation data at an arbitrary time to the equation (2).
• the support 3 descends to the lower chamber 1 B of the processing chamber 1 via the pole screw mechanism 12, and the wafer W is carried in from the opening and closing opening of the gate valve 6 and the lower electrode is moved. 2 Place on top.
• the gate valve 6 is closed and the exhaust system 19 is activated to maintain the processing chamber 1 at a predetermined degree of vacuum.
• He gas is supplied as a back gas from the gas introduction mechanism 15 to increase the thermal conductivity between the wafer W and the lower electrode 2, specifically, the electrostatic chuck 8 and the wafer W to increase the wafer W. Improve the cooling efficiency.
• the processed wafer W is processed in a reverse manner to the loading operation. Carry out from inside, repeat the same process for subsequent wafers W, process a predetermined number of wafers Then, a series of processing ends.
• 25 wafers obtained by mixing 6 wafers W and 19 dummy wafers, which are the same as the actual wafer W, are used as one lot.
• the processing time of [min Z wafer] is processed, and the 11 lots are repeatedly processed every 10 hours or every 5 hours, and the operation data and process characteristic data for the six wafers W are obtained to perform multivariate analysis. Do.
• the PLS method that requires a small number of data since the PLS method that requires a small number of data is used, for example, only the operation data and the process characteristic data of the wafer W in the second and eleventh lots are used, and the PLS method is used.
• the above equation (1) is obtained from these data.
• the six wafers W are inserted in the first to third, fifth, tenth, and twenty-fifth sheets of each lot.
• the temperatures of the shield head (upper electrode) 4 the wall of the upper chamber 1A of the processing chamber 1, and the lower electrode 2 are intermittently detected as operating data.
• These detection signals ⁇ ,, T 2 , ⁇ 3 are sequentially input to the multivariate analyzer 50 via the AZD converter and stored in the operation data storage unit 51.
• the pressure of He gas is intermittently detected as other operation data
• this detection signal P is sequentially input to the multivariate analysis device 50 via the AZD converter, and based on these input values, the multiple The standard deviation is calculated via the variable analysis processing unit 54 and stored in the operation data storage unit 51.
• the voltage of the high frequency power supply 7 is intermittently detected as other operation data.
• this detection signal V is sequentially input to the multivariate analyzer 50 via the AZD converter, and stored in the operation data storage unit 5 "1.
• the average value for each wafer W, and the standard deviation for each wafer W of the operating data for the He gas pressure are obtained via the multivariate analysis processing unit 54.
• the operation for each wafer W The average value and the standard deviation of the data are stored in the operation data storage unit 51, or are prepared for the next processing as they are:
• the detection signal T of the upper electrode temperature of all wafers W and the detection signal of the wall temperature T 2 figure illustrates the time course of the standard deviation of the detection signal P of FIGS. 5 shows.
• Figure 6 shows the change over time in the average value of the high-frequency power detection signal V. The result is shown in Fig. 7.
• the wafer W after processing is taken out, and the shaved amount at 13 points in the surface of the silicon oxide film of the wafer W is transferred from the input / output device 60 to the multivariate analysis device 50.
• the in-plane uniformity is calculated via the multivariate analysis processing unit 54, and the calculated value is stored in the processing result data storage unit 52 as process characteristic data.
• the change over time of such process characteristic data is shown in Fig. 8.
• Operation data and process characteristic data Based on the data, the regression matrix B and the residual matrix E of the above equation (1) were obtained by the PLS method.
• the process characteristic data of the wafer W at the above-mentioned lot and at the other slot than the above-mentioned slot are predicted, and the graph with the X mark is shown in Fig. 9.
• the graph shown by the seal in Fig. 9 is the measured value of the process characteristic data.
• the predicted and measured values of the second and eleventh lots coincide with each other because the wafer W was used at the time of obtaining equation (1). It can be seen that the predicted values of the process characteristic data of other wafers W are also very close to the measured values that fluctuate for each lot (every 10 hours). In particular, a large deterioration in uniformity around 60 hours can be confirmed in both the predicted and measured values.
• Fig. 7 shows the sudden drop in the high-frequency (RF) voltage observed in Fig. 7.
• Fig. 3 to Fig. 6 data reflecting the state inside the processing chamber 1, such as the upper electrode temperature, wall temperature, lower electrode temperature, and He gas pressure, which can detect the fluctuation of the rotor over time.
• Fig. 7 it is difficult to detect lot fluctuations, but it can be seen that it is effective to use both data that reflect the applied state of high-frequency power.
• 3 to 9 show actual measurements of the operation data and process characteristic data for all wafers W in order to compare the predicted values with the actually measured values. It should be noted that, based on the results of such an experiment, the wafer as the process characteristic data of the first embodiment was used. In predicting the in-plane uniformity of the amount of W abrasion, it is particularly important to use the average value of the lower electrode temperature for each wafer W and the standard deviation of the He gas pressure for each wafer as operating data. Was found to be important for raising Thus, in the present embodiment, before processing the actual wafer W, a small number of the same wafers W (12 in the second and 11th lots in the first embodiment) are used. To obtain operating data and process characteristic data as described above.
• the regression equation (1) is obtained by the PLS method, and then when processing actual wafers W, the operation data of any wafer W is detected. Then, the actual in-plane uniformity of the wafer W can be predicted as process characteristic data simply by applying each operation data to the regression equation (2). In addition, extremely accurate process prediction can be performed.
• operation data and processing result data for example, process characteristic data
• a multivariate analysis is performed based on the collected data group (operating data and processing result data), and a correlation between the operating data and the processing result data is obtained through the multivariate analysis.
• the wafer is scraped based on the correlation.
• the processing results for example, process characteristics
• the in-plane uniformity of the amount when actually processing the wafer W, the in-plane surface of the wafer W can be obtained simply by obtaining the operating data of the wafer W. Uniformity can be predicted with high accuracy as a process characteristic.
• multivariate analysis is performed to Since the PLS method was used to determine the correlation between the data and the processing result data, the regression equation 1 can be determined efficiently in a short time. Therefore, according to the first embodiment, it is necessary to manufacture many test wafers as in the past, process many test wafers using the processing apparatus 10, and measure each processing result.
• the processing result can be predicted with higher accuracy than the conventional prediction method.
• the operation data data that easily affects the process characteristic data (in-plane uniformity of the wafer W), that is, the temperatures (upper electrode temperature, upper electrode temperature, The correlation between the operating data and the process characteristic data was used because the wall temperature and lower electrode temperature of processing chamber 1, the pressure in the processing chamber (back gas pressure such as He gas), and electrical data (voltage of high-frequency power) were used. And the process characteristics can be predicted with high accuracy.
• the in-plane uniformity of the wafer W is used as the process characteristic data, it is possible to predict with high accuracy whether the uniformity within the wafer W surface due to etching is good or bad.
• the correlation between the actually measured value and the predicted value was obtained by using the test wafers of the second lot and the 11th lot. However, when the correlation was obtained, the actual process was used. While processing the wafer W, the correlation may be obtained by processing the test wafer periodically, or the correlation may be obtained by processing the test wafer irregularly. Once the correlation has been obtained, data is added using test wafers as appropriate. By updating the correlation, the prediction accuracy can be further improved.
• the temperature of the upper electrode, the temperature of the processing chamber wall surface, and the temperature of the lower electrode are used as the operation data.
• the temperature at the location may be used.
• the lower electrode temperature is preferable.
• the pressure of the He gas was used as the pressure in the processing chamber, but the pressure of the process gas may be used.
• the in-plane pressure difference for example, the pressure difference when the back gas is divided into three systems: center, middle, and edge.
• the voltage of the high-frequency power supply is used as the electrical data of the operation data.
• the fundamental wave, harmonic current, phase, impedance, and the like of the high-frequency power supply may be used.
• the process result data is used as process characteristic data
• the in-plane uniformity of the abrasion amount of the wafer W is used as the process characteristic data.
• data in addition to the wafer W shaving amount, data indicating the etching characteristics such as the line width and the taper angle of the etching pattern may be used.
• a plasma etching apparatus in the case where the present invention is applied to the method for predicting the processing result described above will be described in detail.
• the same components as those in the first embodiment are denoted by the same reference numerals, and detailed description is omitted.
• a parameter used as operation data is changed or added, and a multivariate analysis is performed by using an abrasion amount (for example, an etching rate) of the wafer W in the process characteristic data as the processing result data. Predict the etching rate of w.
• an abrasion amount for example, an etching rate
• a magnet port reactive etching processing apparatus (hereinafter, referred to as “processing apparatus 100”) will be described with reference to FIG.
• the shower head 4 of the processing apparatus 100 shown in FIG. 11 is provided with a spectroscope (hereinafter, referred to as an “optical measuring instrument”) 20 for detecting plasma emission in the processing chamber 1.
• the emission spectrum intensity in a specific wavelength range (for example, 200 to 950 nm) obtained by the optical measuring device 20 is defined as optical data.
• a process gas supply system 18 ′ is connected to the gas inlet 4 A via a pipe 17.
• the process gas supply system 1 8 ', C 5 F 8 gas supply source 1 8 A' has, O 2 gas supply source 1 8 D ', A r gas source 1 8 G'.
• Each gas flow rate can be detected by each mass flow controller 18 C ′, 18 F ′, 18 1 ′.
• the gas flow rate of the C 5 F 8 gas and the gas flow rate of the Ar gas among the gas flow rates are detected.
• the data of these detected gas flow rates is used as trace data.
• the exhaust pipe 1C is equipped with an APC (Auto Pressure Control IIer) valve 1D, and the opening of the APC valve is automatically adjusted according to the gas pressure in the processing chamber 1. Is done.
• the APC opening by the APC valve 1D is detected.
• the detected APC opening is used as trace data.
• a wattmeter 9a for detecting the applied current and applied voltage of the electrostatic chuck 8 is connected between the electrode plate 8A of the electrostatic chuck 8 and the DC power supply 9, a wattmeter 9a for detecting the applied current and applied voltage of the electrostatic chuck 8 is connected.
• the data of the applied current and applied voltage of the electrostatic chuck 8 detected from the wattmeter 9a is used as trace data.
• the gas introduction mechanism 15 for introducing a backside gas is provided with, for example, a mass flow controller (not shown).
• the mass flow controller detects the gas flow of the backside gas.
• the gas flow rate of the backside gas is used as trace data together with the gas pressure of the backside gas detected by the pressure gauge 15B.
• the matching unit 7A includes, for example, two variable capacitors C 1 and C 2, a capacitor C and a coil L, and performs impedance matching via the variable capacitors CI and C 2.
• the positions of the variable capacitors C 1 and C 2 in the matching state are used as trace data.
• the matching unit 7A is provided with a power meter 7a, which measures the voltage Vdc between the high-frequency power supply line (wire) and the ground (ground) of the processing device 100 using the power meter 7a. .
• the voltage Vdc between the high-frequency power supply line (wire) and the ground is used as trace data.
• An electric measuring instrument (for example, a VI probe) 7C is attached to the lower electrode 2 side (high-frequency voltage output side) of the matching device 7A, and is applied to the lower electrode 2 via the electric measuring instrument 7C.
• the fundamental wave (forward and reflected waves of high-frequency power) generated by the high-frequency power P generated in the upper chamber 1A and the high-frequency voltage V, high-frequency current I, high-frequency phase P, and impedance Z of the harmonics are converted into electrical data. Detected as Of these, traveling waves and reflected waves of high frequency power are used as trace data.
• the high-frequency voltage V, high-frequency current I, high-frequency phase P, and impedance Z of the harmonic are VI probe data.
• an integrating unit 7b for integrating the application time of the high-frequency power is connected between the high-frequency power supply 7 and the wattmeter 7B.
• the application integration time of the high-frequency power detected by the integration unit 7b is also used as trace data.
• the cumulative application time is obtained by integrating the time for applying high-frequency power each time the wafer W is processed.
• the integration unit 7b resets the integration time of the application of the high-frequency power to zero every time the processing unit 100 is maintained. Therefore, 'the integration time of high-frequency power applied here is the integration time of application until the next maintenance.
• the above-mentioned maintenance includes, for example, wet cleaning for removing by-products (for example, particles) in the processing apparatus 100 generated by etching, and replacement of consumables and measuring instruments.
• the cumulative application time is reset to zero each time the inkjet cleaning is performed.
• operation data detected from each measuring instrument is divided into optical data, trace data, and VI probe data for use.
• optical data for example, the emission spectrum intensity ⁇ in the wavelength range of 200 to 950 nm detected from the optical measuring instrument 20 described above is used.
• the trace data includes the temperatures (upper electrode temperature ⁇ , wall surface temperature ⁇ 2 , lower electrode temperature ⁇ 2) in the processing chamber 1 described in the first embodiment.
• That gas flow rate of C 5 F 8 gas and A r gas is a process gas, Noku' Qusay Dogasu flow, APC opening by the APC valve 1 D, electrostatic Ji The applied current and applied voltage of the jack 8, the positions of the variable capacitors C 1 and C 2 in the matching device 7 A, the voltage V dc between the high-frequency power supply line and the ground in the matching device 7 A, the traveling wave and reflected wave of the high-frequency power Add the data and the cumulative application time of high-frequency power to the trace data.
• the backside gas pressure and flow rate are, for example, the flow rates at the center and edge of the wafer W, respectively.
• the high-frequency voltage V, high-frequency current I, high-frequency phase P, and impedance Z of the harmonic are used.
• the process characteristic data the scraping amount of the wafer W is used.
• the data of the etching rate (AZ min) when the CVD oxide film formed on the surface of the wafer W by, for example, CVD (chemical vapor deposition) is used.
• the etching rate of the wafer W as one of the process characteristic data is used as the processing result data.
• the regression equation (the relational expression of 1) described in the first embodiment is obtained using, for example, a multivariate analysis program for the PLS method. Then, the operation data is input to the obtained regression equation, and the etching rate of the wafer W is predicted.
• the multivariate analysis processing unit 54 in the second embodiment performs pre-processing on operation data and processing result data before performing multivariate analysis such as calculation of the relational expression (regression equation) in 1. Has become.
• preprocessing for example, OSC (Orthogonal Signal Correction), MSC (Multiplicative Signal Correction) or SNV (Standard Normal Variate Transformation).
• the OSC preprocessing is a preprocessing that removes components (Y and vertical components) unrelated to the objective variable Y from the explanatory variable X.
• the details of the preprocessing by the OSC are described in, for example, Wold, et al., (1998a), orthogonal Signal Correction of Near-Infrared Spectra, Chemometrics and Intelligent Laboratory Systems, 44, 175-185.
• the above preprocessing by SNV generally involves preprocessing in which data is normalized in the data direction for each sample in order to calibrate the effects of variations in the samples (here, operation data and processing result data for each wafer W). It is.
• the pre-processing by the SNV for example, correction is performed by standardizing each sample by a standard deviation.
• the details of the preprocessing by SNV are described in, for example, Barnes, et al., (1989), Standard Normal Variate Transformation and De-trending on Near-infrared Diffuse Reflectance Spectra, Applied Spectroscopy, 43, 772-777. Have been.
• the MSC preprocessing is a preprocessing that obtains the ideal spectrum from the sample and corrects the variance between the samples to be smaller.
• the average is calculated in the wavelength direction for each sample (ideal spectrum), and a linear regression line with the ideal spectrum is calculated for each sample.
• the conditions of the etching process, pressure 5 0 m T in the treatment chamber, the high-frequency power 1 5 0 0 W applied to the lower electrode, the processing gas and C 5 F 8 0 2 and the A r He gas was used as the mixed gas and backside gas.
• the average value of each operation data for each wafer W is obtained via the multivariate analysis processing unit 54.
• the average value of the respective operation data for each wafer W is stored in the operation data storage unit 51, or prepared for the next processing as it is.
• the processed wafer W is taken out, the etching rate of the CVD oxide film of the wafer W is input from the input / output device 60 to the multivariate analyzer 50, and the input value is stored as process characteristic data as processing characteristic data.
• the regression equation (relational expression of 1) is obtained by the PLS method without performing the preprocessing or after performing the preprocessing.
• Figure 13 shows the relationship.
• WC (Wet Cleaning Cycle) 1 is the section until the first cleaning of the processing unit 100 is performed, and WC 2 is the section after the first cleaning of the jet.
• WC3 is the section from the second wet cleaning to the third wet cleaning
• WC4 is the section from the second wet cleaning to the third wet cleaning. This is the section from to the fourth wet cleaning.
• Figures 14 (a) to 14 (a) show the results of the etching rate prediction of the wafer W in the form of a stamped graph.
• the graphs indicated by the triangles are the measured values of the wafer W etching rate data.
• the prediction error (PE) was calculated. This prediction error PE is obtained by subtracting the prediction value from the actual measurement value of each wafer and calculating the sum of the squared values, dividing the sum by the number of processed wafers, and calculating the square root. .
• the prediction error PE is best at 0, and the smaller this value is, the smaller the error between the measured value and the predicted value is.
• the correlation obtained by plotting the relationship between the predicted value and the measured value shown in each figure (a) in Figs. 14 to 29 is shown in each figure (b) in Figs. 14 to 29, respectively.
• the correlation coefficient R was determined for the experimental results shown in Figs. 14 to 29 (b).
• a correlation coefficient R of 1 is best, and a larger value indicates a higher correlation. Therefore, overall, the prediction accuracy is better when the prediction error PE is closer to 0 and the correlation coefficient R is closer to 1.
• WC1 to WC4 were etched under the same etching conditions. Therefore, when calculating the prediction error PE and correlation coefficient, data from WC1 to WC4 were used. I have.
• FIG. 15 shows the case where the above-mentioned optical data and the above-mentioned trace data are used as an explanatory variable.
• Fig. 16 shows the case where the above trace data was used as an explanatory variable
• Fig. 17 shows the case where the above VI probe data was used as an explanatory variable.
• Figures 18 to 21 show the experimental results when multivariate analysis was performed by the PLS method after performing the OSC described above as preprocessing.
• Figure 18 shows FIG. 19 shows a case where the optical data and the trace data are used as explanatory variables.
• Figure 20 shows the case where the above trace data was used as the explanatory variable.
• FIG. 22 shows the case where the above optical data is used as an explanatory variable
• Fig. 23 shows the case where the above optical data and the above trace data are used as an explanatory variable
• Figure 24 shows the case where the above trace data was used as an explanatory variable.
• FIG. 26 shows the case where the above optical data is used as an explanatory variable
• Fig. 27 shows the case where the above optical data and the above trace data are used as an explanatory variable
• Figure 28 shows the case where the above trace data was used as the explanatory variable.
• Fig. 30 shows the prediction errors PE obtained from the experimental results in Figs. 14 to 29 (a) and summarized in a table
• Figure 31 shows the correlation coefficient R obtained from the experimental results in Table 1 and summarized in a table. From a global perspective from the viewpoint of the data used for multivariate analysis, according to Fig. 30, the prediction error PE is largest when optical data is used. In the case of using scientific data and trace data, in the case of using VI probe data, and in the case of using trace data, the size becomes smaller in the order, and the case of using trace data is the smallest. Furthermore, according to Fig.
• the phase relationship number R is the smallest when optical data is used, and increases in the order of using optical data and trace data, using VI probe data, and using trace data. The largest is when trace data is used. Therefore, from the perspective of the data used for the multivariate analysis, from a global perspective, when optical data is used, optical data and trace data are used, VI probe data is used, and trace data is used. The prediction accuracy improves in the order of the cases, and it can be seen that the use of trace data has the best prediction accuracy and is effective for prediction. In the case of using the trace data with the best prediction accuracy, from the perspective of the presence or absence of preprocessing and the type, the prediction error PE is shown in Fig. 30 except for the case of OSC. Preprocessing is smaller than preprocessing.
• the prediction error PE decreases in the order of OSC, SNV, and MSC when preprocessing is performed, and is smallest when MSC is performed as preprocessing. Furthermore, according to Fig. 31, except for the case of OSC, the correlation coefficient R is larger in the case of preprocessing than in the case of no preprocessing. The correlation coefficient R increases in the order of OSC, SNV, and MSC when preprocessing is performed, and is largest when MSC is performed as preprocessing. Therefore, when using the trace data with the best prediction accuracy, From a global perspective in terms of the presence or absence and type of preprocessing, the prediction accuracy is better when preprocessing is performed than when no preprocessing is performed, except when OSC is performed as preprocessing. It turns out to be effective.
• the prediction accuracy is improved in the order of OSC, SNV, and MSC, and the prediction accuracy is more effective when MSC is performed as the preprocessing.
• multivariate analysis was performed using trace data as explanatory variables, and MSC was performed as preprocessing prior to multivariate analysis for the best prediction accuracy. Nari, it turns out to be the most effective.
• Fig. 32 shows a table of the variable influence on projection (VIP) that affects the prediction results for various types of data in the trace data.
• the influence variable VIP indicates the magnitude of the influence of each explanatory variable X when the objective variable Y is predicted. For example, if a is a component, R is a mouth vector, W is a weight vector, and R 2 y is a correlation coefficient of y, the above-mentioned influence variable VIP is (W [a] squared) X (R 2 y [a]) is expressed as a standardized sum of each component. According to Fig. 32, the effect variable VIP has the largest high-frequency voltage (RF voltage) Vpp on the output side of the matching unit 7A, followed by the long integration time of high-frequency power application. Therefore, it can be seen that the application time of the high-frequency voltage Vpp and the high-frequency power greatly affects the prediction results.
• RF voltage radio frequency
• Figure 33 shows the case where only high-frequency voltage Vpp was removed from the trace data.
• Figure 34 shows the case where only the high-frequency power application integration time was used from the trace data.
• Figure 35 shows the trace. In this case, data excluding the high-frequency voltage V pp and the integration time of high-frequency power are used.
• the prediction errors PE were calculated for the experimental results in Figs. 33 to 35 (a), they were 49.7 A / min, 55.1 k / mi ⁇ , and 66.3 AZmin, respectively.
• the prediction errors PE were calculated for the experimental results in Figs. 33 to 35 (a)
• they were 49.7 A / min, 55.1 k / mi ⁇ , and 66.3 AZmin, respectively.
• Fig. 16 (a) Fig. 33 (a) to Fig.
• the high-frequency voltage V pp It was confirmed that the prediction accuracy was lower in all cases where the trace data excluding the power application integration time was used (Fig. 36) than in the case where all the trace data was used. In addition, it was confirmed that the prediction accuracy was the worst when the high-frequency voltage Vpp and the integration time of the high-frequency power were excluded. Therefore, when predicting the etching rate of the wafer W, it is effective to have at least the high-frequency voltage Vpp as the trace data, and it is more preferable to have the integration time of high-frequency power application. As described above, according to the second embodiment, the operation data and the processing result data (for example, process characteristic data) when a small number of test wafers such as wafers in one wet cleaning cycle (WC) are processed.
• the operation data and the processing result data for example, process characteristic data
• a multivariate analysis is performed based on the collected data group (operating data and processing result data), and a correlation between the operating data and the processing result data is obtained through the multivariate analysis.
• the processing result eg, process characteristics
• the amount of wafer W abrasion e.g, etching rate
• the operation data of wafer W is obtained.
• the amount of wafer W scraping eg, etching rate
• the regression equation ⁇ can be obtained efficiently in a short time.
• the second embodiment it is not necessary to fabricate many test wafers as in the past or to process many test wafers using the processing apparatus 10 and measure each processing result. There is no need to spend much man-hours and time to make test wafers and measure processing results. Moreover, the processing result can be predicted with higher accuracy than the conventional prediction method. Further, in the second embodiment, as the operation data, trace data including high-frequency voltage V pp, integration time of high-frequency power application, optical data, VI probe data, and other data that easily affects process characteristic data are stored in the first data. By further adding to the data used in the embodiment, the prediction accuracy of the process characteristic data can be further improved.
• the amount of wafer W abrasion can be estimated. Accuracy can be further improved.
• the prediction accuracy of the Lie process characteristic data can be improved.
• the etching rate of the wafer W is used as the process characteristic data, the quality of the etching of the wafer W by the etching can be predicted with high accuracy. As described above, even if optical data and VI probe data are used as operation data, the prediction accuracy improves.
• the prediction accuracy may decrease. is there.
• the prediction accuracy decreases in the wet cleaning cycle (WC3) other than the wet cleaning cycle (WC1) in which the regression equation (model) based on the multivariate analysis is created.
• the trace data including the high-frequency voltage V pp and the cumulative application time of the high-frequency power is used as the operation data, all the jet cleaning cycles (WC 2 to WC) as shown in Fig. 16 can be obtained. In 4), the prediction accuracy can be improved.
• the integration time of high-frequency power applied to trace data for example, (1) the integration time of application is set to zero each time maintenance such as jet cleaning is performed, so data on the integration time of application in each wet cleaning cycle must be obtained. Can be. Therefore, if the integrated time of high-frequency power application is used as operation data, It is possible to predict with high accuracy even the processing result data whose tendency is changed by performing the training. As described above, according to the present invention, a prediction equation of process characteristics can be obtained only by collecting a small number of operation data and process characteristic data obtained by processing a small number of samples. It is possible to provide a method for predicting a processing result that can easily and accurately predict a process characteristic simply by applying operation data at the time of processing to a prediction formula.
• the process result data is used as the process characteristic data
• the amount of wafer W abrasion eg, etching rate
• the process characteristic data For example, data indicating the etching characteristics such as the line width and the taper angle of the etching pattern may be used.
• the apparatus state data relating to the apparatus state such as the film thickness of by-products in the processing chamber and the consumption of parts such as the focus ring 10a are used. May be used, By using the thickness of by-products and the consumption of parts such as the focus ring 10a as equipment status data, it is possible to predict the cleaning time of the processing unit 10 and the replacement time of parts such as the focus ring 10a. Can also.
• the first and second embodiments the case where the wafer W is subjected to the etching process is described.
• the present invention can be applied to a processing apparatus such as a film forming process other than the etching process. It is not limited to the wafer to be processed.
• the regression equation 1 is obtained by using the PLS method when performing the multivariate analysis.
• other known numerical calculation methods other than the PLS method (for example, the power method
• the eigenvalues and their eigenvectors may be obtained using e.g. INDUSTRIAL APPLICABILITY
• the present invention is applicable to a method and a processing apparatus for predicting a processing result of an object to be processed such as a wafer to be processed in a semiconductor manufacturing apparatus or an apparatus state.
• the present invention can be applied to an apparatus and a method of predicting a processing result in such an apparatus.

Landscapes

• Engineering & Computer Science (AREA)
• Physics & Mathematics (AREA)
• Plasma & Fusion (AREA)
• Chemical & Material Sciences (AREA)
• Analytical Chemistry (AREA)
• Manufacturing & Machinery (AREA)
• Computer Hardware Design (AREA)
• Microelectronics & Electronic Packaging (AREA)
• Power Engineering (AREA)
• Drying Of Semiconductors (AREA)

Priority Applications (1)

Applications Claiming Priority (2)

Publications (1)

Family

ID=19032842

Family Applications (1)

Country Status (3)

Cited By (10)

Citations (6)

• 2002
  • 2002-06-25 JP JP2003509517A patent/JP4220378B2/ja not_active Expired - Fee Related
  • 2002-06-25 WO PCT/JP2002/006348 patent/WO2003003437A1/ja active Application Filing
  • 2002-06-25 TW TW91113908A patent/TWI306269B/zh not_active IP Right Cessation

Patent Citations (6)

Non-Patent Citations (1)

Also Published As

Similar Documents

Legal Events