WO2025089153A1 - Substrate processing method and substrate processing system - Google Patents

Abstract

In the present invention, determining an optimal etching condition includes: acquiring a plurality of etching amount distributions in the radial direction when the surface of a substrate is etched under a plurality of different etching conditions; performing screening processing on the plurality of etching amount distributions, and removing at least one of an etching amount distribution unnecessary for optimization processing and a similar etching amount distribution to select a plurality of effective etching amount distributions; optimizing a combination of effective etching amount distributions used for superposition and the number of times the effective etching amount distributions are superposed so that the shape of the surface of the substrate becomes a target shape by superposing the plurality of effective etching amount distributions using an optimization method; and determining an optimal etching condition by integrating etching conditions corresponding to the optimized combination.

Description

SUBSTRATE PROCESSING METHOD AND SUBSTRATE PROCESSING SYSTEM

This disclosure relates to a substrate processing method and a substrate processing system.

Patent Document 1 discloses a method for determining optimal etching conditions when etching the surface of a substrate. In this method, first, the radial etching amount distribution is obtained when the surface of a substrate is etched under a plurality of different etching conditions. Next, an optimization technique is used to optimize the combination of the etching amount distributions used for superimposition and the number of times the etching amount distributions are superimposed, so that the shape of the substrate surface becomes the target shape by superimposing the etching amount distributions. Next, the etching conditions corresponding to the optimized combination are integrated to determine the optimal etching conditions.

International Publication No. 2023/068066

The technology disclosed herein efficiently optimizes the etching conditions when etching the surface of a substrate.

One aspect of the present disclosure is a substrate processing method for processing a substrate, comprising: optimizing an etching amount distribution to determine optimal etching conditions; and supplying an etching solution to a surface of the substrate based on the optimal etching conditions to etch the surface. Determining the optimal etching conditions includes obtaining multiple radial etching amount distributions when the surface of the substrate is etched under multiple different etching conditions; screening the multiple etching amount distributions to remove at least one of an etching amount distribution unnecessary for the optimization process and a similar etching amount distribution to select multiple effective etching amount distributions; superimposing the multiple effective etching amount distributions using an optimization method to optimize a combination of the effective etching amount distribution used for superimposition and the number of times the effective etching amount distributions are superimposed so that the shape of the surface of the substrate becomes a target shape; and determining the optimal etching conditions by integrating the etching conditions corresponding to the optimized combination.

According to this disclosure, etching conditions can be efficiently optimized when etching the surface of a substrate.

1 is a plan view showing an outline of a configuration of a wafer processing system; FIG. 1 is a side view showing an outline of the configuration of an etching apparatus. FIG. 11 is an explanatory diagram showing a state in which a nozzle moves in a radial direction. FIG. 1 is a flow diagram showing main steps of wafer processing. FIG. 2 is a flow chart showing main steps of a method for determining optimal etching conditions. FIG. 13 is an explanatory diagram showing an example of a learning data acquisition screen displayed on a display panel. FIG. 13 is an explanatory diagram showing an example of a learning data selection screen displayed on a display panel. FIG. 1 is a flow diagram showing the main steps of a method for screening training data using a first pattern of geometric techniques. 1 shows an example of a convex hull obtained by the first pattern. FIG. 11 is an explanatory diagram showing how a plurality of training data are screened using a first pattern geometric method. FIG. 11 is a flow diagram showing the main steps of a training data screening method using a second pattern of graphical techniques. FIG. 13 is an explanatory diagram showing the screening of multiple training data using a second pattern of graphical techniques. FIG. 13 is an explanatory diagram showing the screening of multiple training data using a second pattern of graphical techniques. FIG. 11 is a flow diagram showing main steps of a training data screening method using the third pattern of the QR decomposition technique.

In the manufacturing process of semiconductor devices, the cut surface of a disk-shaped silicon wafer (hereafter referred to as "wafer") obtained by cutting a single crystal silicon ingot with a wire saw or the like is flattened and further smoothed to make the thickness of the wafer uniform. The cut surface is flattened, for example, by surface grinding or lapping. For example, the smoothing is performed by rotating the wafer and moving (scanning) a nozzle back and forth in the radial direction passing through the center of the wafer while supplying an etching solution from the nozzle to the surface of the wafer to etch the surface (hereafter referred to as "scan etching").

The above-mentioned Patent Document 1 discloses a method for determining optimal etching conditions when scan etching the surface of a wafer. In this method, optimal etching conditions are determined by optimization calculations using multiple etching amount distributions (hereinafter sometimes referred to as "learning data") obtained under multiple different etching conditions.

However, in the method disclosed in Patent Document 1, optimization calculations are performed using all learning data, so if there is a large amount of learning data, for example, the optimization calculation time becomes long. Therefore, there is room for improvement in the conventional method of determining optimal etching conditions.

The technology disclosed herein efficiently optimizes the etching conditions when etching the surface of a substrate. Below, a wafer processing system as a substrate processing system and a wafer processing method as a substrate processing method according to this embodiment will be described with reference to the drawings. Note that in this specification and the drawings, elements having substantially the same functional configuration are denoted with the same reference numerals to avoid redundant description.

In the wafer processing system 1 according to this embodiment, a process is performed on a wafer W, which is a substrate obtained by cutting from an ingot, to improve the in-plane thickness uniformity. Hereinafter, the cut surfaces of the wafer W are referred to as the first surface Wa and the second surface Wb. The first surface Wa is the surface opposite the second surface Wb. The first surface Wa and the second surface Wb may also be collectively referred to as the surfaces of the wafer W.

As shown in FIG. 1, the wafer processing system 1 has a configuration in which a loading/unloading station 2 and a processing station 3 are integrally connected. In the loading/unloading station 2, for example, a cassette C capable of housing multiple wafers W is loaded and unloaded between the loading/unloading station 2 and the outside. The processing station 3 is equipped with various processing devices that perform the desired processing on the wafers W.

The loading/unloading station 2 is provided with a cassette mounting table 10 on which multiple, for example, three cassettes C are mounted. A wafer transport device 20 is provided adjacent to the cassette mounting table 10 on the negative side of the X-axis of the cassette mounting table 10. The wafer transport device 20 is configured to be movable on a transport path 21 extending in the Y-axis direction. The wafer transport device 20 also has, for example, two transport arms 22 that hold and transport a wafer W. Each transport arm 22 is configured to be movable horizontally, vertically, around a horizontal axis, and around a vertical axis. The configuration of the transport arm 22 is not limited to this embodiment, and may have any configuration. The wafer transport device 20 is configured to be able to transport a wafer W to the cassette C on the cassette mounting table 10 and to a transition device 30 described later.

The loading/unloading station 2 is provided with a transition device 30 adjacent to the wafer transport device 20 on the negative X-axis direction side of the wafer transport device 20 for transferring the wafer W between the processing station 3.

The processing station 3 is provided with, for example, three processing blocks G1 to G3. The first processing block G1, the second processing block G2, and the third processing block G3 are arranged in this order from the positive side of the X-axis (the loading/unloading station 2 side) to the negative side.

The first processing block G1 is provided with an etching device 40, a thickness measuring device 50, an inversion device 51, and a wafer transport device 60. The etching device 40, the thickness measuring device 50, and the inversion device 51 are arranged in a stacked configuration. Note that the number and arrangement of the etching devices 40, the thickness measuring devices 50, and the inversion devices 51 are not limited to this.

The etching device 40 etches silicon (Si) on the first surface Wa or the second surface Wb after grinding by the grinding device 90 described below. In order to improve the throughput of wafer processing, multiple etching devices 40 may be provided.

As shown in FIG. 2, the etching device 40 has a wafer holder 41, a rotation mechanism 42, a nozzle 43, and a movement mechanism 44.

The wafer holding part 41 holds the outer edge of the wafer W at multiple points, three points in this embodiment. Note that the configuration of the wafer holding part 41 is not limited to the example shown in the figure, and for example, the wafer holding part 41 may be equipped with a chuck (not shown) that suction-holds the wafer W from below. The wafer holding part 41 is configured to be rotatable around a vertical rotation center line 41a by a rotation mechanism 42, thereby allowing the wafer W held on the wafer holding part 41 to be rotated.

The nozzle 43 supplies the etching liquid E to the first surface Wa or the second surface Wb of the wafer W held by the wafer holding part 41. The nozzle 43 is connected to an etching liquid supply source (not shown) that supplies the etching liquid E to the nozzle 43. The nozzle 43 is provided above the wafer holding part 41 and configured to be movable in the horizontal and vertical directions by a moving mechanism 44. In one example, the nozzle 43 is configured to be capable of reciprocating (scanning) or rotating through the rotation center line 41a of the wafer holding part 41, that is, above the center of the wafer W as shown in FIG. 3.

The etching solution E contains hydrofluoric acid (HF), nitric acid (HNO ₃ ), and phosphoric acid (H ₃ PO ₄ ) to properly etch silicon of the wafer W that may be an etching target. In one example, the etching solution E is a mixed solution containing hydrofluoric acid, nitric acid, phosphoric acid, and water. The etching target may be, for example, amorphous silicon.

The thickness measuring device 50 shown in FIG. 1 includes, in one example, a measuring unit (not shown) and a calculating unit (not shown). The measuring unit includes a sensor that measures the thickness of the wafer W after etching at multiple points. The calculating unit obtains the thickness distribution of the wafer W from the measurement results (thickness of the wafer W) by the measuring unit, and further calculates the flatness of the wafer W (TTV: Total Thickness Variation). The calculation of the thickness distribution and flatness of the wafer W may be performed by the control device 130 described below instead of the calculating unit. In other words, a calculating unit (not shown) may be provided in the control device 130 described below. The configuration of the thickness measuring device 50 is not limited to this, and may be configured arbitrarily.

The inversion device 51 inverts the first surface Wa and the second surface Wb of the wafer W in the vertical direction. The inversion device 51 may be configured in any manner.

The wafer transport device 60 is disposed on the negative side of the X-axis of the transition device 30. The wafer transport device 60 has, for example, two transport arms 61 that hold and transport the wafer W. Each transport arm 61 is configured to be movable horizontally, vertically, around the horizontal axis, and around the vertical axis. The wafer transport device 60 is configured to be able to transport the wafer W to the transition device 30, the etching device 40, the thickness measuring device 50, the inversion device 51, the cleaning device 70 described below, the thickness measuring device 71 described below, the buffer device 72 described below, and the inversion device 73 described below.

The second processing block G2 is provided with a cleaning device 70, a thickness measuring device 71, a buffer device 72, an inversion device 73, and a wafer transport device 80. The cleaning device 70, the thickness measuring device 71, the buffer device 72, and the inversion device 73 are arranged in a stacked manner. Note that the number and arrangement of the cleaning devices 70, the thickness measuring devices 71, the buffer device 72, and the inversion device 73 are not limited to this.

The cleaning device 70 cleans at least the first surface Wa or the second surface Wb after grinding by the grinding device 90 described below.

In one example, the thickness measuring device 71 has a configuration similar to that of the thickness measuring device 50 described above. Note that the configuration of the thickness measuring device 71 is not limited to this, and can be configured as desired.

The buffer device 72 temporarily holds the unprocessed wafer W that is transferred from the first processing block G1 to the second processing block G2. The configuration of the buffer device 72 is arbitrary. The buffer device 72 may also have an alignment mechanism (not shown) that adjusts the center position of the wafer W relative to the chucks 93a, 93b (described later) and/or the horizontal orientation of the wafer W.

The inversion device 73 inverts the first surface Wa and the second surface Wb of the wafer W in the vertical direction. The configuration of the inversion device 73 is arbitrary.

The wafer transport device 80 is disposed, for example, on the Y-axis positive side of the cleaning device 70, thickness measuring device 71, buffer device 72, and inversion device 73. The wafer transport device 80 has, for example, two transport arms 81 that transport the wafer W by suction and holding it with an adsorption holding surface (not shown). Each transport arm 81 is supported by an articulated arm member 82 and is configured to be movable horizontally, vertically, around a horizontal axis, and around a vertical axis. The wafer transport device 80 is configured to be able to transport the wafer W to the etching device 40, thickness measuring device 50, inversion device 51, cleaning device 70, thickness measuring device 71, buffer device 72, inversion device 73, and grinding device 90 described below.

The third processing block G3 is provided with a grinding device 90. The grinding device 90 grinds and flattens the first surface Wa or the second surface Wb of the wafer W.

The grinding device 90 has a rotating table 91. The rotating table 91 is configured to be freely rotatable around a vertical rotation center line 92 by a rotating mechanism (not shown). Four chucks 93a, 93b for suction-holding the wafer W are provided on the rotating table 91. Of the four chucks 93a, 93b, the two first chucks 93a are chucks used for grinding at a first processing position B1 described later. These two first chucks 93a are arranged in positions that are point-symmetrical with respect to the rotation center line 92. The remaining two second chucks 93b are chucks used for grinding at a second processing position B2 described later. These two second chucks 93b are also arranged in positions that are point-symmetrical with respect to the rotation center line 92. In other words, the first chucks 93a and the second chucks 93b are arranged alternately in the circumferential direction.

The four chucks 93a, 93b can be moved to the transfer positions A1-A2 and the processing positions B1-B2 by the rotation of the rotary table 91. In addition, each of the four chucks 93a, 93b is configured to be rotatable around a vertical axis by a rotation mechanism (not shown).

The first transfer position A1 is a position on the positive X-axis side and the positive Y-axis side of the rotation center line 92 of the rotating table 91, where the wafer W is transferred to the first chuck 93a when grinding the first surface Wa. The second transfer position A2 is a position on the positive X-axis side and the negative Y-axis side of the rotation center line 92 of the rotating table 91, where the wafer W is transferred to the second chuck 93b when grinding the second surface Wb.

The first processing position B1 is a position on the negative X-axis and negative Y-axis side of the rotation center line 92 of the rotating table 91, and the first grinding unit 100 is disposed therein. The first grinding unit 100 has a grinding section 101 equipped with a grinding wheel (not shown) that is annular and can rotate freely. The grinding section 101 is also configured to be movable in the vertical direction along the support 102. As an example, the first grinding unit 100 grinds the first surface Wa or the second surface Wb of the wafer W held by the first chuck 93a.

The second processing position B2 is a position on the negative X-axis side and the positive Y-axis side of the rotation center line 92 of the rotating table 91, and the second grinding unit 110 is disposed thereat. The second grinding unit 110 has a grinding section 111 equipped with a grinding wheel (not shown) that is annular and can rotate freely. The grinding section 111 is also configured to be movable in the vertical direction along the support 112. As an example, the second grinding unit 110 grinds the second surface Wb or the first surface Wa of the wafer W held by the second chuck 93b.

In addition, a thickness measuring device (not shown) for measuring the thickness of the wafer W after grinding may be provided at the transfer positions A1, A2 or the processing positions B1, B2.

The above-described wafer processing system 1 is provided with a display panel 120. The display panel 120 is, for example, a monitor or a touch panel, and may be attached directly to the wafer processing system 1 or may be capable of being viewed remotely. The display panel 120 displays a screen for operating each process performed in the wafer processing system 1. A signal representing the result of the operation on the display panel 120 is output to the control device 130, which will be described later.

The above wafer processing system 1 is provided with at least one controller 130. The controller 130 processes computer-executable instructions that cause the wafer processing system 1 to perform the various steps described in this disclosure. The controller 130 may be configured to control each element of the wafer processing system 1 to perform the various steps described herein. In one embodiment, some or all of the controller 130 may be included in the wafer processing system 1. The controller 130 may include a processing unit, a storage unit, and a communication interface. The controller 130 is realized, for example, by a computer. The processing unit may be configured to read a program that provides logic or routines that enable various control operations to be performed from the storage unit, and to perform various control operations by executing the read program. This program may be stored in the storage unit in advance, or may be acquired via a medium when necessary. The acquired program is stored in the storage unit, and is read from the storage unit by the processing unit and executed. The medium may be various computer-readable storage media, or may be a communication line connected to the communication interface. The storage medium may be temporary or non-temporary. The processing unit may be a CPU (Central Processing Unit) or one or more circuits. The storage unit may include a RAM (Random Access Memory), a ROM (Read Only Memory), a HDD (Hard Disk Drive), an SSD (Solid State Drive), or a combination thereof. The communication interface may communicate with the wafer processing system 1 via a communication line such as a LAN (Local Area Network).

Next, we will explain the wafer processing performed using the wafer processing system 1 configured as described above. In this embodiment, processing is performed on a wafer W cut from an ingot using a wire saw or the like, or on a lapped wafer W, to improve the in-plane thickness uniformity.

First, a cassette C containing multiple wafers W is placed on the cassette placement table 10 of the loading/unloading station 2. In the cassette C, the wafers W are stored with their first surfaces Wa facing upward and their second surfaces Wb facing downward. Next, the wafers W in the cassette C are removed by the wafer transfer device 20 and transferred to the transition device 30. The wafers W transferred to the transition device 30 are then transferred to the buffer device 72 by the wafer transfer device 60.

Then, the wafer W is transported by the wafer transport device 80 to the grinding device 90 and transferred to the first chuck 93a at the first transfer position A1. The second surface Wb of the wafer W is held by suction in the first chuck 93a.

Next, the rotary table 91 is rotated to move the wafer W to the first processing position B1. Then, the first surface Wa is ground by the first grinding unit 100 (St1 in FIG. 4).

Next, the rotary table 91 is rotated to move the wafer W to the first transfer position A1.

The wafer W is then transported by the wafer transport device 80 to the cleaning device 70. In the cleaning device 70, the first surface Wa of the wafer W is cleaned (St2 in FIG. 4). In St2, the second surface Wb of the wafer W may also be cleaned.

Then, the wafer W is transported to the inversion device 73 by the wafer transport device 80. In the inversion device 73, the first surface Wa and the second surface Wb of the wafer W are inverted vertically (St3 in FIG. 4). That is, the wafer W is inverted so that the first surface Wa faces downward and the second surface Wb faces upward.

Then, the wafer W is transported by the wafer transport device 80 to the grinding device 90 and transferred to the second chuck 93b at the second transfer position A2. The first surface Wa of the wafer W is held by suction in the second chuck 93b.

Next, the rotary table 91 is rotated to move the wafer W to the second processing position B2. Then, the second surface Wb of the wafer W is ground by the second grinding unit 110 (St4 in FIG. 4).

Next, the rotary table 91 is rotated to move the wafer W to the second transfer position A2.

Next, the wafer W is transported by the wafer transport device 80 to the thickness measuring device 71. The thickness measuring device 71 measures the thickness of the wafer W after grinding on both the first surface Wa and the second surface Wb at multiple points to obtain the thickness distribution of the wafer W (St5 in FIG. 4). The thickness measuring device 71 may further calculate the flatness of the wafer W. The obtained thickness distribution of the wafer W is output to, for example, the control device 130, and is used, for example, in the processing of another wafer W that is subsequently processed in the wafer processing system 1. Note that if the grinding device 90 is provided with a thickness measuring device, the thickness of the wafer W after grinding may be measured by the thickness measuring device of the grinding device 90.

Then, the wafer W is transported by the wafer transport device 80 to the cleaning device 70. In the cleaning device 70, the second surface Wb of the wafer W is cleaned (St6 in FIG. 4). In St6, the first surface Wa of the wafer W may also be cleaned.

The wafer W is then transported by the wafer transport device 60 to the etching device 40. In the etching device 40, the second surface Wb of the wafer W is etched with the etching solution E under predefined etching conditions (St7 in FIG. 4). In St7, the second surface Wb is etched under the predefined etching conditions to process the second surface Wb into a target shape.

Then, the wafer W is transported to the inversion device 51 by the wafer transport device 60. In the inversion device 51, the first surface Wa and the second surface Wb of the wafer W are inverted vertically (St8 in FIG. 4). That is, the wafer W is inverted so that the first surface Wa faces upward and the second surface Wb faces downward.

Then, the wafer W is transported by the wafer transport device 60 to the thickness measurement device 50. In the thickness measurement device 50, the thickness of the wafer W after etching is measured at multiple points on the second surface Wb to obtain the thickness distribution of the wafer W, and further calculates the flatness of the wafer W (St9 in FIG. 4). The calculated thickness distribution and flatness of the wafer W are output to, for example, the control device 130.

The control device 130 performs optimization processing based on the thickness distribution and flatness of the wafer W calculated in St9 and output to the control device 130, optimizing the etching amount distribution (etching profile) in the etching process of the first surface Wa and determining the optimal etching conditions for the first surface Wa (St10 in FIG. 4). Note that the etching amount is the amount of the wafer W removed by etching, and the etching amount distribution is the distribution of the etching amount in the radial direction (within the wafer surface) of the wafer W. The method of determining the optimal etching conditions for the first surface Wa in the control device 130 will be described later.

The wafer W is then transported by the wafer transport device 60 to the etching device 40. In the etching device 40, the first surface Wa of the wafer W is etched with the etching solution E under the optimal etching conditions determined in St10 (St11 in FIG. 4). In St11, the first surface Wa is etched under the optimal etching conditions to optimize the etching amount distribution and process the first surface Wa into the target shape.

Then, the wafer W is transported by the wafer transport device 60 to the thickness measurement device 50. The thickness measurement device 50 measures the thickness of the wafer W after etching at multiple points on both the first surface Wa and the second surface Wb to obtain the thickness distribution of the wafer W (St12 in FIG. 4). The thickness measurement device 50 may further calculate the flatness of the wafer W. The obtained thickness distribution of the wafer W is output to, for example, the control device 130, and is used, for example, in the processing of another wafer W that is next processed in the wafer processing system 1.

Then, the wafer W that has been subjected to all the processes is transferred to the cassette C on the cassette mounting table 10 via the transition device 30. This completes the series of wafer processing steps in the wafer processing system 1.

In the above embodiment, the first surface Wa is ground in St1, and then the second surface Wb is ground in St4, but the order of grinding these surfaces may be reversed. Also, the second surface Wb is etched in St7, and then the first surface Wa is etched in St11, but the order of etching these surfaces may be reversed.

In the above embodiment, the etching of the first surface Wa in St11 is performed under the optimal etching conditions determined in St10, but instead, it may be performed under predetermined default etching conditions. In such a case, St9 and St10 in this embodiment are omitted. In addition, the etching of the second surface Wb in St7 is performed under predetermined default etching conditions, but instead, it may be performed under optimal etching conditions. The optimal etching conditions are determined in the same way as in St10.

Next, we will explain the method for determining the optimal etching conditions mentioned above (Step 10 in Figure 4).

First, before processing the wafer W in the wafer processing system 1, a learning process is performed to obtain multiple pieces of learning data (Step 100 in FIG. 5). The learning data is the distribution of the amount of etching of the wafer W under certain etching conditions.

In St100, etching is performed on the dummy wafer under, for example, a plurality of different etching conditions. Specifically, the dummy wafer is etched by changing, for example, the rotation speed R (also called the number of rotations) of the dummy wafer during etching, the scan speed V (also called the swing speed) of the nozzle 43, the scan width L (see the scan width L in FIG. 3, also called the swing radius) of the nozzle 43, or the number of loops N of the nozzle 43. In this case, the etching process time for each dummy wafer is the same. The dummy wafer is etched by rotating the dummy wafer and supplying etching solution E from the nozzle 43 to the dummy wafer while moving the nozzle 43 back and forth, as in the etching in St11. In the following explanation, the back and forth movement of the nozzle 43 between both ends of the dummy wafer is considered as one loop.

The etching of the dummy wafer under each etching condition is carried out for a predetermined desired time (desired number of loops). Then, the etching amount distribution of the dummy wafer is acquired, and this etching amount distribution is output to the control device 130. Furthermore, the control device 130 compresses the output etching amount distribution under each etching condition into an etching amount distribution per unit time (unit number of loops), and stores each compressed etching amount distribution as the above-mentioned learning data.

When learning data is acquired in St100, a learning data acquisition screen 200 is displayed on the display panel 120 as shown in FIG. 6. The learning data acquisition screen 200 displays a list 201 of etching conditions when acquiring learning data. The list 201 of etching conditions displays, for example, the ID of the learning data, the rotation speed R, the scan speed V, the scan width L, the number of loops N, etc.

The learning data acquisition screen 200 also displays an add button 202 for adding learning data. When the user presses the add button 202, an etching condition input screen (not shown) is displayed on the display panel 120. The etching condition input screen displays multiple preset values for each condition, such as the rotation speed R, scan speed V, scan width L, and loop count N, allowing the user to select the value for each condition. Alternatively, the etching condition input screen may be configured so that the user can directly input, for example, the rotation speed R, scan speed V, scan width L, and loop count N. The etching conditions entered on the etching condition input screen are displayed in a list 201 of etching conditions on the learning data acquisition screen 200.

The learning data acquisition screen 200 also displays a delete button 203 for deleting learning data. When the user presses the delete button 203, for example, a learning data deletion screen (not shown) for the learning data to be deleted is displayed. For example, multiple learning data IDs are displayed on the learning data deletion screen, allowing the user to select the learning data ID to be deleted. When the user selects a learning data ID, the etching conditions for that learning data ID are deleted from the list of etching conditions 201 on the learning data acquisition screen 200.

Note that the learning data acquisition screen 200 shown in FIG. 6 is an example, and other items may be displayed.

In the above, an example was described in which the learning data was obtained by etching a dummy wafer, but the etching target when obtaining the learning data is not limited to a dummy wafer. Specifically, for example, the etching process result of a product wafer W processed by the wafer processing system 1 may be stored as the learning data. Also, for example, if a film is formed on the first surface Wa of the wafer W, the etching target may be the film, and the etching process result of the film may be stored as the learning data.

In addition, although the learning data was acquired in the wafer processing system 1, it may be acquired outside the wafer processing system 1. In such a case, the control device 130 determines the optimal etching conditions based on multiple pieces of learning data acquired outside the wafer processing system 1.

Next, a screening process is performed on the multiple learning data (etching amount distributions) acquired in St100, and at least one of unnecessary etching amount distributions and similar etching amount distributions is removed in St111 described below, to select multiple valid learning data (St101 in FIG. 5). In the following description, the etching amount distribution of the valid learning data may be referred to as the "valid etching amount distribution." The method of screening multiple learning data in St101 will be described later.

Next, based on the thickness distribution in the target shape of the wafer W after etching and the thickness distribution in the surface shape of the wafer W after etching obtained in St9 (hereinafter referred to as the "actual shape"), the target etching amount distribution in the etching process in St11 is obtained (St110 in Figure 5). The target etching amount distribution in the etching process can be obtained, as an example, by calculating the difference between the thickness distribution in the target shape of the wafer W and the thickness distribution in the actual shape.

Next, an optimization method (optimization calculation) is used to optimize the effective learning data used in the overlapping and the number of overlapping times of the effective learning data so as to overlap multiple pieces of effective learning data (effective etching amount distribution) to achieve the target etching amount distribution obtained in St110 (St111 in FIG. 5).

In St111, for example, the control of the effective etching amount distribution is applied to a knapsack problem to optimize the number of times that the effective learning data and the effective learning data are overlapped. For example, the etching amount distribution is the knapsack of the knapsack problem, and the effective learning data is the items of the knapsack problem. Then, the number of times that the effective learning data and the effective learning data are overlapped is optimized so that the difference between the overlapped effective etching amount distribution and the target etching amount distribution of St110 is minimized. In other words, the etching amount distribution during etching of the first surface Wa in St11 is optimized.

Next, the etching conditions corresponding to the effective learning data optimized in St111 are integrated to determine the optimal etching conditions (St112 in FIG. 5). Specifically, the optimal etching conditions are determined by integrating the multiple selected etching conditions so that the multiple etching conditions are performed with an optimized number of overlaps. In other words, the optimal etching conditions that optimize the etching amount distribution are determined.

As described above, the optimal etching conditions for the first surface Wa in St10 are determined. In this case, by etching the first surface Wa of the wafer W under the optimal etching conditions in St11, the etching amount distribution can be optimized and the first surface Wa can be processed into the target shape.

The optimal etching conditions for the first surface Wa determined in St10 are stored in the control device 130, and the history of the etching conditions remains in the control device 130. At this time, the learning data used to determine the optimal etching conditions is also stored. In addition, the optimal etching conditions for the first surface Wa may be displayed on an etching condition history screen (not shown) on the display panel 120.

As mentioned above, the etching of the first surface Wa in St11 may be performed under predetermined etching conditions rather than the optimal etching conditions. For this reason, when setting the etching conditions, the user may be allowed to select whether or not to use the learning data.

In such a case, for example, as shown in FIG. 7, a learning data selection screen 210 is displayed on the display panel 120. A learning button 211 and a correction/non-correction button 212 are displayed on the learning data selection screen 210. When the user presses the learning button 211, the use of learning data when etching the first surface Wa is selected. When the user presses the correction/non-correction button 212, the etching conditions are corrected when etching the first surface Wa to determine optimal etching conditions. Then, it is determined whether the etching of the first surface Wa is performed under optimal etching conditions or default etching conditions. Note that the learning data selection screen 210 shown in FIG. 7 is just an example, and other items may be displayed.

Next, the above-mentioned method for screening multiple pieces of training data (Step 101 in FIG. 5) will be described. There are, for example, three patterns of methods for screening multiple pieces of training data. The first pattern is a method using a geometric method, the second pattern is a method using a graph method, and the third pattern is a method using a QR decomposition method.

In the first pattern, a geometric method is used to screen multiple pieces of learning data. First, for each etching condition in the learning process of St100, an etching amount distribution vector is obtained whose components are the etching amounts of multiple measurement points in the etching amount distribution of the learning data. In this embodiment, an etching amount distribution matrix A is obtained as the etching amount distribution vector (St200 in FIG. 8). The etching amount distribution matrix A is a matrix in which the etching amount distribution is (n, m) when the number of measurement points in the etching amount distribution is n and the number of etching conditions in the learning process of St100 is m.

Next, the dimension of the etching amount distribution matrix A acquired in St200 is compressed (St201 in FIG. 8). In St201, the dimension of the etching amount distribution matrix A is compressed from n to r to obtain a matrix A _r of (r, m). Any method for dimensional compression may be used, and for example, low-rank approximation such as singular value decomposition (SVD) or principal component analysis (PCA) may be used. The r dimension may be set arbitrarily.

Next, the vertices of the convex hull are obtained based on the etching amount distribution matrix A _r dimensionally compressed in St201 (St202 in FIG. 8). The convex hull is the smallest convex polygon (convex polyhedron) that includes all the points of the etching amount distribution matrix A _r . In St202, a convex hull algorithm is used to obtain a focal set of the convex hull of a solid (polygon) spanned by the etching amount distribution matrix A _r {a ₀ , a ₁ , ..., a _m }, that is, an r-dimensional polytope (hyperpolyhedron). Note that the convex hull algorithm is arbitrary, and a known algorithm is used.

Fig. 9 shows an example of the convex hull acquired in St 202. Fig. 9 shows a schematic convex hull when the etching amount distribution vector { _a0 , _a1 , _a2 , _a3 , _a4 , _a5 } in which the number of measurement points n is 6 is compressed into two dimensions.

Next, the etching amount distributions present inside the convex hull are removed, and multiple effective etching amount distributions (multiple effective learning data) are selected (St203 in Figure 8). Since the etching amount distribution optimized in St10 is a temporary combination of the learning data (etching amount distributions), a feasible solution in the optimization process of St10 exists inside the convex hull. Note that a feasible solution is a solution in a feasible region in the search space where the design variables and objective function values satisfy the constraint conditions. In this case, it is possible to remove etching amount distributions (learning data) that do not affect the optimization performance of the etching amount distribution in St10, i.e., data that is unnecessary for the optimization process.

9, the convex hull is a polygon spanned by six etching amount distribution vectors, and the etching amount distribution vector _a5 inside the convex hull is removed. The etching amount distribution vector _a5 can be expressed as a linear combination of the etching amount distribution vectors _a0 and _a1 , for example, and is therefore removed.

St200 to St203 are performed as described above, and etching amount distributions that are not necessary for the optimization process of etching amount distribution in St10 are removed, and multiple valid learning data are selected.

10 is an explanatory diagram showing how multiple learning data are screened using the geometric method of the first pattern. FIG. 10(a) shows multiple learning data before screening, and FIGS. 10(b) and (c) show multiple valid learning data after screening. In addition, in FIG. 10(b), the dimension of the etching amount distribution matrix is compressed to four dimensions (r=4), and in FIG. 10(c), the dimension of the etching amount distribution matrix is compressed to three dimensions (r=3). Note that the horizontal axis of FIG. 10 indicates the radial position from the center of the wafer (0 (zero) on the horizontal axis) to the outer periphery, and the vertical axis indicates the etching amount. In this example, the wafer W is, for example, a wafer with a diameter of 300 mm, but is not limited to this. In this example, the numerical values of the etching amount are examples and are not limited to this.

Referring to FIG. 10, the number of learning data shown in FIG. 10(a) is 27, while the number of valid learning data shown in FIG. 10(b) is 23, and the number of valid learning data shown in FIG. 10(c) is 20. Therefore, when the first pattern of geometric method is used, valid learning data can be appropriately selected. Furthermore, the smaller the dimension r compressed in the etching amount distribution matrix, the smaller the number of valid learning data, and the more appropriately the valid learning data can be selected.

Here, if all of the learning data acquired in St100 is used as in the conventional method, the calculation time required for the optimization calculation in St111 in the optimization process of the etching amount distribution in St10 will be long. In other words, the more learning data there is, the longer the calculation time required for the optimization calculation.

If the optimization calculation takes a long time, the throughput of wafer processing may decrease. For example, depending on the transport path of the wafer W, the thickness measurement device 50 may not be able to measure the thickness of the next wafer W in St9 while the optimization calculation in St111 is being performed. In such cases, the waiting time for the next wafer W becomes longer, and the throughput of wafer processing decreases.

In addition, if the amount of training data used in an optimization calculation becomes large, the optimization calculation may not finish. When solving a knapsack problem as an optimization calculation, if the amount of training data is large, a phenomenon known as combinatorial explosion may occur, and a solution may not be found.

In addition, when performing optimization calculations, learning data for new etching conditions may be added to obtain an appropriate solution. However, in such cases, the calculation time for the optimization calculation becomes even longer, making it practically impossible to add learning data.

In this regard, when the geometric method of the first pattern is used, the number of learning data can be appropriately reduced to obtain valid learning data, and as a result, the calculation time for the optimization calculation can be shortened. Therefore, the decrease in throughput of the wafer processing described above can be suppressed, and the throughput can be improved. In addition, the optimization calculation can be performed appropriately, and it is also possible to add learning data for new etching conditions. And, when learning data for new etching conditions is added, the reliability of the optimization process for the etching amount distribution of St10 can be improved, and the optimization accuracy (estimation accuracy) can be improved.

In addition, when the geometric method of the first pattern is used, the calculation time for the optimization calculation can be shortened, or in other words, it is possible to increase the amount of learning data acquired in the original St100. In such a case, it is possible to improve the reliability of the optimization process of the etching amount distribution of St10, and improve the optimization accuracy.

In addition, generally, when the number of learning data used in the optimization calculation in St111 is reduced, the optimization accuracy in the optimization process of the etching amount distribution is likely to change. In this regard, when the geometric method of the first pattern is used, the learning data removed in St203 can be replaced with a combination of other learning data, so that the optimization accuracy in the optimization process of the etching amount distribution in St10 can be maintained. For example, in the example shown in FIG. 9, the removed etching amount distribution vector _a5 can be replaced with a combination of etching amount distribution vectors _a0 and _a1 .

In addition, in the geometric method of the first pattern, dimensional compression of the etching amount distribution matrix of St201 is not essential, and St201 may be omitted. However, if dimensional compression of St201 is not performed, fewer etching amount distribution vectors are contained inside the convex hull obtained in St202, that is, fewer unnecessary etching amount distributions can be removed. For this reason, it is preferable to perform dimensional compression of St201, and in such a case, etching amount distributions unnecessary for the optimization process can be appropriately removed, and effective learning data can be appropriately selected.

In the second pattern, a graph method is used to screen multiple pieces of learning data. First, an etching amount distribution matrix A is obtained as an etching amount distribution vector (St300 in FIG. 11). The etching amount distribution matrix A is a matrix in which the etching amount distribution is (n, m) when the number of measurement points in the etching amount distribution is n and the number of etching conditions in the learning process of St100 is m. The method of obtaining the etching amount distribution matrix A in St300 is the same as in St200, so a detailed explanation will be omitted.

Next, the dimension of the etching amount distribution matrix A acquired in St300 is compressed to acquire an r-dimensional etching amount distribution matrix A _r (St301 in FIG. 11). The dimension compression method in St301 is the same as that in St201, and therefore a detailed description thereof will be omitted.

Next, the similarity or dissimilarity between columns of the etching amount distribution matrix A _r that has been dimension-compressed in St301, i.e., between etching amount distribution vectors, is calculated (St302 in FIG. 11). The method for calculating the similarity or dissimilarity in St302 is arbitrary, and a known method is used.

The following describes the case where the dissimilarity is calculated in St302. In St302, for example, the dissimilarity ∥u _k -u _l ∥ ₂ is calculated between columns of the etching amount distribution matrix A _r . When the similarity between the etching amount distribution vectors is low, or when the L ₂ norm of each etching amount distribution vector is large, the L ₂ norm of the cross product takes a large value, and can be regarded as a dissimilarity.

Next, a first complete graph is obtained in which the etching conditions are the vertices (nodes) and the dissimilarity is the weight of the edge (St303 in FIG. 11). The first complete graph is a simple graph in which every two dissimilar vertices are adjacent, that is, a complete undirected graph in which all vertices are connected by edges. FIG. 12(a) shows an example of the first complete graph obtained in St303. Note that the vertices in the first complete graph may be etching amount distributions instead of etching conditions. Also, the edges in the first complete graph may be similarities instead of dissimilarity.

Next, in the first complete graph obtained in St303, edges whose dissimilarity is equal to or less than the edge cut parameter s are removed to obtain a second complete graph (St304 in FIG. 11). The edge cut parameter s is a predetermined threshold and can be determined arbitrarily. FIG. 12(b) shows an example of the second complete graph obtained in St304. Note that, when similarity is used for the edges of the first complete graph, in St304, edges whose dissimilarity is equal to or more than the predetermined threshold are removed to obtain the second complete graph.

Next, in the second complete graph obtained in St304, the maximum clique problem is solved to find the vertex set of the maximum clique, and the etching amount distribution corresponding to the vertices included in the vertex set is selected as the effective etching amount distribution (effective learning data) (St305 in FIG. 11). In St305, the maximum clique problem is a type of optimization problem that finds the vertex set with the largest number of vertices that induces a complete graph in a simple undirected graph, and the vertex set of the maximum clique is found by solving this maximum clique problem. In addition, the vertices of the second complete graph are etching conditions, and the etching amount distribution corresponding to the etching conditions included in the vertex set is set as the effective etching amount distribution. Note that if the vertices of the second complete graph are etching amount distributions, the vertices included in the vertex set become the effective etching amount distribution as they are.

In this case, when the edges of the first complete graph are removed in St304, the removed vertices are not connected to each other and do not form a clique. Then, when the vertex set that forms the maximum clique is found in St305, all of the vertices in the vertex set are connected to each other. In other words, since only one of the similar vertices is selected, etching amount distributions (learning data) with low dissimilarity, i.e., etching amount distributions with high similarity, can be removed.

Figure 12(c) shows an example of the vertex set of the maximum clique obtained in St305. In Figure 12(c), the vertices painted in black are the vertex set of the maximum clique, and the etching amount distribution corresponding to the vertices included in this vertex set is selected as the effective etching amount distribution.

Steps 300 to 205 are performed as described above, similar etching amount distributions are eliminated, and multiple valid learning data are selected.

FIG. 13 is an explanatory diagram showing how multiple pieces of training data are screened using the second pattern of the graph method. FIG. 13(a) shows multiple pieces of training data before screening, and FIGS. 13(b) and (c) show multiple pieces of valid training data after screening. In addition, in FIG. 13(b), the edge cut parameter s is 0.1 (s=0.1), and in FIG. 10(c), the edge cut parameter s is 0.2 (s=0.2).

Referring to FIG. 13, the number of training data shown in FIG. 13(a) is 27, whereas the number of valid training data shown in FIG. 13(b) is 18, and the number of valid training data shown in FIG. 10(c) is 11. Therefore, when the second pattern of the graph method is used, valid training data can be appropriately selected. Furthermore, the larger the dissimilarity edge cut parameter s is, the smaller the number of valid training data becomes, and the more appropriately valid training data can be selected.

When the second pattern of the graph method is used, the number of learning data can be appropriately reduced to obtain valid learning data, and as a result, the calculation time for the optimization calculation can be shortened. In other words, similar to the first pattern of the geometric method, the throughput of wafer processing can be improved. In addition, the optimization calculation can be performed appropriately, and it is also possible to add learning data for new etching conditions.

Here, in the optimization process of the etching amount distribution in St10, if similar learning data are used, both sets of learning data may be adopted, resulting in multiple combinations. In the optimization process of St10, the expression of the etching amount distribution when switching etching conditions (leaves) lacks accuracy, so the more combinations there are, the larger the optimization error (estimation error) may become.

In this regard, when the second pattern of the graph method is used, similar learning data is removed, so the number of etching conditions (number of leaves) is reduced, the combinations in the optimization process of St10 are simplified, and the optimization error can be kept small.

In addition, in the graph method of the second pattern, dimensional compression of the etching amount distribution matrix of St301 is not essential, and St301 may be omitted.

In addition, in the graph method of the second pattern, instead of St303 to St305, other methods may be used to remove similar learning data. Any method may be used as long as it is possible to remove etching amount distributions for etching conditions in which the similarity or dissimilarity between the etching amount distribution vectors calculated in St302 is equal to or greater than a predetermined threshold, or etching amount distributions for etching conditions in which the dissimilarity is equal to or less than a predetermined threshold.

In the third pattern, multiple learning data are screened using the QR decomposition method. First, the etching amount distribution matrix A is obtained (St400 in FIG. 14). The etching amount distribution matrix A is a matrix in which the etching amount distribution is (n, m) when the number of measurement points in the etching amount distribution is n and the number of etching conditions in the learning process of St100 is m. The method of obtaining the etching amount distribution matrix A in St400 is the same as that in St200, so a detailed explanation will be omitted.

The inventors have considered using, for example, a sensor placement problem for determining optimal sensor positions for multiple sensors as a method for screening multiple training data. In the sensor placement problem, a sensor set is determined for a sensor placement matrix such that the minimum singular value is maximized under the constraint that the number of sensor sets is a desired number p. In other words, a sensor set is determined for which the sum of the singular values of the sensor placement matrix is maximized (the volume of a p-dimensional solid is maximized). However, it is difficult to directly calculate the known formula for this sensor placement problem.

Therefore, the present inventors have conducted extensive research and have come up with the idea of performing pivot selection QR decomposition on the sensor arrangement matrix, i.e., the etching amount distribution matrix A, as an efficient calculation method. That is, the sum of the singular values of the above-mentioned etching amount distribution matrix A is equal to the sum of the diagonal elements r _ii of the upper triangular matrix R obtained by QR decomposing the etching amount distribution matrix A, as shown in the following formula (1). Note that the QR decomposition decomposes the (n, m) etching amount distribution matrix A into the product of an n-th order orthogonal matrix Q and an upper triangular matrix R of (n, m).

Moreover, by performing QR decomposition with pivot selection on the etching amount distribution matrix A as shown in the following formula (2), the diagonal elements r _ii of the upper triangular matrix R are in descending order, that is, in descending order of contribution to the singular values. Note that the pivot is the leftmost non-zero value in a row of the etching amount distribution matrix A. The pivot selection is to interchange the rows or columns of the etching amount distribution matrix A so that the value does not become 0 (zero) or a small value. The pivot selection matrix P is a column that stores the row numbers after the pivot selection.

Then, delete the etching amount distribution data from the end of the pivot selection matrix P until the number of valid training data after screening reaches p.

In order to realize a method corresponding to the above sensor placement problem, QR decomposition with pivot selection is performed on the etching amount distribution matrix A acquired in St400 (St401 in FIG. 14). In St401, when n=M, QR decomposition with pivot selection is performed on the etching amount distribution matrix A. Also, when n≠M, QR decomposition with pivot selection is performed on the product A ^{T A of the inverse matrix A T of} the etching amount distribution matrix and the etching amount distribution matrix A.

Next, the pivot selection matrix P and the total power of the diagonal elements r _ii of the upper triangular matrix R are obtained (St402 in FIG. 14). In St402 of this embodiment, the total power of the diagonal elements r _ii is set to the value shown in the following formula (3) in order to reduce the number of digits of the calculation. In addition, since pivot selection is performed, the diagonal elements r _ii are automatically arranged in ascending order.

Next, the effective total product of the diagonal elements of the upper triangular matrix R, excluding the tail r _nn , is obtained (Step 403 in FIG. 14). The effective total product of the diagonal elements obtained in Step 403 is expressed by the following formula (4).

Next, it is determined whether the effective product of the diagonal elements expressed by the above formula (4) is equal to or less than a predetermined threshold (Step 404 in FIG. 14). The threshold in Step 404 can be determined arbitrarily.

In step 404, if the effective product of the diagonal elements expressed by the above formula (4) is equal to or less than a predetermined threshold, the etching amount distribution corresponding to the end of the pivot selection matrix P is removed (step 405 in FIG. 14). Then, the process returns to step 403.

The above-mentioned steps St403 to St405 are repeated. Then, when the effective sum of the diagonal components expressed by the above formula (4) becomes larger than a predetermined threshold in St404, the series of processes is terminated, and multiple effective etching amount distributions (multiple effective learning data) are selected (St406 in FIG. 14). That is, the pivot selection matrix P is acquired in St402, and the tails r _nn of the diagonal components are removed in St404, so that the etching amount distribution matrix A is maximized in St406, and multiple effective etching amount distributions are selected.

When the QR decomposition method of the third pattern is used, the number of learning data can be appropriately reduced to obtain valid learning data, and as a result, the calculation time for optimization calculation can be shortened. In other words, similar to the geometric method of the first pattern and the graph method of the second pattern, the throughput of wafer processing can be improved. In addition, optimization calculation can be performed appropriately, and it is also possible to add learning data for new etching conditions.

In addition, when the third pattern of the QR decomposition method is used, similar learning data is removed, so the number of etching conditions (number of leaves) is reduced, the combinations in the optimization process of St10 are simplified, and the optimization error can be kept small.

In addition, when using the third pattern QR decomposition method, data unnecessary for the optimization process of the etching amount distribution of St10 can also be removed.

In the QR decomposition method of the third pattern, the dimension of the etching amount distribution matrix A in St400 may be compressed to obtain an r-dimensional etching amount distribution matrix A _r . This dimension compression method is the same as that in St201. Then, in and after St401, the QR decomposition and other processes are performed using the dimension-compressed etching amount distribution matrix A _r .

The above first pattern of geometric method and second pattern of graphical method may be combined to screen multiple learning data. First, in the first pattern of geometric method, steps St200 to St203 are performed to select a first effective etching amount distribution (first effective learning data). Next, in the second pattern of graphical method, steps St300 to St305 are performed using the first effective etching amount distribution to select a second effective etching amount distribution (second effective learning data).

In such a case, the first pattern geometric method can remove data that is not necessary for the optimization process of the etching amount distribution of St10, and the second pattern graphical method can also remove similar etching amount distributions. Therefore, it is possible to more appropriately select valid learning data. Note that the order of the first pattern geometric method and the second pattern graphical method is not limited to this embodiment, and the first pattern geometric method may be performed after the second pattern graphical method.

Similarly, the above-mentioned first pattern of geometric method and the third pattern of QR decomposition method may be combined to screen multiple learning data. First, in the first pattern of geometric method, St200 to St203 are performed to select a first effective etching amount distribution (first effective learning data). Next, in the third pattern of QR decomposition method, St400 to St406 are performed using the first effective etching amount distribution to select a second effective etching amount distribution (second effective learning data).

In such a case, the geometric method of the first pattern can remove data that is not necessary for the optimization process of the etching amount distribution of St10, and further, the QR decomposition method of the third pattern can remove similar etching amount distributions. Therefore, it is possible to more appropriately select valid learning data. Note that the order of the geometric method of the first pattern and the QR decomposition method of the third pattern is not limited to this embodiment, and the geometric method of the first pattern may be performed after the QR decomposition method of the third pattern.

In the above embodiment, the etching amount distribution is used as the etching index distribution (learning data) for controlling the etching process of the wafer W, but the etching amount deviation distribution may also be used. The etching amount deviation distribution is a distribution of values obtained by subtracting the average value of the etching amount from the etching amount within the wafer surface. In such a case, when determining the optimal etching conditions in St10, the etching amount deviation distribution is used instead of the etching amount distribution.

In the above embodiment, an example has been described in which various processes are performed on both sides (first surface Wa and second surface Wb) of a wafer W that has been cut from an ingot using a wire saw or lapped, but various processes may be performed on only one side of the wafer W.

In the above embodiment, various processes are performed on a wafer W that has been cut from an ingot using a wire saw or lapped, but the technology disclosed herein can also be applied to post-processing steps in the manufacturing process of semiconductor devices. Specifically, the technology disclosed herein can also be applied to a laminated wafer formed by bonding a first wafer and a second wafer, in which the first wafer is ground and then the surface of the ground first wafer is etched.

The embodiments disclosed herein should be considered to be illustrative and not restrictive in all respects. The above-described embodiments may be omitted, substituted, or modified in various ways without departing from the spirit and scope of the appended claims. For example, the components of the above-described embodiments may be combined in any manner. Such any combination will naturally provide the functions and effects of each of the components in the combination, as well as other functions and effects that will be apparent to a person skilled in the art from the description in this specification.

Furthermore, the effects described in this specification are merely descriptive or exemplary and are not limiting. In other words, the technology disclosed herein may achieve other effects that are apparent to a person skilled in the art from the description in this specification, in addition to or in place of the above effects.

1 Wafer processing system 40 Etching device 130 Control device W Wafer

Claims (20)

A substrate processing method for processing a substrate, comprising the steps of:
Optimizing the etching amount distribution to determine optimal etching conditions;
supplying an etching solution to a surface of the substrate based on the optimal etching conditions to etch the surface;
Determining the optimal etching conditions includes:
Obtaining a plurality of radial etching amount distributions when etching a surface of a substrate under a plurality of different etching conditions;
performing a screening process on the plurality of etching amount distributions to remove at least one of an etching amount distribution unnecessary for the optimization process and a similar etching amount distribution, thereby selecting a plurality of effective etching amount distributions;
optimizing a combination of the effective etching amount distributions used for superposition and the number of times the effective etching amount distributions are superposed, by using an optimization method, so that the shape of the surface of the substrate becomes a target shape;
and determining the optimal etching conditions by integrating the etching conditions corresponding to the optimized combinations. Selecting the plurality of effective etching amount distributions includes:
acquiring an etching amount distribution vector having etching amounts at a plurality of measurement points in the etching amount distribution as components for each of the etching conditions;
Obtaining a convex hull with the etching amount distribution vector as a vertex;
The substrate processing method according to claim 1 , further comprising: removing the etching amount distribution existing inside the convex hull to select the plurality of effective etching amount distributions. The substrate processing method according to claim 2, further comprising compressing a dimension of the etching amount distribution vector, which is the number of measurement points, and obtaining the convex hull with the dimension-compressed etching amount distribution vector as a vertex. Selecting the plurality of effective etching amount distributions includes:
acquiring an etching amount distribution vector having etching amounts at a plurality of measurement points in the etching amount distribution as components for each of the etching conditions;
Calculating a similarity or a difference between the etching amount distribution vectors;
and selecting the plurality of effective etching amount distributions by removing the etching amount distributions of the etching conditions in which the degree of similarity is equal to or greater than a predetermined threshold, or the etching amount distributions of the etching conditions in which the degree of dissimilarity is equal to or less than a predetermined threshold. obtaining a first complete graph having the etching conditions or the etching amount distribution as vertices and the similarities or the dissimilarities as edges;
removing, from the first complete graph, edges whose similarity is equal to or greater than a predetermined threshold or edges whose dissimilarity is equal to or less than a predetermined threshold, to obtain a second complete graph;
5. The substrate processing method according to claim 4, further comprising: determining a vertex set of a maximum clique in the second complete graph; and selecting the etching amount distributions corresponding to vertices included in the vertex set as the plurality of effective etching amount distributions. The substrate processing method according to claim 4 or 5, further comprising compressing a dimension, which is the number of measurement points, in the etching amount distribution vector, and calculating a similarity or a dissimilarity between the etching amount distribution vectors in which the dimension has been compressed. Selecting the plurality of effective etching amount distributions includes:
acquiring an etching amount distribution matrix having a number of the measurement points in the etching amount distribution as a row number, a number of the etching conditions as a column number, and an etching amount distribution matrix having the etching amounts in the etching amount distribution as components;
performing QR decomposition with pivot selection on the etching amount distribution matrix to obtain a pivot selection matrix;
2. The substrate processing method according to claim 1, further comprising: selecting the plurality of effective etching amount distributions by removing the etching amount distribution corresponding to a tail of the pivot selection matrix. The substrate processing method according to claim 7, further comprising compressing a dimension, which is the number of measurement points, in the etching amount distribution matrix, performing QR decomposition with pivot selection on the etching amount distribution matrix with the dimension compressed, and obtaining the pivot selection matrix. Selecting the plurality of effective etching amount distributions includes:
acquiring an etching amount distribution vector having etching amounts at a plurality of measurement points in the etching amount distribution as components for each of the etching conditions;
Obtaining a convex hull with the etching amount distribution vector as a vertex;
removing the etching amount distribution existing inside the convex hull to select a plurality of first effective etching amount distributions;
Calculating a similarity or a difference between the first effective etching amount distributions;
and selecting a plurality of second effective etching amount distributions by removing the etching amount distributions of etching conditions in which the similarity is equal to or greater than a predetermined threshold value, or the etching amount distributions of etching conditions in which the dissimilarity is equal to or less than a predetermined threshold value. Selecting the plurality of effective etching amount distributions includes:
acquiring an etching amount distribution vector having etching amounts at a plurality of measurement points in the etching amount distribution as components for each of the etching conditions;
Obtaining a convex hull with the etching amount distribution vector as a vertex;
removing the etching amount distribution existing inside the convex hull to select a plurality of first effective etching amount distributions;
acquiring an etching amount distribution matrix having a number of a plurality of measurement points in the first effective etching amount distribution as a row number, a number of the plurality of etching conditions as a column number, and an etching amount distribution matrix having an etching amount in the first effective etching amount distribution as a component;
performing QR decomposition with pivot selection on the etching amount distribution matrix to obtain a pivot selection matrix;
2. The substrate processing method according to claim 1, further comprising: removing the etching amount distribution corresponding to a tail of the pivot selection matrix to select a plurality of second effective etching amount distributions. A substrate processing system for processing a substrate, comprising:
an etching device that supplies an etching solution to a surface of a substrate to etch the surface;
a control device that controls etching of the substrate in the etching device based on optimal etching conditions;
The control device includes:
A control for acquiring a plurality of radial etching amount distributions when the surface of the substrate is etched under a plurality of different etching conditions;
a control for selecting a plurality of effective etching amount distributions by performing a screening process on the plurality of etching amount distributions and removing at least one of an etching amount distribution unnecessary for the optimization process of the etching amount distribution and a similar etching amount distribution;
using an optimization method to optimize a combination of the effective etching amount distributions used for the overlapping and the number of times the effective etching amount distributions are overlapped, so that the shape of the surface of the substrate becomes a target shape;
and determining the optimal etching conditions by integrating the etching conditions corresponding to the optimized combination. The control device includes:
Control for acquiring an etching amount distribution vector having etching amounts at a plurality of measurement points in the etching amount distribution as components for each of the etching conditions;
A control to obtain a convex hull having the etching amount distribution vector as a vertex;
12. The substrate processing system according to claim 11, further comprising: a control for selecting the plurality of effective etching amount distributions by removing the etching amount distribution existing inside the convex hull. The substrate processing system of claim 12, wherein the control device executes control to compress a dimension, which is the number of measurement points, in the etching amount distribution vector and obtain the convex hull with the dimension-compressed etching amount distribution vector as a vertex. The control device includes:
Control for acquiring an etching amount distribution vector having etching amounts at a plurality of measurement points in the etching amount distribution as components for each of the etching conditions;
A control for calculating a similarity or a difference between the etching amount distribution vectors;
and selecting the plurality of effective etching amount distributions by removing the etching amount distributions of the etching conditions in which the similarity is equal to or greater than a predetermined threshold value, or the etching amount distributions of the etching conditions in which the dissimilarity is equal to or less than a predetermined threshold value. The control device includes:
A control for acquiring a first complete graph having the etching condition or the etching amount distribution as vertices and the similarity or the dissimilarity as edges;
a control for removing, from the first complete graph, an edge whose similarity is equal to or greater than a predetermined threshold or an edge whose dissimilarity is equal to or less than a predetermined threshold, to obtain a second complete graph;
15. The substrate processing system according to claim 14, further comprising: a control for determining a vertex set of a maximum clique in the second complete graph, and selecting the etching amount distributions corresponding to vertices included in the vertex set as the plurality of effective etching amount distributions. The substrate processing system according to claim 14 or 15, wherein the control device executes control to compress a dimension, which is the number of measurement points, in the etching amount distribution vector and calculate a similarity or dissimilarity between the etching amount distribution vectors with the compressed dimension. The control device includes:
a control for acquiring an etching amount distribution matrix in which the number of the measurement points in the etching amount distribution is the number of rows, the number of the etching conditions is the number of columns, and the etching amounts in the etching amount distribution are components;
A control of performing QR decomposition with pivot selection on the etching amount distribution matrix to obtain a pivot selection matrix;
12. The substrate processing system according to claim 11, further comprising: a control for selecting the plurality of effective etching amount distributions by removing the etching amount distribution corresponding to a tail of the pivot selection matrix. The substrate processing system of claim 17, wherein the control device executes control to compress a dimension, which is the number of measurement points, in the etching amount distribution matrix, perform QR decomposition with pivot selection on the etching amount distribution matrix with the compressed dimension, and obtain the pivot selection matrix. The control device includes:
Control for acquiring an etching amount distribution vector having etching amounts at a plurality of measurement points in the etching amount distribution as components for each of the etching conditions;
A control to obtain a convex hull having the etching amount distribution vector as a vertex;
a control for selecting a plurality of first effective etching amount distributions by removing the etching amount distribution existing inside the convex hull;
A control for calculating a similarity or a difference between the first effective etching amount distributions;
and selecting a plurality of second effective etching amount distributions by removing the etching amount distributions of etching conditions in which the similarity is equal to or greater than a predetermined threshold value, or the etching amount distributions of etching conditions in which the dissimilarity is equal to or less than a predetermined threshold value. The control device includes:
Control for acquiring an etching amount distribution vector having etching amounts at a plurality of measurement points in the etching amount distribution as components for each of the etching conditions;
A control to obtain a convex hull having the etching amount distribution vector as a vertex;
a control for selecting a plurality of first effective etching amount distributions by removing the etching amount distribution existing inside the convex hull;
a control for acquiring an etching amount distribution matrix in which the number of the measurement points in the first effective etching amount distribution is the number of rows, the number of the etching conditions is the number of columns, and the etching amount distribution matrix has the etching amounts in the first effective etching amount distribution as components;
A control of performing QR decomposition with pivot selection on the etching amount distribution matrix to obtain a pivot selection matrix;
12. The substrate processing system according to claim 11, further comprising: a control for selecting a plurality of second effective etching amount distributions by removing the etching amount distribution corresponding to a tail of the pivot selection matrix.

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