Substrate processing apparatus and temperature control method

Abstract

To perform control of a critical dimension in a substrate with high accuracy while satisfying a restriction of a temperature of each division region.SOLUTION: A substrate processing apparatus has a stage and a calculation part. The stage is provided with a mounting surface on which the substrate is mounted, and is provided with a heater that can adjust a temperature in each division region obtained by dividing the mounting surface. The calculation part is constructed so as to calculate a target temperature of the heater in each division region where a critical dimension of a predetermined measurement point of the substrate when predetermined substrate processing is performed on the substrate mounted on the mounting surface is performed satisfies a predetermined condition while considering a heat transfer between adjacent division regions and a restriction of a settable temperature range of each division region.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present disclosure relates to a substrate processing apparatus and a temperature control method. [Background technology]

[0002] The following Patent Document 1 discloses a method of using a plasma etching system including a substrate support assembly for supporting a substrate during plasma etching, the substrate support assembly including a plurality of independently controllable heater regions disposed under device die positions on the substrate, and a controller for controlling each heater region, the method comprising the steps of: measuring pre-etch critical device parameters at a plurality of device die positions on the substrate; transmitting at least one of the pre-etch critical device parameters and post-etch critical device parameters of a previously etched substrate to the plasma etching system; thereafter supporting the substrate on the substrate support assembly; transmitting process recipe parameters to the plasma etching system and / or loading process recipe parameters from a storage device to the plasma etching system; predicting a target etching temperature at a predetermined position on the substrate from at least one of the process recipe parameters, target post-etch critical device parameters, the pre-etch critical device parameters, and the post-etch critical device parameters; adjusting the temperature at each device die position to the target etching temperature using the controllable heater regions; and plasma etching the substrate. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2016-178316 A Summary of the Invention [Problem to be solved by the invention]

[0004] The present disclosure provides a technique for accurately controlling critical dimensions within a substrate while satisfying temperature constraints for each divided region. [Means for solving the problem]

[0005] A substrate processing apparatus according to an aspect of the present disclosure includes a stage and a calculation unit. The stage is provided with a mounting surface on which a substrate is mounted, and a heater capable of adjusting temperature is provided in each divided region obtained by dividing the mounting surface. The calculation unit is configured to calculate a target temperature of the heater in each divided region at which a critical dimension of a predetermined measurement point on the substrate satisfies a predetermined condition when a predetermined substrate processing is performed on the substrate mounted on the mounting surface, taking into account heat transfer between adjacent divided regions and a constraint on a temperature range that can be set for the heater in each divided region. Effect of the Invention

[0006] According to the present disclosure, it is possible to precisely control the critical dimensions within a substrate while satisfying the temperature constraints of each divided region. [Brief description of the drawings]

[0007] [Figure 1] FIG. 1 is a schematic configuration diagram of a substrate processing system according to an embodiment of the present invention. [Diagram 2] FIG. 2 is a diagram illustrating a schematic configuration of a plasma processing apparatus according to an embodiment. [Diagram 3] FIG. 3 is a plan view illustrating an example of the configuration of an electrostatic chuck according to an embodiment. [Figure 4] FIG. 4 is a cross-sectional view illustrating an example of the configuration of an electrostatic chuck according to an embodiment. [Diagram 5] FIG. 5 is a block diagram showing a schematic configuration of a control unit that controls the plasma processing apparatus according to an embodiment. [Figure 6] FIG. 6 is a diagram showing an example of a temperature distribution. [Figure 7] FIG. 7 is a diagram for explaining the relationship between the divided regions. [Figure 8]FIG. 8 is a diagram illustrating an example of the relationship between the sum of squares of the error and the range. [Figure 9] FIG. 9 is a graph showing an example of the change in equation (19). [Figure 10] FIG. 10 is a graph showing an example of the change in equation (20). [Figure 11A] FIG. 11A is a diagram illustrating the constraints. [Figure 11B] FIG. 11B is a diagram illustrating the constraints. [Figure 11C] FIG. 11C is a diagram illustrating the constraints. [Figure 12A] FIG. 12A is a diagram illustrating an example of a change in value Z of the loss function excluding the constraint function. [Figure 12B] FIG. 12B is a diagram showing an example of a change in equation (20) for constraints 1 and 2. [Figure 12C] FIG. 12C is a diagram illustrating an example of a change in value Z of the loss function including the constraint function. [Figure 13] FIG. 13 is a flowchart showing an example of the flow of the temperature control method according to the first embodiment. [Figure 14] FIG. 14 is a flowchart showing an example of the flow of the temperature control method according to the second embodiment. [Figure 15] FIG. 15 is a diagram illustrating a schematic configuration of a plasma processing apparatus according to the third embodiment. [Figure 16] FIG. 16 is a plan view illustrating an example of the configuration of an electrostatic chuck according to the third embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0008] Hereinafter, embodiments of a substrate processing apparatus and a temperature control method will be described in detail with reference to the drawings. Note that the substrate processing apparatus and the temperature control method disclosed below are not limited to the following embodiments. In addition, the same reference numerals are used for the same or corresponding parts in each drawing. In addition, each embodiment can be appropriately combined within a range that does not cause a contradiction in the processing contents.

[0009] With each generation of semiconductor technology, substrates such as wafers are increasing in diameter, while transistors tend to become smaller, requiring greater precision in substrate processing.

[0010] One of the precisions required for substrate processing is the uniformity of the critical dimensions within the substrate. In substrate processing, the progress of the processing changes depending on the temperature of the substrate. In order to achieve more advanced temperature control of the substrate, some substrate processing apparatuses divide the stage's substrate placement surface into multiple divided areas, provide heaters in each divided area, and adjust the temperature of each divided area so that the critical dimensions at a specified position on the substrate meet specified conditions.

[0011] Incidentally, when the mounting surface of a stage is divided into a plurality of divided regions and the temperature of each divided region is adjusted, the temperature changes near the boundary between each divided region and the adjacent divided region due to the influence of the adjacent divided region. In addition, the adjustable temperature of each divided region of the stage may be restricted. For example, if the temperature difference between the divided regions of the stage is large, hardware defects such as cracks may occur due to stress. In addition, if the temperature difference between the adjacent divided regions of the stage is large, the transfer of heat between the divided regions becomes large, making it impossible to control the temperature with precision. For this reason, the conventional technology may not be able to control the critical dimensions in the substrate with precision. Therefore, a technology that accurately controls the critical dimensions in the substrate while satisfying the temperature constraints of each divided region is expected.

[0012] (First embodiment) [Substrate processing system configuration] First, a schematic configuration of a substrate processing system according to an embodiment will be described. The substrate processing system is a system that performs a predetermined substrate processing on a substrate such as a wafer. In this embodiment, the substrate processing apparatus according to the present disclosure is a plasma processing apparatus, and a case where plasma etching is performed on a substrate as the substrate processing will be described as an example. FIG. 1 is a schematic configuration diagram of a substrate processing system according to an embodiment. The substrate processing system 1000 has a plasma processing apparatus 1 and a measuring apparatus 2. The plasma processing apparatus 1 and the measuring apparatus 2 are connected to each other via a network N so that they can communicate with each other. The network N can be any type of communication network, whether wired or wireless, such as a LAN (Local Area Network) or a VPN (Virtual Private Network).

[0013] The plasma processing apparatus 1 is an apparatus that performs a predetermined substrate processing on a substrate. In this embodiment, the plasma processing apparatus 1 performs plasma etching on a semiconductor wafer (hereinafter, referred to as a "wafer") as the substrate.

[0014] The measuring device 2 is a device that measures a critical dimension at a measurement point, which is a predetermined position on a substrate that has been subjected to substrate processing by the plasma processing device 1. In this embodiment, the measuring device 2 measures the width of a pattern at the measurement point as the critical dimension. Hereinafter, the critical dimension is also referred to as "CD." A plurality of measurement points for measuring the CD are provided at different positions on the substrate. The measuring device 2 measures the width of the pattern at each measurement point. The measuring device 2 may be an inspection device that inspects the substrate for defects. The measuring device 2 transmits CD data for each measured measurement point to the plasma processing device 1.

[0015] In the plasma processing apparatus 1, the mounting surface on which the substrate is placed is divided into multiple divided areas, and based on the CD data of each measurement point received from the measurement device 2, the plasma processing apparatus 1 performs control to adjust the temperature of each divided area so that the CD of each measurement point on the substrate satisfies predetermined conditions.

[0016] [Configuration of plasma processing apparatus 1] Next, the configuration of the plasma processing apparatus 1 will be described. FIG. 2 is a diagram showing a schematic diagram of the plasma processing apparatus 1 according to an embodiment. FIG. 2 shows a schematic diagram of a longitudinal cross-sectional structure of the plasma processing apparatus 1 according to an embodiment. The plasma processing apparatus 1 includes a plasma processing chamber 10, a gas supply unit 20, a power supply 30, and an exhaust system 40. The plasma processing apparatus 1 also includes a substrate support unit 11 and a gas inlet unit. The gas inlet unit is configured to introduce at least one processing gas into the plasma processing chamber 10. The gas inlet unit includes a shower head 13. The substrate support unit 11 is disposed in the plasma processing chamber 10. The shower head 13 is disposed above the substrate support unit 11. In an embodiment, the shower head 13 constitutes at least a part of the ceiling of the plasma processing chamber 10. The plasma processing chamber 10 has a plasma processing space 10s defined by the shower head 13, a sidewall 10a of the plasma processing chamber 10, and the substrate support unit 11. The plasma processing chamber 10 has at least one gas supply port for supplying at least one processing gas to the plasma processing space 10s and at least one gas exhaust port for exhausting gas from the plasma processing space. The plasma processing chamber 10 is grounded. The showerhead 13 and the substrate support 11 are electrically insulated from the housing of the plasma processing chamber 10.

[0017] The substrate support 11 includes a main body 111 and a ring assembly 112. The main body 111 has a central region 111a for supporting the substrate W and an annular region 111b for supporting the ring assembly 112. A wafer is an example of the substrate W. The annular region 111b of the main body 111 surrounds the central region 111a of the main body 111 in a plan view. The substrate W is disposed on the central region 111a of the main body 111, and the ring assembly 112 is disposed on the annular region 111b of the main body 111 so as to surround the substrate W on the central region 111a of the main body 111. Therefore, the central region 111a is also called a substrate support surface for supporting the substrate W, and the annular region 111b is also called a ring support surface for supporting the ring assembly 112.

[0018] In one embodiment, the main body 111 includes a base 1110 and an electrostatic chuck 1111. The base 1110 includes a conductive member. The conductive member of the base 1110 may function as a lower electrode. The electrostatic chuck 1111 is disposed on the base 1110. The electrostatic chuck 1111 includes a ceramic member 1111a and an electrostatic electrode 1111b disposed within the ceramic member 1111a. The ceramic member 1111a has a central region 111a. In one embodiment, the ceramic member 1111a also has an annular region 111b. Note that other members surrounding the electrostatic chuck 1111, such as an annular electrostatic chuck or an annular insulating member, may have the annular region 111b. In this case, the ring assembly 112 may be disposed on the annular electrostatic chuck or the annular insulating member, or may be disposed on both the electrostatic chuck 1111 and the annular insulating member. Also, at least one RF / DC electrode coupled to a radio frequency (RF) power source 31 and / or a direct current (DC) power source 32 described later may be disposed in the ceramic member 1111a. In this case, the at least one RF / DC electrode functions as a lower electrode. When a bias RF signal and / or a DC signal described later is supplied to the at least one RF / DC electrode, the RF / DC electrode is also called a bias electrode. Note that the conductive member of the base 1110 and the at least one RF / DC electrode may function as a plurality of lower electrodes. Also, the electrostatic electrode 1111b may function as a lower electrode. Thus, the substrate support 11 includes at least one lower electrode.

[0019] The ring assembly 112 includes one or more annular members. In one embodiment, the one or more annular members include one or more edge rings and at least one cover ring. The edge rings are formed of a conductive or insulating material, and the cover rings are formed of an insulating material.

[0020] The substrate support 11 may also include a temperature adjustment module configured to adjust at least one of the electrostatic chuck 1111, the ring assembly 112, and the substrate to a target temperature. The temperature adjustment module may include a heater, a heat transfer medium, a flow path 1110a, or a combination thereof. A heat transfer fluid such as brine or gas flows through the flow path 1110a. In one embodiment, the flow path 1110a is formed in the base 1110, and one or more heaters are disposed in the ceramic member 1111a of the electrostatic chuck 1111. The substrate support 11 may also include a heat transfer gas supply unit configured to supply a heat transfer gas to a gap between the back surface of the substrate W and the central region 111a. In an embodiment, the substrate support 11 or the electrostatic chuck 1111 corresponds to a stage of the present disclosure. In an embodiment, the central region 111a corresponds to a mounting surface.

[0021] Here, a configuration of the electrostatic chuck 1111 of the substrate support portion 11 will be described. Fig. 3 is a plan view showing an example of the configuration of the electrostatic chuck 1111 according to an embodiment. Fig. 4 is a cross-sectional view showing an example of the configuration of the electrostatic chuck 1111 according to an embodiment.

[0022] 3 shows a plan view of the upper surface of the electrostatic chuck 1111. The upper surface of the electrostatic chuck 1111 is divided into a central region 111a and an annular region 111b. The central region 111a is a region having a substantially circular shape in a plan view. The substrate W is placed on the upper surface of the central region 111a. The diameter of the central region 111a is substantially the same as that of the substrate W or is slightly smaller than the diameter of the substrate W. The annular region 111b is a region surrounding the central region 111a and extends in a substantially annular shape. In one embodiment, the upper surface of the annular region 111b is located at a lower position than the upper surface of the central region 111a.

[0023] The central region 111a is divided into a plurality of divided regions, and a heater HT is provided in each divided region. For example, as shown in FIG. 3, the central region 111a is divided into a circular divided region at the center. The central region 111a is divided into a plurality of concentric annular regions, and each of the plurality of annular regions is divided into a plurality of arc-shaped divided regions in the circumferential direction. The arc-shaped divided regions are divided so that the angular width and radial width become smaller as they approach the outer periphery. Each divided region is provided with a heater HT. In FIG. 3, the outline of the heater HT provided in each divided region is shown by a dotted line. Also, 1 to 4-6 are attached to positions corresponding to each divided region in order from the inside of the central region 111a. Note that the method of dividing the divided regions shown in FIG. 3 is an example, and is not limited thereto. For example, the central region 111a may be divided into divided regions at a constant angle from the center of the concentric regions. Also, the central region 111a may be divided into divided regions in a lattice shape.

[0024] 4 shows a schematic partial cross section of two divided regions 19 of the electrostatic chuck 1111. An electrostatic electrode 1111b is disposed in the ceramic member 1111a. One electrostatic electrode 1111b is disposed in the ceramic member 1111a corresponding to the central region 111a. A heater HT and a temperature sensor TS are disposed in the ceramic member 1111a for each divided region 19. The heater HT generates heat when power is supplied to heat the divided region 19. The resistance value of the temperature sensor TS changes depending on the temperature.

[0025] Returning to Fig. 2, each heater HT is connected to a heater power supply 60. Each temperature sensor TS is connected to a temperature detection unit 61. Note that in Fig. 2, some of the wiring connecting each heater HT to the heater power supply 60 and each temperature sensor TS to the temperature detection unit 61 is omitted.

[0026] The heater power supply 60 supplies power to each heater HT. The heater power supply 60 is capable of adjusting the power supplied to each heater HT. The heater power supply 60 adjusts the power supplied to each heater HT based on control data input from a control unit 100 described later. Each heater HT generates heat by the power supplied from the heater power supply 60, and heats each divided region.

[0027] The temperature detection unit 61 measures the resistance value of each temperature sensor TS, and detects the temperature of each divided area in which the temperature sensor TS is disposed, based on the measured resistance value.

[0028] The resistance value of the heater HT changes depending on the temperature. The temperature detection unit 61 may measure the current and voltage of the power supplied to each heater HT, calculate the resistance value of each heater HT from the measured current and voltage, and detect the temperature of each divided region based on the calculated resistance value.

[0029] This allows the heat generated by each heater HT to be individually controlled, and the temperatures of the multiple divided regions in the central region 111a to be individually adjusted. At least one measurement point for measuring the CD of the substrate W is provided in each divided region in which the heater HT is provided.

[0030] The shower head 13 is configured to introduce at least one processing gas from the gas supply unit 20 into the plasma processing space 10s. The shower head 13 has at least one gas supply port 13a, at least one gas diffusion chamber 13b, and multiple gas inlets 13c. The processing gas supplied to the gas supply port 13a passes through the gas diffusion chamber 13b and is introduced into the plasma processing space 10s from the multiple gas inlets 13c. The shower head 13 also includes at least one upper electrode. Note that the gas introduction unit may include, in addition to the shower head 13, one or more side gas injectors (SGIs) attached to one or more openings formed in the sidewall 10a.

[0031] The gas supply 20 may include at least one gas source 21 and at least one flow controller 22. In one embodiment, the gas supply 20 is configured to supply at least one process gas from a respective gas source 21 through a respective flow controller 22 to the showerhead 13. Each flow controller 22 may include, for example, a mass flow controller or a pressure-controlled flow controller. Additionally, the gas supply 20 may include one or more flow modulation devices to modulate or pulse a flow rate of the at least one process gas.

[0032] The power source 30 includes an RF power source 31 coupled to the plasma processing chamber 10 via at least one impedance matching circuit. The RF power source 31 is configured to supply at least one RF signal (RF power) to at least one lower electrode and / or at least one upper electrode. This causes a plasma to be formed from at least one processing gas supplied to the plasma processing space 10s. Thus, the RF power source 31 can function as at least a part of a plasma generating unit configured to generate a plasma from one or more processing gases in the plasma processing chamber 10. In addition, a bias potential is generated on the substrate W by supplying a bias RF signal to the at least one lower electrode, and ion components in the formed plasma can be attracted to the substrate W.

[0033] In one embodiment, the RF power supply 31 includes a first RF generating unit 31a and a second RF generating unit 31b. The first RF generating unit 31a is coupled to at least one lower electrode and / or at least one upper electrode via at least one impedance matching circuit, and is configured to generate a source RF signal (source RF power) for plasma generation. In one embodiment, the source RF signal has a frequency in the range of 10 MHz to 150 MHz. In one embodiment, the first RF generating unit 31a may be configured to generate a plurality of source RF signals having different frequencies. The generated one or more source RF signals are supplied to at least one lower electrode and / or at least one upper electrode.

[0034] The second RF generating unit 31b is coupled to at least one lower electrode via at least one impedance matching circuit and configured to generate a bias RF signal (bias RF power). The frequency of the bias RF signal may be the same as or different from the frequency of the source RF signal. In one embodiment, the bias RF signal has a frequency lower than the frequency of the source RF signal. In one embodiment, the bias RF signal has a frequency in the range of 100 kHz to 60 MHz. In one embodiment, the second RF generating unit 31b may be configured to generate a plurality of bias RF signals having different frequencies. The generated one or more bias RF signals are supplied to at least one lower electrode. Also, in various embodiments, at least one of the source RF signal and the bias RF signal may be pulsed.

[0035] The power supply 30 may also include a DC power supply 32 coupled to the plasma processing chamber 10. The DC power supply 32 includes a first DC generator 32a and a second DC generator 32b. In one embodiment, the first DC generator 32a is connected to at least one lower electrode and configured to generate a first DC signal. The generated first bias DC signal is applied to the at least one lower electrode. In one embodiment, the second DC generator 32b is connected to at least one upper electrode and configured to generate a second DC signal. The generated second DC signal is applied to the at least one upper electrode.

[0036] In various embodiments, at least one of the first and second DC signals may be pulsed. In this case, a sequence of voltage pulses is applied to at least one lower electrode and / or at least one upper electrode. The voltage pulses may have a rectangular, trapezoidal, triangular or combination thereof pulse waveform. In one embodiment, a waveform generator for generating a sequence of voltage pulses from the DC signal is connected between the first DC generator 32a and at least one lower electrode. Thus, the first DC generator 32a and the waveform generator constitute a voltage pulse generator. When the second DC generator 32b and the waveform generator constitute a voltage pulse generator, the voltage pulse generator is connected to at least one upper electrode. The voltage pulses may have a positive polarity or a negative polarity. Also, the sequence of voltage pulses may include one or more positive polarity voltage pulses and one or more negative polarity voltage pulses in one period. The first and second DC generating units 32a, 32b may be provided in addition to the RF power supply 31, or the first DC generating unit 32a may be provided in place of the second RF generating unit 31b.

[0037] The exhaust system 40 may be connected to, for example, a gas exhaust port 10e provided at the bottom of the plasma processing chamber 10. The exhaust system 40 may include a pressure regulating valve and a vacuum pump. The pressure in the plasma processing space 10s is adjusted by the pressure regulating valve. The vacuum pump may include a turbomolecular pump, a dry pump, or a combination thereof.

[0038] The plasma processing apparatus 1 includes a controller 100. The controller 100 processes computer-executable instructions that cause the plasma processing apparatus 1 to perform various steps described in this disclosure. The controller 100 can be configured to control each element of the plasma processing apparatus 1 to perform the various steps described herein.

[0039] [Control Unit Configuration] Next, the control unit 100 will be described in detail. Fig. 5 is a block diagram showing a schematic configuration of the control unit 100 that controls the plasma processing apparatus 1 according to an embodiment. The control unit 100 includes a communication interface 101, a process controller 102, a user interface 103, and a storage unit 104.

[0040] The communication interface 101 is capable of communicating with the measuring device 2 via the network N, and transmits and receives various data to and from the measuring device 2. For example, the communication interface 101 receives data of CD transmitted from the measuring device 2.

[0041] The process controller 102 includes a CPU (Central Processing Unit) and controls each part of the plasma processing apparatus 1 .

[0042] The user interface 103 is composed of a keyboard through which a process manager inputs commands to manage the plasma processing apparatus 1, a display that visualizes and displays the operating status of the plasma processing apparatus 1, and the like.

[0043] The storage unit 104 stores a control program (software) for implementing various processes executed in the plasma processing apparatus 1 under the control of the process controller 102, and recipes in which processing condition data and the like are stored. Note that the control program, recipes such as processing condition data, and the like can be used in a state stored in a computer-readable computer recording medium, or can be used online by transmitting them from another device at any time, for example, via a dedicated line. Examples of computer recording media include hard disks, optical disks such as DVDs, flexible disks, and semiconductor memories.

[0044] The process controller 102 has an internal memory for storing programs and data, reads out a control program stored in the storage unit 104, and executes the processing of the read out control program. The process controller 102 functions as various processing units by the operation of the control program. For example, the process controller 102 has the functions of a generation unit 102a, a calculation unit 102b, a plasma control unit 102c, and a heater control unit 102d. In the plasma processing apparatus 1 according to the present embodiment, the process controller 102 has the functions of the generation unit 102a, the calculation unit 102b, the plasma control unit 102c, and the heater control unit 102d, but is not limited to this. The functions of the generation unit 102a, the calculation unit 102b, the plasma control unit 102c, and the heater control unit 102d may be distributed among multiple controllers.

[0045] In substrate processing such as plasma etching, it is desirable that the CD range (the difference between the maximum CD value and the minimum CD value) be small over the entire surface of the substrate W, and that the average CD value be close to a target value. Meanwhile, in substrate processing, the progress of the processing changes depending on the temperature of the substrate W. For example, in plasma etching, the etching progress rate changes depending on the temperature of the substrate W.

[0046] Therefore, in the plasma processing apparatus 1 of this embodiment, a prediction model is used to predict the critical dimension at a specified measurement point on the substrate W using the temperature of each heater HT as a parameter, and the temperature of each divided region is controlled so that the critical dimension within the substrate W satisfies specified conditions.

[0047] Here, the prediction model will be described. In this embodiment, a prediction model in which the critical dimension of the measurement point is modeled as a linear function of the temperature of each heater HT will be described.

[0048] The temperature changes near the boundary between each divided area and the adjacent divided area due to the influence of the adjacent divided area. When the influence of the heater HT temperature of the adjacent divided area on the measurement point is taken into account, the temperature of each measurement point can be expressed as the following formula (1) using the temperature T of the heater HT as a parameter.

[0049]

number

[0050] Here, i is the number of the divided area in which the heater HT including the measurement point is provided, and j is the number of the measurement point included in the divided area in which the heater HT is provided. i represents the temperature of the divided area numbered i. i,j is the temperature and T i This temperature difference is caused by the influence of heat from the adjacent divided areas. i,j also varies depending on the distance of the measurement point from the adjacent divided region.

[0051] δT i,j is obtained as follows. The temperature distribution of the divided regions is measured by infrared thermography with the temperature of the heater HT changed in two adjacent divided regions. The temperature distribution of the divided regions only needs to be obtained at least once in advance. The temperature distribution of the divided regions does not need to be measured using the plasma processing apparatus 1, and may be measured using a substrate support for measurement having a configuration similar to that of the substrate support unit 11. For example, the temperature distribution may be measured using a substrate support for measurement having the same components as the substrate support unit 11. FIG. 6 is a diagram showing an example of the temperature distribution. In the substrate support unit 11 shown in FIG. 6, the central region 111a on which the substrate W is placed is divided into divided regions 19a, 19b, 19c, and 19d. FIG. 6A shows an infrared thermography image when the temperature of the heater HT is changed in the inner divided region 19a and the divided regions 19b, 19c, and 19d. FIG. 6B shows a graph showing the change in temperature with respect to the distance d from the boundary between the divided regions 19a and 19b, with the boundary being set to zero. In the example of Fig. 6(B), the temperature of divided area 19a is set to 29.5°C, and the temperatures of divided areas 19b and 19c are set to 34°C. As shown in Fig. 6(B), the temperature of divided area 19b near the boundary with divided area 19a is not 34°C due to the influence of divided area 19a, and the temperature also changes depending on the distance from divided area 19a.

[0052] For example, two adjacent divided regions 19 are divided regions 19-1 and 19-2, and the temperature of the divided region 19-1 is T 1-1 The temperature of the divided area 19-2 is T 2-1 In this case, the temperature T at a position at a distance d from the boundary of the divided region 19-2 can be expressed by an approximation such as the following equation (2).

[0053]

number

[0054] Here, λ is a constant for approximating the temperature change graph. For example, when approximating the temperature change graph of FIG. 6B, λ is 7.2 mm.

[0055] Equation (1) is δT i,j When expressed as equation (2), it can be expressed as equation (3) below.

[0056]

number

[0057] Here, k is the number of the division area adjacent to the i-th division area. i,j,k is the distance from the adjacent kth divided area to the jth measurement point in the ith divided area. The position of the measurement point is determined in advance, so d i,j,k can be calculated in advance. i,j,k is a constant that represents the influence of the adjacent k-th divided area on the j-th measurement point of the i-th divided area. If the influence of adjacent divided areas is considered to be the same, λ i,j,k For example, when using the measurement results shown in FIG. 6B, λ i,j,k are all 7.2mm.

[0058] FIG. 7 is a diagram for explaining the relationship between the divided regions. In FIG. 7, divided regions 19l to 19t are shown. The divided region 19p is adjacent to the divided regions 19l to 19o and 19s. The divided region 19p includes a measurement point 18. If the number of the divided region 19p is i, the number of the divided regions 19l to 19o and 19s is k. Also, d i,j,k is the distance between the measurement point 18 and the divided areas 19l to 19o and 19s as indicated by the arrows in FIG.

[0059] Next, in order to obtain data used for generating a prediction model, the plasma processing apparatus 1 controls each heater HT to set the temperature of each divided region to several levels, replaces the substrate W at each temperature, and individually performs plasma etching to be actually performed on each substrate W. For example, the plasma processing apparatus 1 controls each heater HT to three or more temperatures, replaces the substrate W at each temperature, and individually performs plasma etching to be actually performed. As an example, the plasma processing apparatus 1 performs plasma etching on the substrate W by setting each heater HT to 50°C. Also, the plasma processing apparatus 1 performs plasma etching on the substrate W by setting each heater HT to 55°C. Also, the plasma processing apparatus 1 performs plasma etching on the substrate W by setting each heater HT to 45°C. Note that, when obtaining data used for generating a prediction model, the temperature of each divided region does not necessarily have to be the same for all divided regions. That is, some divided regions may have a different temperature from the other divided regions. For example, the temperature may be different between a divided region near the center of the central region 111a and a divided region near the outer periphery of the central region 111a.

[0060] Each substrate W on which plasma etching has been performed at each temperature is transported to the measuring device 2. The measuring device 2 measures the CD of each measurement point on each transported substrate W, with a predetermined position set as the measurement point. For example, the measuring device 2 measures the CD of each measurement point on each substrate W on which plasma etching has been performed with each heater HT set to three temperatures of 45°C, 50°C, and 55°C. The measuring device 2 transmits the measured CD data of each measurement point to the plasma processing apparatus 1.

[0061] When predicting the CD of a measurement point as a linear function of the temperature T of each heater HT, the CD of each measurement point can be expressed as the following equation (4-1) using the temperature T of the heater HT as a parameter.

[0062]

number

[0063] Here, i is the number of the divided area in which the heater HT is provided and which includes the measurement point. For example, the divided areas in which the heater HT is provided are sequentially numbered i. j is the number of the measurement point included in the divided area in which the heater HT is provided. For example, the measurement points in each divided area in which the heater HT is provided are sequentially numbered j. CD i,j represents the CD value of the measurement point j included in the divided area i. i,j represents the temperature of the measurement point number j of the divided area number i. A 11_i,j is the CD value of the measurement point j in the divided area i, i,j It is the coefficient of the linear function to calculate from. It represents the average temperature of three or more temperatures measured at the CD of the measurement point number j of the divided area number i. T i,j_a represents the average temperature of three or more temperatures at which the CD of the measurement point number j of the divided area number i is measured. For example, if the CD of the divided area number i is measured at three temperatures of 45°C, 50°C, and 55°C, T i,j_a is 50℃. A 10_i,j represents the average value of CD measured at three or more temperatures at the measurement point numbered j included in the divided area numbered i.

[0064] Equation (4-1) can be expressed as equation (4-2), and the temperature τ l is expressed as the following formula (5-2), and a i,j,l When expressed as the following equation (5-3), it can be expressed as the following equation (5-1).

[0065]

number

[0066] Here, T i represents the temperature of the divided area numbered i. T i_a represents the average temperature of three or more temperatures at which CD is measured in the divided area numbered i. l is the number of the divided area in which the heater HT is provided. For example, if there are 20 divided areas in which the heater HT is provided, l = 1 to 20.

[0067] When generating a prediction model, the plasma processing apparatus 1 controls each heater HT to set the temperature of each divided region to several levels, replaces the substrate W at each temperature, and individually performs the actual plasma etching. For example, the plasma processing apparatus 1 controls each heater HT to three or more temperatures, replaces the substrate W at each temperature, and individually performs the actual plasma etching. As an example, the plasma processing apparatus 1 sets each heater HT to 50°C and performs a plasma etching process on the substrate W. Also, the plasma processing apparatus 1 sets each heater HT to 55°C and performs a plasma etching process on the substrate W. Also, the plasma processing apparatus 1 sets each heater HT to 45°C and performs a plasma etching process on the substrate W.

[0068] Then, each substrate W on which plasma etching processing has been performed at each temperature is moved to the measuring device 2, and a predetermined position on the substrate W is set as the measurement point, and the measuring device 2 measures the CD of the measurement point. That is, the measuring device 2 measures the CD of each measurement point on each substrate W on which plasma etching processing has been performed with each heater HT at three temperatures of 45° C., 50° C., and 55° C. The measuring device 2 transmits the measured CD data of each measurement point to the plasma processing device 1.

[0069] The generation unit 102a generates a prediction model from the received CD data. For example, the generation unit 102a performs fitting using the CD of each measurement point of each substrate W on which plasma etching processing is performed with each heater HT at three temperatures of 45° C., 50° C., and 55° C. and the temperature of each heater HT, to obtain a coefficient A 11_i,j Find the value of .

[0070] Coefficient A 11_i,j Once the value of is found, the coefficient a is calculated from the above formula (5-3). i,j,l is obtained, and the temperature τ l From CD i,j can be calculated.

[0071] The generating unit 102a calculates the coefficient A 11_i,j Substituting the value of into equation (5-3), coefficient a i,j,l The coefficient a is used as a prediction model. i,j,l Generate equation (5-1) by substituting

[0072] The calculation unit 102b calculates the target temperature of the heater HT in each divided region at which the CD of the measurement point on the substrate W satisfies a predetermined condition when plasma etching is performed, taking into account the heat transfer between adjacent divided regions and the constraints of the temperature range that can be set for the heater HT in each divided region. For example, the calculation unit 102b uses the prediction model generated by the generation unit 102a to calculate the temperature of the heater HT in each divided region at which the CD of the measurement point satisfies a predetermined condition and the sum of squares of the error of the CD of each measurement point with respect to the target value μ is minimized.

[0073] A method for calculating the temperature of the heater HT in each divided region that minimizes the sum of squares of the error will be specifically described.

[0074] The above equation (5-1) can be expressed as the following equation (6).

[0075]

number

[0076] Here, m is a number that identifies the measurement point. For example, if there are 400 measurement points, m ranges from 1 to 400. In formula (5-1), the measurement points are numbered in order for each divided area, but in formula (6), the number m is numbered in order for the measurement points in all divided areas. n is the number of the divided area in which the heater HT is provided. CD m CD i,jand represents the CD of the measurement point number m. n is τ l corresponds to the temperature of the heater HT in the divided area numbered n. m,n is a i,j,l corresponds to and represents the coefficient. A 10_m A 10_i,j and represents the average value of CD measured at three or more temperatures at the measurement point numbered m.

[0077] In substrate processing such as plasma etching, it is preferable that the CD range over the entire surface of the substrate W is small and that the average CD value is close to the target value set as the target dimension. m is almost the target value μ(CD m The temperature of the heater HT in each divided area is T * n From the above formula (5-2), τ * n It is assumed that the relationship shown in the following equation (7) holds.

[0078]

number

[0079] The CD of each measurement point may have an error from the target value μ due to the variation of the CD of each measurement point before the substrate processing, the influence of the substrate processing, etc. For this reason, the temperature of the heater HT in each divided area is set to τ * n The CD of each measurement point when m can be expressed as the following equation (8).

[0080]

number

[0081] Here, ε m is the error of CD with respect to the target value μ at the measurement point numbered m.

[0082] From equation (8), the sum of squares of the errors at each measurement point can be expressed as the following equation (9).

[0083]

number

[0084] The point where the sum of squares of the error shown in formula (9) is the smallest is the point where the value is the minimum. At the minimum value, formula (9) satisfies the following formula (10-1), and formulas (10-1) to (10-2) are satisfied.

[0085]

number

[0086] Equation (10-2) is x l,n is expressed by equation (11-2), and y l When expressed by formula (11-3), it can be expressed as the following formula (11-1). For example, when there are 400 measurement points, the sum is calculated for m of 1 to 400 in formulas (11-2) and (11-3).

[0087]

number

[0088] Here, l is the number of the divided region that the heater HT is provided in. For example, if there are 20 divided regions that are provided with the heater HT, l=1 to 20.

[0089] This equation (11-1) can be expressed as a matrix calculation as shown in the following equation (12).

[0090]

number

[0091] The matrix shown in equation (12) can be converted to the matrix shown in equation (13) below by calculating the inverse matrix.

[0092]

number

[0093] x of a matrix l,n is a m,l And, a m,l Corresponding to a i,j,l can be calculated by substituting into equation (11-2). l Also, a m,l Corresponding to a i,j,l , A 10_m A corresponds to 10_i,j This can be calculated by substituting into equation (11-3).

[0094] The calculation unit 102b solves the matrix of the formula (13) to calculate the temperature τ of the heater HT in each divided region that minimizes the sum of squares of the error. * n Calculate.

[0095] However, even if the sum of squares of the error is minimized, the range of CD may not be small. FIG. 8 is a diagram for explaining an example of the relationship between the sum of squares of the error and the range. The horizontal axis of FIG. 8 is the number of the measurement point. The vertical axis of FIG. 8 is the CD at the measurement point. The error at each measurement point is the difference between the target value μ and the CD. When the sum of squares of the error is minimized, it is sufficient that the errors at each measurement point are small as a whole. Therefore, for example, as shown in FIG. 8, even if the error at one measurement point is large with respect to the target value μ, if the errors at many other measurement points are small with respect to the target value μ, the sum of squares of the error will be small. On the other hand, the range of CD is the difference between the maximum value of CD and the minimum value of CD. In the example of FIG. 8, the range of CD does not become small.

[0096] However, there is a strong positive correlation between the range of CD and the variance of the error. The temperature of the heater HT in each divided area where the range of CD is the smallest is the temperature τ * n It is thought to be located in the vicinity of

[0097] Furthermore, the adjustable temperature of each divided region of the substrate support unit 11 may be limited. For example, if the temperature difference between the divided regions of the substrate support unit 11 is large, hardware defects such as cracks may occur due to stress. For example, if the temperature difference between the divided regions of the electrostatic chuck 1111 is large, cracks may occur due to stress. Furthermore, if the temperature difference between the divided regions of the substrate support unit 11 is large, the adhesive bonding the base 1110 and the electrostatic chuck 1111 may peel off due to stress.

[0098] Therefore, a loss function is determined so that the loss function decreases when the critical dimension satisfies a predetermined condition and increases when the temperature of the heater HT in each divided region falls outside the restricted temperature range. Using the determined loss function, the calculation unit 102b calculates the target temperature of the heater HT in each divided region such that the critical dimension of a predetermined measurement point on the substrate W satisfies the predetermined condition and the temperature of the heater HT in each divided region falls within the restricted temperature range.

[0099] Here, a method for setting constraints on the heaters HT in each divided region will be described.

[0100] The matrix T is defined as shown in the following equation (14-1) with the temperature of the heater HT of each divided region and the temperature of the heat transfer fluid such as brine or gas flowing through the flow path 1110a as components, and the matrix T is defined as shown in equation (14-2). All Define.

[0101]

number

[0102] matrix T and matrix T All Components T1 to T n is the set temperature of the heater HT in each divided region. All Component T c is the temperature of the heat transfer fluid flowing through flow path 1110a.

[0103] Matrix T is T1 to T n , T cThe matrix T has n+1 rows and 1 column. All is a matrix with n+1 rows and n+1 columns, with each column being an element of the matrix T.

[0104] The matrix T shown in equation (14-2) All and matrix T All Transpose of matrix t T All The difference between the matrix ΔT in the following equation (15) All It is expressed as the matrix ΔT All is the matrix T All Similarly, it is a matrix with n+1 rows and n+1 columns.

[0105]

number

[0106] matrix ΔT All The diagonal elements are zero, and the nth row and mth column elements are T n -T m The n-row, m-column component T n -T m is the number n and the temperature T of the heater HT in the divided area. n and the temperature T of heater HT in the divided area number m m This is the difference between the two.

[0107] In addition, in response to the constraints on the heater HT of each divided region, the matrix M m Define.

[0108]

number

[0109] m is a number that identifies the constraint to be set. m is the matrix T All Similarly, it is a matrix with n+1 rows and n+1 columns. m is a matrix that specifies whether or not there is a constraint between the divided regions in the constraint number m. m The row and column numbers n+1 of the matrix M are assigned to the numbers of the divided regions.m In the case where there is a constraint between the divided regions with numbers n and m, 1 is set to the components of n row m example and m row n example, and in the case where there is no constraint, 0 is set. The example of formula (16) shows a case where numbers are associated with the divided regions shown in Fig. 3 in order from the inside, and shows the associated divided regions 1, 2-1 to 2-3, and 3-1. In the example of formula (16), 1 is set because there is a constraint between the divided regions 2-1 to 2-3.

[0110] The constraint on the heater HT in each divided region is defined, for example, as shown in the following formula (17).

[0111] Constraint_ m = -F m M m + abs(ΔT All ○ M m ) (17)

[0112] m is a number that identifies the constraint to be set. m is a coefficient that sets the temperature to be constrained by number m. F m M m is a matrix with n+1 rows and n+1 columns. Also, Constraint_ m is also a matrix with n+1 rows and n+1 columns. In the following equation (18), F m =5, M m When Eq.(16) is F m M m Here is an example of F m M m indicates a case where the constraint of number m is set to restrict the temperature difference between adjacent divided regions to 5° C. For example, equation (18) indicates a setting in which the upper limit of the temperature difference between adjacent divided regions 2-1 to 2-3 is restricted to 5° C.

[0113]

number

[0114] In formula (17), "-F m M m" is the coefficient F m and the matrix M m By multiplying by m In the only components where 1 is set, a matrix is ​​obtained with the temperature constraint as a negative value.

[0115] In equation (17), "ΔT All ○ M m " is the matrix ΔT All and the matrix M m The Hadamard product of the matrix ΔT All and the matrix M m Multiply the same n-row and m-column elements of "abs(ΔT All ○ M m )" is the matrix M m A matrix is ​​obtained whose components are the absolute values ​​of the temperature differences between the divided regions only for components set to 1 in

[0116] Constraint_ in Eq. (17) m For the constraint with number m, the calculation is performed for each element of the matrix to subtract the temperature of the constraint from the absolute value of the temperature difference between the divided regions. For example, for the element in row 2, column 3, the calculation is "abs(T2-T3)-5". Constraint_ m is the matrix M m , matrix T All Similarly, it is a matrix with n+1 rows and n+1 columns. m In the case of the temperature difference between the divided regions, the absolute value of the temperature difference between the divided regions exceeds the temperature constraint, and the component has a positive value.

[0117] Constraint_ m For each component, if the value of the component is negative, it is set to 0, and if the value of the component is 0 or positive, the original value of the component is set to the component. For example, in the code of the programming language Python, it can be expressed as the following equation (19).

[0118] y = np.maximum(Constraint_ m , 0) ···(19)

[0119] FIG. 9 is a graph showing an example of the change in equation (19). m If each component of is represented as x, then when x is 0 or less, y = 0. On the other hand, in equation (19), when x is greater than 0, y = x. That is, np.maximum(Constraint_ m , 0) is 0 for the constraint number m if the absolute value of the temperature difference between each divided area where the constraint is set is less than or equal to the constraint temperature, and y = x if the absolute value of the temperature difference between any divided area where the constraint is set is greater than the constraint temperature.

[0120] Equation (19) is the coefficient to multiply np.maximum and Constraint_ m By adding or subtracting a value to , the slope of the fluff and the x-axis intercept can be adjusted. The following equation (20) is an example of adjusting the slope of the fluff and the x-axis intercept of equation (19). Figure 10 is a graph showing an example of the change in equation (20).

[0121] y =100×np.maximum(Constraint_ m +0.1, 0) ···(20)

[0122] Equation (20) is Constraint_ m By adding 0.1 to np.maximum, y increases when the maximum value x is greater than -0.1, as shown in Figure 10. Also, in equation (20), by multiplying np.maximum by 100 as a coefficient, the slope of the fluctuation becomes steeper when x>-0.1.

[0123] The calculation unit 102b calculates the target temperature of the heater HT in each divided region at which the critical dimension of a predetermined measurement point of the substrate W satisfies a predetermined condition when the substrate W placed in the central region 111a is subjected to a predetermined substrate processing, taking into account heat transfer between adjacent divided regions and the constraints of the temperature range that can be set for the heater HT in each divided region. Specifically, the calculation unit 102b calculates the target temperature of the heater HT in each divided region using a loss function that is defined to decrease when the critical dimension satisfies the predetermined condition and to increase when the temperature of the heater HT in each divided region falls outside the restricted temperature range.

[0124] In this embodiment, the loss function is defined, for example, as shown in the following formula (21).

[0125]

number

[0126] The first term in equation (21) is the sum of squares of the CD error at each measurement point relative to the target value μ. The second term in equation (21) is the CD range (the difference between the maximum CD value and the minimum CD value). The third term in equation (21) is the constraint function term that increases when the temperature of the heater HT in each divided area falls outside the constrained temperature range.

[0127] The constraint function is calculated by taking the sum of all components using the above formula (20). For example, in the code of the programming language Python, it can be expressed as the following formula (22).

[0128] Constraint function = np.sum(100 × np.maximum(Constraint_ m +0.1, 0)) (22)

[0129] np.sum() is a function that sums the matrix elements in ().

[0130] A plurality of constraints can be set according to the temperature limit of each divided region of the electrostatic chuck 1111. A number m is assigned to each constraint, and Constraint_ m Set.

[0131] The loss function shown in formula (21) is an example and is not limited to the above. The loss function may be any relational expression as long as it decreases when the CD of each measurement point satisfies a predetermined condition and increases when the temperature of the heater HT of each divided area falls outside the restricted temperature range. For example, the loss function may be configured as the sum of the second and third terms. In other words, the loss function may be the sum of the range of the CD of each measurement point and the restriction function.

[0132] Here, an example of setting a plurality of constraints will be described. For example, as a constraint of number m=1, a temperature difference between circumferentially adjacent divided regions is set for divided regions constituting the same annular region. For example, when a temperature difference between circumferentially adjacent divided regions for divided regions 2-1 to 2-3 and 3-1 to 3-4 is set as a constraint of number m=1, the matrix M1 in equation (17) is set as shown in the following equation (23). Also, as a constraint of number m=1, the coefficient F1 in equation (17) sets a constraint on the temperature difference between circumferentially adjacent divided regions for divided regions 2-1 to 2-3 and 3-1 to 3-4.

[0133]

number

[0134] Fig. 11A is a diagram illustrating constraints. Fig. 11A shows an example of the constraint with number m = 1. With the constraint with number m = 1, as shown in Fig. 11, an upper limit of the temperature difference between adjacent divided regions in the circumferential direction can be set for each of divided regions 2-1 to 2-3 and 3-1 to 3-4.

[0135] Also, for example, as a constraint for number m=2, a temperature difference between divided regions constituting the same annular region is set. For example, when a temperature difference within each of divided regions 2-1 to 2-3 and divided regions 3-1 to 3-4 constituting an annular region is set as a constraint for number m=2, matrix M2 in equation (17) is set as shown in the following equation (24). Also, as a constraint for number m=2, coefficient F2 in equation (17) sets a constraint on the temperature difference within each of divided regions 2-1 to 2-3 and divided regions 3-1 to 3-4. For example, coefficient F2 is set to the same value as the upper limit of the temperature difference for each annular region.

[0136]

number

[0137] Fig. 11B is a diagram illustrating the constraints. Fig. 11B shows an example of the constraint with number m = 2. With the constraint with number m = 2, as shown in Fig. 11B, an upper limit can be set for the temperature difference between the maximum temperature (Max) and the minimum temperature (Min) within each annular region for each of the divided regions 2-1 to 2-3 and the divided regions 3-1 to 3-4.

[0138] For example, an upper limit of the temperature difference between all divided regions is set as a constraint for number m=3. For example, when an upper limit of the temperature difference between all divided regions is set as a constraint for number m=3, the matrix M3 in equation (17) is set as shown in the following equation (25). The matrix M3 is made up of diagonal elements and the T c All components other than the last row and last column, which set the relationship, are set to 1. Also, as a constraint for number m=3, coefficient F3 in equation (17) sets an upper limit on the temperature difference for components other than the diagonal components, the last row, and the last column. For example, coefficient F3 sets the same value as the upper limit on the temperature difference for components other than the diagonal components, the last row, and the last column.

[0139]

number

[0140] Fig. 11C is a diagram for explaining constraints. Fig. 11C shows an example of a constraint with number m=3. With the constraint with number m=3, an upper limit can be set for the temperature difference between the maximum temperature (Max) and the minimum temperature (Min) of each divided area in the entire central area 111a as shown in Fig. 11C. For example, if divided area 3-3 has the maximum temperature (Max) and divided area 4-2 has the minimum temperature (Max) in the entire central area 111a as shown in Fig. 11C, an upper limit can be set for the temperature difference between the maximum temperature (Max) and the minimum temperature (Min) with the constraint with number m=3.

[0141] The constraints are not limited to those described above, and various other constraints can be set.

[0142] The constraint function shown in formula (22) is zero when each constraint is satisfied, and is large when any constraint is not satisfied. Therefore, the loss function shown in formula (21) is small when the critical dimension satisfies a predetermined condition, and is large when the temperature of the heater HT of each divided region is outside the restricted temperature range.

[0143] The calculation unit 102b calculates the temperature τ of the heater HT in each divided region that minimizes the sum of squares of the error. * n Based on the reference, the temperature T of the heater HT in each divided area n For example, the calculation unit 102b calculates the target temperature of the heater HT in each divided region such that the loss function is minimized by changing the temperature τ * nUsing each of these as a reference, the temperature of the heater HT is individually changed in the plus and minus directions by a predetermined temperature to calculate CD at each measurement point, and the loss function shown in formula (21) is calculated. Then, the calculation unit 102b specifies a combination of the heater HT temperatures in each divided area that minimizes the loss function from the calculation result. The predetermined temperature may be a fixed value, may be changed according to the processing conditions, or may be set by an external device. In this embodiment, the predetermined temperature is set to 1 degree. The calculation unit 102b may use a GRG method (Generalized Reduced Gradient method) to calculate the target temperature of the heater HT in each divided area that minimizes the loss function. For example, the calculation unit 102b calculates the target temperature of the heater HT in each divided area that minimizes the loss function using the GRG method, using a value obtained by individually adding a random number to the heater HT temperature in each divided area as an initial value for the specified combination of the heater HT temperatures in each divided area. Note that the calculation unit 102b may calculate the target temperature of the heater HT in each divided area that minimizes the loss function for the specified combination of the heater HT temperatures in each divided area by changing the temperature of the heater HT in each divided area. For example, the calculation unit 102b may calculate the CD of each measurement point by changing the temperature of the heater HT of each divided region randomly or according to a predetermined rule by a temperature range smaller than a predetermined temperature for the identified combination of the heater HT temperatures of each divided region, and calculate the loss function.The calculation unit 102b may then specify the target temperature of the heater HT of each divided region that minimizes the loss function from the calculation result.

[0144] Here, we will briefly explain the reason for including the constraint function in the loss function shown in equation (21). For example, if the constraint function (third term) is removed from the loss function and the loss function is set to the sum of the squares of the error (first term) and the range of CD (second term), the value Z of the loss function is calculated by the temperature T of the heater HT in each divided area. n 12A, the temperature T of the heater HT in each divided region where the loss function value Z is an extreme value changes as shown in FIG. 12A. nis the target temperature of the heater HT in each divided region. However, there are cases where the target temperature of the heater HT in each divided region does not satisfy the constraint of each divided region. Therefore, in this embodiment, the constraint of the heater HT in each divided region is set in accordance with the constraint of the temperature range that can be set for the heater HT in each divided region in the formula (17). For example, when two constraints 1 and 2 with different settable temperature ranges are set, the value y of formula (20) increases as shown in FIG. 12B when the temperature falls outside the restricted temperature range. FIG. 12B is a diagram showing an example of the change in formula (20) for constraints 1 and 2. When the constraint function is the sum of the formulas (20) for each constraint as in the above formula (22) and the constraint function (third term) is included in the loss function as in formula (21), the value Z of the loss function is calculated as follows: n 12C, for example, as shown in FIG. 12C. FIG. 12C is a diagram showing an example of change in the value Z of the loss function including the constraint function. The value Z of the loss function increases when it is outside the temperature range restricted by constraints 1 and 2. In FIG. 12C, the temperature T of the heater HT of each divided region where the value Z of the loss function becomes an extreme value n The temperature T of the heater HT in each divided area is calculated. n is set as the target temperature of the heater HT for each divided region. This makes it possible to calculate the target temperature of the heater HT for each divided region that satisfies the temperature constraints of each divided region and allows for accurate control of the critical dimension in the substrate W.

[0145] The plasma control unit 102c controls the plasma processing by controlling each unit of the plasma processing apparatus 1. For example, the plasma control unit 102c reads out a recipe or the like corresponding to the plasma etching to be performed from the storage unit 104, and controls each unit of the plasma processing apparatus 1 based on the read out recipe or the like.

[0146] The heater control unit 102d, under the control of the plasma control unit 102c, controls the temperature of the heater HT in each divided region to become the target temperature calculated by the calculation unit 102b when performing plasma etching on the substrate W placed on the central region 111a of the substrate support unit 11. For example, the heater control unit 102d controls the heater power supply 60 so that power corresponding to each target temperature is supplied to each heater HT.

[0147] The substrate W on which the plasma etching has been performed is transferred to the measuring device 2. The measuring device 2 measures the CD of the measurement point on the transferred substrate W, and transmits the measured CD data to the plasma processing apparatus 1.

[0148] The calculation unit 102b judges whether the CD range is within the allowable range from the CD data received from the measurement device 2, and if the CD range is not within the allowable range, corrects the prediction model. For example, the calculation unit 102b adds the CD-target value μ of each measurement point to the function of each measurement point of each prediction model, and calculates the temperature τ of the heater HT of each divided region that minimizes the sum of squares of the error again. * n Then, the calculation unit 102b calculates the temperature τ of the heater HT in each divided region that minimizes the sum of squares of the error. * n Based on the reference, the temperature T of the heater HT in each divided area n is changed to calculate the target temperature of the heater HT for each divided region that minimizes the loss function. In the plasma processing apparatus 1 according to this embodiment, when plasma etching is performed on the substrate W at the calculated target temperature of the heater HT for each divided region, if the range of the CD of the measurement point on the substrate W is not within the allowable value, the prediction model is regenerated.

[0149] [Temperature control flow] Next, a description will be given of a temperature control method using the plasma processing apparatus 1 according to the first embodiment. Fig. 13 is a flow chart showing an example of the flow of the temperature control method according to the first embodiment.

[0150] The generating unit 102a initializes the error flag EF to 0 (step S10). The generating unit 102a obtains a function for predicting the temperature of the measurement point by taking into account the influence of the heater HT temperature of the adjacent divided area according to the distance between the measurement point and the divided area adjacent to the divided area including the measurement point, using the temperature of each heater HT as a parameter (step S11). In this embodiment, the generating unit 102a obtains a function for predicting the CD of the measurement point as a linear function of the temperature T of each heater HT. For example, the generating unit 102a obtains the formula (5-1), formula (5-2), and formula (5-3).

[0151] The generating unit 102a obtains data obtained by measuring the CD of each measurement point on the substrate W on which plasma etching has been performed by varying the heater HT of each divided region at several levels (step S12). For example, the plasma processing apparatus 1 controls each heater HT to vary the temperature of each divided region at several levels, and replaces the substrate W at each temperature to individually perform the actual plasma etching. Each substrate W on which plasma etching has been performed at each temperature is moved to the measuring apparatus 2, and the measuring apparatus 2 measures the CD of the measurement point at a predetermined position on the substrate W as the measurement point. The measuring apparatus 2 transmits the measured CD data of each measurement point to the plasma processing apparatus 1. The generating unit 102a obtains data obtained by measuring the CD of each measurement point on the substrate W on which plasma etching has been performed by varying the heater HT of each divided region at several levels by receiving the CD data of each measurement point from the measuring apparatus 2.

[0152] The generating unit 102a generates a prediction model from the acquired data (step S13). For example, the generating unit 102a performs fitting to the obtained function using the measured CD of each measurement point and the temperature of each heater HT, and obtains a function that predicts the CD of the measurement point from the temperature of each heater HT as a prediction model.

[0153] The calculation unit 102b initializes a counter i to 1 (step S14). Then, using the generated prediction model, the calculation unit 102b calculates the temperature τ of the heater HT in each divided region that minimizes the sum of squares of the errors of CD at each measurement point with respect to the target value μ. *n is calculated (step S15).

[0154] The calculation unit 102b calculates the temperature τ of the heater HT in each divided region. * n Using these as the reference, the temperature of the heater HT is individually changed in the plus and minus directions by a predetermined temperature (for example, 1 degree) to calculate CD at each measurement point, and a loss function is calculated. Then, the calculation unit 102b specifies the combination of the heater HT temperatures for each divided region that minimizes the loss function from the calculation results (step S16).

[0155] The calculation unit 102b calculates a random number individually and adds it to the temperature of the heater HT of each of the identified divided regions (step S17). The calculation unit 102b calculates the temperature of the heater HT of each divided region at which the loss function is smallest, for example, by the GRG method, using the value obtained by adding the random number as an initial value (step S18).

[0156] The calculation unit 102b calculates the average value of CD at each measurement point when the heater HT of each divided region is set to the calculated temperature, and determines whether the average value of CD is less than the upper limit of the required specifications (step S19). If the average value of CD is not less than the upper limit of the required specifications (step S19: No), the calculation unit 102b subtracts a predetermined value from the target value μ (step S20).

[0157] On the other hand, if the average value of CD is less than the upper limit of the required specifications (step S19: Yes), the calculation unit 102b judges whether the average value of CD is greater than the lower limit of the required specifications (step S21). If the average value of CD is equal to or less than the lower limit of the required specifications (step S21: No), the calculation unit 102b adds a predetermined value to the target value μ (step S22).

[0158] On the other hand, if the average value of CD is greater than the lower limit of the required specifications (step S21: Yes), the calculation unit 102b stores the data of the average value of CD, the range of CD, and the temperature of the heater HT of each divided region (step S23).

[0159] The calculation unit 102b determines whether the counter i is smaller than the predetermined number of processing times N (step S24). If the counter i is smaller than the predetermined number of processing times N (step S24: Yes), the calculation unit 102b adds 1 to the counter i (step S25) and proceeds to the above-mentioned step S15.

[0160] If the counter i is equal to or greater than the predetermined number of processing times N (step S24: No), the calculation unit 102b adopts the temperature of the heater HT of each divided region of the data with the smallest range of CD from among the stored data as the target temperature (step S26).

[0161] When plasma etching is performed on the substrate W placed on the central region 111a of the substrate support 11, the heater control unit 102d controls the temperature of the heater HT in each divided region to reach the adopted target temperature (step S27).

[0162] The substrate W on which the plasma etching has been performed is transferred to the measuring device 2. The measuring device 2 measures the CD of the measurement point on the transferred substrate W, and transmits the measured CD data to the plasma processing apparatus 1.

[0163] The calculation unit 102b judges whether the CD range is within the allowable range from the CD data received from the measurement device 2 (step S28). If the CD range is not within the allowable range (step S28: No), the calculation unit 102b judges whether the error flag EF is 0 (step S29). If the error flag EF is 0 (step S29: Yes), the generation unit 102a adds the measured CD and heater HT temperature data as data for generating the prediction model (step S30). Thereafter, the process proceeds again to step S13, and the prediction model is regenerated from the measured CD and heater HT temperature data and the data acquired in step S12.

[0164] On the other hand, if the range of CD is within the allowable range (step S28: Yes), the calculation unit 102b initializes the error flag EF to 0 (step S31). Then, the calculation unit 102b waits for processing for a predetermined period of time (step S32). The predetermined period of time may be, for example, a period during which plasma etching is performed on a predetermined number of substrates W, or a period during which a certain amount of time has elapsed.

[0165] The plasma processing apparatus 1 performs plasma etching on the substrate W by controlling the temperature of the heater HT in each divided region to be the adopted target temperature for a predetermined period of time.

[0166] After a predetermined period of time, the calculation unit 102b determines whether the range of CD is within the allowable range based on the CD data received from the measurement device 2 (step S33). If the range of CD is within the allowable range (step S33: Yes), the calculation unit 102b again proceeds to step S32 and waits for processing for a predetermined period of time.

[0167] On the other hand, if the CD range is not within the allowable range (step S33: No), the calculation unit 102b sets the error flag EF to 1 (step S34). The calculation unit 102b corrects the prediction model (step S35). For example, the calculation unit 102b performs correction by adding the value of CD-target value μ of each measurement point to the function of each measurement point of each prediction model. Then, the calculation unit 102b proceeds to step S14 again and calculates the target temperature again.

[0168] On the other hand, if the error flag EF is not 0 (step S29: No), the CD range is not within the allowable range even in the corrected prediction model. In this case, the generation unit 102a cannot generate an appropriate prediction model from the acquired data, so it outputs an error (step S36) and ends the process. For example, the generation unit 102a outputs a message to the user interface 103 requesting that data be reacquired for the measurement points on the substrate W where plasma etching was performed by varying the heater HT in each divided region by several levels, and ends the process.

[0169] When an error is output, the process manager controls each heater HT of the plasma processing apparatus 1 to set the temperature of each divided region to several levels, exchanges the substrate W at each temperature, and individually performs the actual plasma etching to be performed, and again acquires data for generating the prediction model. Then, the process manager again performs the temperature control method according to this embodiment.

[0170] Thus, the plasma processing apparatus 1 according to the first embodiment includes a substrate support unit 11 (stage) and a calculation unit 102b. The substrate support unit 11 is provided with a central region 111a (mounting surface) on which the substrate W is mounted, and a heater HT capable of adjusting temperature is provided in each divided region obtained by dividing the central region 111a. The calculation unit 102b is configured to calculate a target temperature of the heater HT in each divided region at which the critical dimension of a predetermined measurement point of the substrate W satisfies a predetermined condition when a predetermined substrate processing is performed on the substrate W mounted in the central region 111a, taking into account the heat transfer between adjacent divided regions and the constraints of the temperature range that can be set for the heater HT in each divided region. This allows the plasma processing apparatus 1 to accurately control the critical dimension in the substrate W while satisfying the temperature constraints of each divided region.

[0171] The calculation unit 102b is configured to calculate a target temperature of the heater HT in each divided region such that the critical dimension at a predetermined measurement point on the substrate W satisfies a predetermined condition and the temperature of the heater HT in each divided region falls within the restricted temperature range, using a loss function that is determined to decrease when the critical dimension satisfies a predetermined condition and to increase when the temperature of the heater HT in each divided region falls outside the restricted temperature range. This allows the plasma processing apparatus 1 to accurately control the critical dimension in the substrate while satisfying the temperature constraints of each divided region.

[0172] The calculation unit 102b calculates the target temperature of the heater HT of each divided region where the critical dimension of the measurement point satisfies a predetermined condition by using a prediction model that predicts the critical dimension by taking into account the influence of the heater HT temperature of other divided regions according to the distance between the measurement point and the divided region other than the divided region including the measurement point, using the temperature of the heater HT of each divided region as a parameter. The calculation unit 102b is configured to change the temperature of the heater HT of each divided region based on the calculated temperature of each divided region, and calculate the target temperature of the heater HT of each divided region where the loss function is minimized. This allows the plasma processing apparatus 1 to accurately control the critical dimension in the substrate while satisfying the temperature constraints of each divided region.

[0173] The loss function is a function obtained by adding the difference between the maximum and minimum critical dimensions of each measurement point and a constraint function that increases when the temperature of the heater HT of each divided region falls outside the restricted temperature range. This allows the plasma processing apparatus 1 to calculate the target temperature of the heater HT of each divided region where the critical dimensions of the measurement points satisfy a predetermined condition while keeping the difference between the maximum and minimum critical dimensions small.

[0174] The loss function is a function that further adds the sum of squares of the deviations of the critical dimensions at each measurement point. This allows the plasma processing apparatus 1 to calculate the target temperature of the heater HT for each divided region where the critical dimensions of the measurement points satisfy a predetermined condition while keeping small the difference between the maximum and minimum critical dimensions and the sum of the sum of squares of the deviations of the critical dimensions at each measurement point.

[0175] The central region 111a is divided into a plurality of concentric annular regions, and each of the plurality of annular regions is divided into a plurality of divided regions in the circumferential direction. The loss function is set to increase when the temperature difference of the heater HT between the divided regions adjacent in the circumferential direction falls outside the restricted temperature range. This allows the plasma processing apparatus 1 to calculate the target temperature of the heater HT in each divided region where the critical dimension of the measurement point satisfies a predetermined condition while keeping the temperature difference of the heater HT between the divided regions adjacent in the circumferential direction within the restricted temperature range.

[0176] The central region 111a is divided into a plurality of concentric annular regions, and each of the plurality of annular regions is divided into a plurality of divided regions in the circumferential direction. The loss function is set so as to increase for each annular region when the temperature difference between the maximum and minimum temperatures of the heater HT in the plurality of divided regions obtained by dividing the annular region falls outside the restricted temperature range. This allows the plasma processing apparatus 1 to calculate the target temperature of the heater HT in each divided region where the critical dimension of the measurement point satisfies a predetermined condition while keeping the temperature difference between the maximum and minimum temperatures of the heater HT within the restricted temperature range for each annular region.

[0177] The loss function is set to increase when the temperature difference between the maximum and minimum temperatures of the heater HT in all divided regions falls outside the restricted temperature range. This allows the plasma processing apparatus 1 to calculate the target temperature of the heater HT in each divided region, where the critical dimension of the measurement point satisfies a predetermined condition, while keeping the temperature difference between the maximum and minimum temperatures of the heater HT in all divided regions within the restricted temperature range.

[0178] Second embodiment Next, a second embodiment will be described. The substrate processing system 1000 and the plasma processing apparatus 1 according to the second embodiment have the same configurations as those of the substrate processing system 1000 and the plasma processing apparatus 1 according to the first embodiment shown in FIGS. 1 to 5, and therefore the description thereof will be omitted.

[0179] Next, a description will be given of a prediction model according to the second embodiment. The temperature T of each heater HT and the measurement point CD have the relationship shown in the following formula (26).

[0180]

number

[0181] Here, A' is the coefficient of the exponential function of the reciprocal of the absolute temperature of the heater. B' is the activation energy, which is about the same as the physical adsorption energy in the case of CDs. Specifically, B' ≒ 0.25[eV] × 1.7E4[K / eV] = 4.3E3[K].

[0182] CD can be expressed as equation (27) from equation (26).

[0183]

number

[0184] where CD0 is the constant term of CD.

[0185] exp(B´ / T) in equation (27) is the average temperature T at three or more temperatures where CD is measured, as shown in the following equation (28-1). a If the temperature T is expressed as the difference τ with

[0186]

number

[0187] When x is expressed as in the following equation (29-2), equation (28-2) can be expressed as the following equation (29-1).

[0188]

number

[0189] Equation (29-1) can be approximated as equation (30-1) below, and can be expressed as equation (30-2).

[0190]

number

[0191] For example, the average temperature T a = 300 [K] and τ = 10 [K], for example, the first-order term of x in equation (30-2) is 0.47, the second-order term of x is 0.11, and the third-order term is 0.02, and the values ​​become smaller as the order of x increases.

[0192] For example, when equation (30-2) is approximated up to the quadratic term of x, it can be expressed as the following equation (31).

[0193]

number

[0194] Therefore, when equation (31) is used for exp(B' / T), equation (27) can be expressed as the following equation (32).

[0195]

number

[0196] If greater accuracy is required, exp(B' / T) may be approximated by using terms up to and including the second order in equation (30-2). Also, an exponential function may be used as exp(B' / T) as is.

[0197] Equation (32) is A 20 is expressed as the following equation (33-2), and A 21 is expressed as the following equation (33-3), and A 22 When expressed as the following equation (33-4), it can be expressed as the following equation (33-1).

[0198]

number

[0199] As shown in equation (33-1), CD is the average temperature T a Near , it can be approximated by a quadratic function of τ.

[0200] Equation (33-1) is the CD of each measurement point in each divided area where the heater HT is installed. i,j When expressed as an equation, it can be expressed as the following equation (34).

[0201]

number

[0202] Here, i is the number of the divided area in which the heater HT including the measurement point is provided, and j is the number of the measurement point included in the divided area in which the heater HT is provided.

[0203] The generation unit 102a generates a first prediction model by modeling the CD of the measurement point as a linear function of the temperature of the heater HT from the received CD data. For example, the generation unit 102a generates the first prediction model by performing fitting using the CD of each measurement point of each substrate W on which the plasma etching process has been performed and the temperature of each heater HT, as in the first embodiment. For example, the generation unit 102a performs fitting using the CD of each measurement point on each substrate W and the temperature of each heater HT to obtain a function that predicts the CD of the measurement point as a linear function of the temperature T of each heater HT as a first prediction model. For example, the generation unit 102a obtains equations (5-1), (5-2), and (5-3) as the first prediction model.

[0204] Furthermore, the generating unit 102a generates a second prediction model by modeling the CD of the measurement point as a quadratic or higher function of the temperature of the heater HT, or as a sum of an exponential function of the reciprocal of the absolute temperature of the heater and a constant, from the received CD data. For example, the generating unit 102a performs fitting using the CD of each measurement point of each substrate W and the temperature of each heater HT on which plasma etching processing has been performed with each heater HT at three temperatures of 45° C., 50° C., and 55° C., and calculates a coefficient A 20_i,j , A 21_i,j , A 22_i,j Find the value of .

[0205] Coefficient A 20_i,j , A 21_i,j , A 22_i,j Once this is determined, the temperature T l CDs in i,j can be calculated.

[0206] If higher accuracy is required, the generating unit 102a may perform fitting using an approximation formula using terms larger than the quadratic order of exp(B' / T) in formula (30-2) to generate the second prediction model. The generating unit 102a may also perform fitting using an exponential function as exp(B' / T) as is to generate the second prediction model.

[0207] The calculation unit 102b uses the first prediction model and the second prediction model generated by the generation unit 102a to calculate the target temperature of the heater HT in each divided region where the CD of the measurement point satisfies a predetermined condition. For example, the calculation unit 102b uses the first prediction model to calculate the temperature τ of the heater HT in each divided region where the sum of squares of the error of the CD of each measurement point with respect to the target value μ is minimized, as in the first embodiment. * n Calculate.

[0208] Then, the calculation unit 102b changes the temperature of the heater HT in each divided region based on the calculated temperature of the heater HT in each divided region, and calculates the target temperature of the heater in each divided region that minimizes the loss function using the second prediction model. For example, the calculation unit 102b calculates the temperature τ * n Based on the reference, the temperature T of the heater HT in each divided area n By varying the temperature τ of the heater HT in each divided region, the CD of each measurement point is calculated using the above-mentioned formula (3) and formula (34), and the loss function shown in formula (21) is calculated. Then, the calculation unit 102b calculates the target temperature of the heater HT in each divided region that minimizes the loss function from the calculation result. For example, the calculation unit 102b calculates the target temperature τ of the heater HT in each divided region. * nUsing each of these as a reference, the temperature of the heater HT is individually changed in the plus and minus directions by a predetermined temperature to calculate CD at each measurement point, and a loss function is calculated. The calculation unit 102b specifies a combination of the heater HT temperatures for each divided region that minimizes the loss function from the calculation results. The calculation unit 102b calculates the target temperature of the heater HT for each divided region that minimizes the loss function using the GRG method from the specified combination of the heater HT temperatures for each divided region. For example, the calculation unit 102b calculates the target temperature of the heater HT for each divided region using the GRG method, with a value obtained by individually adding a random number to the heater HT temperature for each divided region as an initial value for the specified combination of the heater HT temperatures for each divided region. Note that the calculation unit 102b may calculate the target temperature of the heater HT for each divided region that minimizes the loss function for the specified combination of the heater HT temperatures for each divided region by changing the temperature of the heater HT for each divided region. For example, the calculation unit 102b may calculate the CD of each measurement point by changing the temperature of the heater HT of each divided region randomly or according to a predetermined rule by a temperature range smaller than a predetermined temperature for the identified combination of the heater HT temperatures of each divided region, and calculate the loss function.The calculation unit 102b may then specify the target temperature of the heater HT of each divided region that minimizes the loss function from the calculation result.

[0209] [Temperature control flow] Next, a temperature control method using the plasma processing apparatus 1 according to the second embodiment will be described. Fig. 14 is a flow chart showing an example of the flow of the temperature control method according to the second embodiment. Since the temperature control method according to the second embodiment has some processes that are the same as those of the temperature control method according to the first embodiment shown in Fig. 13, the same processes are denoted by the same reference numerals and their explanations are omitted, and mainly different processes will be described.

[0210] The generating unit 102a generates a first prediction model in which the CD of the measurement point is modeled using a linear function of the temperature of the heater HT from the acquired data. The generating unit 102a also generates a second prediction model in which the CD of the measurement point is modeled using a quadratic or higher function of the temperature of the heater HT, or a sum of an exponential function of the reciprocal of the absolute temperature of the heater and a constant from the acquired data (step S13a). For example, the generating unit 102a performs fitting to the obtained function using the measured CD of each measurement point and the temperature of each heater HT, and obtains a function that predicts the CD of the measurement point using a linear function of the temperature T of each heater HT. The generating unit 102a also obtains a function that predicts the CD of the measurement point using a quadratic function of the temperature T of each heater HT.

[0211] The calculation unit 102b uses the generated first prediction model to calculate the temperature τ of the heater HT in each divided region that minimizes the sum of squares of the error of CD at each measurement point with respect to the target value μ. * n is calculated (step S15a).

[0212] The calculation unit 102b calculates the temperature τ of the heater HT of each divided region. * n Using the second prediction model, the temperature of the heater HT is individually changed in the plus and minus directions by a predetermined temperature (for example, 1 degree) to calculate CD at each measurement point, and a loss function is calculated. The calculation unit 102b specifies the combination of the heater HT temperatures for each divided region that minimizes the loss function from the calculation results (step S16a).

[0213] The calculation unit 102b uses the value obtained by adding the random number as an initial value and calculates the temperature of the heater HT in each divided region at which the loss function is minimized by using the second prediction model, for example, the GRG method (step S18a).

[0214] As a result, the plasma processing apparatus 1 according to the second embodiment can accurately control the critical dimensions within the substrate W while satisfying the temperature constraints of each divided region.

[0215] Third embodiment Next, a third embodiment will be described. The substrate processing system 1000 according to the third embodiment has the same configuration as the substrate processing system 1000 according to the first and second embodiments shown in FIG.

[0216] The configuration of the plasma processing apparatus 1 according to the third embodiment will be described. Fig. 15 is a diagram showing a schematic configuration of the plasma processing apparatus 1 according to the third embodiment. The plasma processing apparatus 1 according to the third embodiment has a configuration similar to that of the plasma processing apparatus 1 according to the first and second embodiments shown in Fig. 2, so the same parts are denoted by the same reference numerals and their description is omitted, and mainly different parts will be described.

[0217] The electrostatic chuck 1111 is provided with a heater HT1 in the central region 111a and a heater HT2 in the annular region 111b.

[0218] Fig. 16 is a plan view showing an example of the configuration of an electrostatic chuck 1111 according to the third embodiment. Fig. 16 shows a plan view of the upper surface of the electrostatic chuck 1111. The upper surface of the electrostatic chuck 1111 is divided into a central region 111a and an annular region 111b.

[0219] The central region 111a is divided into a plurality of divided regions, as in the first and second embodiments, and a heater HT1 is provided in each divided region. The heater HT1 corresponds to the heater HT shown in FIG.

[0220] The annular region 111b is also divided into a plurality of divided regions, and a heater HT2 is provided in each divided region. For example, as shown in FIG. 16, the annular region 111b is divided into a plurality of divided regions in the circumferential direction, and a heater HT2 is provided in each divided region. In FIG. 16, 1 to 5-4 are assigned to positions corresponding to each divided region in order from the inside. Note that the method of dividing the divided regions shown in FIG. 16 is an example, and is not limited to this. The annular region 111b may be divided into more divided regions. For example, the annular region 111b may be divided into divided regions with smaller angular widths and narrower radial widths closer to the outer periphery.

[0221] The heater HT1 and the heater HT2 are individually connected to a heater power supply 60 shown in Fig. 16 via wiring (not shown). Each heater HT1 and each heater HT2 is supplied with individually adjusted power from the heater power supply 60.

[0222] The operation of the plasma processing apparatus 1 configured as above is generally controlled by a control unit 100. The control unit 100 has a configuration similar to that of the control unit 100 according to the first and second embodiments shown in FIG.

[0223] The process controller 102 functions as various processing units by the operation of a control program. For example, the process controller 102 has the functions of a generation unit 102a, a calculation unit 102b, a plasma control unit 102c, and a heater control unit 102d.

[0224] Incidentally, in substrate processing such as plasma etching, when the temperature of the ring assembly 112 is controlled by providing a heater HT2 as in the plasma processing apparatus 1 according to this embodiment, the progress of processing near the outer periphery of the substrate W also changes depending on the temperature of the heater HT2. For example, in plasma etching, when the temperature of the heater HT2 is increased, the temperature of the ring assembly 112 rises. In plasma etching, when the temperature of the ring assembly 112 rises, plasma is consumed near the top of the ring assembly 112, the plasma concentration near the outer periphery of the substrate W decreases, and the progress of etching near the outer periphery of the substrate W slows down.

[0225] Thus, in plasma etching, as the temperature of the substrate W increases, the etching progresses faster, but conversely, as the temperature of the ring assembly 112 increases, the etching progress in the vicinity of the outer periphery of the substrate W slows down.

[0226] Therefore, in the plasma processing apparatus 1 according to this embodiment, the temperatures of the heaters HT1 and HT2 are used as parameters to realize a situation in which the range of the CD over the entire surface of the substrate W is smaller and the average CD value is closer to the target value.

[0227] Here, the prediction model will be explained. When the influence of the temperatures of the heaters HT1 and HT2 is taken into consideration, the CD of the measurement point has the relationship of the following formula (35).

[0228]

number

[0229] Here, CD0 is a term (model part) that predicts the CD of the measurement point from the temperature T of the heater HT1. The formula used to predict CD0 corresponds to the above formula (5-1). T FR is the temperature of the heater HT2 in the ring assembly 112. FR △T FR is a term (model part) that predicts the effect of the temperature of the heater HT2 of the ring assembly 112 on the CD.

[0230] When the effect of the heater HT1 temperature in the other divided areas is taken into account, the temperature T at the measurement point is the average temperature T of the three or more temperatures at which CD is measured. a When the temperature T at the measurement point is close to the average temperature T, it can be approximated by a quadratic function of τ as shown in equation (33-1) above. Furthermore, when the effect of the temperature of the heater HT2 is taken into account, CD is calculated as a and the heater HT2 temperature T FR is the average temperature T FR_a When t is near t, it can be approximated by a linear function using t and ξ as in the following equation (36-1). Also, CD can be approximated by a quadratic function using t and ξ as in the following equation (36-2).

[0231]

number

[0232] Here, τ is the average temperature T of the temperature T at the measurement point, as shown in the above formula (28-1). a ξ is the temperature T of heater HT2 when CD is measured. FR The average temperature T FR_a The temperature is the difference between the temperature and the temperature, and ξ=T FR -T FR_a It is.

[0233] Equation (36-1) is a model approximated by a linear function. The first and second terms on the right side of equation (36-1) are the right side of equation (4-1) described above, and are terms that predict the CD of the measurement point from the temperature τ of heater HT1. A 10 , A 11 is a coefficient. The third term on the right side of equation (36-1) is a term that predicts the effect of the heater HT2 temperature ξ on CD. F 11 is a coefficient.

[0234] Equation (36-2) is a model approximated by a quadratic function. The first to third terms on the right side of equation (36-2) are the right side of equation (33-1) described above, and are terms that predict the CD of the measurement point from the temperature τ of heater HT1. The fourth and fifth terms on the right side of equation (36-2) are terms that predict the effect of the temperature ξ of heater HT2 on the CD. F 21 , F 22 is a coefficient.

[0235] Equation (36-2) is obtained individually as an equation for calculating the CD of each measurement point in each divided area.

[0236] In order to obtain data used for generating a prediction model, the plasma processing apparatus 1 controls each heater HT1 and heater HT2 to set the temperature of each divided region to several levels, replaces the substrate W at each temperature, and individually performs plasma etching to be actually performed on each substrate W. For example, the plasma processing apparatus 1 sets the temperature of each heater HT2 to a constant value, controls each heater HT1 to three or more temperatures, replaces the substrate W at each temperature, and individually performs plasma etching to be actually performed. As an example, the plasma processing apparatus 1 sets each heater HT1 to 50°C and performs plasma etching on the substrate W. Also, the plasma processing apparatus 1 sets each heater HT1 to 55°C and performs plasma etching on the substrate W. Also, the plasma processing apparatus 1 sets each heater HT1 to 45°C and performs plasma etching on the substrate W. Also, the plasma processing apparatus 1 sets the temperature of each heater HT1 to a constant value, controls each heater HT2 to two or more temperatures, replaces the substrate W at each temperature, and individually performs plasma etching to be actually performed.

[0237] Each substrate W that has been plasma etched at each temperature is transported to the measuring device 2. The measuring device 2 measures the CD of a measurement point at a predetermined position for each transported substrate W. The measuring device 2 transmits the measured CD data of each measurement point to the plasma processing device 1.

[0238] As a result, for each measurement point, τ, τ 2 , ξ, ξ 2 , data corresponding to the CD values ​​at the measurement points can be obtained.

[0239]

number

[0240] Here, n is the number of substrates W that have been subjected to plasma etching in order to obtain data used to generate the prediction model. n is the temperature τ of the heater HT1 in the divided region where the measurement point is provided when the nth substrate W is subjected to plasma etching. n is the temperature ξ of the heater HT2 when plasma etching is performed on the nth substrate W. n is the CD value at the measurement point when the nth substrate W is subjected to plasma etching.

[0241] The generating unit 102a generates a first prediction model by modeling the CD of the measurement point as a linear function of the temperatures of the heaters HT1 and HT2 from the received CD data. For example, the generating unit 102a performs fitting to the equation (36-1) using the CD of each measurement point and the temperatures of the heaters HT1 and HT2 to obtain a coefficient A 10 , A 11 , F 11 The generating unit 102a calculates the value of the calculated coefficient A 10 , A 11 , F 11 In this way, a function for predicting the CD of the measurement point as a linear function of the temperature τ of the heater HT1 and the temperature ξ of the heater HT2 is obtained as a first prediction model by substituting the above into the equation (36-1). For example, the generation unit 102a obtains the equation (36-1) as the first prediction model.

[0242] In addition, the generating unit 102a generates a second prediction model in which the CD of the measurement point is modeled with a quadratic function of the heaters HT1 and HT2 from the received CD data. For example, the generating unit 102a performs fitting to the above-mentioned formula (36-2) using the CD of the measurement point and the temperatures of the heaters HT1 and HT2 based on the CD data shown in formula (37) for each measurement point to obtain a coefficient A 20 , A 21 , A 22 , F 21 , F 22 For example, the generation unit 102a performs fitting and finds the coefficient A that minimizes the residual sum of squares. 20 , A 21 , A 22 , F 21 , F 22 Find the value of .

[0243] For example, S ik , S ki is defined as the following equation (38-1), and S iCD is defined as the following equation (38-2), and S i1 is expressed as the following equation (38-3), and x i2 Let x be the following equation (38-4): i3 Let x be the following equation (38-5): i4 is expressed as the following equation (38-6).

[0244]

number

[0245] Here, x j x j is the average value of x K x K is the average of CD. CD is the average of CD.

[0246] When the sum of squared residuals is minimized, the relationships of the following equations (39-1) to (39-5) are satisfied.

[0247]

number

[0248] When a matrix is ​​used, the equations (39-2) to (39-5) can be transformed into the equation (40).

[0249]

number

[0250] The generation unit 102a uses the above-mentioned formula (37) to obtain S ik , S jCD and substitute them into equation (40) to obtain coefficient A 21 , A 22 , F 21 , F 22 Find the value of .

[0251] The generating unit 102a calculates the coefficient A 21 , A 22 , F 21 , F 22 and the average value of τ, τ 2 The average value of τ 2 , the average value of ξ, 2 The average value of 2 Substituting into equation (39-1), coefficient A 20 Find the value of .

[0252] Then, the generating unit 102a calculates the obtained coefficient A 20 , A 21 , A 22 , F 21 , F 22 The second prediction model is generated by substituting into equation (36-2).

[0253] The calculation unit 102b uses the first prediction model and the second prediction model generated by the generation unit 102a to calculate the target temperatures of the heaters HT1 and HT2 in each divided area in which the CD of the measurement points satisfies a predetermined condition.

[0254] For example, the calculation unit 102b uses the first prediction model to calculate the temperature τ of the heater HT1 in each divided region that minimizes the sum of squares of the error of CD at each measurement point with respect to the target value μ, as in the second embodiment. * n , and the temperature of heater HT2, ξ * n Calculate.

[0255] Then, the calculation unit 102b changes the temperature of the heater HT1 and heater HT2 of each divided region based on the calculated temperature of the heater HT1 and heater HT2 of each divided region, and calculates a loss function using the second prediction model.The calculation unit 102b then calculates the target temperature of the heater HT1 and heater HT2 of each divided region that minimizes the loss function from the calculation result.For example, the calculation unit 102b calculates the temperature τ of the heater HT1 of each divided region. * n and the temperature ξ of heater HT2 * n The temperature of heater HT1 and heater HT2 in each divided region is changed based on the temperature τ, and the CD of each measurement point is calculated using the above formula (36-2) to calculate the loss function. Then, the calculation unit 102b calculates the target temperature of heater HT1 and heater HT2 in each divided region that minimizes the loss function from the calculation result. For example, the calculation unit 102b calculates the target temperature of heater HT1 and heater HT2 in each divided region that minimizes the loss function from the temperature τ * n Using these as the reference, the temperature of the heater HT1 is changed individually to the plus and minus by a specified temperature. * nThe temperature ξ of the heater HT2 is changed by a predetermined temperature in plus and minus directions based on the reference temperature ξ to calculate the CD of each measurement point. The calculation unit 102b uses the calculated CD to calculate the loss function shown in formula (21). Then, the calculation unit 102b specifies the temperature combination of the heater HT1 and the heater HT2 of each divided area that minimizes the loss function from the calculation result. The calculation unit 102b calculates the target temperature of the heater HT1 and the heater HT2 of each divided area that minimizes the loss function using the GRG method from the specified combination of the temperatures of the heater HT1 and the heater HT2 of each divided area. For example, the calculation unit 102b calculates the target temperature of the heater HT1 and the heater HT2 of each divided area using the GRG method, using the value obtained by adding a random number to the temperature of the heater HT1 and the heater HT2 of each divided area as the initial value for the specified combination of the temperatures of the heaters HT1 and HT2 of each divided area. The calculation unit 102b may calculate the target temperature of the heater HT of each divided region at which the loss function is minimized by changing the temperature of the heater HT1 and the heater HT2 for the specified combination of the temperature of the heater HT1 and the heater HT2 of each divided region. For example, the calculation unit 102b may calculate the CD of each measurement point by changing the temperature of the heater HT1 and the heater HT2 at a temperature range smaller than a predetermined temperature randomly or according to a predetermined rule for the specified combination of the temperature of the heater HT1 and the heater HT2 of each divided region. The calculation unit 102b calculates the loss function from the calculated CD. The calculation unit 102b may calculate the target temperature of the heater HT1 and the heater HT2 of each divided region at which the loss function is minimized from the calculation result.

[0256] Under the control of the plasma control unit 102c, the heater control unit 102d controls the temperatures of the heaters HT1 and HT2 to the target temperatures calculated by the calculation unit 102b when performing plasma etching on the substrate W. For example, the heater control unit 102d controls the heater power supplies 60 so that power corresponding to the respective target temperatures is supplied to each of the heaters HT1 and HT2.

[0257] As a result, the plasma processing apparatus 1 according to the third embodiment can accurately control the critical dimensions within the substrate W while satisfying the temperature constraints of each divided region.

[0258] In the above embodiment, the substrate W is a semiconductor wafer, but the present invention is not limited to this. The substrate W may be any substrate as long as the progress of the substrate processing is affected by the temperature.

[0259] In the above embodiment, the substrate processing is performed by plasma etching, but the present invention is not limited to this. The substrate processing may be any processing in which the progress of the processing is affected by temperature.

[0260] In the above embodiment, the calculation unit 102b calculates the target temperature of the heater HT in each divided region by using a loss function, but the present invention is not limited to this. The calculation unit 102b may calculate the target temperature of the heater HT in each divided region at which the critical dimension of a predetermined measurement point of the substrate W when a predetermined substrate processing is performed on the substrate W placed in the central region 111a satisfies a predetermined condition, using the restricted temperature range of the heater HT in each divided region as a constraint condition. For example, the calculation unit 102b may calculate the temperature τ of the heater HT in each divided region at which the sum of squares of the error is minimized. * n Based on the above, the temperature T of the heater HT in each divided area is calculated in the restricted temperature range of the heater HT in each divided area. n may be changed to calculate the CD of each measurement point on the substrate W. The calculation unit 102b may then specify a combination of the heater HT temperatures in each divided region that minimizes the range of CD from the calculation results. In this case as well, the plasma processing apparatus 1 can accurately control the critical dimension in the substrate W while satisfying the temperature constraints of each divided region.

[0261] In the above first to third embodiments, the calculation unit 102b calculates the heater target temperature for each divided region that minimizes the difference between the maximum and minimum values ​​of the critical dimensions of each measurement point, but the present invention is not limited to this. The calculation unit 102b may calculate the heater target temperature for each divided region that minimizes the sum of squares of the deviations of the critical dimensions of each measurement point.

[0262] It should be noted that the embodiments disclosed herein are illustrative in all respects and should not be construed as limiting. Indeed, the above-described embodiments may be embodied in various forms. Furthermore, the above-described embodiments may be omitted, substituted, or modified in various forms without departing from the scope and spirit of the appended claims.

[0263] Furthermore, the following supplementary notes are disclosed regarding the above embodiment.

[0264] (Appendix 1) a stage provided with a mounting surface on which a substrate is placed, the mounting surface being divided into divided regions each having a heater capable of adjusting a temperature; a calculation unit configured to calculate a target temperature of the heater in each divided region at which a critical dimension of a predetermined measurement point of the substrate satisfies a predetermined condition when the substrate placed on the placement surface is subjected to a predetermined substrate processing, taking into account heat transfer between adjacent divided regions and a restriction on a temperature range that can be set for the heater in each divided region; and A substrate processing apparatus comprising:

[0265] (Appendix 2) The calculation unit is configured to calculate a target temperature of the heater in each divided region at which the critical dimension of a predetermined measurement point on the substrate satisfies a predetermined condition and the temperature of the heater in each divided region falls within a restricted temperature range, using a loss function that is defined to decrease when the critical dimension satisfies a predetermined condition and to increase when the temperature of the heater in each divided region falls outside a restricted temperature range. 2. The substrate processing apparatus according to claim 1.

[0266] (Appendix 3) The calculation unit is configured to calculate a target temperature of the heater in each divided region at which a critical dimension of a predetermined measurement point of the substrate satisfies a predetermined condition when the substrate placed on the placement surface is subjected to a predetermined substrate processing, using a restricted temperature range of the heater in each divided region as a constraint condition. 2. The substrate processing apparatus according to claim 1.

[0267] (Appendix 4) The calculation unit is configured to calculate a target temperature of the heater in each divided region for which the critical dimension of the measurement point satisfies a predetermined condition by using a prediction model that predicts a critical dimension by taking into account an influence of the heater temperature in the other divided region depending on a distance between the measurement point and the other divided region other than the divided region including the measurement point, with the heater temperature in each divided region as a parameter, and to change the heater temperature in each divided region based on the calculated temperature of each divided region, thereby calculating the target temperature of the heater in each divided region for which the loss function is minimized. 3. The substrate processing apparatus according to claim 2.

[0268] (Appendix 5) The loss function is a function obtained by adding the difference between the maximum and minimum critical dimensions of each measurement point and a constraint function that increases when the temperature of the heater in each divided region falls outside a restricted temperature range. 5. The substrate processing apparatus according to claim 2 or 4.

[0269] (Appendix 6) The loss function is a function obtained by further adding the sum of squares of the deviations of the critical dimensions at each measurement point. 6. The substrate processing apparatus according to claim 5.

[0270] (Appendix 7) The mounting surface is divided into a plurality of concentric annular regions, and each of the plurality of annular regions is divided into a plurality of divided regions in a circumferential direction, The loss function is determined to increase when a temperature difference between the heaters between the divided regions adjacent in the circumferential direction falls outside a restricted temperature range. 7. The substrate processing apparatus according to claim 2, wherein the substrate processing apparatus is a substrate processing apparatus.

[0271] (Appendix 8) The mounting surface is divided into a plurality of concentric annular regions, and each of the plurality of annular regions is divided into a plurality of divided regions in a circumferential direction, The loss function is determined so as to increase for each of the annular regions when a temperature difference between a maximum temperature and a minimum temperature of the heater in a plurality of divided regions obtained by dividing the annular region falls outside a restricted temperature range. 8. The substrate processing apparatus according to claim 2, wherein the substrate processing apparatus is a substrate processing apparatus.

[0272] (Appendix 9) The loss function is determined to increase when the temperature difference between the maximum temperature and the minimum temperature of the heater in all the divided regions falls outside a restricted temperature range. 9. The substrate processing apparatus according to claim 2, wherein the substrate processing apparatus is a substrate processing apparatus.

[0273] (Appendix 10) a step of calculating a target temperature of the heater in each divided region of a stage, the stage being provided with a mounting surface on which a substrate is mounted, the mounting surface being divided into divided regions each of which is provided with a heater capable of adjusting a temperature, the target temperature of the heater in each divided region being calculated so that a critical dimension of a predetermined measurement point of the substrate satisfies a predetermined condition when a predetermined substrate processing is performed on the substrate mounted on the mounting surface, taking into consideration heat transfer between adjacent divided regions of the stage and a temperature range that can be set for the heater in each divided region; controlling the temperature of the heater in each divided region to reach the calculated target temperature when performing substrate processing on the substrate placed on the placement surface; A temperature control method to perform. [Explanation of symbols]

[0274] 1. Plasma processing equipment 2. Measurement equipment 10 Plasma Processing Chamber 11 Substrate support 18 Measurement points 19a~19d, 19-1, 19-2, 19l~19t divided area 60 Heater power supply 61 Temperature detection unit 100 Control section 101 Communication Interface 102 Process Controller 102a Generation part 102b Calculation section 102c Plasma control unit 102d Heater control unit 103 User Interface 104 Storage section 111 Main body 111a Central area 111b Annular region 112 Ring Assembly 1000 Substrate Processing System 1110 Foundation 1110a Flow path 1111 Electrostatic Chuck 1111a Ceramic components 1111b Electrostatic electrode HT, HT1, HT2 Heaters TS Temperature Sensor W substrate

Claims

1. a stage provided with a mounting surface on which a substrate is placed, the mounting surface being divided into divided regions each having a heater capable of adjusting a temperature; a calculation unit configured to calculate a target temperature of the heater in each divided region at which a critical dimension of a predetermined measurement point of the substrate satisfies a predetermined condition when the substrate placed on the placement surface is subjected to a predetermined substrate processing, taking into account heat transfer between adjacent divided regions and a restriction on a temperature range that can be set for the heater in each divided region; and A substrate processing apparatus comprising:

2. The calculation unit is configured to calculate a target temperature of the heater in each divided region at which the critical dimension of a predetermined measurement point on the substrate satisfies a predetermined condition and the temperature of the heater in each divided region falls within a restricted temperature range, using a loss function that is defined to decrease when the critical dimension satisfies a predetermined condition and to increase when the temperature of the heater in each divided region falls outside a restricted temperature range. The substrate processing apparatus according to claim 1 .

3. The calculation unit is configured to calculate a target temperature of the heater in each divided region at which a critical dimension of a predetermined measurement point of the substrate satisfies a predetermined condition when the substrate placed on the placement surface is subjected to a predetermined substrate processing, using a restricted temperature range of the heater in each divided region as a constraint condition. The substrate processing apparatus according to claim 1 .

4. The calculation unit is configured to calculate a target temperature of the heater in each divided region for which the critical dimension of the measurement point satisfies a predetermined condition by using a prediction model that predicts a critical dimension by taking into account an influence of the heater temperature in the other divided region depending on a distance between the measurement point and the other divided region other than the divided region including the measurement point, with the heater temperature in each divided region as a parameter, and to change the heater temperature in each divided region based on the calculated temperature of each divided region, thereby calculating the target temperature of the heater in each divided region for which the loss function is minimized. The substrate processing apparatus according to claim 2 .

5. The loss function is a function obtained by adding the difference between the maximum and minimum critical dimensions of each measurement point and a constraint function that increases when the temperature of the heater in each divided region falls outside a restricted temperature range. The substrate processing apparatus according to claim 2 .

6. The loss function is a function obtained by further adding the sum of squares of the deviations of the critical dimensions at each measurement point. The substrate processing apparatus according to claim 5 .

7. The mounting surface is divided into a plurality of concentric annular regions, and each of the plurality of annular regions is divided into a plurality of divided regions in a circumferential direction, The loss function is determined to increase when a temperature difference between the heaters between the divided regions adjacent in the circumferential direction falls outside a restricted temperature range. The substrate processing apparatus according to claim 2 .

8. The mounting surface is divided into a plurality of concentric annular regions, and each of the plurality of annular regions is divided into a plurality of divided regions in a circumferential direction, The loss function is determined so as to increase for each of the annular regions when a temperature difference between a maximum temperature and a minimum temperature of the heater in a plurality of divided regions obtained by dividing the annular region falls outside a restricted temperature range. The substrate processing apparatus according to claim 2 .

9. The loss function is determined to increase when the temperature difference between the maximum temperature and the minimum temperature of the heater in all the divided regions falls outside a restricted temperature range. The substrate processing apparatus according to claim 2 .

10. a step of calculating a target temperature of the heater in each divided region of a stage, the stage being provided with a mounting surface on which a substrate is mounted, the mounting surface being divided into divided regions each of which is provided with a heater capable of adjusting a temperature, the target temperature of the heater in each divided region being calculated so that a critical dimension of a predetermined measurement point of the substrate satisfies a predetermined condition when a predetermined substrate processing is performed on the substrate mounted on the mounting surface, taking into consideration heat transfer between adjacent divided regions of the stage and a temperature range that can be set for the heater in each divided region; controlling the temperature of the heater in each divided region to reach the calculated target temperature when performing substrate processing on the substrate placed on the placement surface; A temperature control method to perform.

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