Plasma processing device, prediction method, prediction program, and information processing device

Abstract

In the present invention, an acquisition unit periodically acquires: the temperature of a stage on which a substrate is placed; the temperature of a cooling mechanism which is provided on the stage and cools the stage; and the amount of heat generated by a heating mechanism which is provided between a placement surface for placing the stage substrate and the cooling mechanism and heats the stage. A prediction unit, using a calculation formula for predicting the amount of heat input that flows from plasma into the substrate from the amount of heat generated by the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, a first-order time derivative of the temperature of the stage, and a first- or higher-order time derivative of the temperature of the cooling mechanism, predicts the amount of heat input that flows into the substrate from plasma, from the amount of heat generated by the heating mechanism, the temperature of the stage, and the temperature of the cooling mechanism that have been acquired, and the first-order time derivative of the temperature of the stage, and the first- or higher-order time derivative of the temperature of the cooling mechanism.

Description

Plasma processing apparatus, prediction method, prediction program, and information processing apparatus

[0001] The present disclosure relates to a plasma processing apparatus, a prediction method, a prediction program, and an information processing apparatus.

[0002] JP-A-2003-129999 discloses a plasma processing apparatus including: a processing chamber whose interior is evacuated to a reduced pressure; a sample stage provided in the processing chamber and having a sample mounting surface on which a substrate to be processed is placed; a plasma generating device for generating plasma in the processing chamber; a heat transfer gas supply system for supplying a gas for heat transfer to the sample mounting surface; and a coolant passage provided in the sample stage through which a coolant circulates; the sample stage has a heater layer provided between the sample mounting surface and the coolant passage, and the heater layer is divided into a plurality of regions in a radial direction of the sample mounting surface; temperature monitors provided in the sample stage near the heater layer and at positions corresponding to each divided region of the heater layer; and a temperature control device that estimates temperatures at positions corresponding to each divided region of the substrate to be processed placed on the sample mounting surface based on temperature information from each temperature monitor, and controls power supply to the heater layer in each divided region in accordance with the estimated temperature values.

[0003] JP 2008-177285 A

[0004] The present disclosure provides a technique for measuring the amount of heat input from a plasma to a substrate.

[0005] A plasma processing apparatus according to one aspect of the present disclosure includes a stage, a chamber, a cooling mechanism, a heating mechanism, a measurement unit, an acquisition unit, and a prediction unit. The stage has a substrate placed thereon. The chamber has a stage therein, and plasma is generated therein to perform plasma processing on the substrate placed on the stage. The cooling mechanism is provided on the stage and cools the stage. The heating mechanism is provided between the stage's mounting surface on which the substrate is placed and the cooling mechanism, and is capable of controlling the amount of heat generated, thereby heating the stage. The measurement unit measures the temperature of the stage. The acquisition unit periodically acquires the amount of heat generated by the heating mechanism, the temperature of the stage, and the temperature of the cooling mechanism. The prediction unit predicts the amount of heat input flowing from the plasma to the substrate from the amount of heat generated by the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, the first-order time derivative of the stage temperature, and the first-order or higher time derivative of the cooling mechanism temperature, all of which are acquired by the acquisition unit.

[0006] According to the present disclosure, the amount of heat input from the plasma to the substrate can be measured.

[0007] FIG. 1 is a diagram for explaining an example of the configuration of a plasma processing apparatus according to a first embodiment. FIG. 2 is a plan view showing an example of the configuration of an electrostatic chuck according to the first embodiment. FIG. 3 is a cross-sectional view showing an example of the configuration of an electrostatic chuck according to the first embodiment. FIG. 4 is a block diagram showing a schematic configuration of a control unit according to the first embodiment. FIG. 5 is a diagram showing an example of a thermal circuit representing a substrate and a main body according to the first embodiment. FIG. 6 is a flowchart showing an example of the flow of a substrate temperature control process according to the first embodiment. FIG. 7 is a block diagram showing a schematic configuration of an information processing apparatus according to a second embodiment. FIG. 8 is a flowchart showing an example of the flow of a prediction process according to the second embodiment.

[0008] Hereinafter, embodiments of the plasma processing apparatus, the prediction method, the prediction program, and the information processing apparatus disclosed herein will be described in detail with reference to the drawings. Note that the disclosed plasma processing apparatus, the prediction method, the prediction program, and the information processing apparatus are not limited to the embodiments.

[0009] Plasma processing apparatuses that perform plasma processing on substrates such as semiconductor wafers (hereinafter also referred to as "wafers") are known. In plasma processing apparatuses, a technique for measuring the amount of heat input from the plasma to the substrate is expected to be developed in order to understand the state of the plasma processing.

[0010] [First Embodiment] [Apparatus Configuration] An example of a plasma processing apparatus according to the present disclosure will be described. In the embodiment described below, the plasma processing apparatus according to the present disclosure will be described as an example of a plasma processing system having a system configuration for performing plasma processing.

[0011] An example of the configuration of a plasma processing system will be described below: Fig. 1 is a diagram for explaining an example of the configuration of a plasma processing apparatus according to a first embodiment.

[0012] The plasma processing system includes a capacitively coupled plasma processing apparatus 1 and a controller 100. The capacitively coupled 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 11 and a gas inlet. The gas inlet is configured to introduce at least one process gas into the plasma processing chamber 10. The gas inlet includes a showerhead 13. The substrate support 11 is disposed within the plasma processing chamber 10. The showerhead 13 is disposed above the substrate support 11. In one embodiment, the showerhead 13 forms at least a portion of the ceiling of the plasma processing chamber 10. The plasma processing chamber 10 has a plasma processing space 10s defined by the showerhead 13, a sidewall 10a of the plasma processing chamber 10, and the substrate support 11. The plasma processing chamber 10 has at least one gas inlet for supplying at least one processing gas to the plasma processing space 10s and at least one gas outlet for exhausting gas from the plasma processing space 10s. 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.

[0013] 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 a substrate W and an annular region 111b for supporting the ring assembly 112. A wafer is an example of a 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.

[0014] 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 can 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 the annular region 111b may also be provided by another member surrounding the electrostatic chuck 1111, such as an annular electrostatic chuck or an annular insulating member. 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. Furthermore, at least one RF / DC electrode coupled to an RF (Radio Frequency) power supply 31 and / or a DC (Direct Current) power supply 32 (described later) may be disposed within 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 multiple lower electrodes. Furthermore, the electrostatic electrode 1111b may function as a lower electrode. Therefore, the substrate support 11 includes at least one lower electrode.

[0015] 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.

[0016] 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 flow path 1110a has pipes 14a connected to both ends and is connected to the chiller unit 14 via the pipes 14a. The chiller unit 14 stores a coolant, such as brine, and supplies the stored coolant to one of the pipes 14a. The coolant supplied from the chiller unit 14 is supplied to the flow path 1110a via one pipe 14a, flows from one end of the flow path 1110a to the other end, and returns to the chiller unit 14 via the other pipe 14a. The chiller unit 14 is configured to be able to change the temperature of the coolant stored therein. The chiller unit 14 also has a built-in temperature sensor that can measure the temperature of the coolant being supplied. The chiller unit 14 changes the temperature of the coolant stored therein under control of the control unit 100. The chiller unit 14 also outputs the coolant temperature measured by the temperature sensor to the control unit 100. The plasma processing apparatus 1 is configured to be able to control the temperature of the main body 111 by circulating the temperature-controlled coolant from the chiller unit 14 through the flow path 1110a to cool the coolant while heating it with a heater. In the embodiment, the main body 111 corresponds to the stage of the present disclosure. In the embodiment, the central region 111a corresponds to the mounting surface of the present disclosure. In addition, in the embodiment, the coolant, the flow path 1110a, etc. correspond to the cooling mechanism of the present disclosure.

[0017] Here, the configuration of the electrostatic chuck 1111 of the substrate support portion 11 will be described. Fig. 2 is a plan view showing an example of the configuration of the electrostatic chuck 1111 according to the first embodiment. Fig. 3 is a cross-sectional view showing an example of the configuration of the electrostatic chuck 1111 according to the first embodiment.

[0018] 2 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 that is approximately circular in plan view. A substrate W is placed on the upper surface of the central region 111a. The diameter of the central region 111a is approximately 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 that surrounds 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.

[0019] The central region 111a is divided into multiple areas A1 to A14. Hereinafter, the areas A1 to A14 will be referred to collectively as area A when they are not distinguished from one another. Each area A is a division of the central region 111a and constitutes a part of the central region 111a. For example, as shown in FIG. 2, the central region 111a is divided into a circular area A1 at its center. The central region 111a is further divided into multiple concentric annular regions from the circular area A1, and each of the multiple annular regions is divided circumferentially into multiple arc-shaped areas A2 to A14. The arc-shaped areas A2 to A14 have smaller angular widths closer to the periphery. The flow path 1110a is formed within the base 1110 so as to pass under all of the areas A. Note that the method of dividing the areas A shown in FIG. 2 is merely an example and is not limited thereto. For example, the central region 111a may be divided so that the radial width of the arc-shaped area A narrows toward the outer periphery. The central region 111a may also be divided into areas A, each of which is concentrically spaced at a fixed angle from the center. The central region 111a may also be divided into areas A in a lattice pattern. To precisely control the temperature distribution in the central region 111a, the central region 111a may be divided into more areas A. For example, the central region 111a may be divided into 100 or more areas A. While the division method for areas A shown in FIG. 2 illustrates a case in which the annular region 111b is not divided, this is not limiting. The annular region 111b may also be divided into multiple areas A. For example, the annular region 111b may be divided into multiple arc-shaped areas A in the circumferential direction.

[0020] The electrostatic chuck 1111 has a heater HT and a temperature sensor TS provided in each area A. FIG. 3 schematically shows a partial cross section of two areas A of the electrostatic chuck 1111. An electrostatic electrode 1111b is disposed within the ceramic member 1111a. A heater HT and a temperature sensor TS are also disposed within the ceramic member 1111a for each area A. The heater HT generates heat when power is supplied to heat the area A. In the embodiment, the heater HT corresponds to the heating mechanism of the present disclosure. In the embodiment, the temperature sensor TS corresponds to the measurement unit of the present disclosure.

[0021] Returning to Fig. 1, 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 Fig. 1 omits 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.

[0022] 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. For example, the heater power supply 60 performs PWM (Pulse Width Modulation) control of the power supplied to each heater HT. PWM control controls the output power by periodically switching the heater on and off within one cycle. The heater power supply 60 is configured to supply a predetermined amount of power to each heater HT and controls the power supplied to each heater HT by changing the ratio of the on period (duty ratio) within one cycle. The heater power supply 60 adjusts the power supplied to each heater HT based on control data input from the control unit 100. The amount of heat generated by each heater HT can be controlled by PWM control of the power supplied. Each heater HT generates heat using the power supplied from the heater power supply 60 and heats the area A.

[0023] The temperature detection unit 61 measures the resistance value of each temperature sensor TS, and detects the temperature of each temperature sensor TS arranged in each area A based on the measured resistance value.

[0024] The temperature sensors TS may be made of a material whose resistance changes with temperature. For example, the temperature sensors TS may be thermistors. Alternatively, the temperature sensors TS may be thin films made of any of the following materials: tungsten, nickel, molybdenum, copper, silver, platinum, and aluminum. The temperature detection unit 61 may measure the current and voltage of the power supplied to each temperature sensor TS, calculate the resistance of each temperature sensor TS from the measured current and voltage, and detect the temperature of the main body 111 of each area A based on the calculated resistance.

[0025] The showerhead 13 is configured to introduce at least one process gas from the gas supply unit 20 into the plasma processing space 10s. The showerhead 13 has at least one gas supply port 13a, at least one gas diffusion chamber 13b, and multiple gas inlets 13c. The process 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 showerhead 13 also includes at least one upper electrode. In addition to the showerhead 13, the gas inlet may also include one or more side gas injectors (SGIs) attached to one or more openings formed in the sidewall 10a.

[0026] The gas supply unit 20 may include at least one gas source 21 and at least one flow controller 22. In one embodiment, the gas supply unit 20 is configured to supply at least one process gas from a corresponding gas source 21 to the showerhead 13 via a corresponding flow controller 22. Each flow controller 22 may include, for example, a mass flow controller or a pressure-controlled flow controller. Additionally, the gas supply unit 20 may include one or more flow modulation devices to modulate or pulse the flow rate of the at least one process gas.

[0027] The power supply 30 includes an RF power supply 31 coupled to the plasma processing chamber 10 via at least one impedance matching circuit. The RF power supply 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 generates a plasma from at least one process gas supplied to the plasma processing space 10s. Therefore, the RF power supply 31 can function as at least a part of a plasma generating unit configured to generate a plasma from one or more process gases in the plasma processing chamber 10. Furthermore, by supplying a bias RF signal to the at least one lower electrode, a bias potential is generated on the substrate W, thereby attracting ion components in the formed plasma to the substrate W.

[0028] 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 multiple 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.

[0029] The second RF generator 31b is coupled to at least one lower electrode via at least one impedance matching circuit and is 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 generator 31b may be configured to generate multiple bias RF signals having different frequencies. The generated one or more bias RF signals are supplied to at least one lower electrode. In various embodiments, at least one of the source RF signal and the bias RF signal may be pulsed.

[0030] 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 the 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 the 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.

[0031] 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 the 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 either positive or negative polarity. Furthermore, the sequence of voltage pulses may include one or more positive voltage pulses and one or more negative voltage pulses within one period. The first and second DC generating units 32a and 32b may be provided in addition to the RF power supply 31, or the first DC generating unit 32a may be provided instead of the second RF generating unit 31b.

[0032] 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 regulated by the pressure regulating valve. The vacuum pump may include a turbomolecular pump, a dry pump, or a combination thereof.

[0033] The operation of the plasma processing apparatus 1 configured as described above is controlled comprehensively by a control unit 100. The control unit 100 is, for example, a computer, and controls each unit of the plasma processing apparatus 1. The control unit 100 controls the plasma processing apparatus 1 to perform various processes described in this disclosure.

[0034] [Configuration of Control Unit] Next, the control unit 100 will be described. Fig. 4 is a block diagram showing a schematic configuration of the control unit 100 according to the first embodiment. The control unit 100 includes an external interface 101, a user interface 102, a storage unit 103, and a process controller 104.

[0035] The external interface 101 is capable of communicating with each part of the plasma processing apparatus 1 and inputs and outputs various data. The user interface 102 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.

[0036] The storage unit 103 stores a control program (software) and various programs for implementing various processes executed in the plasma processing apparatus 1 under the control of the process controller 104. The storage unit 103 also stores various data used by the programs executed by the process controller 104. For example, the storage unit 103 stores a recipe in which processing condition data and the like are stored, and prediction model data 110. The programs and data may be stored in a computer-readable computer recording medium (e.g., a hard disk, an optical disk such as a DVD, a flexible disk, a semiconductor memory, etc.). The programs and data may also be transmitted as needed from another device, for example, via a dedicated line, for online use.

[0037] The prediction model data 110 is data that stores a prediction model that predicts the amount of heat input from plasma to the substrate W from the heat generation amount of the heater HT, the temperature of the main body 111, the temperature of the coolant, the first-order time derivative of the temperature of the main body 111, and the first-order or higher time derivative of the coolant temperature. In this embodiment, the prediction model is a calculation formula that predicts the amount of heat input from plasma to the substrate W in each area A from the heat generation amount of the heater HT, the temperature of the main body 111, the temperature of the coolant, the first-order time derivative of the temperature of the main body 111, and the first-order or higher time derivative of the coolant temperature. Details of the prediction model will be described later.

[0038] The process controller 104 includes a processor such as a CPU (Central Processing Unit) and an MPU (Micro Processing Unit) and controls each component of the plasma processing apparatus 1. The process controller 104 has an internal memory for storing programs and data, reads a control program stored in the storage unit 103, and executes the processing of the read control program. The process controller 104 functions as various processing units when the control program runs. For example, the process controller 104 has the functions of a plasma control unit 120, an acquisition unit 121, a correction unit 122, a prediction unit 123, a heat generation control unit 124, and an output control unit 125. Note that this embodiment will be described assuming that the process controller 104 has the functions of the plasma control unit 120, the acquisition unit 121, the correction unit 122, the prediction unit 123, the heat generation control unit 124, and the output control unit 125. However, the functions of the plasma control unit 120, the acquisition unit 121, the correction unit 122, the prediction unit 123, the heat generation control unit 124, and the output control unit 125 may be distributed among multiple controllers.

[0039] The plasma control unit 120 controls each part of the plasma processing apparatus 1 and controls the plasma processing.

[0040] The acquisition unit 121 periodically acquires the heat generation amount of each heater HT, the temperature of the main body 111, and the temperature of the refrigerant. In this embodiment, the acquisition unit 121 periodically acquires the temperature of the refrigerant, the heat generation amount of the heater HT for each area A, and the temperature of the main body 111.

[0041] The correction unit 122, the prediction unit 123, and the output control unit 125 will be described in detail later.

[0042] The heat generation control unit 124 controls the heater power supply 60 via the external interface 101 to control the heat generation amount of each heater HT. For example, the heat generation control unit 124 outputs control data specifying the power to be supplied to each heater HT to the heater power supply 60, thereby controlling the heat generation amount of each heater HT. In this embodiment, the heat generation control unit 124 outputs control data specifying the duty ratio of each heater HT to the heater power supply 60. The heater power supply 60 supplies power to each heater HT at the specified duty ratio based on the control data. The heater HT generates heat at an amount corresponding to the supplied power. For example, if the heater power supply 60 is capable of supplying 100 W of power per unit time to one heater HT and the duty ratio is specified as 20%, the heater power supply 60 controls the duty ratio of the power supplied to the heater HT to 20%, thereby supplying 20 W of power per unit time to the heater HT. In this case, the heater HT generates heat at an amount of 20 W per unit time.

[0043] Next, the flow of the plasma processing will be briefly described.

[0044] The substrate W is carried into the plasma processing chamber 10 through a loading / unloading port (not shown) by a transport mechanism such as a transport arm, and placed on the central region 111 a of the substrate support 11 .

[0045] The heat control unit 124 controls the heat generation amount of the heater HT. A set temperature is set in the heat control unit 124. The temperature detection unit 61 detects the temperature of the main body 111 in each area A using each temperature sensor TS. The heat control unit 124 controls the heat generation amount of the heater HT so that the temperature of the main body 111 in each area A detected by the temperature detection unit 61 becomes the set temperature. For example, during plasma processing, the heat generation control unit 124 sets the set temperature of the substrate W stored in the recipe for each area A of the substrate W. The heat generation control unit 124 controls the heat generation amount of the heater HT for each area A so that the temperature of the main body 111 becomes the set temperature.

[0046] The plasma control unit 120 controls the plasma processing. For example, the plasma control unit 120 controls the exhaust system 40 to evacuate the plasma processing chamber 10 to a predetermined vacuum level. The plasma control unit 120 controls the gas supply unit 20 to introduce a processing gas from the gas supply unit 20 into the plasma processing space 10s. The plasma control unit 120 controls the power supply 30 to supply a source RF signal and a bias RF signal from the first RF generation unit 31a and the second RF generation unit 31b in accordance with the introduction of the processing gas, thereby generating plasma in the plasma processing chamber 10.

[0047] Incidentally, in the plasma processing apparatus 1, it is desirable to measure the amount of heat input flowing from the plasma to the substrate W. The amount of heat input flowing from the plasma to the substrate W varies depending on the state of the plasma. Therefore, in the plasma processing apparatus 1, by measuring the amount of heat input flowing from the plasma to the substrate W, the state of the plasma can be grasped. For example, the amount of heat input from the plasma to the substrate W in each area A varies depending on the density distribution of the plasma. Therefore, in the plasma processing apparatus 1, by measuring the amount of heat input from the plasma to the substrate W in each area A, the density distribution of the plasma can be grasped.

[0048] Therefore, the plasma processing apparatus 1 according to this embodiment predicts the amount of heat input from the plasma to the substrate W as follows.

[0049] The acquisition unit 121 periodically acquires the heat generation amount of each heater HT, the temperature of the main body 111, and the temperature of the coolant. In this embodiment, the acquisition unit 121 periodically acquires the temperature of the coolant, the heat generation amount of the heater HT in each area A, and the temperature of the main body 111.

[0050] For example, the acquisition unit 121 acquires the temperature of each temperature sensor TS arranged in each area A from the temperature detection unit 61 via the external interface 101 as the temperature of the main body 111 of each area A. The acquisition unit 121 also acquires the temperature of the refrigerant from the chiller unit 14 via the external interface 101. A thermometer may be added to the pipe 14a to acquire the temperature of the refrigerant flowing into 1110, or the temperature of the refrigerant flowing out from 1110 may be acquired separately.

[0051] The acquisition unit 121 also acquires the heat generation amount of the heater HT in each area A from the heat generation control unit 124. For example, the acquisition unit 121 acquires the power supplied to the heater HT in each area A controlled by the heat generation control unit 124 from the heat generation control unit 124. The acquisition unit 121 identifies the acquired power supplied to the heater HT in each area A as the heat generation amount of the heater HT in each area A. In this embodiment, the acquisition unit 121 acquires the duty ratio of the heater HT in each area A controlled by the heat generation control unit 124 from the heat generation control unit 124. The acquisition unit 121 calculates the power supplied to the heater HT in each area A from the duty ratio of the heater HT in each area A and the power that the heater power supply 60 can supply to the heater HT in each area A. For example, if the duty ratio is 20% and the heater power supply 60 can supply 100 W of power per unit time to the heater HT in area A, the acquiring unit 121 determines the power supply to the heater HT as 20 W per unit time. The acquiring unit 121 determines the determined 20 W per unit time as the heat generation amount of the heater HT.

[0052] The correction unit 122 corrects the refrigerant temperature acquired by the acquisition unit 121 to the refrigerant temperature in each area A along the flow path 1110a.

[0053] The prediction unit 123 predicts the amount of heat input from the plasma to the substrate W in each area A using a prediction model for predicting the amount of heat input from the plasma to the substrate W.

[0054] Here, the prediction model will be described. The prediction model can be expressed as a mathematical model that calculates the amount of heat input flowing from the plasma in each area A to the substrate W. The prediction model calculates the amount of heat input from the plasma in each area A by multiplying the heat generation amount of the heater HT, the temperature of the main body 111, the temperature of the coolant, the first-order time derivative of the temperature of the main body 111, and the first-order or higher time derivatives of the coolant temperature by coefficients and adding them up. For example, the prediction model calculates the amount of heat input flowing from the plasma in each area A to the substrate W by multiplying the coefficients for each area A and all other areas A and adding them up. For example, the prediction model can be expressed as a calculation formula such as the following formula (1) using a thermal network method or a polynomial approximation model.

[0055]

[0056] Here, n is a number assigned to each area A in order. １ ~P ｎ is the amount of heat input flowing into the substrate W from the plasma in the areas A numbered 1 to n. １ ~T ｎ is the temperature of the main body 111 in the area A numbered 1 to n. １ ~p ｎ is the heat generation amount of the heater HT in the area A numbered 1 to n. １ ~T' ｎ is the temperature of the refrigerant in area A numbered 1 to n. １,１ ~a ｎ,ｎ is the temperature T of the main body 111 １ ~T ｎ is the coefficient for b １,１ ~b ｎ,ｎ is the heat generation amount p of the heater HT １ ~p ｎ is the coefficient for １,１ ~c ｎ,ｎ is the temperature T of the main body 111 １ ~T ｎ is the coefficient for the first-order time derivative of . １,１ ~d ｎ,ｎ is the refrigerant temperature T' １ ~T' ｎ is the coefficient for １,１ ~e ｎ,ｎ is the refrigerant temperature T' １ ~T' ｎ is the coefficient for the first-order time derivative of f １,１ ~f ｎ,ｎ is the refrigerant temperature T' １ ~T' ｎ is the coefficient for the second-order time derivative of

[0057] The heat flow in the parts related to the substrate W and the main body 111 can be expressed as a thermal circuit by the thermal network method. Fig. 5 is a diagram showing an example of a thermal circuit representing the substrate W and the main body 111 according to the first embodiment.

[0058] In the thermal circuit shown in Figure 5, the substrates W in areas A numbered 1 to n are represented as nodes #1 to #n, the main body 111 in areas A numbered 1 to n are represented as nodes #n+1 to #2n, and the coolant in the flow path 1110a is represented as nodes #2n+1 to #3n. The coolant flows through the flow path 1110a. Heat transferred to the coolant flows away along with the coolant. For this reason, nodes #2n+1 to #3n are represented as constant potential points using ground symbols.

[0059] In the plasma processing apparatus 1, heat is transferred between the substrate W and the main body 111 and between the main body 111 and the coolant in the flow path 1110a according to the temperature difference for each area A. In the thermal circuit shown in Fig. 5, the thermal resistance between the substrate W and the main body 111 is represented as thermal resistance R1, and the thermal resistance between the main body 111 and the coolant in the flow path 1110a is represented as thermal resistance R2.

[0060] Furthermore, in the plasma processing apparatus 1, heat is transferred between the areas A of the substrate W and the main body 111 according to the temperature difference. In the thermal circuit shown in Fig. 5, the thermal resistance between the areas A of the substrate W is represented as thermal resistance R3, and the thermal resistance between the areas A of the main body 111 is represented as thermal resistance R4.

[0061] In addition, in the plasma processing apparatus 1, a heater HT is provided in the main body 111 for each area A, and the heat generated by the heater HT is transferred to the main body 111. In the thermal circuit shown in Fig. 5, a variable heat source P1 representing a heater HT is connected to each of nodes #n+1 to #2n representing the main body 111.

[0062] Furthermore, the plasma processing apparatus 1 inputs heat from plasma to the substrate W in each area A. In the thermal circuit shown in Fig. 5, the plasma in each area A numbered 1 to n is represented as a variable heat source P2. In the thermal circuit shown in Fig. 5, the variable heat sources P2 representing plasma are connected to nodes #1 to #n representing the substrate W, respectively.

[0063] For nodes #1 to #3n, the simultaneous equations of heat balance can be expressed as the following equations (2-1) to (2-3n).

[0064]

[0065] Here, Q is the heat input (W) at each node. For example, Q１ is the heat input to node #1. G is the thermal conductivity (W / K) between each node. For example, G １,ｉ is the thermal conductivity of node #1 and node #i. T is the temperature (degC) of each node. For example, T １ is the temperature of node #1. t is time (sec). C is the heat capacity of each node. For example, C １ is the heat capacity of node #1.

[0066] The left side of each equation of the simultaneous equations of heat balance is calculated by multiplying the temperature difference between nodes #1 to #3n by the thermal conductivity G for each node, where i is 1 to 3n, to find the sum, and then adding the sum to the heat input Q. For example, the left side of equation (2-1) is calculated by multiplying the temperature difference between nodes #1 to #3n (T ｉ -T １ ) and thermal conductivity G １,ｉ Multiply by to get the sum, and the heat input Q １ and the sum is added.

[0067] Note that equations (2-1) to (2-3n) are expressed as equations that include terms for heat transfer between all nodes #1 to #3n. For nodes between which heat transfer is not taken into consideration, the thermal conductivity G between the nodes is set to, for example, zero. For example, for nodes not connected by the thermal circuit shown in FIG. 5, the thermal conductivity G between the nodes is set to, for example, zero.

[0068] For example, the simultaneous equations for the heat balance of node #1 shown in FIG. 5 can be expressed as the following equation (3).

[0069]

[0070] The above equation (1) can be obtained from the simultaneous equations of the heat balance of nodes #1 to #3n. In addition, the above equation (1) can be obtained in the same way when a polynomial approximation model is used.

[0071] Coefficient a in Equation (1) １,１ ~a ｎ,ｎ , b １,１ ~b ｎ,ｎ , c １,１ ~c ｎ,ｎ , d １,１ ~dｎ,ｎ , e １,１ ~e ｎ,ｎ , f １,１ ~f ｎ,ｎ The values ​​of can be determined by performing fitting using fitting data. The fitting data is generated by measuring, for example, the amount of heat input flowing from the plasma to the substrate W in each area A, the amount of heat generated by the heater HT, the temperature of the main body 111, and the temperature of the coolant using the plasma processing apparatus 1. The fitting data is generated from the amount of heat input from the plasma in each area A, the amount of heat generated by the heater HT, the temperature of the main body 111, the temperature of the coolant, the first-order time derivative of the temperature of the main body 111, the first-order time derivative of the temperature of the coolant, and the second-order time derivative of the temperature of the coolant.

[0072] The amount of heat input flowing from the plasma in each area A to the substrate W is calculated from the simultaneous equations of heat balance for the substrate W in each area A. For example, for nodes #1 to #3n, the simultaneous equations of heat balance shown in the following formulas (2-1) to (2-3n) can calculate the thermal conductivity G from the temperatures of nodes #1 to #3n, their changes over time, and the heat generation amount of the heater HT. The amount of heat input flowing from the plasma in each area A to the substrate W is calculated using the simultaneous equations of heat balance for nodes #1 to #n.

[0073] When generating fitting data, a substrate W is placed in the central region 111a of the substrate support 11. When generating fitting data, the process controller 104 controls the heater power supply 60 to cause each heater HT to generate heat while circulating a coolant from the chiller unit 14 through the flow path 1110a to cool the plasma. The process controller 104 measures the temperature of the substrate W in each area A, the heat generation amount of the heater HT, the temperature of the main body 111, and the temperature of the coolant. The temperature of the substrate W in each area A is measured, for example, by a temperature sensor such as an infrared camera disposed in the plasma processing chamber 10. The temperature of the substrate W in each area A is also measured, for example, by a sensor substrate configured to be able to measure temperature. The process controller 104 periodically measures the temperature of the substrate W in each area A, the heat generation amount of the heater HT, the temperature of the main body 111, and the temperature of the coolant. The process controller 104 periodically measures a plurality of patterns by changing the plasma generation conditions, the coolant temperature, and the heat generation amount of each heater HT, including transitional periods when the temperature is changing. The process controller 104 calculates the amount of heat input flowing from the plasma to the substrate W in each area A based on the temperature of the substrate W in each area A. When generating fitting data, the amount of heat input flowing from the plasma to the substrate W in each area A may be measured using a sensor board or the like configured to be able to measure the amount of heat input from the plasma. The process controller 104 generates fitting data that stores the amount of heat input flowing from the plasma to the substrate W in each area A, the heat generation amount of the heater HT, the temperature of the main body 111, and the temperature of the coolant, along with the measurement time.

[0074] The temperature of the refrigerant in each area A may be the temperature of the refrigerant measured by the chiller unit 14 or may be the temperature of the refrigerant measured by a thermometer installed in the pipe 14a.

[0075] Here, the temperature of the refrigerant flowing through the flow path 1110a gradually increases due to heat input from the base 1110. Therefore, the temperature of the refrigerant in each area A of the fitting data may be corrected to correspond to the temperature increase along the flow path 1110a. For example, the amount of temperature increase of the refrigerant when the refrigerant passes through the flow path 1110a is calculated. Also, the total length from one end of the flow path 1110a where the refrigerant flows in to the other end where the refrigerant flows out is calculated. Also, the length of the flow path 1110a to each area A is calculated. The length of the flow path 1110a to each area A is measured from one end along the flow path 1110a. The total length of the flow path 1110a and the length of the flow path 1110a to each area A may be calculated from the design data of the base 1110, or the base 1110 may be actually measured. In correcting the refrigerant temperature, the amount of increase in refrigerant temperature for each area A is calculated by multiplying the amount of increase in refrigerant temperature over the entire length of flow path 1110a by the ratio of the length of flow path 1110a up to area A to the entire length of flow path 1110a. In correcting the refrigerant temperature, the amount of increase in refrigerant temperature calculated for each area A is added to the refrigerant temperature measured by a thermometer installed in chiller unit 14 or piping 14a to calculate the refrigerant temperature for each area A. Note that the amount of increase in refrigerant temperature for each area A may be determined by simulation or the like.

[0076] By fitting the equation (1) using such fitting data, the coefficient a １,１ ~a ｎ,ｎ , b １,１ ~b ｎ,ｎ , c １,１ ~c ｎ,ｎ , d １,１ ~d ｎ,ｎ , e １,１ ~e ｎ,ｎ , f １,１ ~f ｎ,ｎ can each specify an appropriate value.

[0077] The prediction model data 110 includes the coefficient a １,１ ~a ｎ,ｎ , b １,１ ~b ｎ,ｎ , c １,１ ~c ｎ,ｎ , d １,１ ~d ｎ,ｎ , e１,１ ~e ｎ,ｎ , f １,１ ~f ｎ,ｎ The formula (1) in which the specified values ​​are set is stored.

[0078] The acquisition unit 121 periodically acquires the heat generation amount of each heater HT, the temperature of the main body 111, and the temperature of the coolant. In this embodiment, the acquisition unit 121 periodically acquires the coolant temperature, the heat generation amount of the heater HT, and the temperature of the main body 111 for each area A. The period at which the acquisition unit 121 acquires the coolant temperature, the heat generation amount of the heater HT, and the temperature of the main body 111 may be any period at which the time derivative of the temperature of the main body 111 and the time derivative of the coolant temperature can be calculated. For example, the period is preferably 0.01 to 0.1 seconds, and more preferably 0.0001 to 0.01 seconds.

[0079] The correction unit 122 corrects the refrigerant temperature acquired by the acquisition unit 121 to the refrigerant temperature in each area A in accordance with the temperature increase along the flow path 1110a. For example, the correction unit 122 calculates the amount of refrigerant temperature increase for each area A by multiplying the amount of refrigerant temperature increase over the entire length of the flow path 1110a by the ratio of the length of the flow path 1110a up to the area A to the entire length of the flow path 1110a. The correction unit 122 then calculates the refrigerant temperature for each area A by adding the calculated amount of refrigerant temperature increase for each area A to the refrigerant temperature measured by a thermometer installed in the chiller unit 14 or the piping 14a. Note that the correction unit 122 may also calculate the refrigerant temperature for each area A by adding the amount of refrigerant temperature increase for each area A obtained by simulation or the like to the refrigerant temperature measured by a thermometer installed in the chiller unit 14 or the piping 14a.

[0080] The prediction unit 123 predicts the amount of heat input from the plasma to the substrate W for each area A using the prediction model stored in the prediction model data 110. The prediction unit 123 predicts the amount of heat input from the plasma to the substrate W for each area A based on the corrected coolant temperature in each area A and the acquired heat generation amount of the heater HT and temperature of the main body 111 for each area A. For example, the prediction unit 123 predicts the amount of heat input to each area A using equation (1) from the coolant temperature of each area A, the heat generation amount of the heater HT, the temperature of the main body 111, the first-order time derivative of the temperature of the main body 111, the first-order time derivative of the coolant temperature, and the second-order time derivative of the coolant temperature. For example, the prediction unit 123 substitutes the coolant temperature of each area A, the heat generation amount of the heater HT, the temperature of the main body 111, the first-order time derivative of the temperature of the main body 111, the first-order time derivative of the coolant temperature, and the second-order time derivative of the coolant temperature into equation (1). Then, the prediction unit 123 calculates the amount of heat input from the plasma to the substrate W in each area A by calculating the formula (1). By using the formula (1), the prediction unit 123 can accurately predict the amount of heat input from the plasma to the substrate W.

[0081] The output control unit 125 performs various controls to output the amount of heat input from the plasma to the substrate W in each area A predicted by the prediction unit 123. For example, the output control unit 125 controls the output of information based on the amount of heat input from the plasma to the substrate W in each area A predicted by the prediction unit 123 to the user interface 102. For example, the output control unit 125 controls the display on the user interface 102 of an image showing the distribution of the amount of heat input to each area A on the substrate W. Furthermore, for example, the output control unit 125 outputs data on the amount of heat input from the plasma to the substrate W in each area A predicted by the prediction unit 123 to an external terminal device via a network (not shown). Furthermore, for example, the output control unit 125 controls the storage of data on the amount of heat input from the plasma to the substrate W in each area A predicted by the prediction unit 123 in the storage unit 103.

[0082] [Specific Example of Flow of Prediction Process] Next, a specific example of the flow of the prediction process including the prediction method according to the first embodiment will be described. Fig. 6 is a flowchart showing an example of the flow of the prediction process according to the first embodiment. The prediction process according to the first embodiment is executed when plasma processing is started. When plasma processing is started, the heat control unit 124 is set with the set temperature of the substrate W stored in the recipe for each area A of the substrate W.

[0083] The acquiring unit 121 acquires the heat value of the heater HT, the temperature of the main body 111, and the temperature of the coolant (step S10). For example, the acquiring unit 121 acquires the temperature of the coolant, the heat value of the heater HT, and the temperature of the main body 111 for each area A.

[0084] The correcting unit 122 corrects the refrigerant temperature acquired by the acquiring unit 121 to the refrigerant temperature of each area A (step S11).

[0085] The prediction unit 123 predicts the amount of heat input from the plasma to the substrate W in each area A using the prediction model stored in the prediction model data 110 (step S12). For example, the prediction unit 123 predicts the amount of heat input to each area A using equation (1) from the coolant temperature of each area A, the heat generation amount of the heater HT, the temperature of the main body 111, the first-order time derivative of the temperature of the main body 111, the first-order time derivative of the coolant temperature, and the second-order time derivative of the coolant temperature.

[0086] This allows the plasma processing apparatus 1 according to the first embodiment to measure the amount of heat input from the plasma flowing into each area A of the substrate W.

[0087] The output control unit 125 performs various controls to output the amount of heat input from the plasma in each area A to the substrate W, as predicted by the prediction unit 123 (step S13). For example, the output control unit 125 performs control to display on the user interface 102 an image showing the distribution of the amount of heat input in each area A on the substrate W.

[0088] This allows the process manager to understand the state of the plasma processing by checking the image displayed on the user interface 102. For example, the process manager can understand the plasma density distribution from the image showing the distribution of the heat input amount in each area A.

[0089] The prediction unit 123 determines whether the plasma processing has been completed (step S14). If the plasma processing has not been completed (step S14: No), the process proceeds to step S10. If the plasma processing has been completed (step S14: Yes), the process ends.

[0090] In the above embodiment, the prediction model is described as a prediction model that includes, for each area A, a term for heat transfer from the area A and all other areas A. However, this is not limited to this. For example, the prediction model may be a prediction model that includes, for each area A, a term for heat transfer from the area A and some other areas A. The other some areas A may be areas A where heat transfer occurs to the area A, and may be areas A surrounding the area A, or areas A adjacent to the area A.

[0091] In the above embodiment, the heat input amount from the plasma to the substrate W is predicted for each area A obtained by dividing the central region 111a of the main body 111. However, this is not limited to this. For example, the heat input amount from the plasma to the substrate W may be predicted by treating the central region 111a as a single area A without dividing the central region 111a of the main body 111 into areas A.

[0092] In the above embodiment, the thermal circuit representing the substrate W and the main body 111 is shown as having the configuration in Fig. 5 . However, this is not limiting. The thermal circuit representing the substrate W and the main body 111 may have additional nodes in consideration of heat transfer between the temperature sensor TS and the heater HT within the main body 111. For example, the thermal circuit representing the substrate W and the main body 111 may have a circuit configuration in which additional nodes are added between the nodes #1 to #n and the nodes #n+1 to #2n of the thermal circuit of the configuration in Fig. 5 , and the variable heat source P1 representing each heater HT is connected to the added nodes.

[0093] In the above embodiment, a prediction model (e.g., Equation (1)) calculated from fitting data generated by the plasma processing apparatus 1 is stored in the prediction model data 110. However, this is not limited to this. The prediction model stored in the prediction model data 110 may be a prediction model calculated by another plasma processing apparatus. For example, when multiple plasma processing apparatuses are operated, Equation (1) may be calculated by one of the plasma processing apparatuses, and the calculated Equation (1) may be used by the multiple plasma processing apparatuses. Furthermore, the prediction model stored in the prediction model data 110 may be provided by the manufacturer of the plasma processing apparatus. The prediction model may be adjustable for individual differences between plasma processing apparatuses. For example, a correction term may be added to Equation (1) to absorb individual differences between plasma processing apparatuses. Each plasma processing apparatus 1 may use a prediction model with the correction term adjusted according to the individual differences between the plasma processing apparatuses. For example, a standard Equation (1) is calculated for a standard plasma processing apparatus. Each plasma processing apparatus 1 stores Equation (1) with the adjusted correction term as a prediction model in the prediction model data 110.

[0094] In the above embodiment, the plasma processing is performed on a semiconductor wafer as the substrate W, but the present invention is not limited to this.

[0095] In the above embodiment, the plasma processing apparatus is described as a plasma processing system for performing a plasma etching process. However, the present invention is not limited to this. For example, the plasma processing apparatus may be a film forming apparatus that generates plasma to form a film, or a heat processing apparatus that generates plasma to perform a heat treatment such as ashing.

[0096] In the above embodiment, an example has been described in which information based on the predicted amount of heat input from the plasma to the substrate W is displayed on the user interface 102. However, this is not limited to this. For example, the plasma processing apparatus may control the plasma processing based on the amount of heat input from the plasma to the substrate W. For example, the plasma processing apparatus may calculate the plasma density distribution from the amount of heat input from the plasma to the substrate W in each area A, and control the plasma processing so as to achieve a predetermined density distribution.

[0097] As described above, the plasma processing system (plasma processing apparatus) according to the first embodiment includes the main body 111 (stage), the plasma processing chamber 10 (chamber), a cooling mechanism (coolant, flow path 1110a, etc.), the heater HT (heating mechanism), the temperature sensor TS (measurement unit), the acquisition unit 121, and the prediction unit 123. The main body 111 accommodates a substrate W. The plasma processing chamber 10 includes the main body 111 therein. Plasma is generated inside the main body 111, and plasma processing is performed on the substrate W placed in the main body 111. The cooling mechanism is provided in the main body 111 and cools the main body 111. The heater HT is provided between the cooling mechanism and the support surface of the main body 111 on which the substrate W is placed. The heater HT is capable of controlling the amount of heat generated and heats the main body 111. The temperature sensor TS measures the temperature of the main body 111. The acquisition unit 121 periodically acquires the heat generation amount of the heater HT, the temperature of the main body 111, and the temperature of the cooling mechanism. The prediction unit 123 predicts the heat input amount flowing from the plasma to the substrate W from the heat generation amount of the heater HT, the temperature of the main body 111, the temperature of the cooling mechanism, the first-order time derivative of the temperature of the main body 111, and the first-order or higher time derivative of the temperature of the cooling mechanism, using a calculation formula (e.g., Formula (1)) that predicts the heat input amount flowing from the plasma to the substrate W from the heat generation amount of the heater HT, the temperature of the main body 111, and the temperature of the cooling mechanism acquired by the acquisition unit 121, the first-order time derivative of the temperature of the main body 111, and the first-order or higher time derivative of the temperature of the cooling mechanism. In this way, the plasma processing system according to the first embodiment can measure the heat input amount flowing from the plasma to the substrate W.

[0098] The calculation formula is a prediction model that predicts the amount of heat input from the plasma to the substrate W from the heat generation amount of the heater HT, the temperature of the main body 111, the temperature of the cooling mechanism, the first-order time derivative of the temperature of the main body 111, and the first-order or higher time derivative of the temperature of the cooling mechanism. As a result, the plasma processing system according to the first embodiment can measure the amount of heat input from the plasma to the substrate W using the prediction model.

[0099] The calculation formula is a mathematical model that calculates the amount of heat input flowing from the plasma to the substrate W by multiplying the heat generation amount of the heater HT, the temperature of the main body 111, the temperature of the cooling mechanism, the first-order time derivative of the temperature of the main body 111, the first-order time derivative of the temperature of the cooling mechanism, and the second-order time derivative of the temperature of the cooling mechanism by coefficients and adding them up. The values ​​of the coefficients of the mathematical model are determined using data that has been previously determined regarding the relationships between the amount of heat input flowing from the plasma to the substrate W, the heat generation amount of the heater HT, the temperature of the main body 111, the temperature of the cooling mechanism, the first-order time derivative of the temperature of the main body 111, the first-order time derivative of the temperature of the cooling mechanism, and the second-order time derivative of the temperature of the cooling mechanism. As a result, the plasma processing system according to the embodiment can predict the amount of heat input flowing from the plasma to the substrate W using the mathematical model, and can therefore accurately measure the amount of heat input flowing from the plasma to the substrate W.

[0100] Furthermore, the values ​​of the coefficients of the mathematical model are determined by performing fitting using data. As a result, the plasma processing system according to the embodiment can predict the amount of heat input from the plasma to the substrate W using the mathematical model, and can therefore accurately measure the amount of heat input from the plasma to the substrate W.

[0101] The main body 111 has a mounting surface divided into multiple areas. A cooling mechanism is provided in every area of ​​the main body 111. A heater HT is provided in each area of ​​the main body 111. A temperature sensor TS is provided in each area of ​​the main body 111 and measures the temperature of the main body 111 for each area. The acquisition unit 121 periodically acquires the temperature of the cooling mechanism, the heat generation amount of the heater HT, and the temperature of the main body 111 in each area. The prediction unit 123 uses a calculation formula to predict the amount of heat input from the plasma to the substrate W in each area based on the cooling mechanism temperature acquired by the acquisition unit 121, the heat generation amount of the heater HT and the temperature of the main body 111 in each area, the first-order time derivative of the temperature of the main body 111 in each area, and the first-order or higher time derivative of the temperature of the cooling mechanism. This allows the plasma processing system according to the embodiment to measure the amount of heat input from the plasma to the substrate W in each area A.

[0102] The calculation formula is a mathematical model that calculates the amount of heat input flowing from plasma to the substrate W in each area by multiplying the heat generation amount of the heater HT, the temperature of the main body 111, the temperature of the cooling mechanism, the first-order time derivative of the temperature of the main body 111, the first-order time derivative of the temperature of the cooling mechanism, and the second-order time derivative of the temperature of the cooling mechanism by a coefficient and adding them up for each area. The values ​​of the coefficients of the mathematical model are determined using data that has been previously determined regarding the relationship between the heat generation amount flowing from plasma to the substrate W in each area, the heat generation amount of the heater HT, the temperature of the main body 111, the temperature of the cooling mechanism, the first-order time derivative of the temperature of the main body 111, the first-order time derivative of the temperature of the cooling mechanism, and the second-order time derivative of the temperature of the cooling mechanism. As a result, the plasma processing system according to the embodiment can use the mathematical model to predict the amount of heat input flowing from plasma to the substrate W in each area A, taking into account heat transfer with other areas A.

[0103] Furthermore, the values ​​of the coefficients of the mathematical model are determined by performing fitting using data. As a result, the plasma processing system according to the embodiment can predict the amount of heat input from the plasma in each area A to the substrate W using the mathematical model, and therefore can predict the amount of heat input from the plasma in each area A to the substrate W.

[0104] The calculation formula is a mathematical model that calculates the amount of heat input to each area by multiplying by a coefficient the heat generation amount of the heater HT in that area and all other areas, the temperature of the main body 111, the temperature of the cooling mechanism, the first-order time derivative of the temperature of the main body 111, the first-order time derivative of the temperature of the cooling mechanism, and the second-order time derivative of the temperature of the cooling mechanism, and adding them up. As a result, the plasma processing system according to the embodiment can use the mathematical model to predict the amount of heat input flowing from the plasma in each area A to the substrate W, taking into account heat transfer with all other areas A.

[0105] The cooling mechanism is a flow path through which a coolant flows, the flow path being formed to pass through all areas of the main body 111. The acquisition unit 121 acquires the temperature of the coolant flowing into the flow path. The plasma processing system according to the embodiment further includes a correction unit 122. The correction unit 122 corrects the coolant temperature acquired by the acquisition unit 121 to the coolant temperature in each area along the flow path. The prediction unit 123 uses a calculation formula to predict the heat input in each area from the coolant temperature in each area corrected by the correction unit 122, the heat generation amount of the heater HT and the temperature of the main body 111 in each area acquired by the acquisition unit 121, the first-order time derivative of the temperature of the cooling mechanism in each area, the second-order time derivative of the temperature of the cooling mechanism, and the first-order time derivative of the temperature of the main body 111. As a result, the plasma processing system according to the embodiment can predict the heat input flowing from the plasma in each area A to the substrate W using the coolant temperature in each area A, thereby accurately measuring the heat input flowing from the plasma in each area A to the substrate W.

[0106] Second Embodiment Next, a second embodiment will be described. In the second embodiment, a case will be described in which an information processing apparatus predicts the amount of heat input from plasma to a substrate W. Fig. 7 is a block diagram showing a schematic configuration of an information processing apparatus 200 according to the second embodiment. The information processing apparatus 200 according to the second embodiment has a configuration and function that are partially similar to those of the control unit 100 according to the first embodiment, and therefore, the same components are denoted by the same reference numerals and their descriptions are omitted, and the following mainly describes the different components.

[0107] The information processing device 200 is, for example, a computer, and includes an external interface 201, a user interface 202, a storage unit 203, and a controller 204.

[0108] The external interface 201 is an interface for inputting and outputting various types of data. For example, the external interface 201 is connected to a network and inputs and outputs various types of data to and from external devices. The user interface 202 is composed of a keyboard through which a user such as a process manager inputs commands, a display that can display various types of information, and the like.

[0109] The storage unit 203 stores a control program (software) and various programs for implementing various processes under the control of the controller 204. The storage unit 203 also stores various data used by the programs executed by the controller 204. For example, the storage unit 203 stores the above-mentioned prediction model data 110 and measurement data 211. The programs and data may be stored in a computer-readable computer recording medium (e.g., a hard disk, an optical disk such as a DVD, a flexible disk, a semiconductor memory, etc.). The programs and data may also be transmitted as needed from another device via, for example, a dedicated line and used online.

[0110] The prediction model data 110 is data storing a prediction model for predicting the amount of heat input from the plasma to the substrate W from the heat generation amount of the heater HT, the temperature of the main body 111, the temperature of the coolant, the first-order time derivative of the temperature of the main body 111, and the first-order or higher time derivative of the temperature of the coolant. For example, the prediction model may be a model using a coefficient a １,１ ~a ｎ,ｎ , b １,１ ~b ｎ,ｎ , c １,１ ~c ｎ,ｎ , d １,１ ~d ｎ,ｎ , e １,１ ~e ｎ,ｎ , f １,１ ~f ｎ,ｎ The formula (1) is stored.

[0111] The measurement data 211 is data obtained by periodically measuring the heat generation amount of each heater HT, the temperature of the main body 111, and the temperature of the coolant during plasma processing in the plasma processing apparatus 1. In this embodiment, the measurement data 211 stores the measurement time, the coolant temperature, the heat generation amount of the heater HT, and the temperature of the main body 111 for each area A.

[0112] The controller 204 includes a processor such as a CPU or MPU, and controls the information processing device 200. The controller 204 has an internal memory for storing programs and data, reads a control program stored in the storage unit 203, and executes the processing of the read control program. The controller 204 functions as various processing units when the control program runs. For example, the controller 204 has the functions of the correction unit 122, prediction unit 123, and output control unit 125 described above. Note that this embodiment will be described taking as an example a case where the controller 204 has the functions of the correction unit 122, prediction unit 123, and output control unit 125. However, the functions of the correction unit 122, prediction unit 123, and output control unit 125 may be distributed and realized by multiple controllers.

[0113] The prediction unit 123 uses the prediction model stored in the prediction model data 110 to predict the amount of heat input from the plasma to the substrate W for each area A. For example, the prediction unit 123 reads the heat generation amount of each heater HT, the temperature of the main body 111, and the temperature of the coolant from the measurement data 211 in the order of measurement time.

[0114] The correction unit 122 corrects the readout coolant temperature to the coolant temperature in each area A in accordance with the temperature rise along the flow path 1110 a of the plasma processing apparatus 1 .

[0115] The prediction unit 123 predicts the amount of heat input from the plasma to the substrate W for each area A based on the coolant temperature in each area A corrected by the correction unit 122, the read heat value of the heater HT for each area A, and the temperature of the main body 111. For example, the prediction unit 123 predicts the amount of heat input to each area A from the coolant temperature in each area A, the heat value of the heater HT, the temperature of the main body 111, the first-order time derivative of the temperature of the main body 111, the first-order time derivative of the coolant temperature, and the second-order time derivative of the coolant temperature using equation (1).

[0116] The output control unit 125 performs various controls to output the amount of heat input from the plasma to the substrate W in each area A predicted by the prediction unit 123. For example, the output control unit 125 performs control to output information based on the amount of heat input from the plasma to the substrate W in each area A predicted by the prediction unit 123 to the user interface 202. For example, the output control unit 125 performs control to display on the user interface 202 an image showing the distribution of the amount of heat input to each area A on the substrate W.

[0117] Furthermore, for example, the output control unit 125 outputs data on the amount of heat input from the plasma to the substrate W in each area A predicted by the prediction unit 123 to an external terminal device via a network (not shown). Furthermore, for example, the output control unit 125 performs control to store data on the amount of heat input from the plasma to the substrate W in each area A predicted by the prediction unit 123 in the memory unit 203.

[0118] [Specific example of prediction processing flow] Next, a specific example of the flow of prediction processing including the prediction method according to the second embodiment will be described. Fig. 8 is a flowchart showing an example of the flow of prediction processing according to the second embodiment. The prediction processing according to the second embodiment is executed when a predetermined operation is performed on the user interface 202 to instruct the start of prediction processing.

[0119] The prediction unit 123 reads out the heat generation amount of each heater HT, the temperature of the main body 111, and the temperature of the refrigerant from the measurement data 211 in the order of measurement time (step S20).

[0120] The correcting unit 122 corrects the readout coolant temperature to the coolant temperature in each area A in accordance with the temperature rise along the flow path 1110a of the plasma processing apparatus 1 (step S21).

[0121] The prediction unit 123 predicts the amount of heat input from the plasma to the substrate W in each area A using the prediction model stored in the prediction model data 110 (step S22). For example, the prediction unit 123 predicts the amount of heat input to each area A using equation (1) from the coolant temperature of each area A, the heat generation amount of the heater HT, the temperature of the main body 111, the first-order time derivative of the temperature of the main body 111, the first-order time derivative of the coolant temperature, and the second-order time derivative of the coolant temperature.

[0122] This allows the information processing apparatus 200 according to the second embodiment to measure the amount of heat input flowing into each area A of the substrate W from the plasma during plasma processing in the plasma processing apparatus 1.

[0123] The output control unit 125 performs various controls to output the amount of heat input from the plasma in each area A to the substrate W, as predicted by the prediction unit 123 (step S23). For example, the output control unit 125 controls the user interface 202 to display an image showing the distribution of the amount of heat input in each area A on the substrate W.

[0124] This allows a user, such as a process manager, to understand the state of the plasma processing by checking the image displayed on the user interface 202. For example, the user can understand the plasma density distribution during the plasma processing in the plasma processing apparatus 1 from the image showing the distribution of the heat input amount in each area A.

[0125] The prediction unit 123 determines whether or not reading of data from the measurement data 211 is complete (step S24). If reading of data is not complete (step S24: No), the prediction unit 123 proceeds to step S10 described above. If reading of data is complete (step S24: Yes), the prediction unit 123 ends the process.

[0126] As described above, the information processing apparatus 200 according to the second embodiment includes the storage unit 203 and the prediction unit 123. The storage unit 203 stores measurement data 211 obtained by periodically measuring the heat generation amount of the heater HT, the temperature of the main body 111, and the temperature of the cooling mechanism of the plasma processing apparatus 1 that performs plasma processing on the substrate W placed on the main body 111, while cooling the main body 111 (stage) on which the substrate W is placed by a cooling mechanism (refrigerant, flow path 1110a, etc.) provided in the main body 111 and heating the main body 111 by a heater HT (heating mechanism) provided between the placement surface of the main body 111 on which the substrate W is placed and the cooling mechanism. The prediction unit 123 uses a calculation formula (for example, formula (1)) for predicting the amount of heat input flowing from the plasma into the substrate W from the amount of heat generated by the heater HT, the temperature of the main body 111, the temperature of the cooling mechanism, the first-order time derivative of the temperature of the main body 111, and the first-order or higher time derivative of the temperature of the cooling mechanism to predict the amount of heat input flowing from the plasma into the substrate W from the amount of heat generated by the heater HT, the temperature of the main body 111, the temperature of the cooling mechanism, the first-order time derivative of the temperature of the main body 111, and the first-order or higher time derivative of the temperature of the cooling mechanism, all of which are stored in the measurement data 211. In this way, the information processing apparatus 200 according to the second embodiment can measure the amount of heat input flowing from the plasma into the substrate W.

[0127] It should be noted that the disclosed embodiments are illustrative in all respects and should not be considered 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.

[0128] In addition, the following supplementary notes are disclosed regarding the above-described embodiment.

[0129] a chamber in which the stage is installed and in which plasma is generated to perform plasma processing on the substrate installed on the stage; a cooling mechanism installed on the stage and cooling the stage; a heating mechanism installed between the cooling mechanism and a mounting surface of the stage on which the substrate is installed and capable of controlling the amount of heat generated; a measurement unit that measures the temperature of the stage; an acquisition unit that periodically acquires the amount of heat generated by the heating mechanism, the temperature of the stage, and the temperature of the cooling mechanism; a prediction unit that predicts the amount of heat input flowing from the plasma to the substrate from the amount of heat generated by the heating mechanism, the temperature of the stage, and the temperature of the cooling mechanism acquired by the acquisition unit, and the first-order time derivative of the temperature of the stage and the first-order or higher time derivative of the temperature of the cooling mechanism, using a calculation formula that predicts the amount of heat input flowing from the plasma to the substrate from the amount of heat generated by the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, a first-order time derivative of the temperature of the stage, and a first-order or higher time derivative of the temperature of the cooling mechanism; A plasma processing apparatus comprising:

[0130] (Supplementary Note 2) The plasma processing apparatus according to Supplementary Note 1, wherein the calculation formula is a prediction model that predicts the amount of heat input from the plasma to the substrate based on the heat generation amount of the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, a first-order time derivative of the temperature of the stage, and a first-order or higher time derivative of the temperature of the cooling mechanism.

[0131] (Supplementary Note 3) The plasma processing apparatus according to Supplementary Note 1 or 2, wherein the calculation formula is a mathematical model that calculates the amount of heat input flowing from the plasma to the substrate by multiplying the amount of heat generated by the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, a first-order time derivative of the temperature of the stage, a first-order time derivative of the temperature of the cooling mechanism, and a second-order time derivative of the temperature of the cooling mechanism by coefficients and adding them up, and the values ​​of the coefficients of the mathematical model are determined using data that has been previously determined regarding the relationship between the amount of heat input flowing from the plasma to the substrate, the amount of heat generated by the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, the first-order time derivative of the temperature of the stage, the first-order time derivative of the temperature of the cooling mechanism, and the second-order time derivative of the temperature of the cooling mechanism.

[0132] (Supplementary Note 4) The plasma processing apparatus according to Supplementary Note 3, wherein the values ​​of the coefficients of the mathematical model are determined by performing fitting using the data.

[0133] (Supplementary Note 5) The plasma processing apparatus according to Supplementary Note 1, wherein the stage has a placement surface divided into a plurality of areas, the cooling mechanisms are provided in all areas of the stage, the heating mechanisms are provided in each of the areas of the stage, the measurement units are provided in each of the areas of the stage and measure the temperature of the stage in each area, the acquisition unit periodically acquires the temperature of the cooling mechanism, the heat generation amount of the heating mechanism and the temperature of the stage in each area, and the prediction unit uses the calculation formula to predict the amount of heat input flowing from the plasma to the substrate in each area from the temperature of the cooling mechanism acquired by the acquisition unit, the heat generation amount of the heating mechanism and the temperature of the stage in each area, a first-order time derivative of the temperature of the stage in each area, and a first-order or higher time derivative of the temperature of the cooling mechanism.

[0134] (Supplementary Note 6) The calculation formula is a mathematical model that calculates the amount of heat input flowing from the plasma to the substrate in each area by multiplying the heat generation amount of the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, the first-order time derivative of the temperature of the stage, the first-order time derivative of the temperature of the cooling mechanism, and the second-order time derivative of the temperature of the cooling mechanism by a coefficient in that area and in other areas and adding them up, and the values ​​of the coefficients of the mathematical model are determined using data that has been previously determined regarding the relationship between the heat generation amount of the heating mechanism, the heat generation amount of the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, the first-order time derivative of the temperature of the stage, the first-order time derivative of the temperature of the cooling mechanism, and the second-order time derivative of the temperature of the cooling mechanism.

[0135] (Supplementary Note 7) The plasma processing apparatus according to Supplementary Note 6, wherein the values ​​of the coefficients of the mathematical model are determined by performing fitting using the data.

[0136] (Supplementary Note 8) The plasma processing apparatus according to Supplementary Note 6 or 7, wherein the calculation formula is a mathematical model that calculates the heat input amount in each area by multiplying the heat generation amount of the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, the first-order time derivative of the temperature of the stage, the first-order time derivative of the temperature of the cooling mechanism, and the second-order time derivative of the temperature of the cooling mechanism by a coefficient and adding them up for each area and all other areas.

[0137] (Supplementary Note 9) The plasma processing apparatus according to any one of Supplementary Notes 5 to 8, wherein the cooling mechanism is a flow path through which a coolant flows, the flow path being formed to pass through all areas of the stage, and the acquisition unit acquires the temperature of the coolant flowing into the flow path.

[0138] (Supplementary Note 10) The plasma processing apparatus according to Supplementary Note 9, further comprising a correction unit that corrects the coolant temperature acquired by the acquisition unit to the coolant temperature in each area along the flow path, and the prediction unit uses the calculation formula to predict the heat input in each area from the coolant temperature in each area corrected by the correction unit, the heat generation amount of the heating mechanism and the temperature of the stage in each area acquired by the acquisition unit, the first-order time derivative of the temperature of the cooling mechanism in each area, the second-order time derivative of the temperature of the cooling mechanism, and the first-order time derivative of the temperature of the stage.

[0139] (Supplementary Note 11) A prediction method for a plasma processing apparatus having a stage on which a substrate is placed, a chamber in which the stage is installed and in which plasma is generated and plasma processing is performed on the substrate placed on the stage, a cooling mechanism installed on the stage and cooling the stage, a heating mechanism installed between a mounting surface of the stage on which the substrate is placed and the cooling mechanism, the heating mechanism being capable of controlling the amount of heat generated and heating the stage, and a measurement unit measuring the temperature of the stage, the method comprising: a) periodically acquiring the amount of heat generated by the heating mechanism, the temperature of the stage, and the temperature of the cooling mechanism; b) predicting the amount of heat input flowing from the plasma to the substrate from the acquired heat generation amount of the heating mechanism, the temperature of the stage, and the temperature of the cooling mechanism, as well as the first-order time derivative of the temperature of the stage and the first-order or higher time derivative of the temperature of the cooling mechanism, using a calculation formula that predicts the amount of heat input flowing from the plasma to the substrate from the heat generation amount of the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, a first-order time derivative of the temperature of the stage, and a first-order or higher time derivative of the temperature of the cooling mechanism.

[0140] (Supplementary Note 12) A prediction program for a plasma processing apparatus having: a stage on which a substrate is placed; a chamber in which the stage is installed and in which plasma is generated and plasma processing is performed on the substrate placed on the stage; a cooling mechanism installed on the stage and cooling the stage; a heating mechanism installed between a mounting surface of the stage on which the substrate is placed and the cooling mechanism, the heating mechanism being capable of controlling the amount of heat generated and heating the stage; and a measurement unit measuring a temperature of the stage, the program comprising: a) a step of periodically acquiring the amount of heat generated by the heating mechanism, the temperature of the stage, and the temperature of the cooling mechanism; b) predicting the amount of heat input flowing from the plasma to the substrate from the acquired heat generation amount of the heating mechanism, the temperature of the stage, and the temperature of the cooling mechanism, as well as the first-order time derivative of the temperature of the stage and the first-order or higher time derivative of the temperature of the cooling mechanism, using a calculation formula that predicts the amount of heat input flowing from the plasma to the substrate from the heat generation amount of the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, a first-order time derivative of the temperature of the stage, and a first-order or higher time derivative of the temperature of the cooling mechanism.

[0141] (Supplementary Note 13) An information processing device comprising: a memory unit that stores measurement data of a heat generation amount of a heating mechanism, a temperature of the stage, and a temperature of the cooling mechanism of a plasma processing device that performs plasma processing on a substrate placed on a stage while cooling the stage by a cooling mechanism provided on the stage on which the substrate is placed and heating the stage by a heating mechanism provided between a mounting surface of the stage on which the substrate is placed and the cooling mechanism; and a prediction unit that predicts an amount of heat input flowing from the plasma to the substrate from the heat generation amount of the heating mechanism, the temperature of the stage, and the temperature of the cooling mechanism stored in the measurement data, using a calculation formula that predicts an amount of heat input flowing from the plasma to the substrate from the heat generation amount of the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, a first-order time derivative of the temperature of the stage, and a first-order or higher time derivative of the temperature of the cooling mechanism.

[0142] 1 Plasma processing apparatus 10 Plasma processing chamber 11 Substrate support 14 Chiller unit 14a Piping 60 Heater power supply 61 Temperature detection unit 100 Control unit 101 External interface 102 User interface 103 Memory unit 104 Process controller 110 Prediction model data 111 Main body 111a Central region 111b Annular region 112 Ring assembly 120 Plasma control unit 121 Acquisition unit 122 Correction unit 123 Prediction unit 124 Heat generation control unit 201 External interface 202 User interface 203 Memory unit 204 Controller 211 Measurement data 1110 Base 1110a Flow path 1111 Electrostatic chuck 1111a Ceramic member 1111b Electrostatic electrode A, A1 to A14 Area HT Heater TS Temperature sensor W Substrate

Claims

1. A stage on which a substrate is placed, a chamber provided inside the stage, in which plasma is generated and plasma processing is performed on the substrate placed on the stage, a cooling mechanism provided on the stage for cooling the stage, a heating mechanism provided between the placement surface for placing the substrate on the stage and the cooling mechanism, capable of controlling the amount of heat generated, for heating the stage, a measurement unit for measuring the temperature of the stage, an acquisition unit for periodically acquiring the amount of heat generated by the heating mechanism, the temperature of the stage, and the temperature of the cooling mechanism, and a prediction unit for predicting the amount of heat flowing from the plasma into the substrate from the amount of heat generated by the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, the first-order time differential of the temperature of the stage, and the second-order or higher time differential of the temperature of the cooling mechanism, using a calculation formula for predicting the amount of heat flowing from the plasma into the substrate. A plasma processing apparatus having the above components.

2. The calculation formula is a prediction model for predicting the amount of heat flowing from the plasma into the substrate from the amount of heat generated by the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, the first-order time differential of the temperature of the stage, and the second-order or higher time differential of the temperature of the cooling mechanism. The plasma processing apparatus according to claim 1.

3. The calculation formula is a mathematical model for calculating the amount of heat flowing from the plasma into the substrate by multiplying each of the amount of heat generated by the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, the first-order time differential of the temperature of the stage, the first-order time differential of the temperature of the cooling mechanism, and the second-order time differential of the temperature of the cooling mechanism by a coefficient and adding them together. The value of each coefficient of the mathematical model is determined using data obtained in advance on the relationship between the amount of heat flowing from the plasma into the substrate, the amount of heat generated by the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, the first-order time differential of the temperature of the stage, the first-order time differential of the temperature of the cooling mechanism, and the second-order time differential of the temperature of the cooling mechanism. The plasma processing apparatus according to claim 1.

4. The plasma processing apparatus according to claim 3, wherein the coefficients of each of the mathematical models are determined by performing fitting using the data.

5. The stage has a placement surface divided into a plurality of areas, the cooling mechanism is provided in all areas of the stage, the heating mechanism is provided for each area of the stage, the measuring unit is provided for each area of the stage, measures the temperature of the stage for each area, the acquisition unit periodically acquires the temperature of the cooling mechanism, the calorific value of the heating mechanism in each area, and the temperature of the stage, and the prediction unit uses the calculation formula to calculate the temperature of the cooling mechanism acquired by the acquisition unit, the calorific value of the heating mechanism in each area, the temperature of the stage, the first-order time differential of the temperature of the stage in each area, and the first-order or higher-order time differential of the temperature of the cooling mechanism, and predicts the amount of heat flowing from the plasma to the substrate in each area. The plasma processing apparatus according to claim 1.

6. The calculation formula is a mathematical model that calculates the amount of heat flowing from the plasma to the substrate in each area by multiplying the calorific value of the heating mechanism in the area and other areas, the temperature of the stage, the temperature of the cooling mechanism, the first-order time differential of the temperature of the stage, the first-order time differential of the temperature of the cooling mechanism, and the second-order time differential of the temperature of the cooling mechanism by coefficients for each area and then adding them. The coefficients of each of the mathematical models are determined by using data obtained in advance regarding the relationship between the amount of heat flowing from the plasma to the substrate in each area, the calorific value of the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, the first-order time differential of the temperature of the stage, the first-order time differential of the temperature of the cooling mechanism, and the second-order time differential of the temperature of the cooling mechanism. The plasma processing apparatus according to claim 5.

7. The plasma processing apparatus according to claim 6, wherein the coefficients of each of the mathematical models are determined by performing fitting using the data.

8. The calculation formula is a mathematical model that calculates the heat input amount in each area by multiplying coefficients to and adding the heat generation amount of the heating mechanism in the area and all other areas, the temperature of the stage, the temperature of the cooling mechanism, the first-order time differential of the temperature of the stage, the first-order time differential of the temperature of the cooling mechanism, and the second-order time differential of the temperature of the cooling mechanism for each area. The plasma processing apparatus according to claim 6.

9. The cooling mechanism is a flow path formed to pass through all areas of the stage and through which a refrigerant flows. The acquisition unit acquires the temperature of the refrigerant flowing into the flow path. The plasma processing apparatus according to claim 5.

10. The apparatus further includes a correction unit that corrects the temperature of the refrigerant acquired by the acquisition unit to the temperature of the refrigerant in each area along the flow path. The prediction unit uses the calculation formula to predict the heat input amount in each area from the temperature of the refrigerant in each area corrected by the correction unit, the heat generation amount of the heating mechanism in each area and the temperature of the stage acquired by the acquisition unit, the first-order time differential of the temperature of the cooling mechanism in each area, the second-order time differential of the temperature of the cooling mechanism, and the first-order time differential of the temperature of the stage. The plasma processing apparatus according to claim 9.

11. A prediction method for a plasma processing apparatus, comprising: a stage on which a substrate is placed; a chamber provided inside the stage, in which plasma is generated and plasma processing is performed on the substrate placed on the stage; a cooling mechanism provided on the stage for cooling the stage; a heating mechanism provided between the placement surface of the stage for placing the substrate and the cooling mechanism, capable of controlling the amount of heat generated, for heating the stage; and a measurement unit for measuring the temperature of the stage, the prediction method including: a) periodically acquiring the amount of heat generated by the heating mechanism, the temperature of the stage, and the temperature of the cooling mechanism; and b) using a calculation formula for predicting the amount of heat flowing into the substrate from the plasma from the amount of heat generated by the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, the first-order time differential of the temperature of the stage, and the second-order or higher-order time differential of the temperature of the cooling mechanism, predicting the amount of heat flowing into the substrate from the plasma from the acquired amount of heat generated by the heating mechanism, the temperature of the stage, and the temperature of the cooling mechanism, and the first-order time differential of the temperature of the stage and the second-order or higher-order time differential of the temperature of the cooling mechanism.

12. A prediction program for a plasma processing apparatus, comprising: a stage on which a substrate is placed; a chamber provided inside the stage, where plasma is generated inside and plasma processing is performed on the substrate placed on the stage; a cooling mechanism provided on the stage for cooling the stage; a heating mechanism provided between the placement surface of the stage for placing the substrate and the cooling mechanism, capable of controlling the amount of heat generated, for heating the stage; a measurement unit for measuring the temperature of the stage, which causes a computer to execute: a) a step of periodically acquiring the amount of heat generated by the heating mechanism, the temperature of the stage, and the temperature of the cooling mechanism; b) a step of predicting the amount of heat flowing into the substrate from the plasma using a calculation formula for predicting the amount of heat flowing into the substrate from the plasma from the amount of heat generated by the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, the first-order time differential of the temperature of the stage, and the second-order or higher time differential of the temperature of the cooling mechanism, from the amount of heat generated by the heating mechanism, the temperature of the stage, and the temperature of the cooling mechanism obtained, and from the first-order time differential of the temperature of the stage and the second-order or higher time differential of the temperature of the cooling mechanism.

13. A storage unit that stores measurement data obtained by periodically measuring the amount of heat generated by the heating mechanism, the temperature of the stage, and the temperature of the cooling mechanism of a plasma processing apparatus that cools the stage by a cooling mechanism provided on the stage on which the substrate is placed and heats the stage by a heating mechanism provided between the placement surface of the stage for placing the substrate and the cooling mechanism while performing plasma processing on the substrate placed on the stage; a prediction unit that predicts the amount of heat flowing into the substrate from the plasma using a calculation formula for predicting the amount of heat flowing into the substrate from the plasma from the amount of heat generated by the heating mechanism, the temperature of the stage, the temperature of the cooling mechanism, the first-order time differential of the temperature of the stage, and the second-order or higher time differential of the temperature of the cooling mechanism, from the amount of heat generated by the heating mechanism, the temperature of the stage, and the temperature of the cooling mechanism stored in the measurement data, and from the first-order time differential of the temperature of the stage and the second-order or higher time differential of the temperature of the cooling mechanism.

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