PLATING APPARATUS

Abstract

Provided is a plating apparatus to determine appropriate control parameters for forming plating with high film thickness flatness on a substrate. The plating apparatus includes an estimation unit that estimates a density of a current flowing through an outer edge of the substrate, a current density calculation unit that calculates a density of a plating current flowing through a plating solution into the substrate based on the estimated current density, and a control parameter that specifies an operation mode of the plating apparatus, the current density calculation unit calculating the plating current density for each of a plurality of different operation modes of the plating apparatus, a film thickness calculation unit that calculates a thickness of a plating film formed on the substrate for each of the plurality of operation modes, based on each calculated plating current density, and a control parameter determination unit that determines a control parameter corresponding to an optimal operation mode, based on the calculated plating film thickness for each operation mode of the plating apparatus.

Description

CROSS REFERENCE TO RELATED APPLICATION

This application claims priority to Japanese Patent Application No. 2023-031662 filed Mar. 2, 2023, the entire contents of which are hereby incorporated by reference.

TECHNICAL FIELD

The present invention relates to a plating apparatus.

BACKGROUND ART

A plating apparatus includes a substrate holder that holds a substrate, a plating tank in which a plating solution is stored, and an anode disposed in the plating tank to oppose the substrate held by the substrate holder. In the plating apparatus, a technique has been developed to improve film thickness flatness of plating formed on the substrate (see, for example, PTL 1).

CITATION LIST

Patent Literature

• PTL 1: Japanese Patent No. 7133699

SUMMARY OF INVENTION

Technical Problem

In a plating apparatus, various control parameters are present that affect a film thickness distribution of a plating film formed on a substrate. In performing a plating process by use of a plating apparatus, it is desirable to determine appropriate control parameters for forming plating with high film thickness flatness on the substrate.

Solution to Problem

[Form 1] According to Form 1, a plating apparatus for plating a substrate is provided, and the plating apparatus includes a plating tank to store a plating solution, a substrate holder that holds the substrate, an anode disposed in the plating tank to oppose the substrate held by the substrate holder, a potential sensor disposed in the vicinity of the substrate held by the substrate holder and configured to measure a potential of the plating solution, an estimation unit configured to estimate a density of a current flowing through an outer edge of the substrate based on a value of the potential of the plating solution that is measured by the potential sensor, a current density calculation unit configured to calculate a density of a plating current flowing through the plating solution into the substrate, based on the estimated current density and a control parameter that specifies an operation mode of the plating apparatus, the current density calculation unit calculating the plating current density for each of a plurality of different operation modes of the plating apparatus, a film thickness calculation unit configured to calculate a thickness of a plating film formed on the substrate for each of the plurality of operation modes, based on each of the plating current densities calculated by the current density calculation unit, and a control parameter determination unit configured to determine a control parameter corresponding to an optimal operation mode, based on the plating film thickness for each operation mode of the plating apparatus that is calculated by the film thickness calculation unit, the plating apparatus performing a plating process on the substrate by use of the control parameter determined by the control parameter determination unit.

[Form 2] According to Form 2, in the plating apparatus of Form 1, the operation mode of the plating apparatus is specified by a combination of a plurality of types of control parameters, and the current density calculation unit is configured to calculate the plating current density for each set of the plurality of types of control parameters, and the control parameter determination unit is configured to determine a set of control parameters corresponding to an optimal operation mode, based on the plating film thickness for each operation mode of the plating apparatus that is calculated by the film thickness calculation unit.

[Form 3] According to Form 3, in the plating apparatus of Form 2, the control parameter is a parameter for one or more of i) rotation of the substrate, ii) partial shielding of the substrate, iii) stirring of the plating solution, and iv) a set value of a current flowing between the substrate and the anode.

[Form 4] According to Form 4, in the plating apparatus of Form 1, the control parameter determination unit is configured to determine the control parameter based on flatness of the calculated plating film thickness.

[Form 5] According to Form 5, in the plating apparatus of any one of Forms 1 to 4, the estimation unit is implemented as a state space model configured to estimate the current density by use of a state equation and an observation equation, the state equation being an equation describing time evolution on the density of the current flowing through the outer edge of the substrate, the observation equation being an equation describing a relation between the density of the current flowing through the outer edge of the substrate and the potential of the plating solution at a position of the potential sensor.

[Form 6] According to Form 6, the plating apparatus of Form 5 comprises a plating module including at least the plating tank, the substrate holder, the anode and the potential sensor, wherein the relation between the current density and the potential of the plating solution is based on a function representing a 3D model of the plating module.

[Form 7] According to Form 7, in the plating apparatus of Form 5, the state space model further includes a Kalman filter configured to correct estimation results of the density of the current flowing through the outer edge of the substrate, based on the value measured by the potential sensor.

[Form 8] According to Form 8, in the plating apparatus of Form 1, the outer edge of the substrate is a portion to be gripped with the substrate holder of the substrate.

[Form 9] According to Form 9, in the plating apparatus of Form 8, the plating current density calculated by the current density calculation unit is a density of a current in a region inside the outer edge of the substrate.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a perspective view illustrating an overall configuration of a plating apparatus of an embodiment of the present invention;

FIG. 2 is a plan view illustrating the overall configuration of the plating apparatus of the present embodiment;

FIG. 3 is a longitudinal sectional view schematically illustrating a configuration of a plating module in one embodiment;

FIG. 4 is a schematic view illustrating an enlarged periphery around a conduit of the plating module;

FIG. 5 is a schematic view of a shielding body and a substrate seen from below;

FIG. 6 is a block diagram showing a functional configuration of a control module according to one embodiment;

FIG. 7 is a plan view of the substrate;

FIG. 8 is a block diagram showing a functional configuration of a control module according to another embodiment; and

FIG. 9 is a longitudinal sectional view schematically illustrating a configuration of a plating module according to further embodiment.

DESCRIPTION OF EMBODIMENTS

Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the drawings described below, the same or corresponding components are denoted with the same reference sign and will not be described in duplicate.

First Embodiment

FIG. 1 is a perspective view illustrating the overall configuration of the plating apparatus of this embodiment. FIG. 2 is a plan view illustrating the overall configuration of the plating apparatus of this embodiment. As illustrated in FIGS. 1 and 2, a plating apparatus 1000 includes load ports 100, a transfer robot 110, aligners 120, pre-wet modules 200, pre-soak modules 300, plating modules 400, cleaning modules 500, spin rinse dryers 600, a transfer device 700, and a control module 800.

The load port 100 is a module for loading a substrate housed in a cassette, such as a FOUP, (not illustrated) to the plating apparatus 1000 and unloading the substrate from the plating apparatus 1000 to the cassette. While four load ports 100 are arranged in the horizontal direction in this embodiment, the number of load ports 100 and arrangement of the load ports 100 are arbitrary. The transfer robot 110 is a robot for transferring the substrate that is configured to grip or release the substrate between the load port 100, the aligner 120, and the transfer device 700. The transfer robot 110 and the transfer device 700 can perform delivery and receipt of the substrate via a temporary placement table (not illustrated) to grip or release the substrate between the transfer robot 110 and the transfer device 700.

The aligner 120 is a module for adjusting a position of an orientation flat, a notch, and the like of the substrate in a predetermined direction. While the two aligners 120 are disposed to be arranged in the horizontal direction in this embodiment, the number of aligners 120 and arrangement of the aligners 120 are arbitrary. The pre-wet module 200 wets a surface to be plated of the substrate before a plating process with a process liquid, such as pure water or deacrated water, to replace air inside a pattern formed on the surface of the substrate with the process liquid. The pre-wet module 200 is configured to perform a pre-wet process to facilitate supplying a plating solution to the inside of the pattern by replacing the process liquid inside the pattern with the plating solution during plating. While the two pre-wet modules 200 are disposed to be arranged in the vertical direction in this embodiment, the number of pre-wet modules 200 and arrangement of the pre-wet modules 200 are arbitrary.

For example, the pre-soak module 300 is configured to remove an oxidized film having a large electrical resistance present on a surface of a seed layer formed on the surface to be plated of the substrate before the plating process by etching with a process liquid, such as sulfuric acid and hydrochloric acid, and perform a pre-soak process that cleans or activates a surface of a plating base layer. While the two pre-soak modules 300 are disposed to be arranged in the vertical direction in this embodiment, the number of pre-soak modules 300 and arrangement of the pre-soak modules 300 are arbitrary. The plating module 400 performs the plating process on the substrate. There are two sets of the 12 plating modules 400 arranged by three in the vertical direction and by four in the horizontal direction, and the total 24 plating modules 400 are disposed in this embodiment, but the number of plating modules 400 and arrangement of the plating modules 400 are arbitrary.

The cleaning module 500 is configured to perform a cleaning process on the substrate to remove the plating solution or the like left on the substrate after the plating process. While the two cleaning modules 500 are disposed to be arranged in the vertical direction in this embodiment, the number of cleaning modules 500 and arrangement of the cleaning modules 500 are arbitrary. The spin rinse dryer 600 is a module for rotating the substrate after the cleaning process at high speed and drying the substrate. While the two spin rinse dryers are disposed to be arranged in the vertical direction in this embodiment, the number of spin rinse dryers and arrangement of the spin rinse dryers are arbitrary. The transfer device 700 is a device for transferring the substrate between the plurality of modules inside the plating apparatus 1000. The control module 800 is configured to control the plurality of modules in the plating apparatus 1000 and can be configured of, for example, a general computer including input/output interfaces with an operator or a dedicated computer.

An example of a sequence of the plating processes by the plating apparatus 1000 will be described. First, the substrate housed in the cassette is loaded on the load port 100. Subsequently, the transfer robot 110 grips the substrate from the cassette at the load port 100 and transfers the substrate to the aligners 120. The aligner 120 adjusts the position of the orientation flat, the notch, or the like of the substrate in the predetermined direction. The transfer robot 110 grips or releases the substrate whose direction is adjusted with the aligners 120 to the transfer device 700.

The transfer device 700 transfers the substrate received from the transfer robot 110 to the pre-wet module 200. The pre-wet module 200 performs the pre-wet process on the substrate. The transfer device 700 transfers the substrate on which the pre-wet process has been performed to the pre-soak module 300. The pre-soak module 300 performs the pre-soak process on the substrate. The transfer device 700 transfers the substrate on which the pre-soak process has been performed to the plating module 400. The plating module 400 performs the plating process on the substrate.

The transfer device 700 transfers the substrate on which the plating process has been performed to the cleaning module 500. The cleaning module 500 performs the cleaning process on the substrate. The transfer device 700 transfers the substrate on which the cleaning process has been performed to the spin rinse dryer 600. The spin rinse dryer 600 performs the drying process on the substrate. The transfer device 700 grips or releases the substrate on which the drying process has been performed to the transfer robot 110. The transfer robot 110 transfers the substrate received from the transfer device 700 to the cassette at the load port 100. Finally, the cassette housing the substrate is unloaded from the load port 100.

Note that the configuration of the plating apparatus 1000 described with reference to FIGS. 1 and 2 is merely an example, and the configuration of the plating apparatus 1000 is not limited to the configuration of FIGS. 1 and 2.

Next, a configuration of the plating module 400 will be described. Since 24 plating modules 400 in the present embodiment have the same configuration, one plating module 400 alone will be described. FIG. 3 is a longitudinal sectional view schematically illustrating the configuration of the plating module 400 of one embodiment. The plating module 400 includes a plating tank for storing the plating solution. The plating tank includes a cylindrical inner tank 412 having an open upper surface, and an unillustrated outer tank provided around the inner tank 412 so that the plating solution overflowing from an upper edge of the inner tank 412 is accumulated.

The plating module 400 includes a substrate holder 440 that holds a substrate Wf with a surface to be plated Wf-a being oriented downward. The substrate holder 440 includes a power supply contact point to supply power from an unillustrated power supply to the substrate Wf. The plating module 400 includes an elevating/lowering mechanism 442 that elevates and lowers the substrate holder 440. Further, in one embodiment, the plating module 400 includes a rotation mechanism 448 that rotates the substrate holder 440 about a vertical axis. The rotation mechanism 448 can rotate the substrate holder 440 in a forward direction (for example, clockwise) and a reverse direction (for example, counterclockwise), and can change a rotational speed of the holder. Such rotation of the substrate holder 440 is controlled by the control module 800. The elevating/lowering mechanism 442 and the rotation mechanism 448 can be achieved by a known mechanism such as a motor.

The plating module 400 includes a membrane 420 that separates an inside of the inner tank 412 in the vertical direction. The inside of the inner tank 412 is divided into a cathode region 422 and an anode region 424 by the membrane 420. The cathode region 422 and the anode region 424 are each filled with the plating solution. In the present embodiment, an example where the membrane 420 is provided is described, and alternatively, the membrane 420 need not be provided.

On a bottom surface of the inner tank 412 of the anode region 424, an anode 430 is provided. Also, in the anode region 424, an anode mask 426 for adjusting an electric field between the anode 430 and the substrate Wf is disposed. The anode mask 426 is, for example, a substantially plate-shaped member made of a dielectric material and provided on a front surface of (above) the anode 430 (in FIG. 3). The anode mask 426 has an opening through which a current flowing between the anode 430 and the substrate Wf passes. The anode mask 426 is configured to have a changeable opening dimension and the opening dimension may be adjusted by the control module 800. The opening dimension means a diameter when the opening is circular, and a length of a side or longest opening width when the opening is polygonal. To change the opening dimension in the anode mask 426, a known mechanism can be adopted. In the present embodiment, an example where the anode mask 426 is provided is described, and alternatively, the anode mask 426 need not be provided. Furthermore, the membrane 420 described above may be provided in the opening of the anode mask 426.

In the cathode region 422, a resistor 450 is disposed to oppose the membrane 420. The resistor 450 is a member for uniformly performing the plating process in the surface to be plated Wf-a of the substrate Wf. In the present embodiment, the resistor 450 is configured to be movable in an up-down direction in the plating tank by a drive mechanism 452, and a position of the resistor 450 is adjusted by the control module 800. Alternatively, the plating module 400 need not include the resistor 450. While a specific material of the resistor 450 is not particularly limited, for example, a porous resin such as polyether ether ketone may be used.

In a vicinity of the surface of the substrate Wf in the cathode region 422, a paddle 456 for stirring the plating solution is provided. The paddle 456 is made of, for example, titanium (Ti) or a resin. The paddle 456 reciprocally moves parallel to the surface of the substrate Wf, to stir the plating solution so that sufficient metal ions are uniformly supplied to the surface of the substrate Wf during the plating of the substrate Wf. The paddle 456 may be configured to move perpendicularly to the surface of the substrate Wf. The control module 800 controls movement of the paddle 456 with an unillustrated drive mechanism. Alternatively, the plating module 400 need not include the paddle 456.

The cathode region 422 is provided with a conduit 462. The conduit 462 is a hollow tube and can be made of a resin such as polypropylene (PP) or polyvinyl chloride (PVC) as an example. When the resistor 450 is provided in the cathode region 422, the conduit 462 may be provided between the substrate Wf and the resistor 450. When the paddle 456 is provided, the conduit 462 may be disposed so as not to interfere with the paddle 456, and as an example, the conduit preferably has the same height as the paddle 456 and is preferably disposed on an outer peripheral side of the paddle 456 (in FIG. 3, outside a left-right direction).

FIG. 4 is a schematic view illustrating an enlarged periphery around the conduit 462 of the plating module 400. As illustrated in FIGS. 3 and 4, the conduit 462 has an opening end 464 disposed in a region between the substrate Wf and the anode 430. Specifically, the opening end 464 is located between the substrate Wf and the anode 430 in a direction perpendicular to a plate surface of the substrate Wf and is disposed at a position that overlaps with the substrate Wf seen from the direction perpendicular to the plate surface of the substrate Wf. The opening end 464 is preferably disposed close to the surface to be plated Wf-a, and is preferably configured to face the surface to be plated Wf-a. For example, a distance between the opening end 464 and the surface to be plated Wf-a is in a range of several hundred micrometers to several tens of millimeters. Note that the opening end 464 may be opened in a direction perpendicular to a direction connecting the substrate Wf and the anode 430 (in FIGS. 3 and 4, in the left-right direction), or may be opened inclined toward the surface to be plated Wf-a of the substrate Wf. The conduit 462 extends to a region apart from the region between the substrate Wf and the anode 430. Therefore, the conduit 462 has a first portion 462a disposed in the region between the substrate Wf and the anode 430, and a second portion 462b disposed in the region apart from the region between the substrate Wf and the anode 430. The conduit 462 preferably extends in the direction (left-right direction in FIGS. 3 and 4) perpendicular to the direction (up-down direction in FIGS. 3 and 4) connecting the substrate Wf and the anode 430. In one embodiment, the conduit 462 extends to outside the plating tank. However, without limiting to such examples, the conduit 462 may extend in any direction.

The inside of the conduit 462 is filled with the plating solution in the same manner as in the cathode region 422. The conduit 462 may be provided with a filling mechanism 468 for filling the inside of the conduit 462 with the plating solution. As the filling mechanism 468, various known mechanisms can be adopted, and as an example, an air vent valve, a mechanism for supplying the plating solution, or the like can be adopted. The filling mechanism 468 is provided in the second portion 462b of the conduit 462 as an example.

While FIGS. 3 and 4 illustrate one conduit 462 for ease of seeing, a plurality of conduits 462 may be provided in the plating tank. When the plurality of conduits 462 are provided, the opening ends 464 of the respective conduits 462 may be arranged at different distances from a center of the substrate Wf. When the plurality of conduits 462 are provided, the opening ends 464 of the respective conduits 462 are preferably arranged at positions having an equal distance from the surface to be plated Wf-a of the substrate Wf.

In the second portion 462b of the conduit 462, a potential sensor 470 is provided. While the potential sensor 470 is disposed outside the plating tank in FIGS. 3 and 4, the sensor may be disposed inside the plating tank. The potential sensor 470 detects a potential of the plating solution with which the conduit 462 is filled. The plating solution in the conduit 462 has about the same potential as the plating solution at the opening end 464, and the detected potential by the potential sensor 470 is approximately equal to the potential of the plating solution at the opening end 464. Therefore, the vicinity of the opening end 464 can be a pseudo potential detection position by the potential sensor 470, and the potential sensor 470 provided in the second portion 462b of the conduit 462 can measure a potential near the surface to be plated Wf-a. A detection signal by the potential sensor 470 is inputted into the control module 800.

In one embodiment, it is preferable to provide a potential sensor for reference (not illustrated) in a place of the plating tank where there is relatively little change in potential inside the plating tank, and to acquire a difference between a detected potential by the potential sensor for reference and a detected potential by the potential sensor 470. Since a change in potential measured by the potential sensor 470 is exceedingly small, the measurement is susceptible to noise. For reducing noise, it is preferable to install an independent electrode in the plating solution and connect the electrode directly to ground.

The control module 800 can estimate a thickness of a plating film formed on the substrate Wf based on a detection value of a potential by the potential sensor 470. For example, the control module 800 can estimate a distribution of a plating current in the surface of the substrate during the plating process based on a detection signal from the potential sensor 470 and estimate a film thickness distribution of the plating film on the substrate based on the estimated plating current distribution.

The control module 800 may detect an endpoint of the plating process or may predict a time to the endpoint of the plating process, based on the detection value of the potential sensor 470. As an example, the control module 800 may end the plating process when the film thickness of the plating film estimated based on the detection value of the potential sensor 470 reaches a desired thickness. As an example, the control module 800 may calculate a film thickness increase rate from the film thickness of the plating film that is estimated based on the detection value of the potential sensor 470 and may predict a time until the desired thickness of the plating film is reached, that is, the time to the endpoint of the plating process based on the obtained film thickness increase rate.

Returning to FIG. 3, according to one embodiment, in the cathode region 422, a shielding body 480 is provided for partially or locally shielding the current flowing from the anode 430 to the substrate Wf. The shielding body 480 is, for example, a substantially plate-shaped member made of a dielectric material. FIG. 5 is a schematic view of the shielding body 480 and the substrate Wf of the present embodiment seen from below. FIG. 5 does not illustrate the substrate holder 440 that holds the substrate Wf. The shielding body 480 is configured to be movable to a shielding position (in FIGS. 3 and 5, the position indicated with a dashed line) interposed between the surface to be plated Wf-a of the substrate Wf and the anode 430, and a retracted position (in FIGS. 3 and 5, the position indicated with a solid line) retracted from a region between the surface to be plated Wf-a and the anode 430. In other words, the shielding body 480 is configured to be movable to the shielding position below the surface to be plated Wf-a and the retracted position apart from below the surface to be plated Wf-a. The position of the shielding body 480 is controlled by the control module 800 with the unillustrated drive mechanism. The movement of the shielding body 480 can be performed by a known mechanism such as a motor or solenoid. In the examples illustrated in FIGS. 3 and 5, the shielding body 480 shields a part of an outer peripheral region of the surface to be plated Wf-a of the substrate Wf in a circumferential direction at the shielding position. In the example illustrated in FIG. 5, the shielding body 480 is formed into a tapered shape that becomes thinner toward the center of the substrate Wf. However, without limiting to such examples, the shielding body 480 having any shape predetermined by experiments or the like can be used.

The plating process in the plating module 400 will be described. By immersing the substrate Wf in the plating solution of the cathode region 422 by use of the elevating/lowering mechanism 442, the substrate Wf is exposed to the plating solution. By applying a voltage between the anode 430 and the substrate Wf in this state, the plating module 400 can perform the plating process on the surface to be plated Wf-a of the substrate Wf. In one embodiment, the plating process is performed while rotating the substrate holder 440 by use of the rotation mechanism 448. Through the plating process, a conductive film (plating film) is precipitated on the surface to be plated Wf-a of the substrate Wf. During the plating process, the potential is measured by the potential sensor 470 provided in the conduit 462. When the potential sensor 470 performs measurement with the rotation of the substrate holder 440 (substrate Wf), a measurement position of the potential sensor 470 can be changed, and the potential can be measured for multiple points in the circumferential direction of the substrate Wf or over the entire circumferential direction. The control module 800 then estimates the film thickness of the plating film based on the value of the potential that is detected by the potential sensor 470. This makes it possible to grasp a change in film thickness of the plating film formed on the surface to be plated Wf-a of the substrate Wf in real time during the plating process.

FIG. 6 is a block diagram showing a functional configuration of the control module 800 according to one embodiment in the plating apparatus 1000. The control module 800 is configured to estimate a density distribution of a current flowing through the substrate Wf during the plating process by use of a state space model 804. The state space model 804 includes a state estimation unit 806, an observation value calculation unit 808, and a Kalman filter 810. In addition to the state space model 804, the control module 800 includes a 3D model creation unit 802, a current density calculation unit 812, a film thickness calculation unit 814, and an endpoint determining unit 816. The control module 800 can be configured as a computer including, for example, an input/output device, an arithmetic device, and a storage device. For example, the control module 800 is configured to achieve functions of the respective units 802, 806, 808, 810, 812, 814, and 816 by reading and executing computer program stored in the storage device with the arithmetic device (for example, a processor).

The 3D model creation unit 802 creates a three-dimensional (3D) model of the plating module 400. The 3D model of the plating module 400 is data obtained by modeling and describing shapes, arrangements, physical property values, and the like of various components in the plating module 400. The 3D model incorporates at least components that affect an electric field inside the plating tank (inner tank 412) of the plating module 400. Such components include, for example, the anode 430, the anode mask 426, the membrane 420, the resistor 450, the substrate Wf, a seed layer provided on the substrate Wf, the plating solution stored in the plating tank, the conduit 462, and the potential sensor 470. The 3D model of the plating module 400 can be composed of information on the shapes, arrangements, and physical property values (for example, conductivity, dielectric constant, etc.) for these components. As an example, these pieces of information may be inputted to the control module 800 via an input/output interface of the control module 800 by an operator of the plating apparatus 1000, and the 3D model of the plating module 400 may be created based on the input information by the 3D model creation unit 802. Some pieces of the above information, for example, some physical property values, may be stored in advance in the storage device of the control module 800, and the operator may select an appropriate value from the physical property values.

The state estimation unit 806 is configured to estimate a “state” of the plating module 400 by use of a state equation. Specifically, the state estimation unit 806 estimates the density of the plating current at the outer edge of the substrate Wf as the “state” of the plating module 400.

FIG. 7 illustrates a plan view of the substrate Wf. The substrate Wf has an outer edge 62 that is a portion with which the substrate Wf is held by the substrate holder 440 and that is not exposed to the plating solution. As illustrated in FIG. 7, the substrate Wf includes one or more electrical contacts 441 on the outer edge 62. In the example of FIG. 7, the substrate Wf includes six electrical contacts 441 evenly spaced on the outer edge 62. Each electrical contact 441 is connected to a negative terminal of a power supply (not illustrated) via electrical wiring (not illustrated) built into the substrate holder 440, and the plating current flows through the substrate Wf through the electrical contacts 441.

Hereinafter, the density of the plating current at the outer edge 62 of the substrate Wf will be referred to as the “outer edge current density”, and the outer edge current density at time t will be described as j_t(θ), wherein θ indicates a position in the outer edge 62 of the substrate Wf that is measured by an angle around the center of the substrate Wf (see FIG. 7). The outer edge current density j_t(θ) is expressed in Fourier series as follows.

$\left[\mathrm{Formula}1\right]$ $\begin{array}{cc}{j}_t\left(\theta \right)=j_0+{\sum }_{i=1}^n\left(a_{i,t}\cos i\theta +b_{l,t}\sin i\theta \right)& \left(1\right)\end{array}$

The estimation of the outer edge current density j_t(θ) comes down to estimation of Fourier coefficients a_i,t and b_i,t. In one embodiment, the state estimation unit 806 estimates (predicts) the outer edge current density j_t(θ) at time t from the outer edge current density j_t-1(θ) at time t−1 by use of the following state equation.

$\left[\mathrm{Formula}2\right]$ $\begin{array}{cc}\left(\begin{array}{c}{a}_{i,t}\\ b_{i,t}\end{array}\right)=F_i\left(\begin{array}{c}{a}_{i.t-1}\\ b_{i,t-1}\end{array}\right)+{\nu }_t& \left(2\right)\end{array}$

The matrix Fi is given by the following equation and represents the rotation of the substrate Wf using the rotation mechanism 448. The vector v_t is noise. In this model, it is assumed that the outer edge current density at the time t is given by rotating the outer edge current density at the time t−1 with the rotation of the substrate Wf. In the following equation, ω is an angular velocity of the rotation of the substrate Wf, and Δt is a time step (a time difference between the time t and the time t−1).

$\left[\mathrm{Formula}3\right]$ $\begin{array}{cc}{F}_i=\frac{1}{1+c_i^2}\left(\begin{array}{cc}1-c_i^2& -2c_i\\ 2c_i& 1-c_i^2\end{array}\right)& \left(3\right)\end{array}$ $\begin{array}{cc}{c}_i=\frac{i\omega \Delta t}{2}& \left(4\right)\end{array}$

To estimate the outer edge current density, a state equation other than the above equation may be used.

The observation value calculation unit 808 is configured to estimate an “observation value” from the “state” of the plating module 400 by use of an observation equation. Specifically, the observation value calculation unit 808 estimates (calculates) the value of the potential of the plating solution in the plating tank that is expected to be measured by the potential sensor 470 from the outer edge current density j_t(θ) as the “observation value” in the plating module 400. Hereinafter, the value calculated by the observation value calculation unit 808 will be referred to as a “potential estimate value”, and the potential estimate value at time t will be described as ϕ_t.

As described above, the potential measured by the potential sensor 470 is the potential in the vicinity of the surface to be plated Wf-a of the substrate Wf that is plated. This potential is determined by the distribution of the plating current flowing through the plating solution in the plating tank to the substrate Wf. The distribution of this plating current is then dependent on a physical structure of the plating module 400. Therefore, the potential estimate value ϕ_t can be calculated using the 3D model of the plating module 400 that is created in the 3D model creation unit 802. That is, the potential estimate value ϕ_t can be represented as in the following equation.

$\left[\mathrm{Formula}4\right]$ $\begin{array}{cc}{\varphi }_t=F\left(a_{1,t},b_{1,t},\dots \right)& \left(5\right)\end{array}$

Here, F is a function representing the 3D model of the plating module 400, and a_i,t, b_i,t, and others are Fourier coefficients of the above-described outer edge current density j_t(θ). Note that the function F can be numerically determined based on the 3D model acquired from the 3D model creation unit 802. Taylor expansion of the function F in the above equation around a_i,t=0 and b_i,t=0 is performed as follows. The following equation is an approximate expression to terms of a first order, and terms of second or more orders may be considered.

$\left[\mathrm{Formula}5\right]$ $\begin{array}{cc}{\varphi }_t\approx F\left(0,0,\dots \right)+{\sum }_{i=1}^n\left(\frac{\partial F}{\partial a_{i,t}}{a}_{i,t}+\frac{\partial F}{\partial b_{i,t}}{b}_{i,t}\right)& \left(6\right)\end{array}$

In one embodiment, the observation value calculation unit 808 calculates the potential estimate value ϕ_t at time t from the outer edge current density j_t(θ) at time t by use of the following observation equation, wherein w_t is noise.

$\left[\mathrm{Formula}6\right]$ $\begin{array}{cc}{\varphi }_t=F\left(0,0,\dots \right)+H\left(\begin{array}{c}{a}_{1,t}\\ b_{1,t}\\ ⋮\\ a_{n,t}\\ b_{n,t}\end{array}\right)+w_t& \left(7\right)\end{array}$ $\begin{array}{cc}H=\left(\frac{\partial F}{\partial a_{1,t}}\frac{\partial F}{\partial b_{1,t}}\dots \frac{\partial F}{\partial a_{n,t}}\frac{\partial F}{\partial b_{n,t}}\right)& \left(8\right)\end{array}$

This observation equation is based on the Taylor expansion equation of the function F representing the 3D model of the plating module 400 illustrated above. Alternatively, an observation equation different from the above equation may be used to obtain the potential estimate value ϕ_t.

The Kalman filter 810 is configured to correct the “state” of the plating module 400 that is estimated by the state estimation unit 806 by use of actual measurement results in the plating module 400. Specifically, the Kalman filter 810 uses, for the correction, the actual measured value of the potential that is obtained from the potential sensor 470. In one embodiment, the Kalman filter 810 corrects the outer edge current density j_t(θ) (Fourier coefficients a_i,t and bit) estimated by the state estimation unit 806, depending on a difference between the measured potential value obtained from the potential sensor 470 and the potential estimate value ϕ_t calculated by the observation value calculation unit 808.

Since the substrate Wf is rotated by the rotation mechanism 448 as described above, measured values of the potential at a large number of measurement points along the circumferential direction of the substrate Wf are obtained from the potential sensor 470. Therefore, corrections can be made by use of the measured values at these measurement points to obtain an accurate outer edge current density.

The outer edge current density j_t(θ) estimated and corrected by use of the state space model 804 in this manner is outputted to the current density calculation unit 812. The current density calculation unit 812 calculates the density of the plating current in a region 64 (see FIG. 7) inside the outer edge 62 of the substrate Wf based on the outer edge current density obtained from the state space model 804. The region 64, unlike the outer edge 62 of the substrate Wf, is not held by the substrate holder 440 and is exposed to the plating solution. A current flows through the plating solution in the plating tank into the region 64. Specifically, the current density calculation unit 812 calculates the density of the current flowing from the plating solution in the plating tank through an interface between the plating solution and the substrate Wf into the substrate Wf. The thickness of the plating film formed on the substrate Wf depends on this current density. Hereinafter, this current density will be referred to simply as the “plating current density”, and the plating current density at position k on the substrate Wf (region 64) and at time t will be described as j_k,t.

The plating current density j_k,t is connected in a specific relation to the outer edge current density j_t(θ). Specifically, the plating current density is determined by the outer edge current density and the physical structure of the plating module 400. Therefore, the plating current density j_k,t can be similarly represented as in the following equation using the 3D model of the plating module 400 in the same manner as the potential estimate value ϕ_t described above.

$\left[\mathrm{Formula}7\right]$ $\begin{array}{cc}{j}_{k,t}=G_k\left(a_{1,t},b_{1,t,}\dots \right)& \left(9\right)\end{array}$

In the equation, G_k is a function representing the 3D model of the plating module 400, and a_i,t, b_i,t, and others are Fourier coefficients of the outer edge current density j_t(θ). The function G_k can be numerically determined based on the 3D model of the plating module 400 that is acquired from the 3D model creation unit 802. The function G_k in the above equation is then Taylor expanded around a_i,t=0 and b_i,t=0 as follows. The following equation is an approximate expression to the term of the first order, and terms of second or more orders may be considered.

$\left[\mathrm{Formula}8\right]$ $\begin{array}{cc}{j}_{k,t}\approx G_k\left(0,0,\dots \right)+{\sum }_{i=1}^n\left(\frac{\partial G_k}{\partial a_{i,t}}{a}_{i,t}+\frac{\partial G_k}{\partial b_{i,t}}{b}_{i,t}\right)& \left(10\right)\end{array}$

In one embodiment, the current density calculation unit 812 can calculate the plating current density jkt by use of the above formula.

The film thickness calculation unit 814 is configured to calculate the thickness of the plating film formed on the substrate Wf based on the plating current density j_k,t obtained from the current density calculation unit 812. In one embodiment, the film thickness calculation unit 814 uses the following equation to calculate a plating film formation rate v_k,t and film thickness w_k,t at position k on the substrate Wf and at time t.

$\left[\mathrm{Formula}9\right]$ $\begin{array}{cc}{v}_{k,t}=\frac{M}{zF\rho }{j}_{k,t}& \left(11\right)\end{array}$ $\begin{array}{cc}{w}_{k,t}={\sum }_{i=0}^t{v}_{k,l}\Delta t& \left(12\right)\end{array}$

In the equation, M and ρ are a molecular weight and density of the plating precipitated on the substrate Wf, z is a valence of plating reaction, and F is a Faraday constant. The film thickness calculation unit 814 may predict the future plating current density and film formation rate by use of the state equation described above, to calculate not the current film thickness w_k,t but the film thickness w_k,t at an endpoint (time t=T) of the plating process.

The endpoint determining unit 816 determines the endpoint of the plating process on the substrate Wf based on the plating film thickness obtained by the film thickness calculation unit 814. For example, the endpoint determining unit 816 may end the plating process when the estimated current film thickness w_k,t reaches a desired thickness, or alternatively may predict a time to the endpoint of the plating process based on the estimated current film thickness w_k,t and the predicted future film formation rate v_k,s (s=t, . . . , T).

As described above, according to the plating apparatus 1000 of the present embodiment, the film thickness of the plating film can be estimated based on the measured value of the potential sensor 470 by use of the state space model. This makes it possible to grasp the change in film thickness of the plating film formed on the surface to be plated Wf-a of the substrate Wf in real time during the plating process.

Second Embodiment

FIG. 8 is a block diagram illustrating a functional configuration of a control module 800 according to another embodiment. In the present embodiment, a current density calculation unit 812 calculates a plating current density jkt (the density of a current flowing through a plating solution into a substrate Wf) based on control parameters that specify an operation mode of a plating module 400 in addition to an outer edge current density obtained from a state space model 804. For example, even if the outer edge current density is the same, the plating current density j_k,t can vary depending on whether a shielding body 480 is at a shielding position or a retracted position. When a plating process is performed while rotating a substrate holder 440 by use of a rotation mechanism 448, the plating current density j_k,t can vary depending on a rotation direction or a timing to switch rotation in forward and reverse directions. Furthermore, the plating current density j_k,t can vary depending on whether or not to stir the plating solution with a paddle 456 driven during the plating process, or a set value of the plating current outputted from a power supply. The current density calculation unit 812 uses these control parameters for the operation mode of the plating module 400 in calculating the plating current density j_k,t.

More specifically, the current density calculation unit 812 calculates the plating current density j_k,t for each of a plurality of different operation modes of the plating module 400 according to the control parameters. For example, a control parameter for a position of the shielding body 480 may be “on (shielding position)” or “off (retracted position)”, and the current density calculation unit 812 calculates a plating current density j_k,t corresponding to “on” (the plating current density when the shielding body 480 is at the shielding position) and a plating current density j_k,t corresponding to “off” (the plating current density when the shielding body 480 is at the retracted position). Another control parameter for the rotation of the substrate holder 440 may be “f (forward rotation; forward)” or “r (reverse rotation; reverse)”, and the current density calculation unit 812 calculates a plating current density j_k,t corresponding to “f” (the plating current density when the plating process is performed while rotating the substrate holder 440 in the forward direction), and a plating current density j_k,t corresponding to “r” (the plating current density when the plating process is performed while rotating the substrate holder 440 in the reverse direction). The control parameter is not limited to two stages, such as “on” and “off”, or “f” and “r” and may be in multiple stages. For example, the control parameter for the position of the shielding body 480 may include an “intermediate position” in addition to “on” and “off”, and the control parameter for the rotation of the substrate holder 440 may include four parameters for “fast forward rotation”, “slow forward rotation”, “fast reverse rotation”, and “slow reverse rotation”. The current density calculation unit 812 calculates the plating current density jkt for each of such plurality of operation modes of the plating module 400.

The plurality of operation modes of the plating module 400 can be represented by a combination of control parameters. For example, continuing with the above examples, the control parameters represented by the combination of the position of the shielding body 480 and the rotation of the substrate holder 440 can be “on, f” (the shielding body 480 is at the shielding position and the substrate holder 440 rotates in the forward direction), “on, r” (the shielding body 480 is at the shielding position and the substrate holder 440 rotates in the reverse direction), “off, f” (the shielding body 480 is at the retracted position and the substrate holder 440 rotates in the forward direction), and “off, r” (the shielding body 480 is at the retracted position and the substrate holder 440 rotates in the reverse direction). Based on such a combination of control parameters, the current density calculation unit 812 calculates the plating current density j_k,t for each operation mode of the plating module 400. In this example, the current density calculation unit calculates the plating current density j_k,t (on, f) corresponding to the control parameter “on, f”, the plating current density j_k,t (on, r) corresponding to the control parameter “on, r”, the plating current density j_k,t (off, f) corresponding to the control parameter “off, f”, and the plating current density j_k,t (off, r) corresponding to the control parameter “off, r”. As described above, the control parameter may be divided into three or more stages, and the number of the plating current densities j_k,t to be calculated corresponds to the number of combinations of control parameters. The control parameters may be combined, for example, with or without the stirring of the plating solution by the paddle 456, in addition to the position of the shielding body 480 and the rotation of the substrate holder 440. When the position of the shielding body 480 is in two stages of “on” and “off”, the rotation of the substrate holder 440 is in two stages of “f” and “r”, and the stirring by the paddle 456 is in two stages of “with stirring” and “without stirring”, the plating current density j_k,t is calculated for 2³=8 types of operation modes according to the combination of these control parameters. Without limiting to these examples, any combination of control parameters is possible.

A film thickness calculation unit 814 uses the plating current density j_k,t corresponding to each of the operation modes of the plating modules 400 that is calculated as described above, to calculate the thickness w_k,t of the plating film formed on the substrate Wf for each operation mode of the plating module 400. For example, the film thickness calculation unit 814 uses the plating current density j_k,t (on, f) to calculate a plating film thickness w_k,t (on, f) corresponding to the control parameter “on, f” (the operation mode in which the shielding body 480 is at the shielding position and the substrate holder 440 rotates in the forward direction); uses the plating current density j_k,t (on, r) to calculate a plating film thickness w_k,t (on, r) corresponding to the control parameter “on, r” (the operation mode in which the shielding body 480 is at the shielding position and the substrate holder 440 rotates in the reverse direction); uses the plating current density j_k,t (off, f) to calculate a plating film thickness w_k,t (off, f) corresponding to the control parameter “off, f” (the operation mode in which the shielding body 480 is at the retracted position and the substrate holder 440 rotates in the forward direction); and uses the plating current density j_k,t (off, r) to calculate a plating film thickness w_k,t (off, r) corresponding to the control parameter “off, r” (the operation mode in which the shielding body 480 is at the retracted position and the substrate holder 440 rotates in the reverse direction). The film thickness calculation unit 814 calculates the plating film thickness w_k,t in this manner for all the plating current densities j_k,t calculated in the current density calculation unit 812.

A control parameter determination unit 818 determines an optimal operation mode of the plating module 400 (an optimal control parameter or an optimal set of control parameters) based on the plating film thickness w_k,t for each operation mode of the plating module 400 that is calculated by the film thickness calculation unit 814. This determination can be made, for example, based on flatness of the calculated plating film thickness w_k,t. Continuing with the above examples, for example, the control parameter determination unit 818 compares respective degrees of flatness of the plating film thicknesses w_k,t (on, f), w_k,t (on, r), w_k,t (off, f), and w_k,t (off, r) calculated for the four operation modes of the plating module 400 and selects the plating film thickness having the highest flatness. It should be noted that subscript k represents a position on the substrate Wf (refer to the definition of the plating current density j_k,t described above), and the plating film thickness w_k,t (on, f) and the like represent a plating film thickness distribution on the substrate Wf. The control parameter determination unit 818 can optimally determine the operation mode (the control parameter or the set of control parameters) of the plating module 400 corresponding to the film thickness distribution having the highest flatness.

A plating process control unit 820 controls the plating module 400 according to the optimal control parameter or the optimal set of control parameters determined by the control parameter determination unit 818. For example, when it is determined that the plating film thickness w_k,t (on, f) has the highest flatness, the plating process control unit 820 controls the plating module 400 to perform the plating process while moving the shielding body 480 to the shielding position and rotating the substrate holder 440 in the forward direction. The plating process control unit 820 performs this control for each time step Δt (it is additionally assumed that the current density calculation unit 812, film thickness calculation unit 814 and control parameter determination unit 818 also perform the above described operations, respectively). For each time step Δt, the position of the shielding body 480 and the rotation of the substrate holder 440 (furthermore, the stirring of the plating solution with the paddle 456, etc.) are thus controlled in an optimal state. As a result, plating with high film thickness flatness can be formed on the substrate Wf.

In the above-described example using the control parameter combinations “on, f”, “on, r”, “off, f”, and “off, r”, the current density calculation unit 812 can calculate the plating current density j_k,t for each operation mode of the plating module 400 by use of the following equation, for example. First, an outer edge current density at time t can be described as j_t(θ, ψ). Here, θ represents an angular position on the substrate Wf (the angular position seen in a substrate coordinate system), and ψ represents a rotation angle of the substrate Wf by the substrate holder 440. Note that θ is the same as in Formula (1) described above.

$\left[\mathrm{Formula}10\right]$ $\begin{array}{cc}{j}_t\left(\theta ,\psi \right)=j_0+{\sum }_{i=1}^n\left(a_{i,t}\cos i\left(\theta -\psi \right)+b_{i,t}\sin i\left(\theta -\psi \right)\right)& \left(13\right)\end{array}$

The rotation angle ψ of the substrate Wf is related to the control parameters “f” and “r”. For example, time profile ψ(t) of the rotation angle can represent the forward rotation and reverse rotation (or alternating between the forward rotation and the reverse rotation) of the substrate holder 440. The current density calculation unit 812 can calculate the plating current density j_k,t on the substrate Wf according to the following equation from the outer edge current density of Formula (13).

$\left[\mathrm{Formula}11\right]$ $\begin{array}{cc}{j}_{k,t}=\alpha G_{on}\left(a_{1,t},b_{1t},\dots ;\theta ,\psi \right)+\left(1-\alpha \right)G_{\mathrm{oft}}\left(a_{1,t},b_{1,t},\dots ;\theta ,\psi \right)& \left(14\right)\end{array}$

As in Formula (9) of the first embodiment, G_on and G_off are functions representing a 3D model of the plating module 400 and are numerically determined based on the 3D model of the plating module 400 acquired from a 3D model creation unit 802. The function G_on corresponds to the 3D model of the plating module 400 when the shielding body 480 is at the shielding position, and the function G_off corresponds to the 3D model of the plating module 400 when the shielding body 480 is at the retracted position. Since a physical structure of the plating module 400 changes depending on whether the shielding body 480 is at the shielding position or the retracted position, the function G_on is different from the function G_off.

The coefficient α of Formula (14) takes α=1 when the shielding body 480 is at the shielding position and takes α=0 when the shielding body 480 is at the retracted position. That is, the coefficient α corresponds to the control parameters “on” and “off”. The time profile α(t) of the coefficient α can represent movement of the position of the shielding body 480. An intermediate value α between 0 and 1 may indicate that the shielding body 480 is at an intermediate position between the shielding position and the retracted position.

The current density calculation unit 812 thus specifies the rotation angle φ of the substrate Wf and the coefficient α for the 3D model of the plating module 400 (or specifies the time profile φ(t) and α(t)) and can accordingly calculate the plating current density for each of the control parameters “on, f”, “on, r”, “off, f” and “off, r”. Note that each term on the right side of Formula (14) can be calculated using, for example, the approximate expression (10) of the first embodiment.

Third Embodiment

FIG. 9 is a longitudinal sectional view schematically illustrating a configuration of a plating module 400A according to another embodiment. In this embodiment, a substrate Wf is disposed vertically. Specifically, the substrate Wf is held with its plate surface oriented horizontally. As illustrated in FIG. 9, the plating module 400A includes a plating tank 410A that holds a plating solution inside, an anode 430A disposed in the plating tank 410A, and a substrate holder 440A. The substrate Wf may be either a rectangular substrate or a circular substrate.

The anode 430A is disposed to oppose the plate surface of the substrate Wf in the plating tank. The anode 430A is connected to a positive electrode of a power supply 90, and the substrate Wf is connected to a negative electrode of the power supply 90 via the substrate holder 440A. When a voltage is applied between the anode 430A and the substrate Wf, a current flows through the substrate Wf, and a metal film is formed on the surface of the substrate Wf in the presence of the plating solution.

The plating tank 410A includes an inner tank 412A in which the substrate Wf and the anode 430A are arranged, and an overflow tank 414A adjacent to the inner tank 412A. The plating solution in the inner tank 412A overflows a side wall of the inner tank 412A to flow into the overflow tank 414A.

One end of a plating solution circulation line 58a is connected to a bottom of the overflow tank 414A, and the other end of the plating solution circulation line 58a is connected to a bottom of the inner tank 412A. To the plating solution circulation line 58a, a circulation pump 58b, a constant temperature unit 58c and a filter 58d are attached. The plating solution overflows the side wall of the inner tank 412A to flow into the overflow tank 414A and is then returned to the inner tank 412A through the plating solution circulation line 58a from the overflow tank 414A. Thus, the plating solution circulates between the inner tank 412A and the overflow tank 414A through the plating solution circulation line 58a.

The plating module 400A further includes a regulation plate 454 that regulates a potential distribution on the substrate Wf. The regulation plate 454 is disposed between the substrate Wf and the anode 430A and has an opening 454a for limiting an electric field in the plating solution.

The plating module 400A also includes a conduit 462A in the plating tank 410A. The conduit 462A can be, as an example, made of a resin such as polypropylene (PP) or polyvinyl chloride (PVC). The conduit 462A, in the same manner as the conduit 462 of the above embodiments, includes a first portion 462Aa including an opening end 464A disposed in a region between the substrate Wf and the anode 430A, and a second portion 462Ab disposed in a region apart from the region between the substrate Wf and the anode 430A. Furthermore, a potential sensor 470A is provided in the second portion 462Ab of the conduit 462A. A detection signal by the potential sensor 470A is inputted into a control module 800. The control module 800 is the same as described with reference to FIG. 6 or 8.

In the plating module 400A in the present embodiment, detection by the potential sensor 470A can be performed during a plating process in the same manner as the plating module 400 of the embodiment illustrated in FIG. 3. The control module 800 then operates in the same manner as in the first or second embodiment. Thereby, a change in film thickness of the plating film formed on a surface to be plated of the substrate Wf can be measured in the plating process in the same manner as in the first embodiment. Furthermore, plating with high film thickness flatness can be formed on the substrate Wf in the same manner as described in the second embodiment.

The embodiments of the present invention have been described above based on several examples, and the above embodiments of the present invention are described to facilitate understanding of the present invention and are not intended to limit the present invention. Needless to say, the present invention may be changed or modified without departing from the spirit, and the present invention includes equivalents to the invention. Also, in a range in which at least some of the above-described problems can be solved or a range in which at least some of effects are exhibited, arbitrary combination or omission of respective constituent components described in claims and description is possible.

REFERENCE SIGNS LIST

• • 1000 plating apparatus
  • 100 load port
  • 110 transfer robot
  • 120 aligner
  • 200 pre-wet module
  • 300 pre-soak module
  • 400 plating module
  • 500 cleaning module
  • 600 spin rinse dryer
  • 700 transfer device
  • 800 control module
  • 412 inner tank
  • 420 membrane
  • 422 cathode region
  • 424 anode region
  • 426 anode mask
  • 430 anode
  • 440 substrate holder
  • 441 electrical contact
  • 442 elevating/lowering mechanism
  • 448 rotation mechanism
  • 450 resistor
  • 452 drive mechanism
  • 456 paddle
  • 462 conduit
  • 464 opening end
  • 468 filling mechanism
  • 470 potential sensor
  • 480 shielding body
  • 802 3D model creation unit
  • 804 state space model
  • 806 state estimation unit
  • 808 observation value calculation unit
  • 810 Kalman filter
  • 812 current density calculation unit
  • 814 film thickness calculation unit
  • 816 endpoint determining unit
  • 818 control parameter determination unit
  • 820 plating process control unit
  • 62 outer edge
  • 90 power supply

Claims

1. A plating apparatus for plating a substrate, comprising: a plating tank to store a plating solution,a substrate holder that holds the substrate,an anode disposed in the plating tank to oppose the substrate held by the substrate holder,a potential sensor disposed in the vicinity of the substrate held by the substrate holder and configured to measure a potential of the plating solution,an estimation unit configured to estimate a density of a current flowing through an outer edge of the substrate based on a value of the potential of the plating solution that is measured by the potential sensor,a current density calculation unit configured to calculate a density of a plating current flowing through the plating solution into the substrate, based on the estimated current density and a control parameter that specifies an operation mode of the plating apparatus, the current density calculation unit calculating the plating current density for each of a plurality of different operation modes of the plating apparatus,a film thickness calculation unit configured to calculate a thickness of a plating film formed on the substrate for each of the plurality of operation modes, based on each of the plating current densities calculated by the current density calculation unit, anda control parameter determination unit configured to determine a control parameter corresponding to an optimal operation mode, based on the plating film thickness for each operation mode of the plating apparatus that is calculated by the film thickness calculation unit, the plating apparatus performing a plating process on the substrate by use of the control parameter determined by the control parameter determination unit.

2. The plating apparatus according to claim 1, wherein the operation mode of the plating apparatus is specified by a combination of a plurality of types of control parameters, and the current density calculation unit is configured to calculate the plating current density for each set of the plurality of types of control parameters, andthe control parameter determination unit is configured to determine a set of control parameters corresponding to an optimal operation mode, based on the plating film thickness for each operation mode of the plating apparatus that is calculated by the film thickness calculation unit.

3. The plating apparatus according to claim 2, wherein the control parameter is a parameter for one or more of i) rotation of the substrate, ii) partial shielding of the substrate, iii) stirring of the plating solution, and iv) a set value of a current flowing between the substrate and the anode.

4. The plating apparatus according to claim 1, wherein the control parameter determination unit is configured to determine the control parameter based on flatness of the calculated plating film thickness.

5. The plating apparatus according to claim 1, wherein the estimation unit is implemented as a state space model configured to estimate the current density by use of a state equation and an observation equation, the state equation being an equation describing time evolution on the density of the current flowing through the outer edge of the substrate, the observation equation being an equation describing a relation between the density of the current flowing through the outer edge of the substrate and the potential of the plating solution at a position of the potential sensor.

6. The plating apparatus according to claim 5, comprising a plating module including at least the plating tank, the substrate holder, the anode and the potential sensor, wherein the relation between the current density and the potential of the plating solution is based on a function representing a 3D model of the plating module.

7. The plating apparatus according to claim 5, wherein the state space model further includes a Kalman filter configured to correct estimation results of the density of the current flowing through the outer edge of the substrate, based on the value measured by the potential sensor.

8. The plating apparatus according to claim 1, wherein the outer edge of the substrate is a portion to be gripped with the substrate holder of the substrate.

9. The plating apparatus according to claim 8, wherein the plating current density calculated by the current density calculation unit is a density of a current in a region inside the outer edge of the substrate.