Patent Publication Number: US-2023152077-A1

Title: Plating apparatus and film thickness measuring method for substrate

Description:
TECHNICAL FIELD 
     The present invention relates to a plating apparatus and a film thickness measuring method for substrate. 
     BACKGROUND ART 
     Conventionally, there has been known what is called a cup type plating apparatus as a plating apparatus that can perform a plating process on a substrate (for example, see PTL 1). The plating apparatus includes a plating tank that stores a plating solution and internally includes an anode, a substrate holder disposed above the anode and holds the substrate as a cathode, and a rotation mechanism that rotates the substrate holder when performing the plating process on the substrate. 
     CITATION LIST 
     Patent Literature 
     
         
         PTL 1: Japanese Unexamined Patent Application Publication No. 2008-19496 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     A conventional plating apparatus such as the one described above was not configured to be capable of measuring the film thickness of the substrate in the plating process. 
     The present invention has been made in view of the above, with an object to provide a technique for measuring the film thickness of the substrate in the plating process. 
     Solution to Problem 
     [Aspect 1] To achieve the above-described object, a plating apparatus according to one aspect of the present invention includes a plating tank, a substrate holder, a rotation mechanism, a plurality of contact members, a coil, a current sensor, and a film thickness measuring device. The plating tank is configured to store a plating solution and internally includes an anode. The substrate holder is disposed above the anode and configured to hold a substrate as a cathode. The rotation mechanism is configured such that the rotation mechanism rotates the substrate holder when a plating process is performed on the substrate. The plurality of contact members are disposed in the substrate holder and arranged in a circumferential direction of the substrate holder. The plurality of contact members are configured to contact an outer peripheral edge of a lower surface of the substrate to supply electricity to the substrate in the plating process. The coil is configured to generate a current by an electromagnetic induction due to a magnetic field caused by a current flowing into the contact member. The contact member is configured to rotate together with the substrate holder in the plating process. The current sensor is configured to detect the current generated in the coil. The film thickness measuring device is configured to measure a film thickness of the substrate based on the current detected by the current sensor in the plating process. 
     According to this aspect, the film thickness of the substrate can be measured in the plating process. 
     [Aspect 2] In aspect 1 described above, the coil may be disposed to have a space from the substrate holder outside the substrate holder in a radial direction of the substrate holder. 
     [Aspect 3] In aspect 1 or 2 described above, the plurality of contact members are disposed equally in the circumferential direction of the substrate holder, and the current sensor may be configured to detect a current generated in the coil by the electromagnetic induction due to the magnetic field caused by the contact member that has most closely approached the coil, among the contact members configured to rotate together with the substrate holder in the plating process. 
     According to this aspect, a distribution of a film thickness in the circumferential direction of the substrate can be measured. 
     [Aspect 4] To achieve the above-described object, a film thickness measuring method for substrate according to one aspect of the present invention uses a plating apparatus. The plating apparatus includes a plating tank, a substrate holder, a rotation mechanism, a plurality of contact members, and a coil. The plating tank is configured to store a plating solution and internally includes an anode. The substrate holder is disposed above the anode and configured to hold a substrate as a cathode. The rotation mechanism is configured such that the rotation mechanism rotates the substrate holder when performing a plating process on the substrate. The plurality of contact members are disposed in the substrate holder and arranged in a circumferential direction of the substrate holder. The plurality of contact members are configured to contact an outer peripheral edge of a lower surface of the substrate to supply electricity to the substrate in the plating process. The coil is configured to generate a current by an electromagnetic induction due to a magnetic field caused by a current flowing into the contact member. The contact member is configured to rotate together with the substrate holder in the plating process. The film thickness measuring method includes: detecting the current generated in the coil in the plating process; and measuring a film thickness of the substrate based on the detected current. 
     According to this aspect, the film thickness of the substrate can be measured in the plating process. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a perspective view illustrating an overall configuration of a plating apparatus according to an embodiment. 
         FIG.  2    is a plan view illustrating the overall configuration of the plating apparatus according to the embodiment. 
         FIG.  3    is a schematic diagram for describing a configuration of a plating module of the plating apparatus according to the embodiment. 
         FIG.  4    is a schematic diagram illustrating a state where a substrate is immersed in a plating solution in a plating process. 
         FIG.  5 A  is an enlarged schematic cross-sectional view illustrating a part A 1  in  FIG.  3   . 
         FIG.  5 B  is a schematic cross-sectional view illustrating a state where a cross-sectional surface of a peripheral configuration of a contact member is viewed from an upper side. 
         FIG.  6    is a schematic diagram for describing a film thickness measuring method according to the embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     The following describes embodiments of the present invention with reference to the drawings. The drawings are schematically illustrated for ease of understanding features of matters, and a dimensional proportion of each component or the like is not always identical to that of an actual component. Furthermore, for some drawings, X-Y-Z orthogonal coordinates are illustrated for reference purposes. Of the orthogonal coordinates, the Z direction corresponds to the upper side, and the −Z direction corresponds to the lower side (the direction where gravity acts). 
       FIG.  1    is a perspective view illustrating the overall configuration of a plating apparatus  1000  of this embodiment.  FIG.  2    is a plan view illustrating the overall configuration of the plating apparatus  1000  of this embodiment. As illustrated in  FIGS.  1  and  2   , the 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 the 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 deaerated 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 the plating solution to the inside of the pattern by replacing the process liquid inside the pattern with a 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 or the like 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 for performing 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 substrates. 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 to dry the substrate. While the two spin rinse dryers  600  are disposed to be arranged in the vertical direction in this embodiment, the number of spin rinse dryers  600  and arrangement of the spin rinse dryers  600  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 in 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 . 
     The configuration of the plating apparatus  1000  described in  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   . 
     Subsequently, the plating module  400  will be described. Since a plurality of the plating modules  400  included in the plating apparatus  1000  according to this embodiment have similar configurations, only one plating module  400  will be described. 
       FIG.  3    is a schematic diagram for describing a configuration of the plating module  400  of the plating apparatus  1000  according to this embodiment.  FIG.  4    is a schematic diagram illustrating a state where a substrate Wf is immersed in a plating solution Ps when performing the plating process. The plating apparatus  1000  according to the embodiment is a cup type plating apparatus. The plating module  400  of the plating apparatus  1000  mainly includes a plating tank  10 , a substrate holder  20 , a rotation mechanism  30 , an elevating mechanism  40 , a contact member  50 , a coil  60 , a current sensor  65 , and a film thickness measuring device  70 . In  FIGS.  3  and  4   , cross-sectional surfaces of a part of the members of the plating apparatus  1000  (such as the plating tank  10  and the substrate holder  20 ) are schematically illustrated. 
     The plating tank  10  according to this embodiment is configured by a container having an opening in its upper side and having a bottom. Specifically, the plating tank  10  has a bottom portion  10   a  and an outer peripheral portion  10   b  that extends upward from the outer peripheral edge of this bottom portion  10   a , and an upper portion of this outer peripheral portion  10   b  is opened. Although the shape of the outer peripheral portion  10   b  of the plating tank  10  is not specifically limited, the outer peripheral portion  10   b  according to this embodiment has a cylindrical shape as an example. 
     The plating tank  10  internally stores a plating solution Ps. It is only necessary that the plating solution Ps is a solution that contains metallic element ions for constituting the plating film, and the specific examples are not particularly limited. In this embodiment, a copper plating process is used as an example of the plating process, and a copper sulfate solution is used as an example of the plating solution Ps. Furthermore, in this embodiment, the plating solution Ps contains a predetermined additive. However, it is not limited to this configuration, and the plating solution Ps may have a configuration that does not contain the additive. 
     The plating tank  10  is provided with a supply port (not illustrated) for supplying the plating solution Ps to the plating tank  10 , and a discharge port (not illustrated) for discharging the plating solution Ps from the plating tank  10 . After the plating solution Ps discharged from the discharge port is temporarily stored in a reservoir tank (not illustrated), the plating solution Ps is pressure-fed by a pump (not illustrated), and supplied to the plating tank  10  from the supply port again. 
     The plating tank  10  internally includes an anode  11 . A specific type of the anode  11  is not particularly limited, and a soluble anode and/or an insoluble anode may be used. In this embodiment, an insoluble anode is used as the anode  11 . A specific type of this insoluble anode is not particularly limited, and platinum, iridium oxide, and the like may be used. 
     Above the anode  11  inside the plating tank  10 , a porous ionically resistive element  12  is disposed. Specifically, the ionically resistive element  12  is configured by a porous plate member having a plurality of holes (pores). The plating solution Ps below the ionically resistive element  12  can pass through the ionically resistive element  12  and flow above the ionically resistive element  12 . The ionically resistive element  12  is a member disposed for ensuring uniformization of an electric field formed between the anode  11  and the substrate Wf. Thus, since the ionically resistive element  12  is disposed in the plating tank  10 , a uniformization of a film thickness of a plating film (plated layer) formed on the substrate Wf can be easily ensured. The ionically resistive element  12  is not an essential configuration in this embodiment, and the plating apparatus  1000  may have a configuration without the ionically resistive element  12 . 
     The substrate holder  20  is a member capable of holding the substrate Wf as the cathode. Specifically, the substrate holder  20  is disposed above the anode  11  (further above the ionically resistive element  12  in this embodiment). The substrate holder  20  holds the substrate Wf such that the lower surface Wfa of the substrate Wf opposes the anode  11  and the ionically resistive element  12 . The lower surface Wfa of the substrate Wf corresponds to the surface to be plated. 
       FIG.  5 A  is an enlarged schematic cross-sectional view of a part A 1  in  FIG.  3   . The substrate holder  20  according to the embodiment has a first holding member  21  and a second holding member  22 . The first holding member  21  holds an upper surface Wfb of the substrate Wf. The second holding member  22  holds an outer peripheral edge of the lower surface Wfa of the substrate Wf via a sealing member  23 . The substrate holder  20  holds the substrate Wf by sandwiching the substrate Wf with the first holding member  21  and the second holding member  22 . The first holding member  21  has a circular plate shape, and the second holding member  22  has an approximate ring shape. The sealing member  23  is for suppressing the plating solution Ps from contacting the contact member  50  when the substrate Wf is immersed in the plating solution Ps. The sealing member  23  has a ring shape. 
     The above-described configuration of the substrate holder  20  is merely an example, and the substrate holder  20  is not limited to the above-described configuration insofar as the substrate holder  20  can hold the substrate Wf. 
     With reference to  FIG.  3    again, the substrate holder  20  is connected to the rotation shaft  31  of the rotation mechanism  30 . The rotation mechanism  30  is a mechanism for rotating the substrate holder  20 . As the rotation mechanism  30 , a known mechanism can be used, such as a motor. The elevating mechanism  40  is supported by a spindle  45  extending in the vertical direction. The elevating mechanism  40  is a mechanism for elevating the substrate holder  20  and the rotation mechanism  30  in the vertical direction. As the elevating mechanism  40 , a known elevating mechanism can be used, such as a linear motion type actuator. The rotation mechanism  30  and the elevating mechanism  40  are controlled by the control module  800 . 
     When performing the plating process on the substrate Wf the rotation mechanism  30  rotates the substrate holder  20 , while the elevating mechanism  40  moves the substrate holder  20  downward, and immerses the substrate Wf in the plating solution Ps in the plating tank  10  (see  FIG.  4   ). In a state where the substrate Wf is immersed in the plating solution Ps, an energization device (not illustrated) causes electricity to flow between the anode  11  and the substrate Wf. Accordingly, a plating film is formed on the lower surface Wfa of the substrate Wf. 
     An operation of the plating module  400  is controlled by the control module  800 . The control module  800  includes a microcomputer, and the microcomputer includes a Central Processing Unit (CPU)  801  as a processor, a storage unit  802  as a non-transitory storage medium, and the like. The control module  800  controls the rotation mechanism  30  and the elevating mechanism  40  in the plating module  400 , by the operation of the CPU  801  according to commands of a program stored in the storage unit  802 . 
       FIG.  5 B  is a schematic cross-sectional view illustrating a state where a cross-sectional surface (cross-sectional surface of the B 1 -B 1  line) of a peripheral configuration of the contact member  50  is viewed from an upper side. In  FIG.  5 B , an illustration of the first holding member  21  is omitted. With reference to  FIGS.  5 (A) and  5 (B) , the contact member  50  is a member for supplying electricity to the substrate Wf by contacting the outer peripheral edge of the lower surface Wfa of the substrate Wf. The plurality of contact members  50  are disposed in the substrate holder  20  (specifically, the second holding member  22  in this embodiment) and arranged in a circumferential direction of the substrate holder  20 . 
     Specifically, the plurality of contact members  50  according to the embodiment are disposed equally in the circumferential direction of the substrate holder  20 . The number of the plurality of contact members  50  is not specifically limited, but in this embodiment, as an example, there are 12 pieces. The plurality of contact members  50  are electrically connected to the energization device (not illustrated), and provides the electricity supplied from the energization device to the substrate Wf. 
     Subsequently, the following describes the coil  60 , the current sensor  65 , and the film thickness measuring device  70 . With reference to  FIGS.  3 ,  4 ,  5   (A), and  5 (B), the coil  60  according to the embodiment is disposed outside the substrate holder  20  in a radial direction of the substrate holder  20 . Furthermore, the coil  60  according to the embodiment is disposed to have a space from the substrate holder  20  (that is, so as not to contact the substrate holder  20 ). 
     The coil  60  is secured to the plating module  400  via a holding member (not illustrated) for holding the coil  60 . The coil  60  is configured not to rotate even when the substrate holder  20  rotates. Furthermore, the coil  60  is configured to move up and down together with the substrate holder  20  when the substrate holder  20  moves up and down. Specifically, the coil  60  according to the embodiment is connected to the elevating mechanism  40  via the holding member (not illustrated). Thus, when the substrate holder  20  moves up and down, the coil  60  moves up and down with the substrate holder  20 . 
     Furthermore, as illustrated in  FIG.  4   , in the embodiment, a disposed position of the coil  60  is set, such that the coil  60  does not get immersed in the plating solution Ps even when the substrate Wf is immersed in the plating solution Ps. However, it is not limited to this configuration, and for example, it may be a configuration in which the coil  60  also gets immersed in the plating solution Ps when the substrate Wf gets immersed in the plating solution Ps. 
     Furthermore, as illustrated in  FIG.  5 A , in this embodiment, the coil  60  is disposed such that a coil shaft  60   a  of the coil  60  extends in the vertical direction. However, the extending direction of the coil shaft  60   a  is not limited to this. For example, the coil shaft  60   a  may extend in the horizontal direction. Alternatively, the coil shaft  60   a  may extend in an inclined direction at an angle of more than 0° and less than 900 with respect to the horizontal direction. 
       FIG.  6    is a schematic diagram for describing the film thickness measuring method.  FIG.  6    illustrates a state where the second holding member  22 , the contact member  50 , and the coil  60  are viewed from the same direction as  FIG.  5 B . 
     When performing the plating process on the substrate Wf, a current flowing into the contact member  50  causes a magnetic field MA around the contact member  50 . In the plating process, since the contact member  50  rotates with the substrate holder  20 , the magnetic field MA rotates with the substrate holder  20 . An electromagnetic induction due to the rotating magnetic field MA generates a current (specifically, a faint current) in the coil  60 . That is, the current generated in the coil  60  is an electromagnetic current generated by the electromagnetic induction. 
     Specifically, a disposed position of the coil  60  according to the embodiment is adjusted such that a current is generated in the coil  60  by an electromagnetic induction due to a magnetic field MA caused by the contact member  50  that has most closely approached the coil  60 , among the contact members  50  rotating together with the substrate holder  20  in the plating process. 
     The current sensor  65  is electrically connected to the coil  60  and detects a value of the current that has been generated in the coil  60 . Specifically, the current sensor  65  according to the embodiment is configured to detect a value of a current that has been generated in the coil  60  by the electromagnetic induction due to the magnetic field MA caused by the contact member  50  that has most closely approached the coil  60 , among the contact member  50  that rotates with the substrate holder  20 . 
     The film thickness measuring device  70  is electrically connected to the current sensor  65 . The film thickness measuring device  70  is disposed outside the plating tank  10  and measures a film thickness of a plating film (that is, “the film thickness of the substrate Wf”) formed on the lower surface Wfa of the substrate Wf based on a current detected by the current sensor  65 . 
     Specifically, the film thickness measuring device  70  according to the embodiment includes a microcomputer. The microcomputer includes a CPU  71  as a processor, a storage unit  72  as a non-transitory storage medium, and the like. The storage unit  72  stores a program. The film thickness measuring device  70  measures the film thickness of the substrate Wf by the operation of the CPU  71  according to commands of a program stored in the storage unit  72 . A specific example of the film thickness measurement of the film thickness measuring device  70  is described in the following. 
     First, the smaller the value of the current flowing into the contact member  50  is (consequently, the weaker the magnetic field MA caused by the current is), the smaller the film thickness of the substrate Wf tends to become. Therefore, the smaller the film thickness of the substrate Wf is, the smaller the value of the current generated in the coil  60  becomes. Thus, a correlation relationship exists between the film thickness of the substrate Wf and the value of the current generated in the coil  60 . Therefore, the film thickness measuring device  70  according to the embodiment uses the correlation relationship between the film thickness of the substrate Wf and the value of the current generated in the coil  60  to measure the film thickness of the substrate Wf. 
     Specifically, in the storage unit  72  of the film thickness measuring device  70  according to the embodiment, a data map specifying the relationship between the value of the current generated in the coil  60  and the film thickness of the substrate Wf is stored in advance. This data map specifies the relationship between the value of the current generated in the coil  60  and the film thickness of the substrate Wf such that the smaller the value of the current generated in the coil  60  is, the smaller the film thickness of the substrate Wf becomes. The film thickness measuring device  70  obtains the value of the current detected by the current sensor  65  (that is, the value of the current generated in the coil  60 ), extracts the film thickness of the substrate Wf corresponding to the value of the obtained current from the data map of the storage unit  72 , and obtains the film thickness of the extracted substrate Wf as a measured value of the film thickness of the substrate Wf. As described above, the film thickness measuring device  70  measures the film thickness of the substrate Wf. 
     Furthermore, as described above, since the current sensor  65  according to the embodiment detects the current generated in the coil  60  by the electromagnetic induction due to the magnetic field MA caused by the contact member  50  that has most closely approached the coil  60 , the film thickness measuring device  70  according to the embodiment measures the film thickness of the substrate Wf corresponding to the rotation phase (θ) of the contact member  50  that has most closely approached the coil  60 . 
     For example, the current sensor  65  shown in  FIG.  6    detects a current generated in the coil  60  by an electromagnetic induction due to the magnetic field MA caused by the contact member  50  at a position of 180° in rotation phase (θ). Subsequently, the film thickness measuring device  70  measures the film thickness of the substrate Wf at a location of 180° in rotation phase (θ) based on the current detected by the current sensor  65 . This is performed every time the plurality of contact members  50  approach the coil  60 . Accordingly, the film thickness measuring device  70  can measure a distribution of the film thickness in a circumferential direction of the substrate Wf (in other words, the film thickness of each rotation phase of the contact member  50 ). 
     The film thickness measuring method for the substrate Wf according to the embodiment is achieved by the above-described plating apparatus  1000 . The description of the film thickness measuring method will be omitted due to duplication with the description of the plating apparatus  1000 . 
     According to the embodiment described above, the film thickness of the substrate Wf can be measured in the plating process. Furthermore, according to the embodiment, the distribution of the film thickness in the circumferential direction of the substrate Wf can be measured as well. 
     As described above, while the details of the embodiment of the present invention have been described, the present invention is not limited to the specific embodiments and modifications, and various kinds of modifications and changes can further be made within the spirit of the present invention described in the claims. 
     REFERENCE SIGNS LIST 
     
         
         
           
               10  . . . plating tank 
               11  . . . anode 
               20  . . . substrate holder 
               30  . . . rotation mechanism 
               50  . . . contact member 
               60  . . . coil 
               65  . . . current sensor 
               70  . . . film thickness measuring device 
               400  . . . plating module 
               1000  . . . plating apparatus 
             Wf . . . substrate 
             Wfa . . . lower surface 
             Ps . . . plating solution 
             MA . . . magnetic field