ELECTRODE AND APPARATUS FOR ELECTROLYTICALLY TREATING A WORKPIECE, ASSEMBLY FOR FORMING A CELL OF THE APPARATUS AND METHOD AND COMPUTER PROGRAM

Abstract

An electrode for an apparatus (1) for electrolytically treating a workpiece (3), the apparatus (1) being of a type arranged to convey the workpiece (3) with a surface to be treated past and directed towards a surface of the electrode, is divided into segments (23a-e) at at least this surface of the electrode. The segments (23a-e) are arranged next to each other in a first direction (x). Adjacent segments (23a-e) are separated from each other along respective segment edges (24a-f) such as to allow adjacent segments (23a-e) to be maintained at different respective voltages. The segment edges (24a-f) extend at least partly in a second direction (y) from a common value (y.sub.0) of a co-ordinate in the second direction (y) to an edge (25,26) of at least an electrically conducting part of the electrode surface, the second direction (y) being transverse to the first direction (x) and corresponding to a direction of movement of the workpiece, in use. The segment edges (24a-f) between at least one pair of adjacent segments (23a-e) extend along respective paths of which an angle to the electrode surface edge (25,26) decreases from the common value (y.sub.0) of the co-ordinate to the electrode surface edge (25,26).

Claims

1. Electrode for an apparatus (1) for electrolytically treating a workpiece (3), the apparatus (1) being of a type arranged to convey the workpiece (3) with a surface to be treated past and directed towards a surface of the electrode, wherein the electrode is divided into segments (23a-e) at at least this surface of the electrode, wherein the segments (23a-e) are arranged next to each other in a first direction (x), wherein adjacent segments (23a-e) are separated from each other along respective segment edges (24a-f) such as to allow adjacent segments (23a-e) to be maintained at different respective voltages, and wherein the segment edges (24a-f) extend at least partly in a second direction (y) from a common value (y.sub.0) of a co-ordinate in the second direction (y) to an edge (25,26) of at least an electrically conducting part of the electrode surface, the second direction (y) being transverse to the first direction (x) and corresponding to a direction of movement of the workpiece, in use characterised in that the segment edges (24a-f) between at least one pair of adjacent segments (23a-e) extend along respective paths of which an angle to the electrode surface edge (25,26) decreases from the common value (y.sub.0) of the co-ordinate to the electrode surface edge (25,26).

2. Electrode according to claim 1, wherein, at least within each half of the electrode seen in the first direction (x), the paths extend in a same one of opposite senses in the first direction (x) from the common value (y.sub.0) of the co-ordinate to the electrode surface edge (25,26), so that the paths are all inclined in the same direction, at least within each half of the electrode seen in the first direction (x).

3. Electrode according to claim 1, wherein the paths from the common value (y.sub.0) of the co-ordinate to the electrode surface edge (25,26) are curves.

4. Electrode according to claim 1, wherein at least the electrically conducting part of the electrode surface comprises two halves (28,29), seen in the second direction (y), wherein respective sections of the segment edges (24a-f) in one half (28,29) are a mirror image of respective sections of the segment edges (24a-f) in the other half (28,29) with respect to a line (27) of symmetry located at the common value (y.sub.0) of the co-ordinate.

5. Electrode according to claim 1, wherein a point at the electrode surface edge (25,26) on a path of a first of the segment edges (24a-f) of each segment (23a-e) is at the same co-ordinate value or removed in the first direction (x) from a point at the common value (y.sub.0) of the co-ordinate on the path of the other of the segment edges (24a-f) of that segment (23a-e).

6. Electrode according to claim 1, wherein a width of the segments (23a-e), corresponding to a distance between the edges (24a-h) of a segment (23a-e) at the common value (y.sub.0) of the co-ordinate, increases from segment (23a-e) to segment (23a-e), so that the segments (23a-e) become progressively wider with distance in the first direction (x) from an electrode edge (22), or wherein this condition holds true within each half of the electrode, seen in the first direction (x).

7. Electrode according to claim 1, wherein an angle to the electrode surface edge (25,26) of the paths of a pair of segment edges (24a-f) between a pair of adjacent segments (23a-e) at the surface edge increases from pair to pair with distance in the first direction (x) from an electrode edge (22), or wherein this condition holds true within each half of the electrode, seen in the first direction (x).

8. Assembly for forming a cell (2a-e) of an electrolytic processing apparatus (1), wherein the assembly comprises at least one electrode (16) according to claim 1.

9. Assembly according to claim 8, further comprising at least one shielding device, extending in the first and second directions (x,y) in front of the electrode surface of one of the at least one electrodes (16).

10. Assembly according to claim 9, wherein the shielding device comprises a plate (19), provided with a multitude of through-going channels pervious to liquid and distributed in the first and second directions (x,y).

11. Electrolytic processing apparatus comprising at least one processing cell (2a-e), the processing cell (2a-e) comprising at least one assembly according to claim 8.

12. Method comprising at least a computer-implemented step (34-42) of designing an electrode (16) according to claim 1, wherein the design step (34-42) includes determining the shapes of the paths.

13. Method according to claim 12, wherein determining the shapes of the paths includes determining (35) respective coefficients of a polynomial, e.g. a second-degree polynomial, of the co-ordinate in the first direction (x), the polynomial representing a co-ordinate in the second direction (y), and wherein, seen in plan view onto the electrode surface, each path from the common value (y.sub.0) of the co-ordinate in the second direction corresponds to the polynomial with a respective set of coefficients, optionally with a superimposed deviation.

14. Method according to claim 13, wherein the coefficients are obtained by calculating a voltage drop-off function, being a function of the co-ordinate in the first direction (x) and representing a voltage change in the first direction (x) along the surface of the workpiece (3).

15. Computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the design step (34-42) of a method according to claim 12.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0080] The invention will be described in further detail with reference to the accompanying drawings, in which:

[0081] FIG. 1 is a very schematic top plan view of an electrolytic processing apparatus;

[0082] FIG. 2 is a cross-sectional detailed view of a clamp arm for contacting a workpiece conveyed through the electrolytic processing apparatus;

[0083] FIG. 3 is a schematic plan view of a surface of an anode for a cell of the electrolytic processing apparatus;

[0084] FIG. 4 is a plan view corresponding to that of FIG. 3, but onto an opposite side of the anode;

[0085] FIG. 5 is a plan view of a shielding device for placement between the anode and the workpiece;

[0086] FIG. 6 is a detailed view of a section of the shielding device;

[0087] FIG. 7 is a diagram illustrating steps in a method used to obtain the anode;

[0088] FIG. 8 is a diagram illustrating an implementation of one of the steps of FIG. 7;

[0089] FIG. 9 is a diagram illustrating voltage differences between segments of the anode and the workpiece, the voltage dropoff in an electrolyte bath between the workpiece and the anode and the voltage dropoff in an electrically conducting layer on the surface of the workpiece facing the anode;

[0090] FIG. 10 is a schematic plan view of one half of the anode to illustrate how segment edge shapes are determined;

[0091] FIG. 11 is a diagram showing a first phase in a determination of the target current density averages for the segments;

[0092] FIG. 12 is a diagram showing a result of the determination of the target current density averages; and

[0093] FIG. 13 is a diagram showing a percentage deviation of a current density at positions along a workpiece length from an average current density, calculated by simulating a cell comprising an anode of the type illustrated in FIGS. 3, 4 and 10 and a shielding device as shown in FIGS. 5 and 6.

DESCRIPTION OF EMBODIMENTS

[0094] An electroplating apparatus 1 comprises a number of processing cells 2a-d for plating a planar workpiece 3a-f. The planar workpiece 3a-f may be a foil or panel, e.g. made mainly of dielectric material. The surfaces parallel to the plane of the workpiece are referred to herein as the major surfaces. At least one of these major surfaces is to be plated by the apparatus 1. This includes plating the side walls of any vias through the workpiece 3a-f or of trenches in the workpiece 3a-f.

[0095] Only the electrolytic plating apparatus 1 is described and illustrated here. This apparatus 1 will generally be preceded by apparatus for effecting preliminary processing steps, including ablation, desmearing, ionic activation and electroless deposition to form an electrically conducting precursor layer on the workpiece 3a-f.

[0096] It is convenient to define a first direction x, the dimension of the workpiece 3a-f also being referred to herein as the width. A second direction y, transverse to the first direction x, corresponds to a direction of movement of the workpieces 3a-f through the apparatus 1.

[0097] The apparatus 1 comprises an enclosure 4 defining a bath of circulated electrolyte. Rollers 5a-c support the workpieces 3a-f up to a point of entry into the enclosure 4, where they are engaged by a conveying system 6, shown schematically as comprising a series of clamps 7 for engaging the major surfaces of the workpieces 3a-f at a proximal edge 8a-f. A distal edge 9a-d is located at what is referred to herein as a window of each cell 2a-d, where the electrolyte flows out of the cell 2a-d. In the illustrated embodiment, the workpieces 3a-f are not held at the distal edge 9a-d. The workpieces 3a-f are also not supported by any solid structures between the edges 8,9. The workpieces 3a-f are immersed in the electrolyte, however. In alternative embodiments, support elements may be provided. The workpieces 3a-f may also be clamped on both sides, seen in the first direction x.

[0098] The clamps 7 automatically engage the workpieces 3a-f as the latter enter the enclosure 4 and disengage when the workpieces 3a-f leave the enclosure 4. The clamps 7 are supported on an endless belt 10, which may be a belt with a toothed profile or a chain, for example, driven by one or more drums 11a,b around which the endless belt 10 is arranged and by which the endless belt 10 is supported.

[0099] It is noted that FIG. 1 is schematic. In a practical implementation, the clamps 7 will extend into the cells 2a-d, so that the workpieces 3a-f protrude only little or not at all at their proximal edges 8a-f.

[0100] The clamps 7 comprise an arm 12 (FIG. 2) on each side of the workpiece 3a-f. The arm 12 comprises an electrically conducting core part 13 covered by an electrically insulating shielding 14 except for a surface section 15 for engaging the major surface of the workpiece 3. The or each clamp 7 that engages the workpiece 3 forms part of an electrical circuit comprising the workpiece 3, which functions as a cathode, and an anode 16.

[0101] In a cell 2 for plating both major surfaces of the workpiece 3, the arrangement is mirrored. The present discussion will focus on only those components for plating one major surface of the workpiece 3, in the illustrated embodiment the major surface facing upwards.

[0102] The anode 16 of the example comprises two layers 17,18 (FIG. 2). In alternative embodiments, there may be one layer or even more layers. At least a lower layer 18 proximate to the workpiece 3 comprises mesh sections. The mesh is pervious to the electrolyte. An upper layer 17 may also be a mesh layer or, as in the illustrated example, a layer made of apertured plate sections. Electrolyte can thus flow through the anode 16 towards the workpiece 3.

[0103] A shielding device comprising a shielding plate 19 made of electrically insulating material and provided with through-going channels is situated between the anode 16 and the workpiece 3. The shielding plate 19 functions to protect against short-circuits due to contact between the workpiece 3 and the anode 16. The shielding plate 19 may be omitted in some embodiments. The shielding plate 19 extends in the first direction x and the second direction y in front of the anode surface facing the workpiece 3. The shielding plate 19 may be essentially co-extensive with the anode 16. In the illustrated embodiment, there is a slight deviation, as will be explained.

[0104] In the illustrated embodiment, a clamp anode 20 (FIG. 2) extends in the second direction y along an edge 22 (FIGS. 3 and 4) proximal to the clamp 7 and in a third direction z, transverse to the first direction x and the second direction y. The clamp anode 20 is provided with a separately controlled current supply (not shown in detail). The clamp anode 20 is arranged to a certain extent to prevent current from flowing from the anode 16 to the clamp 7 or a region of the workpiece 3 at an edge of the workpiece 3 where the workpiece 3 is contacted by the clamp 7. In addition, the clamp anode 20 compensates for deposition of metal on the clamp 7 instead of the workpiece 3 by providing an additional current flow to the workpiece 3. This further contributes to the uniformity of the layer formed on the workpiece 3. If the workpiece 3 is a printed circuit board, the clamp anode 20 provides a plated edge region, generally up to 25 mm wide, which is needed for contacting at subsequent processing stages,

[0105] In an embodiment, a surface 21 of the clamp anode 20 facing the anode 16 is covered by electrically insulating material. This is useful because the current from the clamp anode 20 is controlled independently of that from the anode 16, so that there may be a potential difference between the two.

[0106] At least the layer 18 of the anode 16 of which the surface faces the workpiece 3 is divided into segments 23a-e. Adjacent segments 23a-e are separated from each other along respective segment edges 24a-h (FIG. 3). The segment edges 24a-e between adjacent segments 23 form a pair. The pair may be separate by a gap or by electrically insulating material. The width of the gap or separating strip of electrically insulating material imposes a limit on the number of segments 23a-e that can be provided, but need not be determinative of the maximum number of segments 23a-e.

[0107] In any case, the separation means that the segments 23a-e are mutually electrically insulated. There is a small coupling due to the fact that the electrolyte between the workpiece 3 and the anode 16, as well as the electrically conducting starter layer on the surface of the workpiece 3 are electrically conducting. The manner in which the segments 23a-e are separated is such as to allow adjacent segments 23a-e to be maintained at different respective voltages. The coupling is lower than the range that needs to be controlled to apply an adjustable current to each individual segment 23a-e. Each segment's voltage difference to the clamp 7 is independently controllable by an associated respective rectifier (not shown). This voltage difference will be referred to as the anode-clamp voltage Uc.sub.i, where i is the number of the segment 23 counting from the segment 23a proximal to the clamp 7 in the first direction x.

[0108] The segment edges 24a-e extend partly in the second direction y from a common value y.sub.0 of the y-co-ordinate to a first electrode edge 25 extending in the first direction x. In the illustrated embodiment, the segment edges 24a-e also extend partly in the opposite sense in the second direction y from the common value y.sub.0 of the y-co-ordinate to a second electrode edge 26 extending in the first direction x. The first and second electrode edges 25,26 are thus opposite edges. A line of symmetry 27 is located at the common value y.sub.0 of the y-co-ordinate. The anode 16 can be regarded as comprising two halves 28,29, seen in the second direction y.

[0109] The segment edges 24a-e extend along respective paths of which an angle to the first electrode edge 25 decreases from the common value y.sub.0 of the y-co-ordinate to the first electrode edge 25. Also, the angle to the second electrode edge 26 decreases from the common value y.sub.0 of the y-co-ordinate to the second electrode edge 26.

[0110] The sections of the segment edges 24a-e in a first half 28 of the first and second halves 28,29 extend in the same sense in the first direction x from a point at the common value y.sub.0 of the y-co-ordinate to the first electrode edge 25, i.e. the value of the x-co-ordinate increases along the path towards the first electrode edge 25. The sections of the segment edges 24a-e in the second half 29 extend in the same sense in the first direction x from a point at the common value y.sub.0 of the y-co-ordinate to the second electrode edge 26, i.e. the value of the x-co-ordinate increases along the path towards the second electrode edge 26.

[0111] In the illustrated embodiment, the paths of the segment edges 24a-e are curves. In other embodiments, they may be piecewise linear curves.

[0112] In the illustrated embodiment, a point at the first electrode edge 25 on a path of a first of the segment edges 24a-h of each segment 23a-e has the same x-co-ordinate or a smaller value of the x-co-ordinate as a point at the common value y.sub.0 on the path of the other of the segment edges 24a-h of that segment 23a-e. Taking the third segment 23c as an example (FIG. 3), a first segment edge 24d extends from the point (x.sub.1,y.sub.0) to the point (x.sub.2,y.sub.1). A second segment edge 24e extends from the point (x.sub.3,y.sub.0) to the point (x.sub.4,y.sub.1), where x.sub.4≥x.sub.3. It follows that each point on the surface of the workpiece 3 faces at most two electrode segments 23a-e.

[0113] Counting the segments 23a-e from the proximal electrode edge 22, a width of the segments 23a-e, corresponding to a distance between the segment edges 24a-h at the common value y.sub.0 of the y-co-ordinate, increases from segment to segment in the x-direction. The segments 23a-e become progressively wider, reflecting the fact that the voltage at the surface of the workpiece 3 changes most steeply in the x-direction at the proximal electrode edge 22 when the workpiece 3 is only contacted at that edge 22.

[0114] The segment edges 24a-e also become progressively more curved in the x-direction. In other words, an angle to the first electrode edge 25 of the paths of a pair of segment edges 24a-h between a pair of adjacent segments 23a-e at the first electrode edge 25 increases from pair to pair in the x-direction (the paths of the segment edges 24a-h forming such a pair are essentially identical in shape). This holds true mutatis mutandis for the angle to the second electrode edge 26.

[0115] The shielding plate 19 is provided with a multitude of essentially regularly distributed through-going channels, with some adjacent channels being interconnected to form a single channel with a larger cross-sectional area and channels being omitted at certain locations (cf. FIG. 6).

[0116] From the top view of FIG. 4, it will be appreciated that the anode 16 is provided with electrical contacts 30a-f extending to the lower layer 18 to contact the segments 23a-e. The electrical contacts 30a-f are provided at respective locations having a respective x-co-ordinate. An integral of the channel areas in a strip of the shielding plate 19 extending in the second direction y at a corresponding x-co-ordinate is lower than the integral of the channel areas in adjacent parallel strips of the same width. This width will generally be approximately the width of the electrical contact 30a-f. Thus, the tendency of current to flow directly to the location of the electrical contact 30a-f is countered.

[0117] In a similar manner, the shielding plate 19 is fixed by at least one fastener 31a-g (only some are shown in FIG. 5 for clarity reasons) extending in a direction transverse to the shielding plate 19 and located at an associated position having a respective x-co-ordinate. The fastener 31 has a cross-section with a certain width at a surface of the shielding plate 19 distal to the anode 16. An integral of the cross-sectional areas of the channels in sections of a strip of the shielding plate 19 with the certain width an extending in the second direction y at the x-co-ordinate is higher than in adjacent sections of adjacent parallel strips of the same width. In other words, the permeability is increased in the strip sections on either side of where the fastener 31 attaches to the shielding plate 19 to compensate for the fact that the fastener 31 behaves as a non-conductive element, despite being made of electrically conducting material.

[0118] The shielding plate 19 is also configured to compensate for edge effects.

[0119] A proximal shielding plate edge 32 (FIG. 5) proximal in the first direction x to the clamp 7, in use, has an irregular shape. This is to increase an integral of the liquid-pervious area in a strip of the plate extending in the second direction y along that proximal shielding plate edge 32 relative to the corresponding integral in an adjacent parallel strip of the same width. Otherwise, there would be a decrease in current density along the edge of the workpiece 3. The decrease is in principle not a problem, but a local decrease gives rise to an increase in an adjacent strip of the workpiece 3. This is avoided by the increase in permeability at the proximal shielding plate edge 32. Because the channels are of the same size and distributed regularly (with the same pitch), the result is an irregular proximal shielding plate edge 32.

[0120] A distal shielding plate edge 33 is configured to counter a steep decrease in current density, in particular if the workpiece 3 has a smaller extent in the first direction x than the anode 16 and the shielding plate 19. An integral of a liquid-pervious area of the channels in a strip of the shielding plate 19 extending in the second direction y along the distal shielding plate edge 33 is lower than in an adjacent parallel strip of the same width. This helps avoid the formation of a rib of plating material along the corresponding distal edge 9 of the workpiece 3.

[0121] In a method of obtaining the anode 16, the separation between adjacent segments 23a-e is neglected, as illustrated in FIGS. 9 and 10. Each segment edge 24a-h is a second-order polynomial. Seen in the first direction x, a point at the first electrode edge 25 of each segment edge 24a-h but the last is at the same co-ordinate value x as the point at the common value y.sub.0 of the next segment edge 24a-h. The number of segments 23a-e and the dimensions of the anode 16 are also fixed. Within these constraints, it remains to find the coefficients of the second-order polynomials defining the segment edges 24a-h, as well as the potential difference Uc.sub.i with respect to the clamp, where i indicates the number of the segment 23a-e, counting from the proximal segment 23a in the first direction x.

[0122] The potential difference across the bath at the centre of the i.sup.th segment, seen in the first direction x, is Umb.sub.i. The voltage difference between the corresponding position in the surface layer on the workpiece 3 and the clamp position is Um.sub.i, where the clamp is assumed to be at the origin, i.e. x=0. Referring to FIG. 9, the following equations obtain:

[00001]$\begin{array}{cc}\mathrm{Umb}=\mathrm{Uc}-\mathrm{Um},& \left(1\right)\end{array}$$\begin{array}{cc}\mathrm{Um}=\frac{\alpha /3\left(x_{i+1}^3-x_i^3\right)+b/2\left(x_{i+1}^2-x_i^2\right)+c\left(x_{i+1}-x_i\right)}{x_{i+1}-x_i}.& \left(2\right)\end{array}$

[0123] The dashed graph (FIG. 9) shows the voltage target distribution. Note that Um is simply the average voltage in a segment of the surface layer on the workpiece 3 opposite a particular one of the segments 23a-e. The voltage drop-off in the surface layer is a second-order polynomial.

[0124] In a first step 34 (FIG. 7) of the design process, the design parameters are obtained. These include the thickness of the layer of electrically conducting material on the workpiece 3, the dimensions of the workpiece 3 in the first direction x and the second direction y, the resistivity of the electrolyte, a distance between the surface of the workpiece 3 and a surface of the anode 16 and the resistivity of the conducting material on the workpiece 3. A further requirement is a nominal current density average, the average being over an area of the anode 16. From this result target current density averages for each segment 23a-e, according to a formula:

CDA[i]=m.Math.i.sup.p+n  (3),

where i is the segment number, p is an empirically determined fixed value and the values for m and n follow by taking the nominal current density average value for the final segment (e.g. i=5 in the illustrated embodiment) and a particular value for the first segment (i=1), which is determined through trial and error. This process is illustrated in FIGS. 11 and 12. FIG. 11 shows the result of taking too large a value for the current density average in the first segment CDA[1]. FIG. 12 shows the result of adjusting this value down to an appropriate value. The values of the current density average for all the other segments 23a-e are obtained using equation (3).

[0125] In a next step 35, the shapes of the paths of the segment edges are determined.

[0126] As illustrated in FIG. 8, this step 35 involves an initialisation (step 36) and calculation (step 37) of the target current density average for each segment 23a-e, according to equation (3).

[0127] Thereafter follow a series of iterations of steps.

[0128] First (step 38), the current density average is calculated for each segment 23a-e. This involves dividing the first half 28 into narrow strips extending from the proximal electrode edge 22 to the opposite edge in the first direction x, each strip having a relatively small dimension in the second direction y. With the voltage drop-off function and the values of the segment voltages Uc.sub.i, the current contributions for each segment 23a-e can be calculated for that narrow strip. The contributions of all the narrow strips are then summed to find the current for each segment 23a-e, which is divided by the area of that segment. The resulting values are compared with the target values and the values Uc.sub.i are adjusted to decrease the deviations (step 39). The calculation (steps 39,38) is repeated to bring the current density averages for the segments 23a-e closer to the target values or until another stop criterion (e.g. a certain number of iterations) is met.

[0129] Next (step 40), the segment edges 24a-h are adjusted.

[0130] FIG. 10 shows the first half 28 of the anode 16. The dashed lines correspond to paths that a point on the workpiece 3 faces as the workpiece 3 is moved in the second direction y. In an electroplating process, the amount of metal deposited is proportional to the electric charge Q. The electrical charge Q is defined by the electrical current I multiplied by the time t:

Q=I.Math.t  (3).

[0131] It is assumed that a velocity v of the workpiece 3 is constant:

v=L/t,  (4)

where L is the dimension of the first half 28 of the anode 16 in the second direction y. At each position in the first direction x, the time t is the same, so that the charge is the product of the current I and the length L for each point on the workpiece 3 that moves past only one segment 23a-e.

[0132] To achieve an equal metal deposition for each location x[i] in the first direction x, the collected electrical charge Q must be the same. This leads to the following constraints:

L.sub.S5,x[i].Math.I.sub.S5,x[i]+L.sub.S4,x[i].Math.I.sub.S4,x[i]=Q[i].Math.v,

L.sub.S5,x[i+1].Math.I.sub.S5,x[i+1]+L.sub.S4,x[i+1].Math.I.sub.S4,x[i+1]=Q[i+1].Math.v,

L.sub.S5,x[i+2].Math.I.sub.S5,x[i+2]+L.sub.S4,x[i+2].Math.I.sub.S4,x[i+2]=Q[i+2].Math.v,

where v and Q are constants.

[0133] The anode segments 23a-e are divided into narrow strips of equal size extending in the y-direction. Each strip extends through two neighbouring segments 23a-e. Because the segments 23a-e are at different voltages, the local currents that enter the workpiece 3 are also different. The currents along the strips are summed, reflecting the fact that the workpiece 3 passes in front of the entire anode 16.

[0134] The conducting layer on the workpiece 3 is modelled as a one-dimensional chain of resistances, each having a length in the x-direction corresponding to the distance between one strip to the next. This allows one to model the currents as entering at the nodes of the chain of resistances. From this results a voltage drop-off allowing to calculate a new voltage drop-off function. This function is a second-order polynomial, as mentioned. The coefficients of the polynomial determine the shapes of the segment edges 24a-h, which are corresponding second-order polynomials. With the new shapes of the segment edges 24a-h obtained in the second step 40, the method returns to the calculation of the segment voltages Uc.sub.i.

[0135] The iterations are repeated until a break-off criterion is satisfied (e.g. a fixed number of iterations, a particular maximum deviation of the current density averages from the target values, or the like). The break-off criterion in one particular embodiment is that the respective current contributions of the strips defined in the step 40 of adjusting the segment edges 24a-h are equal (or differ by less than a pre-determined maximum allowable deviation).

[0136] In an optional further step 41 (FIG. 7), the current density is calculated by means of simulation across the surface of the workpiece 3. The permeability of the shielding plate 19 is then (optional step 42) locally adjusted such as to reduce the deviations of the current density from an average value. This takes account of the separation between adjacent segments 23a-e neglected in the calculation of the shape of the segment edges 24a-h. The two steps 41,42 are carried out iteratively to arrive at an optimal aperture distribution for the shielding plate 19.

[0137] Finally (step 43), the anodes 16 are manufactured to the design.

[0138] A simulation of an anode 16 designed in such a process shows that the deviations from the average current density remain within 5% across the extent of the workpiece 3 in the first direction x (FIG. 13), except for small strips at the edges 8,9.

[0139] The invention is not limited to the embodiments discussed above, which may be varied within the scope of the accompanying claims. An improvement in the uniformity of the current density is, for example, also achieved without the shielding plate 19 discussed above.

TABLE-US-00001 List of reference numerals  1 apparatus  2a-d cells  3a-f workpieces  4 enclosure  5a-c rollers  6 conveying system  7 clamp  8a-f proximal workpiece edges  9a-d distal workpiece edges 10 belt 11a, b drums 12 arm 13 core part 14 core part shielding 15 core part surface section 16 anode 17 upper layer 18 lower layer 19 shielding plate 20 clamp anode 21 clamp anode surface 22 proximal electrode edge 23a-e segments 24a-h segment edges 25 first electrode edge 26 second electrode edge 27 line of symmetry 28 first half 29 second half 30a-f electrical contacts 31a-g fasteners 32 proximal shielding plate edge 33 distal shielding plate edge 34 step (obtain design parameters) 35 step (determine path shapes) 36 step (initialisation) 37 step (calculate target current density average for each segment) 38 step (determine actual current density average values for each segment) 39 step (adjust segment voltages) 40 step (determine new segment edge shapes) 41 step (perform simulation) 42 step (optimise shielding plate) 43 step (manufacture anode to design)