Method of coating substrates

Abstract

The disclosure relates to a method of determining a velocity profile for the movement of a substrate to be coated relative to a coating source.

Claims

1. A method of determining a velocity profile for the movement of a substrate to be coated relative to a coating source during a coating operation of the substrate in order to achieve a defined target layer thickness profile, wherein the method comprises the steps of: (a) describing a deposition rate, wherein the deposition rate is the rate at which the coating is applied to the substrate, and wherein the deposition rate is described by an approximation function comprising a product of at least two functions depending on the substrate coordinates and depending on the position of the substrate relative to the coating source, wherein the product of at least two functions comprises several parameters; (b) describing the velocity profile to be determined by an approximation function comprising one or more parameters; (c) coating the substrate using a defined velocity profile, wherein the substrate to be coated is moved during the coating operation relative to the coating source in a straight line along a first direction using this velocity profile; (d) measuring the actual layer thickness profile of the coated substrate achieved by the coating operation; (e) determining one or more of the parameters of the approximation function for the deposition rate on the basis of a comparison of the measured actual layer thickness profile with the defined target layer thickness profile; and (f) determining the velocity profile by determining one or more of the parameters of the approximation function for the velocity profile to be determined on the basis of the parameter(s) determined in step (e).

2. The method according to claim 1, wherein the coating operation is carried out by the coating source in a coating range, wherein the coating range has a first extension in the first direction, and wherein the first extension is at least 100 mm.

3. The method according to claim 1, wherein the defined target layer thickness profile is a constant layer thickness, and wherein the coating operation is carried out by the coating source in a coating range, wherein the coating range has a first extension in the first direction, and the substrate has a second extension in the first direction of movement, and wherein the ratio of the first extension to the second extension is at least 0.2.

4. The method according to claim 1, wherein the defined target layer thickness profile is a variable layer thickness, wherein the coating operation is carried out by the coating source in a coating range, wherein the coating range has a first extension in the first direction, and wherein the defined target layer thickness profile has a profile length along this first direction of movement, and wherein the ratio of the first extension to the profile length is at least 0.2.

5. The method according to claim 1, wherein, as one factor, the product contains a function which accounts for the geometry and depends on the coating source coordinates and is independent of the position of the substrate relative to the coating source, and wherein, as a further factor, the product contains a function which accounts for the movement of the substrate and depends on the position of the substrate relative to the coating source and is independent of the coating source coordinates.

6. The method according to claim 1, wherein the at least two functions are each described by an approximation function comprising one or more parameters.

7. The method according to claim 1, wherein steps (a) to (f) are repeated, wherein the parameters of the previous run determined in step (e) are used in step (a) of the subsequent run, and the defined velocity profile in step (c) of the subsequent run corresponds to the velocity profile determined in step (f) of the previous run.

8. The method according to claim 7, wherein steps (a) to (f) are repeated until the deviation between the measured actual layer thickness profile of the coated substrate and the defined target layer thickness profile is less than 1.0%.

9. A method of coating a substrate comprising the steps of: (a) determining a velocity profile for the movement of the substrate to be coated relative to a coating source in order to achieve a defined target layer thickness profile according to any one of the preceding claims; and (b) coating the substrate using the previously determined velocity profile, wherein the substrate to be coated is moved during the coating operation relative to the coating source in a straight line along a first direction using this velocity profile.

10. The method according to claim 9, wherein the defined target layer thickness profile is a constant layer thickness, and wherein the determined velocity profile is not constant.

11. The method according to claim 9, wherein the deposition rate of the coating source depends on the position of the substrate relative to the coating source, and wherein the determined velocity profile is configured such that a variation in the deposition rate of the coating source is at least partially compensated for by a variation in the velocity of the substrate.

12. The method according to claim 9, wherein a layer thickness non-uniformity generated by the dependence of the deposition rate of the coating source on the position of the substrate relative to the coating source is at least partially compensated for by the predetermined velocity profile.

13. A device for coating a substrate comprising: a coating source; a substrate support adapted to move the substrate to be coated relative to the coating source in a straight line along a first direction during a coating operation; and a control unit adapted and configured to vary the velocity of the substrate along the first direction during the coating operation according to a predetermined velocity profile depending on the position of the substrate in order to obtain a coating having a target layer thickness profile defined along the first direction, wherein the control unit is adapted and configured to determine the predetermined velocity profile according to a method which comprises the steps of: (a) describing a deposition rate, wherein the deposition rate is the rate at which the coating is applied to the substrate, and wherein the deposition rate is described by an approximation function comprising a product of at least two functions depending on the substrate coordinates and depending on the position of the substrate relative to the coating source, wherein the product of at least two functions comprises several parameters; (b) describing the velocity profile to be determined by an approximation function comprising one or more parameters; (c) coating the substrate using a defined velocity profile, wherein the substrate to be coated is moved during the coating operation relative to the coating source in a straight line along a first direction using this velocity profile; (d) measuring the actual layer thickness profile of the coated substrate achieved by the coating operation; (e) determining one or more of the parameters of the approximation function for the deposition rate on the basis of a comparison of the measured actual layer thickness profile with the defined target layer thickness profile; and (f) determining the velocity profile by determining one or more of the parameters of the approximation function for the velocity profile to be determined on the basis of the parameter(s) determined in step (e).

14. The device according to claim 13, wherein the coating operation is carried out by the coating source in a coating range, wherein the coating range has a first extension in the first direction, and wherein the first extension is at least 200 mm.

15. The device according to claim 13, wherein the coating operation is carried out by the coating source in a coating range, wherein the coating range has a first extension in the first direction, wherein the first extension is at least 300 mm.

16. The device according to claim 14, wherein the defined target layer thickness profile is a constant layer thickness, and wherein the coating operation is carried out by the coating source in a coating range, wherein the coating range has a first extension in the first direction, and the substrate has a second extension in the first direction, and wherein the ratio of the first extension to the second extension is at least 0.3.

17. The device according to claim 16, wherein the defined target layer thickness profile is a constant layer thickness, wherein the ratio of the first extension to the second extension is at least 0.5.

18. The device according to claim 17, wherein the ratio of the first extension to the second extension is at least 1.0.

19. The method according to claim 1, wherein the coating operation is carried out by the coating source in a coating range, wherein the coating range has a first extension in the first direction, and wherein the first extension is at least 50 mm.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Preferred embodiments of the present disclosure are described in more detail below with reference to the Figures, wherein:

(2) FIG. 1a schematically shows the geometry of an LDD coating operation in a cross-sectional view for the case of a magnetron sputtering cathode;

(3) FIG. 1b schematically shows the geometry of the LDD coating operation according to FIG. 1a in a perspective view;

(4) FIG. 2 schematically shows the movement of the substrate through the coating range during an LDD coating operation as well as the associated velocity profile;

(5) FIG. 3 shows the coordinate systems used in the context of the present disclosure;

(6) FIG. 4a schematically shows the relevant proportions during an LDD coating operation;

(7) FIG. 4b schematically shows the relevant proportions during an LDD coating operation;

(8) FIG. 4c schematically shows the relevant proportions during an LDD coating operation;

(9) FIG. 4d schematically shows the relevant proportions during an LDD coating operation;

(10) FIG. 4e schematically shows the relevant proportions during an LDD coating operation;

(11) FIG. 5a schematically shows an LDD coating operation according to the prior art;

(12) FIG. 5b schematically shows an LDD coating operation according to the prior art;

(13) FIG. 5c schematically shows an LDD coating operation according to the prior art;

(14) FIG. 6a shows a contour plot of R(x_m; x_k) from a simulation calculation;

(15) FIG. 6b shows values of R(x_m; x_k) for various x_m from a simulation calculation;

(16) FIG. 7a shows measured layer thicknesses for different velocity profiles; and

(17) FIG. 7b shows the velocity profiles belonging to FIG. 7a.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

(18) FIG. 1 schematically shows the geometry of a conventional LDD coating method both in a cross-sectional view (FIG. 1a) and in a perspective view (FIG. 1b), in which a substrate 1 is moved relative to a sputtering cathode 2 comprising a magnet array 3 and a sputtering target 4. The linear movement of the substrate 1 along a first direction relative to the sputtering cathode is indicated by the arrow 5 on the substrate 1. In this Figure, the sputtering cathode 2 is a long cathode whose long axis is perpendicular to the direction of movement of the substrate 1. The reference sign B (cf. FIG. 1a) indicates the coating range and the reference sign U (cf. FIG. 1a) indicates the vicinity of the cathode (e.g. shielding plates).

(19) FIG. 2 schematically shows the movement of the substrate 1 through the coating range B, wherein, prior to the coating operation, the substrate 1a moves through the coating range B in a straight line along the arrow, and, after the coating operation has been performed, is provided with the reference sign 1b. The static deposition rate is schematically indicated by the curve 6. At the bottom of FIG. 2, the velocity profile 7 of the substrate is shown with respect to the sputtering cathode, wherein in the present case the velocity profile 7 has an area with a constant velocity corresponding to that part of the profile in which a coating operation takes place.

(20) In the following, a particularly preferred embodiment for an algorithm for determining the velocity profile 7 will be explained in detail. Even if the following embodiment is directed to the special case of the LDD coating method using a sputtering cathode, this algorithm can analogously be applied for other coating sources and in particular PVD sources.

(21) Since, as explained above, a certain degree of layer thickness uniformity can already be achieved with the LDD method even without the method described herein, a rate distribution of the following form is assumed hereinafter to simplify matters:
R(x.sub.k;x.sub.m)=R.sub.g(x.sub.k)*P.sub.ν(x.sub.m)  (3)

(22) R.sub.g(x.sub.k) is the rate distribution unaffected by the movement of the substrate as a function of the position under the cathode x.sub.k. P.sub.ν(x.sub.m) describes the effect of the substrate movement on the total distribution and has a value in the order of 1, since this effect is not large. This also justifies the approach according to equation (3). Thus, equation (la) and equation (1b) respectively result in

(23) $\begin{array}{cc}d\left(x_s^{\prime }\right)={\int }_{-k-x_s^{\prime }}^{k-x_s^{\prime }}\frac{R_g\left(x_s^{\prime }+x_m\right)*P_v\left(x_m\right)}{v\left(x_m\right)}d{x}_m\mathrm{and}& \left(1c\right)\\ d\left(x_s^{\prime }\right)={\int }_{-k}^k\frac{R_g\left(x^{*}\right)*P_v\left(x^{*}-x_s^{\prime }\right)}{v\left(x^{*}-x_s^{\prime }\right)}d{x}^{*}& \left(1d\right)\end{array}$

(24) In the case of ν(x*−x′.sub.s)=ν.sub.0, equation (1d) likewise results in relation (2). An improvement of the layer thickness uniformity to a deviation of below 0.5% and in particular of significantly below 0.5% is extremely difficult due to the effects discussed at the beginning, in particular when the coating range between ±k is an extended range, which is always the case in practice. However, various applications of the LDD coating method—some of which have already been mentioned at the beginning—require deviations from the target layer thickness of down to less than 0.1% on large substrates.

(25) From relation (1c), as will be shown in the following, a method of determining the course of the velocity ν(x.sub.m) can be derived by means of which predetermined profiles of the layer thickness d(x.sub.s) can be achieved with minimum effort. In particular, (even extremely small) deviations from a target layer thickness can be compensated for and thus extremely good layer thickness uniformity can be achieved. It is essential—and this is one of the advantages of the present disclosure—that the method can be applied to the case which is always existing in practice, i.e., the case in which the extension of the coating range from −k to +k is approximately of the same order of magnitude as the extension of the substrate from −w to +w. Previously known methods similar to LDD technology, in which a layer thickness adjustment is to be achieved by varying the substrate velocity, are always based on a coating range that is very small compared to the substrate (k<<w)—usually without explicitly mentioning this.

(26) In DE 10 2006 036 403 A1, for example, a heuristic relation is described which takes account of the self-evident relation d˜1/ν (see above). This relation can be in principle derived as a special case of the method presented herein from equation (la) for an infinitely small coating range k.fwdarw.0
d.sub.i(x′.sub.s)=2*k*R(0;−x′.sub.s)/ν.sub.i(−x′.sub.s),  (4a)
wherein the index I already takes into account the i-th step of the iteration for the optimization of the layer thickness as described in DE 10 2006 036 403 A1. With d.sub.i(x′.sub.s)*ν.sub.i(−x′.sub.s)=2*k*R(0, −x′.sub.s) the next iteration step i+1 results in
ν.sub.i+1(x′.sub.s)=ν.sub.i(x′.sub.s)*d.sub.i(−x′.sub.s)/d0  (4b)
This is essentially the relation indicated in DE 10 2006 036 403 A1. d.sub.i+1(−x′.sub.s) was replaced by the target layer thickness d0 of the iteration. The algebraic signs are due to the given geometry, in which the velocity of the entire substrate always refers to the center of the substrate. As noted in DE 10 2006 036 403 A1, this calculation method is for extended coating sources only an approximation, without defining the numerical limits of this approximation. The analysis of the geometric conditions immediately shows the problem, see FIG. 5: For an approximation according to equation (4b) to be carried out, the substrate point would have to be located in the very small coating range which is the prerequisite for the derivation of equation (4b) (see also FIG. 4b). In the case of the extended coating range addressed herein, this situation is not existent. For the calculation according to equation (4b), for example, the substrate point would have to be directly below the cathode center. In the case of this extended coating range, however, the substrate will be already coated when the front edge of the extended substrate is not yet below the cathode center (cf. FIG. 5a, reference arrow pointing downwards). Thus, it is not possible to determine a velocity according to equation (4b) in this situation. This is only possible when the substrate continues to move, namely as long as a point of the substrate moves below the cathode center (cf. FIG. 5b). After the rear edge of the substrate has left the cathode center (see FIG. 5c), the substrate velocity cannot be determined again. This analysis shows that even an approximate determination of ν by means of the iteration according to equation (4b) or according to DE 10 2006 036 403 A1 is not possible for the practically always existing case of an extended coating range and extended substrates.

(27) According to the disclosure, this problem is taken into account by the fact that the unknown functions R(x*; x*−x′.sub.s) or R.sub.g(x.sub.k) and P.sub.ν(x.sub.m) can be approximately described by “simple” functions. The course of this “simple” function is determined by parameters which can be determined, if necessary also iteratively, by measuring the layer thickness of already coated substrates using standard methods. Using these “simple” functions and the parameters determined from the measured values, the velocity profile ν(x.sub.m) can also be determined by approximation using the equations indicated above.

(28) In the following, the derivation and description of the algorithm for obtaining an optimized velocity profile according to a preferred embodiment of the disclosure will be explained in detail. This algorithm is unrestrictedly applicable to the case important in the praxis of the LDD technology in which the coating range defined by ±k is not significantly smaller than the substrate size or the envisaged structures of the desired layer thickness profile in the direction of travel. In the coating range, the deposition rate is described by the function R(x.sub.k, x.sub.m) or R.sub.g(x.sub.k)*P.sub.ν(x.sub.m). Basically, it would be possible to measure R(x.sub.k, x.sub.m) by placing test substrates fixedly (without movement) statically under the cathode at different positions x.sub.m and after the deposition—by measuring the respective layer thickness profiles resulting at a sufficient number of measuring points x.sub.k (i.e., in the direction of travel). However, this approach is very complex. Experience with coating by, e.g., cathode sputtering shows namely that static coating profiles depend to a greater or lesser extent on the parameters determining the coating operation, such as, i.e., cathode power, gas pressure, target age. This approach would also be prone to errors, since the coating profile sought can also depend on the movement itself. Thus, in practice, it must be assumed that R(x.sub.k; x.sub.m) or the two functions R.sub.g(x.sub.k) and P.sub.ν(x.sub.m) are not known.

(29) In a first preferred embodiment, the method according to the disclosure consists in that the function R(x.sub.k; x.sub.m) is approximately described by a polynomial:
R(x.sub.k;x.sub.m)≈Σ.sub.i,jR.sub.ij*x.sub.k.sup.i*x.sub.m.sup.j  (5a)

(30) and the parameters or constants R.sub.ij are determined on the basis of measured values. However, the method will be explained in the following by means of a further implementation in which the functions R.sub.g(x.sub.k) and P.sub.ν(x.sub.m) as well as subsequently ν(x.sub.m) are approximately described by polynomials:

(31) $\begin{array}{cc}{R}_g\left(x_k\right)\approx R_g^{\Sigma }\left(x_k\right)=\underset{i=0}{\overset{iz}{.Math.}}{R}_i*x_k^i& \left(5b\right)\\ P_v\left(x_m\right)\approx P_v^{\Sigma }\left(x_m\right)=1+\underset{j=1}{\overset{jz}{.Math.}}{P}_j*x_m^j& \left(5c\right)\\ v\left(x_m\right)\approx v^{\Sigma }\left(x_m\right)=\underset{l=0}{\overset{lz}{.Math.}}{v}_l*x_m^l& \left(5d\right)\end{array}$

(32) and by respectively inserting these polynomials into equation (1c) instead of the original functions. The numbers iz, jz and lz have to be set appropriately. On the assumption that the parameters or constants R.sub.i, P.sub.j and ν.sub.l are known, the integral in equation (1c) can be calculated, e.g., by numerical methods. Programming can be carried out, for example, by means of the EXCEL spreadsheet program.

(33) The step-by-step determination of the sought constants ν.sub.l is first described in the following for the case that deviations from an (average) target layer thickness d.sub.z caused by the movement of the substrate are to be minimized.

(34) Step 1: To this end, a coating operation is carried out and during this coating operation the substrate is moved through the coating range at a constant velocity ν.sub.0. The velocity ν.sub.0 is set such that the average layer thickness d.sub.m corresponds to the envisaged target layer thickness.

(35) Step 2: The layer thickness d.sub.m(x.sub.s,h) on the substrate (the superscript “m” stands for measurement) is then measured at measuring points x.sub.s,h using a suitable method.

(36) Step 3: At each of these points, the integral in equation (1d) is then numerically calculated using the polynomials R.sub.g.sup.Σ(x.sub.k), P.sub.ν.sup.Σ(x.sub.m) and for a constant velocity (ν.sup.Σ(x.sub.m)=ν.sub.0), and the “approximate” layer thicknesses d.sup.s(x.sub.s,h) are determined therewith. First, iz=0 is set for this calculation, i.e., R.sub.g=R.sub.0 is constant. This restriction is based on equation (2), which shows that at a constant substrate velocity ν.sub.0 a position dependence of R.sub.g does not entail a position dependence of the layer thickness. The parameters P.sub.j are arbitrarily set in this step, e.g., P.sub.j=0, j=1 . . . 6, i.e., jz=6 Due to the fact that arbitrary constants are used in the polynomials R.sub.g.sup.Σ(x.sub.k) and P.sub.ν.sup.Σ(x.sub.m), of course, these polynomials do not describe the unknown functions R.sub.g(x.sub.k) and P.sub.ν(x) in any way.

(37) Step 4: Subsequently, the parameters R.sub.0 and P.sub.j, j=1 . . . 6 are determined by variation so that the sum of the deviation squares

(38) $\begin{array}{cc}{\chi }^2=\underset{h=0}{\overset{m}{.Math.}}{\left[d^m\left(x_{s,h}\right)-d^s\left(x_{s,h}\right)\right]}^2.fwdarw.\mathrm{MIN}!& \left(6a\right)\end{array}$
becomes minimal. Established iterative numerical methods can be used for the minimalization, such as, e.g., the simplex method. The calculation of all values of d.sup.s(x.sub.s,h) according to equation (1d) has to be carried out for each set of parameters until the minimum according to equation (6a) is reached. As a result of this minimalization, in particular the course of P.sub.ν(x.sub.m) is approximately available due to the now found values of R.sub.0 and P.sub.j, j=1 . . . 6. The information for this approximation was obtained from the measured values d.sup.m(x.sub.s,h).

(39) Step 5: Using these parameters now set, the velocity coefficients ν.sub.l, l=0 . . . 6, i.e., lz=6, are determined, again by minimalization as described in detail in step 4, according to

(40) $\begin{array}{cc}{\chi }^2=\underset{h=0}{\overset{m}{.Math.}}{\left[d_Z-d^s\left(x_{s,h}\right)\right]}^2.fwdarw.\mathrm{MIN}!& \left(6b\right)\end{array}$

(41) Thus, the course of the velocity ν(x.sub.m)≈ν.sup.Σ(x.sub.m) according to equation (5d) has been approximately found.

(42) A new coating operation using the course of the velocity ν.sup.Σ(x.sub.m) shows that a clear improvement of the layer thickness uniformity is achieved already after this first optimization cycle, see FIG. 7a. If further optimization is required, steps 1 to 5 can be repeated. The values for R.sub.0 and P.sub.j, j=1 . . . 6 as already known from the first pass as well as the velocity profile ν.sup.Σ(x.sub.m) with the parameters ν.sub.l, l=0 . . . 6 as already obtained are then the starting point for this next run. Since now the velocity of the substrate is no longer constant and thus the prerequisite of a constant substrate velocity is no longer true (see equation (2)), the parameters R.sub.i, i=1 . . . 6 can now also be included in the minimalization operation, see FIG. 7a.

(43) The determination of the constants ν.sub.l for the case that a predetermined layer thickness profile in the direction of travel of the substrate is to be generated by the coating operation by means of a variable velocity is performed in a way analogous to that for the constant layer thickness by executing steps 1 to 5. However, the minimalization for determining the velocity coefficients must now be carried out by means of

(44) $\begin{array}{cc}{\chi }^2=\underset{h=0}{\overset{m}{.Math.}}{\left[d_p\left(x_{s,h}\right)-d^s\left(x_{s,h}\right)\right]}^2& \left(6c\right)\end{array}$
instead of equation (6b). d.sub.p(x.sub.s,h) is the layer thickness at the measuring points x.sub.s,h as they result from the predetermined layer thickness profile.

(45) For the approximate determination of R(x.sub.k; x.sub.m) or the two functions R.sub.g(x.sub.k) and P.sub.ν(x.sub.m) as well as of ν(x.sub.m), other suitable functions can also be used. In the linear case according to equations (5b) to (5d), for example, a cubic splines algorithm is an appropriate option, in which both the nodes and the constants of the cubic segments can be used for a fit according to equation (6b) and equation (6c). In each case, criteria for the selection of approximation functions will be that a good description of the unknown original functions can be achieved with as few parameters as possible.

(46) FIGS. 4a to 4e schematically illustrate the proportions of some dimensions or lengths characteristic of, for example, the LDD coating operation in various exemplary situations. The reference signs 1 and 2 (according to FIG. 1) denote the substrate and the sputtering cathode, respectively. The reference sign 6 indicates the static deposition rate distribution, which depends, i.e., on the cathode width. Since the proportions are discussed herein using the example of the LDD coating operation, all sizes refer to the direction of movement of the substrate 1 relative to the cathode 2. The reference sign B denotes the extension of the coating range along the direction of movement (cf. also FIG. 1a). The same applies to the dimension D of the substrate 1.

(47) FIG. 4a shows the case of an ideal “line source”, which can only be implemented by special slit diaphragms (reference sign 9) directly above the substrate. In this case, the relation B<<D holds. The reference sign 8 denotes the layer or the layer thickness profile. In such an arrangement, a large part of the material flow from the target to the substrate is “screened out”. This leads to an extremely low deposition rate in combination with a large loss of material due to the slit diaphragms. Therefore, this arrangement is hardly used in practice. As explained above, this case is included as a special case in the presented technique.

(48) In FIGS. 4b, 4c a typical deposition rate 6 (e.g., similar to a Gaussian distribution) is shown. FIG. 4b shows the case of a constant target layer thickness 8, in which a maximum degree of layer thickness uniformity is aimed at. FIG. 4c shows the case in which a linear increase 8 (greatly exaggerated in the Figure for the sake of illustration) of the layer thickness over the entire substrate width is to be produced with a deviation of the layer thickness from this linear profile as small as possible. In both cases, the relation B≈D holds.

(49) FIGS. 4d to 4e exemplarily show alternative layer thickness target profiles 8 (greatly exaggerated in the Figures for the sake of illustration). These profiles are typically characterized by a characteristic length S which is smaller than the dimension D of the substrate 1. In the case of FIG. 4d, this characteristic length S is smaller than the coating range B, but still in the same order of magnitude. The layer thickness target profile 8 of FIG. 4e, on the other hand, has a sharp edge or step for which the characteristic length S of the layer thickness target profile approaches zero: S.fwdarw.0.

(50) As is readily apparent from FIG. 4e, a precise step profile with a perfectly sharp edge cannot be achieved with a cathode that has an extended coating range, i.e., if B>>S. The coating operation with an extended coating range would lead to a “softening” of the step in the deposited profile. Such profiles can only be generated with the aid of an (ideal) line source with B.fwdarw.0 (see FIG. 4a). However, the present disclosure enables the layer thicknesses of profiles with correspondingly large characteristic lengths to be manufactured efficiently with maximum precision, even with large coating ranges, i.e., B≈D.

(51) The fact that this is not possible using conventional methods, such as those described, for example, in DE 10 2006 036 403 A1, is illustrated once again in FIGS. 5a to 5c, which show that a velocity profile ν(x.sub.m) cannot be determined, not even approximately, with a simple method applicable only for ideal line sources according to FIG. 4a. In the case of an extended substrate area, the substrate is already coated here when the front edge of the extended substrate is not yet below the cathode center (cf. FIG. 5a). Thus, the determination of the velocity on the basis of a different layer thickness below the arrow (reference sign 10) is not possible. FIGS. 5b and 5c show the passage of the substrate 1 through the extended coating range B.

(52) FIGS. 6 and 7 exemplarily show the results of an optimization according to the disclosure for the case of a constant target layer thickness, with the values k=70 mm (i.e., with a coating range having a width of 140 mm, cf. FIG. 2) and w=50 mm (i.e., a substrate extension of 100 mm, cf. FIG. 3). The “measured value” d.sup.m(x.sub.s,h) were auxiliary calculated using a simulation function R(x.sub.k; x.sub.m). The dependence of this simulation function is based on calculation methods for the deposition rate of longitudinal cathodes (see, e.g., “Schichtdickengleichmäβigkeit” von aufgestäubten Schichten—Vergleich zwischen Berechnungen und praktischen “Ergebnisse” (Layer Thickness Uniformity of Sputtered Layers—Comparison between Calculations and Practical Results), G. Deppisch, Vakuumtechnik 30 (1981) 106). The initial function thus determined for the “measure” layer thickness for a constant, non-optimized velocity profile is shown in FIG. 7a (diamond-shaped symbols).

(53) FIG. 6a shows the “contour plot” of the thus determined values of R(x.sub.k; x.sub.m). In order to illustrate the good functioning of the method according to the disclosure, the effect of the substrate movement, i.e., the dependence R on x.sub.m is greatly exaggerated. In the case of this simulation, the minimum values of R are approximately 50 (arbitrary units) and the maximum values are 130. In LDD practice, such a great change in the rate R due to the substrate movement is normally not observed. In addition to FIG. 6a, FIG. 6b shows the course of R(x.sub.k; x.sub.m) for different values x.sub.m. FIG. 7a shows the “measure” layer thickness as a result of optimization in the order without optimization, after first optimization and after second optimization. Despite the great exaggeration of the dependence of the rate R on x.sub.m, a degree of layer thickness uniformity of 0.21% is achieved already after the second optimization step. FIG. 7b shows the velocity profiles corresponding to FIG. 7a.