CONTROLLED DEPOSITION OF A FUNCTIONAL MATERIAL ONTO A TARGET SURFACE

Abstract

A plate including functional material to be deposited onto a target surface using monochromatic radiation having a wavelength is described. The plate further includes a substrate with a first surface directed towards the target surface and with a second surface to receive the monochromatic radiation. The first surface is patterned with recessed areas that have a dielectric coating and that are filled with the functional material. The dielectric coating includes a sequence of dielectric coating layers alternating in refractive index. The dielectric coating therewith has a relatively high reflectivity for said monochromatic radiation incident perpendicular to the dielectric coating in comparison to a reflectivity for said monochromatic radiation incident at an angle of 45 degrees to the dielectric coating. As such shear forces are mitigated without requiring a high alignment accuracy. The present application further describes a deposition device including the plate and a method involving the plate.

Claims

1. A method for controlled deposition of a functional material onto a target surface using monochromatic radiation having a wavelength, the method comprising: providing a transparent carrier plate having a substrate with a first surface and a second surface opposite to the first surface, therewith providing the first surface with one or more recessed areas; depositing a dielectric coating comprising a sequence of dielectric coating layers alternating in refractive index on the first surface, the dielectric coating having a relatively high reflectivity for the monochromatic radiation incident perpendicular to the dielectric coating in comparison to a reflectivity for the monochromatic radiation incident at an angle of 45 degrees to the dielectric coating; filling the one or more recessed areas with the functional material; positioning the transparent carrier plate between the monochromatic radiation source and the target surface, with the first surface facing the target surface; directing the monochromatic radiation towards the second surface of the plate, the monochromatic radiation having an intensity and a duration that causes a transfer of functional material from the one or more recessed areas to the target surface.

2. The method according to claim 1, wherein the dielectric coating layers have a thickness in a range of 0.05 to 0.15 times the wavelength of the monochromatic radiation.

3. The method according to claim 1, further comprising, before providing the first surface with one or more recessed areas, depositing a reflective coating at the first surface that substantially reflects the monochromatic radiation incident thereto.

4. The method according to claim 1, wherein a scanning laser is used to generate the monochromatic radiation.

5. The method according to claim 4, wherein the monochromatic radiation is directed via a telecentric lens to the second surface of the plate to ensure that the angle of incidence is equal over the area covered by the monochromatic radiation.

6. The method according to claim 4, wherein an excimer laser is used to generate the monochromatic radiation.

7. The method according to claim 1, further comprising the step of depositing a photon radiation absorbing layer subsequent to the depositing the dielectric coating, and preceding the filling the one or more recessed areas with the functional material.

8. A plate comprising: a functional material to be deposited onto a target surface using monochromatic radiation having a wavelength; and a substrate with a first surface to be directed towards the target surface and with a second surface to receive the monochromatic radiation, wherein the first surface is patterned with one or more recessed areas having a dielectric coating and being filled with said-the functional material, and wherein the dielectric coating comprises a sequence of dielectric coating layers alternating in refractive index, the dielectric coating having a relatively high reflectivity for the monochromatic radiation incident perpendicular to the dielectric coating in comparison to a reflectivity for the monochromatic radiation incident at an angle of 45 degrees to the dielectric coating.

9. The plate according to claim 8, wherein the dielectric coating layers have a thickness in a range of 0.05 to 0.15 times the wavelength of the monochromatic radiation.

10. The plate according to claim 8, wherein the dielectric coating covers the first surface in a blanketwise manner.

11. The plate according to claim 8, wherein the dielectric coating is covered with a protective layer.

12. The plate according to claim 8, wherein non-recessed portions of the first surface are provided with a reflective coating that substantially reflects the monochromatic radiation.

13. The plate according to claim 8, comprising at least in the one or more recessed areas a photon radiation absorbing layer between the dielectric coating and the functional material.

14. The plate according to claim 8, being provided at its second surface with a gray-scale mask to control a heat flux of the monochromatic radiation to cooperate with the dielectric coating to provide for an at least substantially homogeneous transmitted heat flux at the inner surface of the one or more recessed areas and/or to suppress transmission of the radiation outside these areas.

15. A deposition device comprising: a plate comprising: a functional material to be deposited onto a target surface using monochromatic radiation having a wavelength; and a substrate with a first surface to be directed towards the target surface and with a second surface to receive the monochromatic radiation, wherein the first surface is patterned with one or more recessed areas having a dielectric coating and being filled with the functional material, and wherein the dielectric coating comprises a sequence of dielectric coating layers alternating in refractive index, the dielectric coating having a relatively high reflectivity for the monochromatic radiation incident perpendicular to the dielectric coating in comparison to a reflectivity for the monochromatic radiation incident at an angle of 45 degrees to the dielectric coating; a holder configured to hold a target with a target surface facing the first surface of the plate; a monochromatic radiation source configured to render the monochromatic radiation to be directed towards the second surface of the plate; a controller configured to cause the monochromatic radiation source to render the monochromatic radiation with an intensity and a duration that causes a transfer of functional material from the one or more recessed areas to the target surface.

16. The deposition device according to claim 15, wherein the dielectric coating layers have a thickness in the range of 0.05 to 0.15 times the wavelength of the monochromatic radiation.

17. The deposition device according to claim 15, wherein the dielectric coating covers the first surface in a blanketwise manner.

18. The deposition device according to claim 15, wherein the dielectric coating is covered with a protective layer.

19. The deposition device according to claim 15, wherein non-recessed portions of the first surface are provided with a reflective coating that substantially reflects the monochromatic radiation.

20. The deposition device according to claim 15, wherein the plate comprises at least in the one or more recessed areas a photon radiation absorbing layer between the dielectric coating and the functional material.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0029] These and other aspects are described in more detail with reference to the drawings. Therein

[0030] FIG. 1, 1A schematically shows a stage in a prior art deposition process;

[0031] FIG. 2 shows an embodiment of a deposition device including a plate as claimed herein;

[0032] FIG. 3A, 3B illustrate aspects of the plate;

[0033] FIG. 4 schematically shows a normalized transmitted heat flux as a function of a wall angle in a first embodiment of the plate;

[0034] FIG. 5 schematically shows a normalized transmitted heat flux as a function of a wall angle in a second embodiment of the plate;

[0035] FIG. 6 shows another embodiment of a deposition device including a plate as claimed herein;

[0036] FIG. 7 shows an embodiment of a method as claimed herein;

[0037] FIG. 8 schematically shows exemplary aspects of the method;

[0038] FIG. 9A-9C show alternative embodiments of the plate as claimed herein.

DETAILED DESCRPTION OF EMBODIMENTS

[0039] FIG. 2 schematically shows a deposition device to controllably deposit a functional material 2 onto a target surface 51 of a target 5 using monochromatic radiation R3 having a wavelength λ.sub.R3. The deposition device of FIG. 2 comprises a carrier plate 1, a holder 7 to hold the target 5, a monochromatic photon radiation source 3 and a controller 8 to control the monochromatic radiation source 3.

[0040] As schematically shown in FIG. 2, the carrier plate 1 has a substrate 10 with a first surface 11 to be directed towards the target surface 51 and a second surface 12 to receive the monochromatic photon radiation R3. The first surface 11 is patterned with one or more recessed areas 111. In the example of FIG. 2 only one recessed area 111 is shown, but in practice, the carrier plate 1 may have a plurality of recessed areas. Recessed areas may be of any type, e.g. circular wells, curved or straight trenches and the like. The recessed areas may for example have a width of 10 micron and smaller, but also larger sized recessed areas may be contemplated depending on the application. In the example shown in FIG. 2, the entire first surface 11 provided with a dielectric coating 4. Alternatively, the dielectric coating 4 may be exclusively provided in the portions of the first surface 11 defined by the recessed area(s) 111, and be absent outside these areas. The recessed areas 111 are filled with the functional material 2 to be deposited on the target. As schematically shown further in FIG. 2, the dielectric coating 4 comprises a sequence of dielectric coating layers 41, 42, 43 that alternate in refractive index. The dielectric coating layers 41, 42, 43 are applied with a uniform thickness so that the dielectric coating 4 has a relatively high reflectivity for monochromatic radiation R3B incident thereto in a perpendicular direction and has a relatively low reflectivity for monochromatic radiation R3S incident thereto in a direction deviating from said perpendicular direction, i.e. at an angle of 45 degrees.

[0041] In operation of the deposition device the controller 8 causes the monochromatic radiation source 3 to render monochromatic photon radiation R3 with an intensity and a duration that causes a transfer of functional material 2 from the one or more recessed areas 111 to the target surface 51. The monochromatic radiation source 3 directs the monochromatic radiation R3 towards the second surface 12 of the carrier plate 1. To that end the monochromatic radiation source 3 may include a laser, e.g. an excimer laser or a scanning laser and optional further optical components, such as a telecentric lens.

[0042] As shown schematically in FIG. 2, for monochromatic radiation R3B directed towards the bottom 111B of the recessed area 111 is incident to the dielectric coating 4 in a perpendicular direction so that a relatively large portion is reflected. Contrary thereto monochromatic radiation R3S directed towards the side wall 111S of the recessed areas 111 is incident to the dielectric coating 4 in a direction deviating from the perpendicular direction, so that only a relatively small portion thereof is reflected. Therewith the radiation intensity at the bottom 111B of the recessed area(s) 111 is reduced as compared to the case wherein a dielectric coating 4 is absent. As a consequence a difference between the heat flux developed near the sidewall 111S and the bottom 111B is reduced.

[0043] A first example is shown in more detail in FIG. 3A, 3B. Therein FIG. 3A shows a portion of the bottom 111B of a recessed area 111, and FIG. 3B shows a portion of the side wall 1115 of a recessed area 111. In the example shown the substrate 10 of the plate is of silicon dioxide, and a dielectric coating 4 is provided with a first high refractive index (n=2.4) layer 41 of TiO2 with a thickness of 40 nm, a first low refractive index (n=1.45) layer 42 of SiO2 with a thickness of 40 nm, and a second high refractive index layer 43 of TiO2 with a thickness of 40 nm. Also a protective coating layer 45 of Al2O3 with a thickness of 40 nm is provided. The latter has a refractive index n=1.75.

[0044] It is noted that in dielectric mirrors the thickness of the layers multiplied with their refractive index is typically a quarter of the wavelength of the radiation to be reflected, so that the high refractive index layers are thinner than the layers with a lower refractive index. In the present application it is not necessary that the dielectric coating reflects all radiation, but it is sufficient that the radiation directed towards the bottom of the recessed portions is attenuated to a sufficient extent to achieve a substantially homogeneous distribution of the transmitted heat flux over the inner surface of the recessed areas. Suitable coatings that meet this requirement can selected without undue effort using a simulation. For example starting from the following input, a wavelength XR.sub.3 of the monochromatic radiation used, a slanting angle of the walls of the recessed elements a number of dielectric layers in the dielectric coating and a selection of the mutually different dielectric materials for these layers, the thickness can be varied in the simulation to determine for which thickness the required attenuation is achieved. It can be presumed in the simulation that the thickness of the layers is equal, or that the layer thicknesses for high- and low refractive index layers mutually have a fixed thickness ratio. Therewith only one parameter needs to be varied in the simulation. https://www.filmetrics.com/reflectance-calculator provides a simulator suitable for this purpose.

[0045] At each interface 10-41, 41-42, 42-43 and 43-45 and 45, a reflection occurs and these reflections reinforce or cancel each other depending on the path length difference. The path length through each layer is the product of the layer thickness (d) and its refractive index (n).

[0046] The strength of the reflection at the interface of mutually subsequent layers depends on their refractive indices (n.sub.o, n.sub.s) according to the following relationship.

[00001]$R={\left(\frac{n_0-n_S}{n_0+n_S}\right)}^2$

[0047] The extent to which reflections mutually cancel each other depends on their phase difference.

[0048] In an example, the wavelength λ.sub.R3 of the monochromatic radiation source used is 532 nm. Therewith for the layers 41, 42, 43, 45 the bidirectional optic path length (*λ.sub.R3) for radiation incident in the direction of the surface normal expressed as a fraction of the wavelength is as follows:

TABLE-US-00001 Layer Material n.d *λ.sub.R3 41, 43 TiO2 (n = 2.4) 96 0.36 42 SiO2 (n = 1.45) 58 0.22 45 Al2O3 (n = 1.75) 70 0.26

[0049] In the center of the recessed area, the incident angle of the light is transverse to the plane of the layers. The various partial reflections are out of phase but are not fully in counter phase, so that part of the radiation R3B is reflected, and does not arrive at the bottom 111B of the recessed area 111.

[0050] In the case of FIG. 3B, showing the radiation R3S directed to the side wall 111S of the recessed areas 111, the path length is increased, as the radiation R3S has a direction deviating from the normal direction of the coating 4. Therewith the partial reflections occurring at the layer interfaces are to a larger extent out of phase, so that a relatively small part of the radiation R3S is reflected. Therewith a larger part can reach the side wall 111S of the recessed area 111.

[0051] FIG. 4 shows the relationship between the normalized heatflux (normalized power density) and the angle of incidence of the beam. In this example, the normalized heatflux gradually increases from about 1 to 1.8 when increasing the angle from 0 to 45 degrees, and decreases to 0 when the angle is further decreased to 90 degrees. For an angle of 70 degrees, corresponding to the angle of the sidewall the 111S, the normalized heatflux is approximately equal to 1, so that a substantially uniform heatflux is achieved within the recessed area 111. It is noted that the heat flux transmitted through a surface is defined as the power density (W/m.sup.2) in the normal direction of the surface. The normalized heat flux is a dimensionless value obtained by dividing the heat flux for a particular angle by the heat flux at an angle of 0. In some cases, it may be desired that the heat flux through the side walls of the recessed area is slightly higher (e.g. about 5 or 10%) than the heat fllux through the bottom, so that the side releases just before the bottom releases. Therewith a risk of occurrence of a shear force can be further mitigated.

[0052] In another example, the wavelength λ.sub.R3 of the monochromatic radiation source used is 308 nm and the dielectric coating 4 is provided with a first high refractive index (n=2.1) layer 41 of HfO2 with a thickness of 38 nm, a first low refractive index (n=1.45) layer 42 of SiO2 with a thickness of 38 nm, and a second high refractive index layer 43 of HfO2 with a thickness of 38 nm. Also a protective coating layer 45 of Al2O3 with a thickness of 25 nm is provided. The latter has a refractive index n=1.75.

TABLE-US-00002 Layer Material n.d *λ.sub.R3 41, 43 HfO2 (n = 2.1) 55 0.36 42 SiO2 (n = 1.45) 80 0.51 45 Al2O3 (n = 1.75) 44 0.28

[0053] FIG. 5 shows for this example the normalized heat flux as a function of the angle of incidence. The dependency of the normalized heat flux on the angle of incidence is qualitatively the same as in preceding example, but quantitatively there is a difference. With an angle in a range of 0 to about 65 degrees, the normalized heat flux does not differ more than about 10% from the reference value 1. Therewith recessed areas 111 with a variety of side wall angles within this range of angles can be provided in the carrier plate, all having a substantially uniform distribution of heat flux over their bottom wall and side wall.

[0054] FIG. 6 shows an alternative embodiment of the claimed deposition device. Parts therein corresponding to those in FIG. 2 have the same reference. As an additional feature the non-recessed portions of the first surface 11 of the carrier plate are provided with a reflective coating 6, e.g. a reflecting metal coating or a further dielectric coating 6 that substantially reflects (R3R) the monochromatic radiation R3. The dielectric coating 4 extending over the further dielectric coating 6 can therewith cooperates with the latter. This is because the dielectric coating 4 is already designed to partially reflect incident radiation perpendicular to the surface. The further dielectric coating 6 below the dielectric coating 4 provides additional dielectric coating layers that further enhance the reflectivity outside the recessed areas.

[0055] Therewith it is avoided that any functional material 2″ present in these areas is transferred to the target surface 51, even if the monochromatic radiation R3 is directed thereto. It is not necessary that a reflective coating 6 fully reflects the radiation R3. It is sufficient if the monochromatic radiation R3 is sufficiently reduced in strength to avoid the transfer.

[0056] In the embodiment shown in FIG. 6 the recessed area 111 is further provided with a photon radiation absorbing layer 9 between the dielectric coating 4 and the functional material 2. Therewith the photon radiation is very efficiently converted into heat, regardless the type of functional material 2 used.

[0057] FIG. 7 schematically shows a method for controlled deposition of a functional material onto a target surface using monochromatic radiation having a wavelength. The method comprises a step S1, wherein a transparent carrier plate is provided having a substrate with a first and a second mutually opposite surfaces, therewith providing the first surface with one or more recessed areas. In an embodiment step S1 comprises a first sub-step S1A, wherein the transparent carrier plate is provided, e.g. made of glass or silicon oxide, and a second sub-step S1B, wherein the first surface is provided with one or more recessed areas.

[0058] In the embodiment of FIG. 7, an additional sub-step S1C is performed. In this sub-step S1C, a reflective coating is deposited at the first surface that substantially reflects the monochromatic radiation incident perpendicular to the reflective coating. Sub-step S1C comprises for example depositing a reflecting metal coating, e.g. a silver layer. Preferably however a dielectric coating is applied using a sequence of sub-sub-steps wherein dielectric coating layers are subsequently deposited to form a dielectric mirror that (optionally in combination with a dielectric coating 4) substantially reflects perpendicularly incident monochromatic radiation of said wavelength. With a dielectric mirror an amount of heat absorption van be relatively modest as compared to when using a metal coating, therewith reducing the risk of damage. In the example of FIG. 7, sub-step S1C is performed before providing in step S1B the first surface with one or more recessed areas. As a result, a plate is obtained as used in the deposition device of FIG. 6, wherein non-recessed portions of the first surface 11 of the plate 1 are provided with a reflective coating 6 that substantially reflects the monochromatic radiation R3. As discussed with reference to FIG. 6, therewith the risk that materials are unintendedly transferred outside the recessed portions is reduced. Because in this embodiment of the method sub-step S1B is performed subsequent to sub-step S1C, it is not necessary to accurately align the deposition process in sub-step S1C. In sub-step S1C, the dielectric coating 6 or other reflective coating can simply be deposited over the entire first surface of the plate, and in sub-step S1B this coating is locally removed in the portions of the first surface occupied by the recessed portions. Nevertheless, it may be contemplated to perform sub-step S1C subsequent to sub-step S1B provided that care is taken that the first surface occupied by the recessed portions remains free from the material used for the reflective coating.

[0059] In step S2 of the method, a dielectric coating is deposited Step S2 comprises a sequence of sub-steps wherein in each subsequent sub-step a dielectric coating layer is deposited having a refractive index different from that of the dielectric coating layer deposited in the preceding sub-step. It is sufficient that the dielectric coating obtained therewith extends within the portions of the first surface defined by the one or more recessed areas, but alternatively the dielectric coating may also extend beyond the one or more recessed areas. Typically the dielectric coating is deposited over the entire surface of the plate, therewith obviating masking and aligning issues.

[0060] The dielectric coating has a reflectivity for the monochromatic radiation incident perpendicular thereto that is relatively high in comparison to a reflectivity for said monochromatic radiation incident at an angle of 45 degrees to the dielectric coating.

[0061] In a subsequent step S3 the one or more recessed areas are filled with the functional material, e.g. copper, aluminum, tungsten, chromium, polysilicon to be deposited. Other materials than metal are also suitable for use as a functional material. The functional material may for example be provided as an ink wherein conductive particles are suspended. Rheological properties of the functional material may be modified by additives or solvent, for example to obtain a shear-thickening, a shear-thinning, a thixotropic, a rheopectic or a Bingham plastic behavior. In particular donor materials with a shear-thinning behavior are favorable. Donor materials with this behavior have a viscosity that decreases with the rate of shear strain. Shear-thinning donor materials remain as a stable layer on the donor substrate, but are relatively easily morphed at the time of deposition. By way of example, the functional material is a viscous silver nanoparticle ink with a high metal load.

[0062] It is noted further process steps may take place before the one or more recessed areas are filled with the functional material. For example a photon radiation absorbing layer may be deposited subsequent to the step of depositing the dielectric coating, and preceding the step of filling the one or more recessed areas with said functional material. As noted above this improves the conversion of the monochromatic radiation into heat. Alternatively or additionally a vaporizable material may be deposited the one or more recessed areas before filling with the functional material.

[0063] After the one or more recessed areas are filled in step S3 with the functional material, the transparent carrier plate is ready for use in a deposition device, for example as shown in FIG. 2 or FIG. 6.

[0064] Therewith the transparent carrier plate 1 is positioned between the monochromatic radiation source 3 and the target surface 51 of a target, with the first surface 11 facing the target surface 51, as shown in FIGS. 2 and 6 for example.

[0065] In operation the monochromatic radiation R3 of the monochromatic radiation source 3 is directed in step S4 towards the second surface 12 of the plate 1. Therewith the monochromatic radiation R3 has an intensity and a duration that causes a transfer S5 of functional material 2 from the one or more recessed areas 111 to the target surface 51. Optimal values for intensity and duration can be determined by routine tests for a selected functional material and the transmissivity of the coating layers. The duration of the heat irradiation is typically short, e.g. in terms of microseconds, usually even shorter, nano-seconds. In practice good results with modest technical requirements may be obtained with a pulse duration in the order of a few to a few tens of ns. Nevertheless, in some cases an even shorter pulse duration may be applied, e.g. in the range of 10-500 ps. In a test phase the intensity can be varied from a relatively low value (e.g. corresponding to an exposure (fluence) of about 0.1 J/cm.sup.2) to a relatively high value (e.g. corresponding to an exposure (fluence) of about 1 J/cm.sup.2) to determine for which value or value range the transfer of the functional material 2 is optimal in terms of deposition accuracy.

[0066] According to one approach, the entire second surface 12 of the plate 1 is irradiated with a beam of homogeneous power density. In that case a homogeneous exposure is achieved having an exposure value equal to the product of the power density and the exposure time.

[0067] According to another approach, as illustrated in FIG. 8, a scanning beam is used that is scanned with a speed v in a scanning direction Sy, parallel to axis y, along the second surface 12 opposite the recessed area 111 (here a trench shown in dotted lines) at the first surface.

[0068] In this case, the exposure E(x,y) can be determined as:

E(x,y)=∫.sub.t=−∞.sup.+∞P(x,v,t)Q(t)dt

Wherein P( . , . ) specifies the spatial distribution of the beam R3 and Q( ) specifies how the total beam power varies in time t.

[0069] FIG. 8 shows the footprint 31 of the scanning beam when it is pulsed during scanning. Previous pulses are indicated as dotted circles, e.g. 31″. As a result of said scanning, uniformity of the energy density at the second surface is obtained in the scanning direction provided that the distance between subsequently pulsed areas 31″, 31 is subsequently small, e.g. the distance should be smaller than one third times the size of the footprint in the scanning direction. Also in the direction x, perpendicular to the scanning direction, exposure variations may be limited. For example, it may be required that the maximum exposure Emax and the minimum exposure Emin in the range x1<x<x2 are bounded with the following relationship:

[00002]$\left(\frac{E\max -E\min }{E\max +E\min }\right)<0.05$

[0070] This may be achieved with a highly uniform beam. Alternatively, as shown in FIG. 8, a beam may be applied having a footprint extending beyond the boundaries of the recessed area 111, which is sufficiently uniform within these boundaries. When using a pulsed laser, the pulse frequency should be sufficiently high to uniformly heat the functional material, for example a frequency of 100 kHz or higher. A continuous wave laser can also be used where the timed release is controlled by the scan speed.

[0071] As noted with reference to FIG. 6, precautions can be taken to reduce the risk that functional material accidently is transferred as result of exposure of the plate by the beam in areas outside the recessed areas.

[0072] Returning to FIG. 7, it is further shown therein that upon completion of the deposition process in step S4, S5, recessed areas of the carrier plate can be refilled with functional material in step S3, so that the carrier plate is ready for reuse. Optionally, the carrier plate, in particular its first surface may be cleaned in an additional step S6 before refilling in step S3.

[0073] FIG. 9A-9C show further embodiments of a transparent carrier plate 1. Parts therein corresponding to those in FIG. 2 and FIG. 6 have the same reference number. For clarity, the dielectric coating 4 is shown without further detail. The dielectric coating 4 at the first surface 11 may for example have a stack of dielectric coating layers 41, 42, 43 as shown in more detail in FIG. 3A, 3B and described above with reference to FIGS. 3A, 3B, 4 and 5. Also other layers may be provided such as a protective coating. In the embodiments shown in FIG. 9A-9C, the transparent carrier plate 1 is additionally provided with a gray-scale mask 122 to control a heat flux of the monochromatic photon radiation R3.

[0074] In the example shown in FIG. 9A, gray-scale mask 122 has a transparent first zone 122BS which corresponds to an area defined by the recessed areas 111. The gray-scale mask 122 has second opaque zones 1220 complimentary thereto. Upon exposure of the plate 1 to radiation R3, the portion of the radiation incident at the transparent first zone 122BS is transmitted towards the dielectric coating 4 in the recessed area 111, with which it is achieved that a transmitted heat-flux in the surface of the side wall 1115 and a transmitted heat-flux in the surface of the bottom wall 111B have substantially the same magnitude.

[0075] In the example shown in FIG. 9B, gray-scale mask 122 has a central zone 122B corresponding to the surface area of the bottom wall 111B of the recessed area 111, a boundary zone 122S corresponding to the surface area of the side wall 111S of the recessed area 111 and a complementary zone 122O. In this example the gray-scale mask 122 is provided to control a heat flux of the monochromatic photon radiation R3 to cooperate with the dielectric coating 4 to provide for an at least substantially homogeneous transmitted heat flux at the inner surface of the one or more recessed areas 111. Therewith an additional degree of freedom is available. For example if recesses with side walls with mutually different slanting angles are provided therein, the gray-scale mask 122 can be designed to achieve the at least substantially homogeneous transmitted heat flux, even if the dielectric coating would not be capable to provide the proper compensation for the full range of side wall angles. For example in case the plate provided with the coating described with reference to FIG. 4 comprises in addition to recesses with a wall angle of 70 degrees also recesses with a wall angle of 45 degrees or 80 degrees. In the example shown in FIG. 9B, the central zone 122B for example has a transmissivity of 60% and the boundary zone 1225 has a transmissivity of approximately 100%. In that case for a recession with a side wall at an angle of 80 degrees, using the coating described with reference to FIG. 4, a substantially homogeneous transmitted heat flux would be available over the inner surface of the recession. In the example of FIG. 9B, the transmissivity of the complementary zone 1220 is also approximately 100%.

[0076] In the example shown in FIG. 9C, the gray-scale mask 122 combines the functionalities provided in the examples of FIGS. 9A and 9B.