WO2010121652A1

WO2010121652A1 - Mastering method, mastering device and substrate master

Info

Publication number: WO2010121652A1
Application number: PCT/EP2009/054759
Authority: WO
Inventors: Johan Nessaether
Original assignee: M2 Engineering Ab
Priority date: 2009-04-21
Filing date: 2009-04-21
Publication date: 2010-10-28

Abstract

The invention relates to a mastering method for producing a substrate master, a mastering device for producing a substrate master and a substrate master, in particular for use in an optical storage media replication process, the mastering method comprising the following steps: providing a substrate (1) with a substantially planar surface (11); coating the planar surface (11) of the substrate (1) with a patterning layer (3); and patterning the patterning layer (3) by exposing the patterning layer to a patterning radiation (5) at one or more writing spots (33) along an exposure path (31), such that a thickness modulation or a continuous change of thickness is induced in the patterning layer (3) along the exposed exposure path (31).

Description

Title:

Mastering Method, Mastering Device and Substrate Master

Description:

The present invention relates to a mastering method, a mastering device and a substrate master.

For the mass production of optical storage media such as compact discs (CDs), DVDs, Blu-Ray discs (BDs), and similar formats, the digital information is transferred onto the media by means of a so called stamper. The stamper is a device, which is generally made of a metal and has a flat surface, on which the digital information is provided as thickness variation in form of bumps and / or dips. The thickness variation, which extends along a spiral on the circular stamper, is transferred onto an optical medium either after or during the production of the medium. In the latter case, the stamper may be utilized as a surface inside an injection molding chamber, inside which the optical storage medium is produced.

The stamper itself is obtained by metalizing the surface of a substrate master comprising a substrate made of glass (in which case it is called a glass master), or other suitable material providing a supportive structure. On the flat surface of the substrate, a structured layer comprising a thickness variation is provided such that the surface of the substrate master replicates the desired surface of the optical storage media to be produced. During the sequence of making the stamper and using it to produce the optical storage medium, the surface structure of the substrate master is copied into an inverted image onto the stamper surface, which is copied again into an inverted image onto the surface of the medium. In some cases, additional copying stages are introduced between metalizing the substrate master and making the final stamper. The structured layer on the surface of the substrate master is generally made by coating the substrate with a photoresist, patterning the photoresist with a laser beam, and finally developing the photoresist in order to remove the regions exposed to the laser beam and obtaining the substrate master. There follows a metallization process comprising electroforming to obtain a thick metal layer on the structured surface of the substrate master. This thick metal layer is used either as the stamper or as a pre-form for the stamper.

In the method for producing the substrate master as described above, the success of the substrate master production is to a large degree dependent on parameters of the developing process such as temperature and concentration of the developer as well as developing time, which are hard to control. This may lead to uncertain results and significant amount of waste. Furthermore, the additional step of developing adds cost and time to the production process.

It is therefore the objective of the invention to provide for the production of substrate masters, in particular for optical storage media manufacturing, leading to higher throughput at lower costs as well as more consistent results.

This problem is solved in the invention by the mastering method with the features according to claim 1 , by the mastering device with the features according to claim 16, and by the substrate master with the features according to claim 17. Preferred embodiments are described in the dependent claims.

The invention is based on the idea that certain types of material experience a significant change in volume when exposed to radiation, and exploiting this effect for the manufacturing of substrate masters, for example for use in an optical storage media replication process. By utilizing such material for creating a patterning layer on the substrate surface and exposing the patterning layer to a patterning radiation at one or more writing spots along an exposure path, a thickness modulation will be induced along this path. In a case where a continuous or very long writing spot is exposed to radiation with a substantially constant intensity, a continuous change of thickness will result. Such a continuous well or trough is useful for example for creating a writable BD (BD-R) or a rewritable BD (BD-RE), which have a continuous trough spiraling from the center to the border of the disc.

The change in thickness resulting from the volume change upon exposure to radiation may be a purely thermal effect, or it may result from a combination of a thermal effect and an effect due to interaction of the radiation with the material of the patterning layer, e.g. a photo-chemical reaction in case of use of electromagnetic radiation.

The exposure path along which the exposure takes place does not have to be a straight line. In fact, for usual optical storage media, a spiraling line is necessary in order to allow for a continuous readout of the manufactured medium while it is rotated. By exposing the writing spots to radiation, bumps or pits are created at these spots on the surface of the patterning layer, depending on whether the material used contracts or expands upon exposure.

It should be noted that other material layers may be deposited onto or applied to the substrate before the application of the patterning layer. For example, an adhesive layer may be applied in order to provide for a good connection between the patterning layer and the substrate surface. The substrate itself may be made of glass or other suitable material allowing for a substantially smooth and flat surface, preferably up to a nanometer scale, such as for example a silicon wafer. Furthermore, there may be a baking step introduced after application of the patterning layer, although the baking step may be omitted in other embodiments, thus simplifying the fabrication process. Whether a baking step is applied or not, and the parameters of the baking process, such as temperature and duration, may affect the response of the patterning layer to the patterning radiation.

The substrate master described herein may also be used in order to fabricate devices other than optical storage media. Such devices include lab-on-a-disc devices comprising microfluidic channels, which are formed on a device - A - substrate using the stamper described above. For being able to fabricate such microfluidic channels, the features created on the substrate master by exposure of the patterning layer need to be of suitable width, for example on the order of or larger than one or two μm. This may be implemented e.g. by raising the focus size of the patterning radiation beam or by defocusing it. Alternatively, a writing spot corresponding to a channel may be exposed in multiple passages in order to obtain wider wells or troughs. Furthermore, the patterning radiation needs to be movable on the surface of the patterning layer in two dimensions independently, in order to be able to expose the patterning layer along one or more exposure paths which are oriented in different angles towards each other, in particular perpendicular to each other. In a similar way, a substrate master may be created for optical devices comprising waveguides. In this case, the writing spots on the substrate master correspond to the waveguides desired on the optical device.

In a preferred embodiment, the substrate is coated with a patterning layer comprising a material that leads to an increase in layer thickness upon exposure to the patterning radiation. In other words, the digital information will be coded as bumps on the surface of the patterning layer. Because in the finished storage medium the information is usually provided in form of pits (rather than bumps) on the medium surface or in the surfaces of lower lying layers in the medium, there might be a need for one or more further inverted images to be created during fabrication of the stamper as described above.

Preferably, the substrate is coated with a patterning layer comprising a novolak based material. Novolaks are phenol-formaldehyde type polymers or resins. In order to use them as photoresist, a photosensitive substance is usually added, such as DNQ (diazonaphthoquinone). One example for a patterning layer material is the photoresist S1805 manufactured by Rohm and Haas. However, other similar substances may be used instead. For example the photoresist may be applied to the substrate surface undiluted or diluted with a solvent at a ratio of about 1 :1 , 1 :2, or 1 :4 (i.e. 1 part photoresist, 4 parts solvent). According to an advantageous embodiment, the induced thickness modulation or continuous change of thickness is on the order of about 10 nm to 100 nm, preferably about 30 nm to 70 nm, more preferably about 60 nm. Whereas the target thickness modulation, e.g. the bump height for substrate masters for BDs, is about 60 nm, the target change of thickness for BD-REs is about 20 nm.

In any case, it may be of importance to obtain a significant change in thickness or a significant thickness variation upon exposure, in order to allow for reliable detection of the digital information on the finished storage medium. In this case, significant means that the thickness variation is at least on the order of a half or one percent of the layer thickness. In terms of the patterning layer thickness, the induced thickness modulation may advantageously be above 0.5 % of the patterning layer thickness, preferably on the order of about 1% to 10 %, more preferably between about 3% and 6%.

In a preferred embodiment, the induced thickness modulation or continuous change of thickness has a width perpendicular to the direction of the exposure path, with lies in a range of about 100 nm to 300 nm, preferably about 80 nm to 200 nm, more preferably about 150 nm. Here as well as for the other width and length measurements of bumps or pits, full-width half-maximum values are provided. As an example, for a BIu -Ray disc, the center to center distance from one track to a neighboring track is approximately 320 nm. Thus in order to minimize intersymbol interference between neighboring tracks, the target width of the induced thickness modulation or continuous change of thickness is about 150 nm.

The exposed writing spots have, in one advantageous embodiment, lengths along the direction of the exposure path, which lie in a range of about 100 nm to 800 nm, preferably about 150 nm to 700 nm. It is assumed here that the exposure of a writing spot leads to a bump or a pit with an approximately corresponding length. The smaller lengths may generally correspond to bumps denoted as so called "12 marks", while the larger lengths may generally correspond to so called "18 marks" or "19 marks".

Advantageously, the substrate is being rotated during the patterning step. In this case, the radiation may be directed along the exposure path describing a spiral on the patterning layer by moving the radiation from the center of the substrate, which coincides with rotation axis, to the periphery or border of the substrate, or from the periphery to the center.

Preferably, the patterning radiation comprises an electromagnetic radiation, for example from a laser source. However, alternatively any radiation that can deposit a sufficient amount of energy in a localized area for the material to react may be suitable. The radiation may be directed and / or focused onto the patterning layer by suitable mirrors and lenses. In case of electromagnetic radiation, near field optics such as the end of an optical fiber may be utilized for irradiating the patterning layer. As an example for electromagnetic radiation, ultraviolet light might be used, having the advantage of allowing a very small focus size, leading to sufficiently small patterns for BD manufacturing. The ultraviolet light might for example have a wavelength of around 375 nm or 420 nm. At such wavelengths, an objective lens used for focusing the radiation onto the patterning layer surface might have a numerical aperture of NA=0.90.

In a preferred embodiment, during the patterning step, a focus of the patterning radiation is adjusted in its vertical position with respect to the planar surface of the substrate, by using focus control means. Such focus control means may comprise optical distance measurement and adjustment means. Alternatively, the focus of the patterning radiation may be adjusted and held at substantially constant height above the patterning layer by focus control means in form of an airbearing holding the focusing device for the patterning radiation such as a lens. When providing for a sufficiently conductive surface, e.g. underneath the patterning layer, the focus control means may be provided for distance measurement through capacitance coupling.

However, preferably the focus control means direct a sampling radiation onto the patterning layer at a fixed distance from a patterning radiation spot. Although a separate sampling beam may also be utilized in a case where the patterning layer is developed after exposure to a patterning beam, it is of particular advantage in the present case of inducing a thickness change directly by the patterning beam. As the thickness changes due to the exposure, the reflected radiation from the patterning beam changes as well. An attempt to monitor this reflected radiation, e.g. by monitoring its collimation, in order to judge whether the beam is still focused onto the surface of the patterning layer, does thus not lead to reliable results.

Instead, a vertical distance of the patterning layer surface for example to a writing head of the mastering device is monitored via a sampling radiation directed to a spot on the patterning layer which has not yet been exposed to the patterning radiation. Depending on the direction of writing, this spot might be towards a center or towards a border of the substrate, relative to the writing spot. It can also be at the same distance from the center of the substrate as the writing spot, as long as it is ahead of the patterning radiation in a writing direction.

The sampling radiation may come from the same source as the patterning radiation, for example by using a beam splitter to split off a part of the patterning radiation for sampling purposes which is small enough in intensity in order to not affect the patterning layer significantly by itself. In a simpler and more cost effective embodiment, a separate radiation source might be used for the focus control means. When using electromagnetic sampling radiation, one may use a wavelength towards the red part of the spectrum in order to lower the energy being deposited in the patterning layer by the sampling radiation. Using a separate radiation source has furthermore the advantage that the focus control can also be performed while the patterning radiation is turned off. On the patterning layer, the beams of the patterning radiation and of the sampling radiation should be sufficiently spaced apart in order for any change in thickness induced by the patterning radiation not to affect the focus control. A distance of about two track widths, corresponding to around 600 nm in the example given above, may be sufficient. In general, a distance between the two beams along the patterning layer of between about 1 and 1.5 micrometer may be used.

According to one preferred embodiment, during the patterning step, the patterning radiation intensity is raised during the exposure of a writing spot. When creating bumps at the writing spots, by exposing them to a patterning radiation of constant intensity, the region adjacent to the bump in the writing direction often experiences a drop in layer thickness. This effect becomes more pronounced for longer writing spots. By raising the radiation intensity towards the end of the writing spot, this effect may be reduced or substantially eliminated.

The patterning radiation intensity may be ramped or raised in steps during the exposure of the writing spot. When ramping the intensity, one might begin at a very low intensity, which is then gradually increased to a maximum intensity at the end of the writing spot. Alternatively, the intensity at the beginning of the writing spot may already be at a value sufficient for creating thickness changes in the patterning layer. In this case, the intensity ramp will be set on top of this value, e.g. starting around the middle of the writing spot. To keep the process simple, however, the intensity may be increased in one or more steps.

Preferably, the patterning radiation intensity is raised by between about 10 % and 90 %, preferably about 30 % and 70 %, more preferably by about 50 % during the exposure of the writing spot. In other words, when at the beginning of the writing spot the intensity is sufficient for creating thickness changes, this intensity may be raised to said values by the end of the writing spot. As described above, this change in intensity may be distributed over one or more intensity steps.

The patterning radiation may be from a continuous wave (CW) source or from a pulsed source. In the latter case, a change in intensity may be implemented by pulse width modulation.

In a preferred embodiment, during the patterning step, the patterning radiation intensity is set to between about 0.5 and 5 milliwatts at the one or more writing spots, preferably between about 1 and 3 milliwatts, more preferably at about 2 milliwatts. When using a sampling radiation, the sampling radiation intensity may preferably be between about 100 and 1000 microwatts, preferably on the order of about 500 microwatts.

After the patterning step, the patterned patterning layer may in a preferred embodiment be coated by a metal layer, e.g. made of nickel, in particular for producing a stamper for use in an optical storage media replication process or in the process of manufacturing other devices such as lab-on-a-disc devices or optical devices. Deposition of an initial metal layer may be done for example by sputtering. In order to obtain a thicker metal layer, an electroforming process may be used. As described above, the metal layer created this way may be directly used as a stamper after separating it from the substrate master. However, due to the inverted character of the pattern on the patterning layer, the metal layer may be used itself for forming a second metal layer thereon via electroforming deposition, which in turn serves as a stamper.

The above described mastering method can be performed using a Mastering device, in particular for producing a substrate master for use in an optical storage media replication process, comprising: a substrate holder designed to hold a substrate with a substantially planar surface; a coating device designed to coat the planar surface of the substrate with a patterning layer; and a patterning device comprising a patterning radiation source and designed to pattern the patterning layer by exposing the patterning layer to a patterning radiation at one or more writing spots along an exposure path, such that a thickness modulation or a continuous change of thickness is induced in the patterning layer along the exposed exposure path. The mastering device may be adapted by adding necessary means and structural features such that the mastering device performs the mastering method in any of its embodiments as described above.

The mastering method described above leads to the fabrication of a substrate master, in particular for use in a storage media fabrication process, comprising a substrate with a substantially planar surface, a patterning layer coating the planar surface of the substrate, wherein the patterning layer comprises a thickness modulation or a continuous change of thickness along an exposure path created by exposing the patterning layer to a patterning radiation at one or more writing spots along an exposure path. The substrate master may comprise further features in accordance to any embodiment of the mastering method employed to fabricate the substrate master, which lead to structural features of the substrate master. To avoid duplication of these features here, reference is being made to the corresponding description of the mastering method embodiments above.

In the following description, the invention is described in view of a preferred embodiment with reference to the accompanying figures:

Fig. 1a) to 1d) showing a cross section of a substrate master at different stages in the manufacturing process;

Fig. 2 showing a top view of a section of the substrate master shown in Fig. 1d); and

Fig. 3a) to 3d) showing diagrams of different patterning radiation intensities as functions in time.

The Fig. 1a) to 1d) show a cross section of a substrate master at four different stages in the manufacturing process. First, as shown in Fig. 1a), a substrate 1 , e.g. made of glass, silicon or other suitable material, is provided, comprising a substantially flat and even surface 11. As shown in Fig. 1 b), a patterning layer 3 is applied to the surface 11 of the substrate 1. The patterning layer 3 is applied via spin-coating, preferably at a low speed of about 200 to 300 revolutions per minute in order to obtain a layer thickness of about 1 to 2 μm. The substance used for the patterning layer 3 creation is a photoresist from the company Rohm and Haas, with the product code S1805, either undiluted or diluted at 1 :4.

After spin-coating the substrate 1 , the writing process begins, since there is no need for baking the patterning layer 3. However, baking of the patterning layer 3 may be useful in some cases in order to optimize layer properties like sensitivity to the patterning radiation 5. During the writing process, as shown in Fig. 1 c), a beam of patterning radiation 5 is directed onto the patterning layer 3 along an exposure path 31. It should be noted that the cross sections shown in Fig. 1a) to 1 d) are taken along the exposure path 31 , along which the patterning layer 3 is exposed to the patterning radiation 5.

Although the patterning radiation 5 appears as a collimated beam in Fig. 1 c), it is actually focused onto the patterning layer 3, either on a top or a bottom surface in contact with the surface 11 of the substrate 1. As the patterning radiation 5 advances along the writing direction R due rotational movement of the substrate 1 as well as a translational movement of the patterning radiation 5, the focus may shift vertically. In order to keep the focus at a constant vertical height with respect to the patterning layer 3, focus means are used, which are not shown in Fig. 1. Preferable, a separate radiation source is used in order to create a sampling radiation which would illuminate the patterning layer 3 at a distance from the patterning radiation 5. A reflection of the sampling radiation is then monitored in order to detect changes in the vertical height of the surface of the patterning layer 3 and adjust the focus of the patterning radiation 5 accordingly.

As the patterning radiation 5 travels along the exposure path 31 in a writing direction R, it is turned on and off, for example with the help of a shutter or by switching a radiation source on and off, such that the exposure of the patterning layer 3 takes place at desired writing spots 33. As shown in Fig. 1c), the exposure to the patterning radiation 5 leads to a thickness change in the patterning layer 5 at the writing spots 33 to form bumps 33.

The resulting substrate master after the writing process is shown in cross section in Fig. 1d). The bumps 33, having varying lengths L, are lined up along the exposure path 31. The length L of each bump 33 depends in the digital information to be represented by the bumps 33. It varies between about 150 nm and about 700 nm, corresponding to so called I2 and I8 marks or I9 marks.

A top view on a section of the substrate master shown in Fig. 1d) is depicted in a schematic in Fig. 2. This schematic shows also a further exposure path 31 , along which the patterning radiation 5 has exposed the patterning layer 5 to produce bumps 33 at writing spots 33. The two exposure paths 31 are parts of one spiral path extending from a center to a border of the substrate master. The two paths 31 shown in Fig. 2 are therefore approximately circular on a larger scale, although they appear as straight lines on the micrometer scale shown in Fig. 2. They represent neighboring tracks on the final optical storage media product and are spaced apart on the patterning layer 3 at a distance D.

As shown in Fig. 2, the bumps 33 have a substantially constant width W along the exposure path 31. In order to write the bumps 33, the patterning radiation 5 can be kept at a substantially constant intensity. However, as explained above, this might lead to pits being formed adjacent to the bumps 33 in the writing direction R. In order to prevent such an effect, the intensity of the patterning radiation 5 is raised towards the end of the writing spot 33.

Fig. 3a) to 3d) show diagrams of four different intensity progressions for the patterning radiation 5 for exposing a writing spot 33. In each diagram, the radiation intensity is plotted along the ordinate axis in arbitrary units, while the abscissa denotes either time or distance along the path 31 , also in arbitrary units.

As shown in Fig. 3a), the radiation intensity of the patterning radiation 5 may be constant over the course of the exposure of one writing spot 33. The exposure of the writing spot 33 begins at a beginning point B, which may be a point in time, when the patterning radiation 5 intercepts the patterning layer 3 at one end of the desired writing spot 33, and ends at a later ending point E, corresponding to the other end of the writing spot 33. Between those two points B and E, the radiation intensity is set to a first value I₁, corresponding to a value, which is suitable for creating the bumps 33, for example on the order of about 2 milliwatts.

Radiation intensities that are raised during the exposure of a writing spot 33 are depicted in Fig. 3b) to 3d). The diagrams in Fig. 3b) and 3c) each show a progression, wherein the exposure begins initially at a first intensity value I₁ and is raised to a second intensity value I₂ during the course of the exposure of the writing point 33. While the intensity is raised according to Fig. 3b) in a step, the intensity is ramped in the case shown in Fig. 3c) from the first I₁ to the second value I₂. The change in intensity from the first value I₁ the second value I₂ may be performed using multiple steps and intermediate intensity values.

Finally, in the case shown in Fig. 3d), the intensity begins at a very low or substantially zero intensity and is being ramped up to the second intensity value I₂ towards the end of the exposure. Alternatively, the intensity at the beginning point B in Fig. 3d) may start at the first intensity value I₁ as in the previous Fig. 3a) to 3c), while immediately starting to ramp up. In any of the cases shown in Fig. 3a) to 3d), the second intensity level I₂ is preferably about 50 % higher than the first intensity level I₁. Reference Numerals:

1 substrate

11 substrate surface

3 patterning layer

31 exposure path

33 writing spot (bump)

5 patterning radiation

R writing direction

L bump / writing spot length

W bump / writing spot width

D track to track distance

B exposure beginning point

E exposure end point li first intensity value

I₂ second intensity value

Claims

Claims:

1. Mastering method for producing a substrate master, in particular for use in an optical storage media replication process, comprising the following steps: providing a substrate (1 ) with a substantially planar surface (11 ); coating the planar surface (11 ) of the substrate (1 ) with a patterning layer (3); and patterning the patterning layer (3) by exposing the patterning layer to a patterning radiation (5) at one or more writing spots (33) along an exposure path (31 ), such that a thickness modulation or a continuous change of thickness is induced in the patterning layer (3) along the exposed exposure path (31 ).

2. Mastering method according to claim 1 , characterized in that the substrate (1 ) is coated with a patterning layer (3) comprising a material that leads to an increase in layer thickness upon exposure to the patterning radiation (5).

3. Mastering method according to claim 1 or 2, characterized in that the substrate (1 ) is coated with a patterning layer (3) comprising a novolak based material.

4. Mastering method according to one of the previous claims, characterized in that the induced thickness modulation or continuous change of thickness is on the order of about 10 nm to 100 nm, preferably about

30 nm to 70 nm, more preferably about 60 nm.

5. Mastering method according to one of the previous claims, characterized in that the induced thickness modulation or continuous change of thickness has a width perpendicular to the direction of the exposure path, which lies in a range of about 100 nm to 300 nm, preferably about 80 nm to 200 nm, more preferably about 150 nm.

6. Mastering method according to one of the previous claims, characterized in that the exposed writing spots have lengths along the direction of the exposure path, with lie in a range of about 100 nm to 800 nm, preferably about 150 nm to 700 nm.

7. Mastering method according to one of the previous claims, characterized in that the substrate is rotated during the patterning step.

8. Mastering method according to one of the previous claims, characterized in that the patterning radiation comprises an electromagnetic radiation.

9. Mastering method according to one of the previous claims, characterized in that during the patterning step, a focus of the patterning radiation is adjusted in its vertical position with respect to the planar surface of the substrate, by using focus control means.

10. Mastering method according to claim 9, characterized by focus control means that direct a sampling radiation onto the patterning layer at a fixed distance from a patterning radiation spot.

11. Mastering method according to one of the previous claims, characterized in that during the patterning step, the patterning radiation intensity is raised during the exposure of a writing spot.

12. Mastering method according to claim 11 , characterized in that during the patterning step, the patterning radiation intensity is ramped or raised in steps during the exposure of the writing spot.

13. Mastering method according to claim 11 or 12, characterized in that during the patterning step, the patterning radiation intensity is raised by between about 10 % and 90 %, preferably about 30 % and 70 %, more preferably by about 50 % during the exposure of the writing spot.

14. Mastering method according to one of the previous claims, characterized in that during the patterning step, the patterning radiation intensity is set to between about 0.5 and 5 milliwatts at the one or more writing spots, preferably between about 1 and 3 milliwatts, more preferably at about 2 milliwatts.

15. Mastering method according to one of the previous claims, characterized in that after the patterning step, the patterned patterning layer is coated by a metal layer for producing a stamper for use in an optical storage media replication process.

16. Mastering device, in particular for producing a substrate master for use in an optical storage media replication process, comprising: a substrate holder designed to hold a substrate with a substantially planar surface; a coating device designed to coat the planar surface of the substrate with a patterning layer; and a patterning device comprising a patterning radiation source and designed to pattern the patterning layer by exposing the patterning layer to a patterning radiation at one or more writing spots along an exposure path, such that a thickness modulation or a continuous change of thickness is induced in the patterning layer along the exposed exposure path.

17. Substrate master, in particular for use in a storage media fabrication process, comprising a substrate with a substantially planar surface, a patterning layer coating the planar surface of the substrate, wherein the patterning layer comprises a thickness modulation or a continuous change of thickness along an exposure path created by exposing the patterning layer to a patterning radiation at one or more writing spots along an exposure path.