Patent Publication Number: US-2009224180-A1

Title: Apparatus and method for processing a wafer

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to a concept of processing a wafer and in particular to an apparatus and a method for beam processing a processing surface of a wafer to obtain a bulk acoustic wave (BAW) device having trimmed characteristics, e.g. a trimmed resonance frequency. 
     BAW devices generally include a piezoelectric layer, which is at least partially arranged between opposing electrodes. The individual layers of a BAW device are manufactured in thin film technology. The resonance frequency in such BAW device strongly depends on the layer thickness of the individual layers (electrode layers, piezoelectric layers etc). The layer thicknesses hereby vary within the substrate (wafer) and from substrate to substrate. 
     BAW devices are preferably used in filters of high frequency applications up to the GHz frequency area. An exemplary filter configuration is a band pass filter, which is among others used in mobile communication devices. For such applications, the required accuracy in thin film technology lies below 0.1% (max-min) for the location of the resonance frequency. 
     In order to achieve the required accuracy of the resonance frequency position, a method for manufacturing a layer having a default layer thickness profile is known, wherein on a substrate after the deposition of the BAW device, the resonance frequency is determined at several positions of the substrate/wafer by measurement. Based on the deviation of the measured frequency from the specified target frequency a required thinning of a top layer of the individual piezoelectric oscillating circuits is determined. This thinning is achieved in this known method by a local sputtering off of the top layer using an ion-beam. 
       FIG. 7  shows a meander path trimming using conventional x-y scanning system. Using Cartesian coordinates in way that the (x,y)-plane is parallel to the processing surface  100  of a wafer  105  and an ion-beam  200  starts exemplary with a motion along the x-direction  710 , followed by a motion along the negative y-axis  720 , followed by a motion along the negative x-direction  730  and again a subsequent motion along the negative y-direction  720 . These motions are successively repeated until the ion-beam  200  has reached the point  750  and the whole processing surface  100  has been processed. 
     The conventional tool representing the use of mechanical scanning systems utilize two linear drives in order to scan the ion-beam  200  over the device wafer  105 . The ion-beam  200  thins down the topmost layer of the device and increases the resonance frequency accordingly. The ion-beam  200  is typically Gaussian shaped and has a half-maximum diameter around 10 to 15 mm. Using Cartesian coordinates (x, y), the wafer  105  is mounted in typical systems to the x-y scanning table and moves in the meander-path  710 ,  720 ,  730  with a spacing of less than 10 mm in y-direction. The local speed in x-direction has to be accurately controlled as it determines the local removal. However, significant accelerations are required in x-direction to obtain accurate results in regions where a high gradient of frequency must be corrected. 
     A problem with systems as described above is that the x-y scanning table needs to be very powerful and mechanically robust. As a whole system operates in a vacuum chamber, the vacuum chamber to accommodate the scanning table will be much larger than other typical vacuum chambers in semiconductor industry. The large size of the vacuum chamber causes the tool to be huge and the pumping times for evacuating the chamber after chamber opening quite long. 
     At turning points  720  of the meander  710 ,  730  the x-drive slows down, reverses direction and accelerates to a high speed. Depending on the required removal at the wafer edges the x-drive will move at maximum speed at the wafer edge, move on towards a predefined turning point, decelerate to zero speed, move y-drive into the next meander line, accelerate x-drive to maximum speed and move towards the wafer edge. The turning points are typically quite far (&gt;40 mm) outside of the wafer  105  in order to avoid unintentional additional removal on the wafer area. As a consequence, a significant portion of the total processing time is wasted for reaching the turning points  720  outside the wafer  105  and returning to the wafer center. Hence, conventional ion-beam processing as shown in  FIG. 7  implies in particular a loss of time as well as additional wear and tear. 
     BRIEF SUMMARY OF THE INVENTION 
     In accordance with embodiments of the present invention an apparatus for processing a processing surface  100  of a wafer  105  by means of a processing-beam  200  comprises a means for moving the wafer  105  and the processing-beam  200  relative to each other so that the processing-beam  200  scans the processing surface  100  of the wafer  105  in a scanning path having a curved course with continuously or stepwise changing radiuses. 
     In accordance with a further embodiment of the present invention an apparatus for processing a processing surface  100  of a wafer  105  by means of a processing-beam  200 , the processing-beam  200  scans the processing surface  100  in a scanning path having a curved course with continuously or stepwise changing radiuses comprises a rotational driving means for the wafer  105  and a linear driving means for the processing-beam  200 . 
     In accordance with a further embodiment of the present invention a method for processing a processing surface  100  of a wafer  105  by means of a processing-beam  200  comprises moving the wafer  105  and the processing-beam  200  relative to each other so that the processing-beam  200  scans the processing surface  100  of the wafer  105  in a scanning path having a curved course with continuously or stepwise changing radiuses. 
     In accordance with a further embodiment of the present invention a method for processing a processing surface  100  of a wafer  105  by means of a processing-beam  200 , the processing-beam  200  scans the processing surface  100  in a scanning path having curved course with continuously or stepwise changing radiuses comprises rotating the wafer  105  and moving the processing-beam  200 . 
     The present invention also comprises a computer program for implementing the inventive methods. 
     Advantages of embodiments of the present invention are that a trimming of BAW devices can be achieved in higher quality, shorter processing time and with an increased reliability. In particular, the advantages comprise the following aspects. A smoother speed profile is achieved by avoiding of turning points of the scanning path. As there is no need for high accelerations, a rotational stage needs much less space and can easily be integrated within a vacuum chamber. An angular acceleration can easily be generated. Using a spindle drive allows to eliminate one degree of freedom in the control system. Due to a higher velocity, a removal rate can be made very small at the edges of the wafer  105 . 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       Features of the invention will be more readily appreciated and better understood by reference to the following detailed description, which should be considered with reference to the accompanying drawings, in which: 
         FIG. 1   a  shows a scanning path with a spiral trimming course for a beam-processing a processing surface  100  of a wafer  105  in accordance to the present invention; 
         FIG. 1   b  shows a scanning path with a circular trimming course with stepwise changing radiuses for beam-processing a processing surface  100  of a wafer  105  in accordance to the present invention; 
         FIG. 2  shows a processing arrangement according to an embodiment of the present invention where the wafer  105  rotates and the processing-beam  200  moves along a linear path; 
         FIG. 3  shows a processing arrangement according to an embodiment of the present invention where the wafer  105  rotates and the processing-beam  200  moves forward and backward along the linear path; 
         FIG. 4  shows a cross-sectional view of a processing arrangement according to an embodiment, which is embedded in a vacuum chamber; 
         FIG. 5  shows an alternative processing arrangement according to an embodiment of the present invention where the wafer  105  is fixed and the processing-beam source is mounted on a linear stage that is rotatable so that the processing-beam  200  performs both, the rotation as well as the linear motion; 
         FIG. 6  shows an alternative processing arrangement according to an embodiment of the present invention where the processing-beam is fixed and the wafer  105  rotates and moves at the same time along a linear path; and 
         FIG. 7  shows the meander path trimming using a conventional x-y scanning system. 
     
    
    
     In the subsequent description of the preferred embodiments of the present invention, same or equivalent elements or elements having the same effect or function are provided with the same reference numerals. 
     DETAILED DESCRIPTION OF THE INVENTION  
       FIG. 1   a  shows a schematic view on a spiral path, comprising an ingoing spiral course  110  and an outgoing spiral course  120 , wherein the drawing plane coincides with the wafer surface. It shows moreover a processing-beam  200  at a position X(r,φ).  FIG. 1   a  shows in addition a top view of a processing or treating surface  100 . According to the present invention, the processing surface  100  is at least a part of the wafer surface, wherein in the embodiment of  FIG. 1  the processing surface  100  coincides with the wafer surface that is processed by the processing-beam  200  which is generated by a processing-beam source (not shown in  FIG. 1   a ). The processing beam  200  can comprise an ion-beam or an ionized and/or reactive gas cluster beam. 
     A resonance frequency of a BAW device depends as explained before, besides on a used material, strongly on thicknesses of the layers and therefore these thicknesses have to be adjusted accurately. In this embodiment, the processing-beam  200  follows first the ingoing spiral course  110  towards the center point  230  of the processing surface  100 , where r=0, and an outgoing spiral course  120  away from the center point  230  of the processing surface  100 . An initial or final position of the processing-beam is indicated by a line  130 . Each point X(r,φ) of the ingoing and outgoing spiral course corresponds to a particular radial position r and angular position expressed by the angle φ. 
     A motion of the processing-beam  200  along the scanning path  110  is generated, in general, by two independent drives for the processing-beam  200  and dependent on these drives, a usage of different coordinates is appropriate so that each drive changes one of the coordinates. Besides the usual Cartesian coordinates (x,y), a point X on the scanning path  110  on the processing surface  100  can be identified by angular coordinates, i.e. by using a radial distance r of the point X(r,φ) to the center point  230  of the processing surface  100  and the angular variable φ, which measures the angle between an imaginary axis  140  and a line  150  connecting the center point  230  of the processing surface  100  with the point X(r,φ). In the simplest case the imaginary axis  140  can be identified with the x-axis of the (x,y)-coordinates, but any other axis can also be chosen. Typically, different scans correspond to the usage of different drives for the motion of the processing-beam  200 , e.g. an x-drive changes the position along the x-coordinate and hence is a linear drive, whereas a φ-drive changes the angular variable and hence is a rotational drive and changes the angle φ. 
     Therefore, a combined radial and angular motion generates the spiral course and the present invention is based on an r-φ scanning (e.g. spiral path) instead of an x-y scanning (meander path) used in conventional processing-beam scanning of a processing surface  100  of a wafer  105 . Along the ingoing course  110  the radius value r decreases and angular value φ increases, at the center point  230  with r=0 the processing-beam  200  crosses the rotational axis and the outgoing spiral course  120  is along increasing radius values r as well as increasing angular values φ. 
     In an embodiment, the wafer  105  is mounted on a rotational stage or a rotational drive, wherein the rotation axis  230  is perpendicular to the processing surface  100 , in order to scan the angle. Since the central point  230  and the rotation axis  230 , which is perpendicular to the drawing plane, are identical in this and the following top views, the same reference number will be used in order to provide a simplified notation. The radius scan will be done by a linear stage or linear drive mounted in a way that the processing-beam  200  will come close to the center point  230  of the processing surface  100  where the radial position vanishes, i.e. r=0. 
       FIG. 1   b  shows an embodiment of the present invention, where the scanning path  110  on the processing surface  100  is circular with gradually changing radiuses. The circular path is only one example; the scanning path on the processing surface  100  can also be elliptic or can have any other curved form. The coordinates are the same, as the ones used in  FIG. 1   a , i.e. the processing-beam  200  is at the position X(r,φ), which is parameterized by the radial position r and the angular position given by the angle φ. Therefore, for this scanning path  110  the radius r changes not continuously. In this embodiment the scanning path  110  terminates at the center point  230 , but the motion can also be reversed so that the processing-beam  200  moves towards its initial position or the linear motion crosses the processing surface  100  (cp.  FIG. 1   a ). 
     The spiral course  110  is only one example for a scanning path and, in further embodiments, the scanning path can comprise also elliptic or more general curved courses. Generally, the scanning path can comprise any curved, circular, spiral or elliptic course with gradually, continuously or stepwise changing radiuses. A particular scanning path is defined by a particular way of changing the radial position r and the angular position φ with time, i.e. by specific controlling the radial and angular drive. In the following it will be assumed that the scanning path  110  comprise a spiral course, although more general scanning paths as discussed in the context of  FIG. 1   a  and  FIG. 1   b  are possible for the following embodiments. 
       FIG. 2  is a top view of a processing arrangement to implement the scanning path  110  as shown in  FIG. 1   a  or  1   b  according to an embodiment of the present invention.  FIG. 2  shows a wafer  105  with a processing surface  100 , the processing surface  100  being processed by the processing-beam  200  and the drawing plane coincides with the wafer surface. In accordance with an embodiment of the present invention the wafer  105  rotates in a direction as indicated by arrows  220  about a rotation axis  230 . At the same time the processing-beam  200  describes a linear path  210 . The linear path  210  begins with respect to the rotational axis  230  in this exemplary top view on the left hand side and follows the linear path  210  by crossing the rotation axis  230  and continuing towards the right hand side in relation to the drawing plane of the wafer  105 . The specific form of the spiral course is adjustable by an angular velocity for the rotation about the axis  230  as well as by a linear velocity of the processing-beam  200  along the linear path  210 . 
       FIG. 3  depicts another top view of a processing arrangement comprising the processing-beam  200  and the wafer  105  with the processing surface  100 . The wafer  105  rotates about the rotation axis  230  with a rotation sense indicated by the arrows  220 . In this embodiment the processing-beam  200  moves along a linear path  310  towards the rotation axis  230  and returns from this point along the same path, i.e. the processing-beam  200  does not cross completely the processing surface  100  and instead reverse its motion towards the initial position from where the scan started. In the ideal case the final position is the same as the initial position where the scan started. The resulting scanning path on the processing surface  100  obtained from this embodiment will show differences at the center point  230  in comparison to the scanning path  110  shown in  FIG. 1   a . These differences are due to the fact that the processing-beam  200  stops at the central point  230  and reverses its motion along the linear drive. 
     As indicated by a dotted line in  FIG. 3 , in further embodiments the turning point is not at the rotation axis  230 , but at another point along the path  310  or there are multiple turning points, i.e. multiple motions along the radial coordinate are performed with reversed direction to scan the processing surface  100 . 
     According to a further embodiment of the present invention the scanning velocity along the radial coordinate r and the scanning velocity along the angular coordinate φ can be adjusted independently so that a rate of removal of wafer material can be adjusted for each region on the processing surface  100 . 
     In a further embodiment the radial velocity and the angular velocity are not independently, but instead are in an adjustable fixed relationship to each other. This can be achieved by a so-called spindle drive so that the radius position is a function of the accumulated angle, i.e. r=f(φ±n·360°) (n=number of complete rotations). By means of a spindle drive one degree of freedom is eliminated so that only one velocity needs to be adjusted. A hardware implementation of the so-called spindle drive can be obtained by using gear or gear trains. On the other hand, the linear and rotational drives can be controlled by software and in this case, the so-called spindle drive can be implemented by a particular software, i.e. by a software that ensures the relationship between the radial position r and the angular position φ. 
     In terms of software it is also possible to setup other scanning paths in a way that a computer controls the correct trimming of the BAW device, i.e. adjust a scanning velocity of the processing-beam  200  with respect to the processing surface  100  as well as, if necessary, control the radial and angular drive to perform a multiple scanning of a part of the scanning surface  100  for the case if more wafer material has to be removed. 
     In addition, the linear path  210  and  310 , as shown in  FIG. 2  and in  FIG. 3  are only examples. In the preferred embodiment the linear path  210  and/or  310  crosses the rotational axis  230 , but it can also be shifted parallel to the drawing plane from the central point  230  along the processing surface  100  with the consequence that a region around the central point  230  is not processed. In addition, the linear path  210  and  310  can have different orientations in the drawing plane with respect to the wafer surface so that the linear path is not along the horizontal direction in this drawing plane, but is inclined in the drawing plane. Finally, the rotation sense as indicated by the arrows  220  is only an example. In further embodiments of the present invention, the rotation sense is opposite or changes. 
       FIG. 4  is a cross-sectional view of an arrangement according to an embodiment of the present invention as discussed in the context of the  FIGS. 1-3 . The wafer  105  with the processing surface  100  is mounted on a holder  410 , which is rotatable about the rotation axis  230  and is connected with a drive motor  420 . The radial motion of the processing-beam  200  is along a linear stage  210 . In this embodiment the wafer  105 , the holder  410 , a processing-beam source  205  for providing a processing-beam  200  and the linear stage  210  are arranged inside a vacuum chamber  430 . The rotational axle  230  is fed-through a wall of the vacuum chamber  430  and the drive motor  420  is located outside the vacuum chamber  430 . This is only a schematic view and further details like the vacuum pump, the driving motor for the linear motion along the linear stage  210  and a power supply are not explicitly shown in  FIG. 4 . In  FIG. 4  the edges of the surface of the wafer  105  are indicated by A and B whereas the processing surface  100  is bounded by A′ and B′. In further embodiments both surfaces coincide, i.e. A=A′ and B=B′, but the processing surface  100  can also be smaller than the surface of the wafer  105  as shown in  FIG. 4 . Also a rotational sense as indicated by the arrows  220  is only an example and in different embodiments the rotation sense is opposite or is changed during operation. 
     The embodiment as discussed in the context of  FIG. 2  corresponds to the case where the processing-beam  200  moves from the left hand side  440  of the linear stage  210  toward the right hand side  450  of the linear stage  210  or the other way around. On the other hand, in the embodiment as discussed in the context of  FIG. 3  the processing-beam  200  moves only to the point  460 , where the linear stage  210  crosses the rotation axis  230  indicated by a dashed line and returns to a starting point, which can either be on the left hand side  440  or on the right hand side  450  in the cross-sectional view of  FIG. 4 . In further embodiments, the turning point of the processing-beam  200  is at a different point  460 ′, which is on the processing surface  100 , i.e. in-between A′ and B′, or there are multiple turning points (not shown in  FIG. 4 ). 
       FIG. 5  shows a top view on an alternative arrangement of processing the processing surface  100  of the wafer  105  with the processing-beam  200 . In this embodiment the wafer  105  is fixed and the processing-beam  200  moves along the linear stage  210 , which at the same time rotates about the rotational axis  230  in the direction as indicated by the arrows  220 . Again, the rotation direction as well as the direction of the linear motion along the linear stage  210  are only examples and in different embodiments the rotation as well as the linear motion could be implemented in a reversed way. As in the embodiment discussed in the context of  FIG. 3  the linear motion of the processing-beam  200  can also comprise a forward and backward motion, i.e. the motion stops for example at the point where the linear stage crosses the axis of rotation  230  and moves backwards towards an initial position from which the scan started. It is also possible to use a spindle drive, where the motion along the linear stage  210  is in a fixed relationship to the angular motion in the direction  220 . 
       FIG. 6  shows a top view on another alternative arrangement of processing a processing surface  100  of the wafer  105 . In this embodiment the processing-beam  200  is fixed and the wafer  105  rotates about the rotation axis  230 , which is perpendicular to the processing surface  100  of the wafer  105 . The rotation of the wafer  105  is in a direction  220 . In this embodiment the rotational drive for the wafer  105  is combined with the linear drive so that the wafer  105  rotates and moves linearly along the direction  210 . Combining both motions, the resulting path of the processing-beam  200  will describe a spiral course on the processing surface  100  of the wafer  105 . 
     It is an advantage of embodiments of the present invention, that these trimming tools, used during manufacturing of BAW devices, can be improved significantly with regard to required clean-room space, throughput, pumping times and cost of ownership. 
     It is a further advantage of embodiments of the present invention that changing the trimming from meander path to a spiral course results in much smoother speed profiles, because most frequency profiles to be corrected have a dominantly rotational symmetry. In addition, turning points can be avoided completely and no processing time is wasted. 
     It is a further advantage of embodiments of the present invention that the linear drive for the radius scan can be relatively slow and made by uncomplicated means. There is no need for very high accelerations because the relative speed and acceleration of the processing-beam  200  with respect to the wafer  105  is merely generated by the rotational stage. This is in contrast to conventional trimming tools, where significant accelerations are required in x-direction to obtain accurate results in regions where a high gradient of frequency must be corrected. As the acceleration will be small in embodiments according to the present invention, it may be possible to put the processing-beam source  205  on a linear stage for radius scan rather than the wafer  105 . 
     It is an advantage of embodiments of the present invention, that the rotational stage will need much less space in the vacuum chamber  430  as compared to an x-y scanning system. It is much easier to generate high angular acceleration than it is to generate linear acceleration, because it is possible to use mechanical transmissions in a rotating stage, which will increase torque by simple means. Under the condition that the radius scan is done by moving the processing-beam source  205  the stage will have a stationary rotational axis  230 . It may be possible to use a vacuum feed-through for the axle and place a powerful drive motor outside the vacuum chamber  430  thus eliminating the need for complicating cooling systems inside the vacuum chamber  430  and reduce the chamber volume even further. 
     It is also an advantage of embodiments of the present invention, that it is possible to use mechanical transmissions (spindle drive) so that the radius position (r-value) of the linear drive is a function of the accumulating angle (φ-value) of the rotational stage, thus eliminating one degree of freedom in the control system. In this case there is a fixed locus (path) of the processing-beam  200  on the processing surface  100  of a wafer  105  and only the speed at which the processing-beam  200  moves along the path determines the local removal. 
     It is a further advantage of the embodiments of the present invention that the minimum removal can be made extremely small at the edges of a wafer  105  because the wafer  105  can be rotated at a very high angular rate without compromising safety of the system. If it is required to start the path far away from the wafer edges the wasted processing time will be much shorter. The system is fail-proof by itself; the rotational axis  230  stores most of the kinetic energy and in contrast to linear stages there is no end position, which the moving mass could hit in case of a failure. On the other hand in conventional meander scanning path, the processing-beam  200  was accelerated and decelerated rapidly at each turning point and a failure for deceleration could damage the conventional trimming tool. 
     Using a spiral course  110  in accordance with embodiments of the present invention offers a clear advantage of higher dynamics on most of the wafer area, which enables to etch gradients as steep as the Gaussian beam itself allows. Only the center of the wafer  105  will have lower effective dynamics and a higher minimum removal, but this is acceptable because on typical wafers most material needs to be removed in the center anyways. 
     In accordance with an embodiment, the present invention utilizes one rotational drive and one linear drive in order to move a processing-beam  200  and the processing-beam source  205  generating the processing-beam  200 , respectively, along a spiral course  110  on a wafer  105 . The processing beam can comprise an ion-beam or an ionized and/or reactive gas cluster beam. The linear drive and the rotational drive operate independently or in further embodiments operate with a fixed relationship (spindle drive). 
     The rate of removal of wafer material can be adjusted either by the velocity of the processing-beam  200  with respect to the processing surface  100  or by the number of processing cycles, i.e. by repeating the scanning path  110  a higher rate of removal can be achieved. Finally, a varying height of the processing-beam  200  over the processing surface  100  or a lens for the processing-beam  200  can intensify the rate of removal or direct the processing-beam  200  appropriately. 
     While this invention has been described in terms of several preferred embodiments, there are alterations, permutations and equivalents, which fall within the scope of the invention. It should also be noted that there are many alternative ways of implementing the methods and compositions of the present invention. It is therefore intended that the following appended claims be interpreted as including all such alterations, permutations, and equivalents that fall within the true spirit and scope of the present invention. 
     Some examples of these alterations and combinations of embodiments of the present invention are given as follows. In the embodiment discussed in the context of  FIG. 5  the wafer  105  was fixed, but in further embodiments the wafer  105  can also rotate, i.e. not only the linear stage  220  rotates, but independently also the wafer  105  can rotate about the rotation axis  230  or about another axis (not shown in the figure). In addition, the rotation axis  230  of the linear stage can be shifted to any position on the processing surface  100  and thereby scanning only a part of the processing surface  100  along a spiral course. Further embodiments comprise also a drive to adjust the height of the processing-beam  200  over the processing surface  100 . This allows for example, that the scanning path comprises only an ingoing path  110  and the processing-beam  200  is uplifted at the central point  230  or at any other point along the scanning path  110 . Note, in the embodiment as shown in  FIG. 1   a  every region of the processing surface  100  is scanned twice. If the resulting rate of removal is to high, it may have an advantage to uplift the processing-beam  200  at the central point so that each region of the processing surface  100  is scanned only once. Of course, in further embodiments the scan can also start at the central point  230  and moves towards to the edge of the processing surface  100  of the wafer  105 . Moreover, the scanning path  110  in the embodiments discussed so far is very symmetric. In other embodiments, the scanning path  110  can have different forms as e.g. an elliptic or any other curved form. One example is the embodiments shown in  FIG. 1   b.    
     In the embodiments discussed with the different figures, the center point  230  of the processing surface  100  coincides with a center of the wafer surface. In further embodiments the processing surface  100  is only a part of the wafer surface, the wafer surface having a different center point. According to any embodiment of the present invention, the processing beam  200  can comprises an ion-beam or an ionized and/or a reactive gas cluster beam. The processing-beam  200  is typically Gaussian shaped and, for example, has a half-maximum diameter of around 1 to 15 mm. However, according to inventive concept of the present invention, the half-maximum diameter of the processing beam  200  has a lower limit given by a single die (of about 1 mm or less) and an upper limit given by the wafer size (of about 150 mm or more). Therefore, according to inventive concept of the present invention, the half-maximum diameter of the processing-beam  200  may be within a range of about 1 to 150 mm, preferably within a range of about 1 to 50 mm, and especially in a range of 1 to 15 mm. 
     Depending on certain implementation requirements of the inventive methods, the inventive methods can be implemented in hardware or in software. The implementation can be performed using a digital storage medium, in particular a disk or a CD having electronically readable control signals stored thereon, which cooperate with a programmable computer system such that the inventive methods are performed. 
     Generally, the present invention is, therefore, a computer program product with a program code stored on a machine readable carrier, the program code being operative for performing the inventive methods when the computer program product runs on a computer. In other words, the inventive methods are, therefore, a computer program having a program code for performing at least one of the inventive methods when the computer program runs on a computer. 
     LIST OF REFERENCES 
       100  a processing surface
   105  a wafer
   110  a scanning path
   120  an outgoing spiral course
   130  a final position of the processing-beam
   140  an imaginary axis
   150  a connecting line
   200  a processing-beam
   205  a processing-beam source
   210  a linear path
   220  a rotation sense
   230  a center point
   310  another linear path
   410  a holder
   420  a drive motor
   430  a vacuum chamber
   440  a left hand side of the linear path
   450  a right hand side of the linear path
   460  an end point
   460 ′ a different end point
   710  a motion along the x-direction
   720  a motion along the y-direction
   730  a motion along the negative x-direction
   750  a final point