HOMOGENIZER WITH REDUCED INTERFERENCE
CROSSREFERENCE TO RELATED APPLICATIONS
This application claims the benefit under 35 U.S. C. 119(e)(l) of U.S. Provisional Application No. 60/812,220, filed 09.06.2006.
The disclosure of U.S. Provisional Application 60/812,220, filed 09.06.2006 and US 2005/0127184 Al is considered part of and is incorporated by reference in the disclosure of this application.
BACKGROUND OF THE INVENTION
The present invention relates to a method for creating a target intensity distribution in a target field from a first input light beam propagating in a first propagation direction and a second input light beam, whereby said first input light beam and said second input light beam enter a light entrance surface of a cylindrical lens array of a homogenizer.
The present invention relates to an optical system for creating a target intensity distribution in a target field from one or two light beams having an intensity distribution.
The invention further relates to a material processing apparatus, in particular to a laser annealing apparatus comprising an optical system previously mentioned.
Additionally, the invention relates to a pulse stretcher being capable of generating said aforementioned first and said second laser beams.
The present invention is useful, for example, in annealing of large substrates, in the field of light (e.g. laser) induced crystallization of substrates, in the field of flat panel display, such as liquid crystal display (LCD) (for example: thin film transistor displays (TFT) etc.) or luminescence display (inorganic or organic light emitting diode (LED, OLED),
electroluminescence (EL)) manufacturing processes. Furthermore, the present invention may be used for the fabrication of thin film photovoltaic devices.
In particular, the present invention is useful in order to generate an apparatus being capable of crystallizing amorphous Silicon (a-Si) films thus forming polycrystalline Silicon (p-Si). Such polycrystalline Silicon thin films are widely used in microelectronics and display techniques as mentioned above. P-Si has higher charge carrier mobility as compared to a- Si which is useful for the fabrication of higher speed switching or integration of higher quality driver electronics on the display substrate. Furthermore, p-Si has a lower absorption coefficient for light in the visual spectral range enabling p-Si to be used as a rear electrode for LCD-applications allowing backlight to be transmitted. Lastly, the defect density of p- Si is lower as compared with a-Si which is a prerequisite for the fabrication of high efficient solar cells.
The conversion of a-Si into p-Si maybe employed by heat treatment at around 1000 0C. Such a procedure may only be used for a-Si on heat resistant substrates such as quartz. Such materials are expensive compared to normal float glass for display purposes. Light induced crystallization of a-Si allows the formation of p-Si from a-Si without destroying the substrate by the thermal load during crystallization. Amorphous Silicon may be deposited by a low cost process such as sputtering or chemical vapor deposition (CVD) on substrates such as glass, quartz or synthetics. The crystallization procedures are well known as excimer laser crystallization (ELC), sequential lateral solidification (SLS) or thin beam crystallization procedure (TDX). An overview of these different fabrication procedures is e.g. given by D. S. Knowles et al. "Thin Beam Crystallization Method: A New Laser Annealing Tool with Lower Cost and Higher Yield for LTPS Panels" in SD 00 Digest, 1- 3; Ji-Yong Park et al. "P-60: Thin Laser Beam Crystallization method for SOP and OLED application" in SD 05 Digest, 1-3 in a brochure of the TCZ GmbH Company entitled "LCD Panel Manufacturing Moves to the next Level- Thin-Beam Directional X'tallization (TDX) Improves Yield, Quality and Throughput for Processing Poly-Silicon LCDs".
Line beams with a typical size of e.g. 0.5 mm x 300 mm and a homogeneous intensity distribution are for example applied in silicon annealing on large substrates using excimer
laser crystallization (ELC). State-of-the- art optical systems use refractive optical illumination systems containing crossed cylindrical lens arrays to create the desired intensity distribution. These arrays, the functionality of which is e.g. described in US 2003/0202251 Al, are examples of a more general group of homogenization schemes that divide the input beam into multiple beams using suitably shaped sub apertures. The superposition of these multiple beams in the field plane averages out intensity variations and homogenizes the beam. Typically, two perpendicular directions, namely the so called short axis direction and the so called long axis direction, are homogenized separately using cylindrical optics.
WO 2006/066706 A2 discloses the generation of a line beam with a short axis full width at half maximum (FWHM) dimension of 4 to 7 μm and a long axis dimension of 700 mm. The homogenizer for the long axis dimension comprises a cylindrical fly's eye converter and a rod.
In a laser homogenization scheme containing a fly's eye as an integrator the uniform intensity distribution is achieved by overlapping different portions of the laser profile at a certain field point. This method is e.g. described by Yoshiharu Ozaki and Kiichi Takamoto in their article "Cylindrical fly's eye lens for intensity redistribution of an excimer laser beam" being published in APPLIED OPTICS / Vol. 28, No. 1 / 1 January 1989, pages 106 to 110.
Due to this overlapping of different portions of the laser profile at a certain field point interference can occur. The contrast of the interference pattern depends on the number of independent spatial coherence cells of the laser. A spatial coherence cell of a laser means an area when two beams are coherent to each other.
For many applications the residual interference pattern has to be reduced. Different methods and arrangements for reducing residual interference patterns are known.
US 6,594,090 B2 for example discloses a homogenizer consisting of a fly's eye integrator and a condensing lens. The fly's eye integrator comprising two cylindrical lens arrays is arranged in front of the condensing lens. In order to reduce the interference pattern a
rotating diffuser is used in front of the fly's eye. The effect of the rotating diffuser is to change the relative phase between beams which can interfere at the image plane. The rotating diffuser enhances the etendue, i.e. how "spread out" the light is in area and angle, in both perpendicular directions. While there exist a lot of applications where an increase in etendue does not imply a drawback, especially in laser annealing applications with a very high aspect ratio of the homogenized beam at the substrate an increase in etendue in the short axis is a disadvantage.
US 6,650,480 B2 discloses another possibility to reduce interference in a homogenizer containing a fly's eye. An example described therein refers to the use of a distributed delay device in front of the homogenizing cylindrical lens array. The distributed delay device is i.e. a quartz block with a stepped shape such that optical path differences are successively created. The dimension of one step should be equivalent to the size of one lens in the cylindrical lens array. If the introduced path length difference is larger than the coherence length of the laser beam the interference of rays from different positions at the lens array condensed at a certain field point in the image plane can be reduced. In order to be independent of laser beam fluctuations a large number of cylindrical lenses in the fly's eye are advantageous. In this case a small step size of the distributed delay device is required. This makes the manufacturing of this element very difficult.
A reduction in speckle contrast with the use of pulse stretchers is described in US 6,693,930 Bl. The reduction in contrast is performed based on the fact that laser beams entering a diffuser at a different angle or position produce a changed speckle pattern leaving the diffuser. With the use of pulse stretchers multiple incoherent beams are generated which produce multiple speckle patterns which reduce the residual contrast.
US 6,191,887 discloses another system for speckle reduction. This system divides the pulse into successions of temporally separated and spatially aberrated pulse lets. Spatial aberrators are located along the delay lines and modify the wave front shapes. Due to the aberrations different speckle patterns are generated at the image plane.
Except of the prior art optical apparatus with distributed delay device all other cited optical arrangements according to the prior art have the disadvantage of modifying the angular and
wave front distributions due to diffusers or aberrators. Especially in laser annealing applications this effect in the short axis direction is not acceptable.
SUMMARY OF THE INVENTION
It is an object of the present invention to provide a method in order to reduce interference in laser beam homogenizers which use cylindrical lens arrays.
Another object of the present invention is to provide an optical system/apparatus for creating a homogenized target intensity distribution in a target field from an input light beam having an intensity distribution.
Still another object of the present invention is to provide a material processing apparatus having a highly homogenized target intensity distribution with high aspect ratio of preferably more than 30 000 due to a reduction of interference effects.
A further object of the present invention is to provide a pulse stretcher being capable of generating two incoherent laser beams propagating in different directions out of one coherent incoming laser beam.
These and other objects are solved by a method according to claim 1, an optical system according to claim 27, a material processing apparatus and in particular a laser annealing apparatus according to claim 49 as well as a pulse stretcher according to claim 50.
Advantageous embodiments are disclosed in the dependent claims.
The method for creating a target intensity distribution in a target field premises a first (preferably non-diverging) input light beam propagating in a first propagation direction and a second (preferably non-diverging) input light beam. Said first input light beam and said second input light beam enter a light entrance surface of a cylindrical lens array of a homogenizer. According to the invention said second input light beam propagates in a second propagation direction differing from said first propagation direction. The
interference patterns of both said first input light beam and said second input light beam overlap in said target field resulting in a reduction of residual interferences. This effect may be derived assuming that said first input light beam comprises a plurality of coherent sub beams and said second input light beam also comprises a plurality of coherent sub beams. The interference analysis and the result of said respective calculation will be shown in the following paragraphs based on the drawings 1 to 3.
Preferably, said cylindrical lens array comprises a plurality of cylindrical lenslets each having a straight apex line running in parallel and in that said first input light beam and said second input light beam enclose an angle in a plane normal to said apex lines. The superposition of such oriented input light beams leads to an increased reduction of undesired residual interferences while angular orientations in other planes lead to generally lower reductions.
According to a preferred variant of said method according to the invention said angle holds the following relation:
λ sin(α) = ■ {2i + l), (1)
2 * mP
wherein P is the pitch of said cylindrical lens array and i, m are integers.
The residual interference pattern in said target field is in an ideal case minimized if it is further assumed that said first input light beam and said second input light beam are incoherent to each other and that the peak intensity of said first input light beam and/or the peak intensity of said second input light beam is/are adjusted such that said peak intensities of said first and said second input light beams are almost the same.
Since in real homogenizers the superposition of two input light beams of the type mentioned above and in particular having identical peak intensities does not necessarily result in a target intensity distribution in said target field having a flat top hat profile, according to the invention said peak intensity/ies of said first and/or said second input light beam/s can be adjusted in order to minimize said residual interference pattern in said target
field. This may be for example achieved by measuring the beam profile in said target field and coupling this measurement back as a control variable for adjusting said peak intensity/ies of said first and/or said second input light beam/s.
It is possible that said first and second input light beams are generated by different light sources. In this case in general there is no phase relationship between the different light beams (if not enforced by a respective clock pulse). Nevertheless, it is preferred that said first and said second input light beams are generated by a single light source. This arrangement has the advantage that in most cases the phase relationship between said first and said second light beams will be known or it will be possible to calculate the phase relationship taking into consideration the design parameters of the optical system.
It is to be noted that not only two input light beams, i.e. the first and second input light beams above, may be involved in the homogenization scheme according to the invention but also one additional or a plurality of input light beams, in the following named as at least one additional input light beam. Each additional input light beam may propagate in another propagation direction differing from the propagation directions of the first and second beams as well as -if more than one additional input light beam is involved- also differing from the propagation directions of the other additional input light beams. All input light beams, namely the first and second input light beams and the one or the plurality of additional input light beams, may be adjusted in its respective peak intensities such that a residual interference pattern in said target field is minimized.
In a preferred embodiment a light beam emitted by said single light source is split into a first light beam and a second light beam and where applicable one or more additional light beams. Said first light beam propagates through a pulse stretcher without delay. Said second (and where applicable said additional) light beam(s) is/are delayed and deflected with respect to said first light beam by said pulse stretcher. Said first light beam may be used as said first input light beam and said delayed and deflected second light beam may be used as said second input light beam and if applicable said one or said plurality of additional light beam(s) may be used as said additional input light beam(s). This embodiment has the advantage that both or said plurality of input light beams may be
generated by an optical beam shaping apparatus, namely a pulse stretcher, which is frequently part of an optical system.
The deflection of said second beam (or said one or plurality of additional light beam(s)) with respect to said first beam may easily be generated by arranging a wedge in the beam path of said second (or said one or plurality of additional) light beam(s). Alternatively, a wedge may also be arranged in the beam path of said first light beam.
Another preferred embodiment consists in that that said first propagation direction and/or said second propagation direction and/or said additional propagation direction(s) are automatically or manually adjusted. Said adjustment allows minimizing said residual interference pattern in said target field.
In the case where said light beam is split by at least one beam splitter, the reflectivity of said at least one beam splitter preferably is chosen such that a residual interference pattern in said target field is minimized. A minimization of the residual interference pattern may be achieved by choosing an adequate polarization dependency of the beam splitter for light entering the beam splitter. Another possibility consists in choosing an adequate overall reflectivity of the beam splitter for incoming light. As will be shown in the following with reference to the Figures, preferably, the reflectivity of the beam splitter is 2/3, or when accepting a certain tolerance of reflectivity between 60% and 70%. This holds in particular for beam splitters the reflectivity of which is polarization independent.
In a preferred embodiment of the invention two or more pulse stretchers are arranged in series in order to split said light beam into said first, said second and said one or said plurality of additional light beam(s). The use of two or a plurality of pulse stretchers in series does not only allow to generate a plurality of beams with different propagation directions but also the propagation directions of said plurality of beams may be predetermined in order to fulfil predetermined interference conditions in said target field as required in order to minimize a residual interference pattern.
The optical system for creating a target intensity distribution in a target field according to the invention comprises:
- a first light source for generating a first input light beam and a second light source for generating a second input light beam, or a single light source for generating a light beam and a beam splitter for splitting said light beam into said first input light beam and said second input light beam,
- a homogenizer having a cylindrical lens array with a light entrance surface for being entered by said first input light beam and said second input light beam,
- a first directing device for directing said first input light beam to propagate in a first propagation direction when entering said light entrance surface and - a second directing device for directing said second input light beam propagating in a second propagation direction differing from said first propagation direction when entering said light entrance surface.
The problem mentioned above is completely solved by this optical system according to the invention.
Preferably, said cylindrical lens array comprises a plurality of cylindrical lenslets each having a straight apex line running in parallel and in that said first input light beam and said second input light beam enclose an angle in a plane normal to said apex lines. The superposition of input light beams having such angular orientation with respect to each other leads to a reduction of undesired residual interferences while angular orientations in other planes lead to reductions with in general much less degree.
A preferred embodiment of said optical system according to the invention is characterized by said cylindrical lens array having a pitch and said angle holding relation (1) given above.
Preferably, said first input light beam and said second input light beam are incoherent to each other and the peak intensities of both input light beams are identical.
In general, said first and/or second light sources or said single light source are one or more lasers.
The optical system according to the invention in a preferred embodiment comprises a pulse stretcher for transmitting a first light beam mainly not delayed and for delaying and deflecting a second light beam with respect to said transmitted first light beam. On the one hand said transmitted first light beam forms said first input light beam and on the other hand said delayed and deflected second light beam forms said second input light beam.
Preferably, a wedge is arranged in the beam path of said second light beam for deflecting said second light beam.
The optical system according to the invention preferentially comprises a propagation direction adjusting device for automatically and/or manually adjusting said first propagation direction and/or said second propagation direction. Said propagation direction adjusting device may be a mirror being movable, in particular rotatable and/or linearly slidable.
Alternatively or additionally, said optical system according to the invention may comprise a peak intensity adjusting device for automatically and/or manually adjusting a peak intensity of said first input light beam and/or a peak intensity of said second input light beam. Said peak intensity adjusting device may serve for adjusting said peak intensities of said first and second input light beams in order to minimize a residual interference pattern in said target field. In an ideal case said peak intensity adjustment device may serve for adjusting said peak intensities of said first and second input light beams to be equal. As a peak intensity adjusting device e.g. an attenuator may be used.
As already mentioned in the introductory part of present application the invention may be useful when constructing machines for laser annealing of large substrates. The invention therefore also focuses on a material processing apparatus, in particular a laser annealing apparatus, for creating a target intensity distribution in a target field from an input light beam have an intensity distribution, whereby said intensity distribution in said target field have an expansion in a first dimension and an expansion in a second dimension whereby said expansion in said first dimension exceeds that expansion in said second dimension by more than 30 000. According to the invention said material processing apparatus comprises an optical system according to one of the previously described types.
A pulse stretcher according to the invention which stretches an incoming light beam and which is capable of generating first and second input light beams of the aforementioned kind comprises:
- a beam splitter for splitting an incoming light beam into a first light beam and a second light beam, whereby said first light beam passes said beam splitter mainly not delayed and propagates in a first propagation direction,
- a delay line for delaying said second light beam with respect to said transmitted first light beam, and
- a deflecting device for deflecting said delayed second light beam with respect to said transmitted first light beam such that said delayed second light beam propagates in a second direction.
The pulse stretcher according to a preferred embodiment of the invention may comprise a wedge being arranged in the beam path of said second light beam for deflecting said second light beam.
The pulse stretcher preferably comprises a propagation direction adjusting device for automatically and/or manually adjusting said first propagation direction and/or said second propagation direction. Said propagation direction adjusting device may for example be a mirror being movable, in particular rotatable and/or linearly slidable.
A preferred embodiment of a pulse stretcher according to the invention may also comprise a peak intensity adjusting device for automatically and/or manually adjusting a peak intensity of said first light beam and/or a peak intensity of said second light beam. Exemplarily, the peak intensities of said first and second input light beams are adjusted to be equal.
BRIEF DESCRIPTION OF THE DRAWINGS
Exemplary embodiments will be described hereafter in detail with reference to the accompanying drawings, in which
Fig. 1 shows a state-of-the-art homogenizer comprising two cylindrical lens arrays and a condenser being illuminated by two beams with different propagation direction, whereby only the sub beams hitting neighboring cylindrical lenslets interfere in the field plane, Fig. 2 shows an interference pattern calculated for a beam consisting of a first set of sub beams propagating in parallel to each other prior to transmitting said state-of-the-art homogenizer according to Fig. 1, Fig. 3 shows an interference pattern composed of a first and a second set of sub beams, whereby the sub beams of each set propagate in parallel to each other prior to transmitting said state-of-the-art homogenizer according to Fig. 1 and said sub beams of different sets propagate not in parallel to each other prior to transmitting said state-of-the-art homogenizer according to Fig. 1,
Fig. 4 shows a pulse stretcher being modified with respect to a pulse stretcher according to prior art forming said first set of sub beams delivering said interference pattern according to Fig. 2,
Fig. 5 shows a pulse stretcher according to the invention forming said first and second sets of sub beams delivering said interference pattern according to Fig. 3, Fig. 6 shows another pulse stretcher according to the invention forming said first and second sets of sub beams delivering said interference pattern according to Fig. 3, Fig. 7 shows the pulse stretcher according to Fig. 5 generating a set of delayed pulses due to multiple internal beam splitting, each subsequent delayed pulse exiting the pulse stretcher in a propagation direction with respect to the propagation direction of the preceding pulse deviating by the same angle,
Fig: 8 shows the intensities of the transmitted pulse and delayed pulses out-coupled from a pulse stretcher according to Fig. 5 or Fig. 6 when using a beam splitter having a reflectivity of 60%,
Fig. 9 shows the intensities of the transmitted pulse and delayed pulses out-coupled from a pulse stretcher according to Fig. 5 or Fig. 6 when using a beam splitter having a reflectivity of 66,67%,
Fig. 10 shows the state-of-the-art homogenizer according to Fig. 1 being illuminated by two beams with different propagation direction, whereby the sub beams hitting three adjacent cylindrical lenslets interfere in the field plane, Fig. 11 shows the condition for constructive interference for sub beams being separated by the pitch of a the cylindrical lens array according to Fig. 10,
Fig. 12 shows the condition for constructive interference for sub beams being separated by two times the pitch of a the cylindrical lens array according to Fig. 10,
Fig. 13 shows two pulse stretchers being arranged in series being capable of eliminating an interference pattern in the target field when the lateral coherence length of a beam hitting a cylindrical lens array of a fly's eye homogenizer exceeds twice the array pitch.
Homogenizers with cylindrical lens arrays produce a spatial interference pattern at the image plane which depends on the pitch of the lens array and the focal length of the condenser lens. This matter of fact will be explained in the following:
Figure 1 shows a plane view of a typical configuration for a homogenizer in the xz-plane of a Cartesian coordinate system having the coordinates x, y, z. The homogenizer comprises two cylindrical lens arrays Ia and Ib, a first cylindrical lens array Ia and a second cylindrical lens array Ib, and a cylindrical condenser 2 being arranged along the z- direction and in planes 13, 14, 15 being in parallel to the xy-plane of said Cartesian coordinate system x, y, z.
In the arrangement shown in Fig. 1 the first array Ia is located in the focal plane 13, i.e. at a focal distance fib, of the second array Ib. The condenser 2 is located at a distance d from the second array Ib. A plane located at the focal distance f2 of said condenser 2 forms a field plane. This field plane in the following is indicated with the reference numeral 3.
Said cylindrical lens arrays Ia and Ib each comprise a plurality of preferably identical cylindrical lenslets 8a, 8b, 8c, 8d, 9a, 9b, 9c and 9d. The wording cylindrical lenslet does
not include lenslets in the form of cylinders with circular cross section, only, but also "cylinders" with in particular semi circular cross section or non-circular concave or non- circular convex cross section. For simplicity reasons only four of said identical cylindrical lenslets 8a, 8b, 8c, 8d, 9a, 9b, 9c and 9d for each cylindrical lens array Ia and Ib are shown in Fig. 1. Said identical cylindrical lenslets 8a, 8b, 8c, 8d, 9a, 9b, 9c and 9d of one of said cylindrical lens arrays Ia and Ib are arranged adjacent to each other in x-axis direction. The apex lines 10a, 10b, 10c, 1Od, 11a, l ib, l ie, Hd, 12a, 12b of said individual cylindrical lenslets 8a, 8b, 8c, 8d, 9a, 9b, 9c and 9d of said cylindrical lens arrays Ia and Ib and said cylindrical condenser 2 follow the y-direction of said Cartesian coordinate system x, y, z.
The distance between the apex lines 10a, 10b, 10c, 1Od, 11a, l ib, l ie, Hd of adjacent cylindrical lenslets 8a, 8b, 8c, 8d, 9a, 9b, 9c and 9d within one cylindrical lens array Ia and Ib in the following is called pitch 16, 17. In the present example the pitches 16, 17 of said cylindrical lens arrays Ia, Ib are identical.
For the following explanations one or more light sources (not shown) are assumed to be arranged on the left hand side of said first cylindrical lens array Ia. Said one or more light sources emit one or more light beams being directed to said first cylindrical lens array Ia. Light in this case means electromagnetic radiation of any wavelength.
First, we assume a first beam 4 being emitted from one of said light sources and propagating in z-direction and second we assume a second beam 5 being emitted from said one light source or another light source and propagating in a direction having an angle (measured in said xz-plane) differing from 0° with respect to said z-axis-direction. Each of said first and second beams 4, 5 comprise a plurality of sub beams 4a, 4b, 5a, 5b. Two of each first and second beams being spaced in x-direction by the pitch 16, 17 of said cylindrical lens arrays Ia, Ib are shown in Fig. 1.
Both beams 4, 5 hit a front surface of said first cylindrical lens array Ia on a position 6a, 6b, pass said homogenizer and cross said field plane 3. In this case the position 7a, 7b of a sub beam 4a, 5a or 4b, 5b at the field plane 3 only depends on the position 6a, 6b at the first array Ia and is in a certain range independent of the entrance angle O41, α5a, θ4b, α5b of
the sub beam 4a, 5a or 4b, 5b when entering said first array Ia. Figure 1 indicates the entrance angle O41, αsa, Okb, α5b as being the angle between the z-axis direction and the propagation direction of the respective sub beam 4a, 5a or 4b, 5b in the xz-plane. Here we exemplarily assume oi4a= α4b = 0° and αsa,= αsb≠ 0°.
Due to overlapping of multiple sub beams 4a, 5a or 4b, 5b homogenization in said field plane 3 can be achieved. The sub beams 4a and 4b hit the first lens array Ia at two positions 6a, 6b which are spaced by the pitch 16 of said first array Ia. The two sub beams 4a and 4b are deflected in an equivalent way and are condensed at the same field point 7a in the field plane 3. If the two sub beams 4a and 4b are coherent to each other interference occurs at the field plane 3. The spatial distribution of the interference pattern at the field plane 3 depends on the pitch 16, 17 of the arrays Ia, Ib and the focal length f2 of the condensing lens 2.
Figure 2 shows for simplicity reasons the interference pattern 18 of said first beam 4 consisting of said two sub beams 4a and 4b, only, in said field plane 3 after having passed said homogenizer shown in Fig. 1. It is to be noted that the pattern is calculated for the sub beams 4a and 4b shown in Fig. 1, only. If additional sub beams 4c, 4d,... (not shown) were propagating in z-direction when hitting the front surface of said first cylindrical lens array Ia (but not necessarily being spaced by the pitch 16 of said first cylindrical lens array Ia) these sub beams 4c, 4d,... (not shown) would also contribute to the interference and the interference pattern 18 would be more complex. Nevertheless, the contrast of 100 % would be the same.
Also shown in the Figure 1 are two sub beams 5 a, 5b of said second beam 5 which are incident onto the first array Ia under a different angle αsa,= α5b with respect to the sub beams 4a and 4b of said first beam 4 but hit the first array Ia at the same positions. Due to the working principle of the two cylindrical lens arrays Ia, Ib the two sub beams 5a, 5b leave the second cylindrical lens array Ib under identical angles β5a = βsb = β4a = β4b as compared to the sub beams 4a and 4b. Therefore the two sub beams 5a and 5b of the second beam 5 are condensed at the same field point 7b = 7a as compared to the two sub beams 4a and 4b of the first beam 4. If the sub beams 4a and 4b of the first beam 4 are coherent to each other and also the sub beams 5a and 5b of the second beam 5 are coherent
to each other the residual interference can be reduced to a high degree if the two beams 4 and 5 are incoherent to each other, and the phase difference Δ(p5a>5b between sub beams 5 a and 5b is different by a (2i+l)*π from the phase difference Δ(p4aj4b of the sub beams 4a and 4b, whereby i is an integer.
The phase difference Δφ4;s between beams 4 and 5 can be achieved if relation (1) is fulfilled for the incidence angle α = α5a - 04a = α5b - okb, namely
sin(α) = ^ * (2/ + l), (2)
whereby P is the pitch of the first cylindrical lens array Ia and i is said integer.
If the amplitudes A of beams 4 and 5 are the same and the angle α fulfills the above relation the interference patterns 18, 19 of both beams 4 and 5 look like that shown in Figure 3. The summation 20 of the two incoherent interference patterns 18, 19 leads to a constant intensity which is indicated by a straight line at the normalized intensity value 1 in Figure 3.
The following embodiments generate such two beams 4 and 5 from a single light source in order to compensate for residual interference drawbacks when using a fly's eye homogenizer. The embodiments focus on the generation of said different beams 4 and 5 in a pulse stretcher.
Figure 4 shows a typical configuration of an imaging pulse stretcher for lengthening the propagation path of a light beam 100 in the xz-plane of a Cartesian coordinate system having the coordinates x, y, z. Similar pulse stretchers are also described in US 2005/0127184 Al, US 6,928,093 B2 and WO 2005/050799 Al.
The pulse stretcher shown in Fig. 4 comprises four spherical mirrors 103, 104, 105, 106, in the following referred to as first spherical mirror 103, second spherical mirror 104, third spherical mirror 105 and fourth spherical mirror 106. The radii rl, r2, r3 and r4 of curvature of the mirrors 103, 104, 105 and 106 are identical. The first mirror 103 and the
third mirror 105 are arranged on a common axis of symmetry with their concave sides situated opposite one another, to be precise at a mirror distance Dl corresponding to the radii rl and r3 of curvature. In a similar manner the second mirror 104 and the fourth mirror 106 are arranged on another common axis of symmetry with their concave sides situated opposite one another and at a mirror distance D2=D1 corresponding to the radii r2 and r4 of curvature. The arrangement is thus a confocal or 4f arrangement of the mirrors 103, 104, 105 and 106, with the result that this arrangement has the properties of a 1 : -1 imaging optic. Besides said mirrors 103, 104, 105 and 106 the pulse stretcher according to Fig. 4 comprises a beam splitter 101 being arranged in the center between the first and third mirrors 103, 105 and being tilted by 45° with respect to the z-axis direction. In addition to the prior art a compensation plate 102a is inserted into the delayed beam path. This compensation plate 102a is also tilted with respect to the z-axis direction but by an angle of -45°, i.e. being arranged transverse to the beam splitter 101.
In the following the principle of the pulse stretcher is described:
A light beam 100 is generated for example by a laser, such as an excimer laser (not illustrated). The pulse stretcher has a coupling-in area 118 which serves for coupling the light beam 100 into the space between the first and third mirrors 103, 105. In the present case the coupling-in area 118 is formed by said beam splitter 101 tilted by 45° with respect to the incident light beam 100.
The laser beam 100 hits the beam splitter 101. The incoming beam 100 is split into a transmitted portion 107 and a reflected portion 108. The reflected portion 108 travels to the third mirror 105 and is reflected there. From the third mirror 105 the light beam 108 passes to the second mirror 104, is reflected there and passes to the fourth mirror 106, where the light beam 108 is then reflected. From there the light beam 108 passes to the first mirror 103 where the beam 108 is again reflected. The reflected portion 108 thus has run through the confocal distributed configuration and is imaged again to the beam splitter 101. The "rear side" of the coupling-in area 118 of the beam splitter 101, which is formed in reflective fashion, serves as coupling-out area 120 for coupling the light beam 108 out of the space between the two mirrors 103 and 105. In accordance with arrow 109, the delayed light beam 108 thus leaves the pulse stretcher after four circulations, the out-coupled light
beam 109 and the in-coupled light beam 100 lying on the same optical axis and having the same shape and cross-sectional area after the pulse stretcher, through the use of the spherical mirrors 103, 104, 105 and 106, images the in-coupling area 18 1:1 onto the out- coupling area 20. The propagation path of the light beam 100 has thus been lengthened in the pulse stretcher by approximately 4-times the mirror distance D.
The additional compensation plate 102a being arranged in the propagation path of said delayed light beam 108 in front of said beam splitter 101 serves for compensation the shift of the beam splitter 101, only. If the compensation plate 102a has the same thickness d and refraction index n as has the beam splitter 101 and if the compensation plate 102a is oriented 45° to the reflected portion 108 after having been reflected by the first mirror 103 as shown in the Figure 4, the transmitted beam 107 and the delayed beam 108 leave the pulse stretcher without an offset and with the same angle forming one single out-coupled light beam 109.
Of course the residual property of the delayed beam 108 depends on the adjustment of the pulse stretcher. In laser annealing applications the divergence and pointing in the short axis for the delayed beam 108 has to be close to the divergence of the incoming laser beam 100. If this requirement is achieved also the divergence and pointing in the long axis is very close to the properties of the incoming beam 100.
If we assume transmitted beam 107 forms said first beam 4 of Figure 1 and delayed beam 108 forms said second beam 5, the sub beams 5a and 5b in Figure 1 will have almost the same properties as the sub beams 4a and 4b. This means that the interference patterns will not differ significantly. Although the beams 4, 5 are incoherent the summation does not lead to a significant reduction of interference.
Therefore, in a preferred embodiment according to the invention which is shown in Figure 5 the compensation plate 102b is a wedge which introduces a pointing in a predetermined direction. The angle γ of the wedge 102b should be dimensioned so that the resulting angle CC of the delayed beam 108 fulfills the relation (1) given above. The predetermined direction is the same where the integration with the fly's eye Ia, Ib, 2 occurs. The reflectivity of the beam splitter should be designed so that the transmitted beam 107 and
the delayed beam 108 have almost the same peak intensity. In this case the reduction of contrast is very effective.
Figure 6 shows another embodiment according to the invention for splitting a laser beam 100 into a transmitted beam 107 and a delayed beam 108 in the xz-plane of a Cartesian coordinate system having the coordinates x, y, z.. The difference to the embodiment of Figure 4 is the use of plane mirrors 112, 113, 114, 115, namely the first plane mirror 112, the second plane mirror 113, the third plane mirror 115 and the fourth plane mirror 114, instead of the spherical mirrors 103, 104, 105 and 106. The plane mirrors 112 and 114 are tilted by -45° with respect to the z-axis and the plane mirrors 113 and 115 are tilted by 45° with respect to the z-axis. Said plane mirrors 112, 113, 114, 115 are pair wise arranged with their reflective sides on rectangles opposite to each other. In the center between said first and said third mirror 112, 115 a beam splitter 111 is located. The beam splitter 111 has the same orientation as that in Figure 4, namely tilted by 45° with respect to the z-axis.
If we again assume a laser beam 100 propagating in negative x-axis direction. The laser beam 100 hits the beam splitter 111. The incoming beam 100 is split into a transmitted portion 107 and a reflected portion 108. The transmitted portion 107 is two times deflected, namely at the front surface 118 and at the back surface 121 of the beam splitter 111. In accordance with arrow 110, the transmitted portion 107 leaves the pulse stretcher. The out- coupled transmitted light beam 110 and the in-coupled light beam 100 again lie on the same optical axis and have the same shape and cross-sectional area. The reflected portion 108 travels to the third mirror 115 and is reflected there. From the third mirror 115 the light beam 108 passes to the fourth mirror 114, is reflected there and passes to the second mirror 113, where the light beam 108 is then reflected. From there the light beam 108 passes to the first mirror 112 where the beam 108 is again reflected. The reflected portion 108 thus has run through the distributed configuration and is reflected from the first mirror 112 again to the beam splitter 101. The "rear side" of the coupling-in area 118 of the beam splitter 101, which is formed in reflective fashion, serves as out-coupling area 120 for coupling the light beam 108 out of the space between the two mirrors 112 and 115. In accordance with arrow 109, the light beam 108 thus leaves the pulse stretcher after reflections at the four plane mirrors 112, 113, 114, 115, the out-coupled light beam 109 and the in-coupled light beam 100 lying on different optical axis but having the same shape
and cross-sectional area. The propagation path of the light beam 100 has thus been lengthened in the pulse stretcher by approximately the sum of the distances between the mirrors 112, 113, 114, 115. The difference due to the use of plane mirrors 112, 113, 114, 115 instead of the use of spherical mirrors 103, 104, 105, 106 consists in that that the plane mirrors 112, 113, 114, 115 don't image the incoming laser beam 100.
In the case of a small delay line, i.e. without imaging, but with a delay line longer than the coherence length of the laser, the additional broadening of the delayed beam 108 could be probably accepted.
An advantageous modification of this embodiment consists in having at least one of the plane mirrors (here mirror 112) being rotatable. This rotatable mirror 112 enables the angle α of the beams 5a and 5b in Figure 1 to be continuously adjusted due to rotation of the mirror 112. If the intensity distribution in the plane 3 is monitored the angle of the mirror 112 can be adjusted to minimize the residual interference pattern.
A further advantageous modification of this embodiment consists in having at least one of the plane mirrors (here also mirror 112) being shiftable. The advantage of the possibility to shift the mirror is to adjust the beam position of the delayed beam 108.
In order to make sure that the delayed beam is fully reflected, the beam splitters 101 as in Fig. 5 or 111 as in Fig. 6 can e.g. be polarizing beam splitters, which transmit one portion of the input beam 100 and reflect another portion (the delayed beam 108), which is then completely reflected when hitting the beam splitter the second time, and leaves the pulse stretcher.
In general however, the beam splitters 101 or 111 will not fully reflect the delayed beam 108, but split the delayed beam 108 again and generate another beam 122 which makes one more round trip in the pulse stretcher, which is then partly reflected and out-coupled and partly transmitted again, and so on. As a consequence, a whole series of pulses is generated by the pulse stretcher, each pulse being further delayed by a constant time. Fig. 7 shows the respective situation in case of the beam stretcher shown in Fig. 5 for the central ray.
The relative intensity of the pulses is determined by the reflectivity of the beam splitter. If optical losses in the pulse stretcher (e.g. by absorption) can be neglected, the intensity of the pulses (relative to the input beam) is given by the formulae:
Intensity of transmitted pulse (0. pulse) t
Intensity o f first delayed pulse ( 1 st pulse) r2
Intensity of second delayed pulse (2nd pulse) t r2
(2)
Intensity of n-th delayed pulse (n-th pulse) tnA r2
total sum 1
where r is the reflectivity of the beam splitter and t = 1-r is the transmission.
For r = 60%, the relative intensities of the different pulses are exemplarily shown in Fig. 9.
If wedge 102b is inserted in the pulse stretcher instead of the compensation plate 102a, or mirror 112 is adjusted in order to introduce an angular shift cc of the first delayed beam 108, each subsequent pulse will also be deflected by an angle which is CCn = n α for the n-th pulse (see Fig. 7).
If now a cylindrical lens array, for example said cylindrical lens array Ia of the arrangement according to Fig. 1, is illuminated with these multiple beams, the phase difference of the n-th beam with respect to the direct beam is approximately (for small angles) n-times the phase difference of the first beam and the direct beam. So if the angle α is adjusted for a phase difference of (2i+l) π according to formula (1 (i.e. first delayed beam out of phase) in order to minimize interference, the n-th beam will have a phase difference of n (2i+l) π and beams with even number n will be in phase with the direct beam, beams with odd numbers n will be out of phase and all of them will add up to form the final interference pattern. A similar consideration applies if CC is chosen to be different from (2i+l) π, but in general this case is less favorable.
This means that if multiple beams are present from the pulse stretcher, the relative intensities of the multiple beams have to be adjusted such that the total interference pattern disappears. Since there is only one easily accessible means to adjust the intensities, namely the reflectivity of the beam splitter, the reflectivity of the beam splitter has to be chosen such that the total interference is minimized. For the above case with even-numbered beams in phase and odd-numbered beams out of phase, the condition for perfect cancellation is that the added intensities of these two groups are equal (i.e. each 50% of the input beam intensity). The formulae from above can be used to determine the optimum reflectivity:
Intensity of transmitted pulse (0. pulse) t
Intensity of first delayed pulse (1. pulse) r
Intensity of second delayed pulse (2. pulse) t r
Intensity of third delayed pulse (3. pulse) t2 r2 (3) Intensity of fourth delayed pulse (4. pulse) t3 r2
Intensity of fifth delayed pulse (5. pulse) t4 r2
total sum t + t r2/(l -t2) r2/(l -t2)
The condition of equal intensities then yields r = 2/3 = 66.67%. The resulting relative intensities are shown in Fig. 9.
It can be shown that if reflectivity r deviates from this optimum value, the remaining interference contrast, defined as
is |(2-3r)/(2-r)|, whereby Imax is the maximum intensity and Imm is the minimum intensity of the remaining interference pattern. For example, for r = 50%, the interference contrast is 33.33%.
The above calculations base on the assumption that interference only of subbeams transmitting neighboring lenslets of a lens array such as for example lenslets 8a and 8b or
8b and 8c of lens array Ia of Fig. 1 will occur. But, if the lateral coherence length of the input beam exceeds twice the array pitch P, there is interference not only between the subbeams from adjacent lenslets, but also from lenslets with larger separation (for example lenslets 8a and 8c or 8a and 8d in Fig. 10). For these multiple interference paths with different distances of the interfering rays at the starting surfaces, one pulse stretcher as described above in general cannot eliminate the interference pattern completely. For example, if there is interference between rays with distance P (as is e.g. shown in Fig. 11) and 2P (as is e.g. shown in Fig. 12), the conditions (from formula (I)):
sin(α) = λ (2i+l) / 2P (5) and sin(α) = λ (2j+l) / 4P (6)
would have to be fulfilled at the same time, which is impossible for all integers i, j.
In this case, -as is shown in Fig. 13- the interference can be eliminated by using two pulse stretchers 123, 124. Starting from an input beam 125 the first pulse stretcher 123 generating pulses 126, 127 with propagation directions enclosing an angle CCi that fulfills condition (5) and the second pulse stretcher 124 generating pulses 128, 129, 130, 131, 132, 133 with propagation directions enclosing a different angle CC2 that fulfills condition (6). The beams 126, 127 leaving the first pulse stretcher 123 then serve as input beams for the second pulse stretcher 124.
More general, one pulse stretcher or any other angle-generating device can be used for each interference pattern (i.e. each separation of interfering rays) that needs to be eliminated, each generating an angle CCk which satisfies
sin(cck) = λ (2jk+l) / 2 pk (7)
for the respective separation pk of interfering rays.
The total number of pulse stretchers can be reduced if one or more of the generated angles CCk satisfy formula (7) for more than one of the separations pk of rays at the same time.
For example, for regularly spaced/^ = k P (multiples of array pitch, k is an integer), the number of pulse stretchers can be reduced to m = ceiling [Iog2 k], were ceiling[ ] is the mathematical operation of rounding up to the next integer. The angles αm must then satisfy the condition
sin(αm) = λ (2/m+l) / 2m /> (8)