an amplitude defect in a reflective multilayer coating can be caused by the imbedding of a particle near or at the top of the coating . the particle reduces the local reflectivity of the coating in two ways : the particle directly shadows the underlying layers , and thereby reduces the reflected field due to the absorption of light by the particle . the particle damages the multilayer structure in its vicinity , either in the actual imbedding process , or during the growth of the multilayer around the particle . there is no contribution to the reflected field from the damaged region of the multilayer , and hence the local reflectivity is reduced due to absorption in the damaged region . even in the case where the particle does not remain imbedded in the coating , the residual damaged region of the multilayer acts as an amplitude defect in this case , the defect will physically appear as a pit or scratch in the top of the multilayer coating . it is also important to emphasize that the repair of amplitude defects in the multilayer coating is to be performed on the mask blank , prior to the deposition of the absorber layer . the basic principle of the repair method is to restore the local reflectivity by removing the particle ( if it exists ) and the damaged part of the coating , while exposing the intact underlying layers of the multilayer coating . this process must satisfy two constraints . first , the intact underlying layers must not be damaged in the repair process . second , the repaired region must not produce a significant variation of contrast in the bright field intensity of the lithographic image . the repair method can be generally divided into two steps as shown schematically in fig2 a - 2 c . fig2 a shows a particle 30 embedded a multilayer reflective coating 32 . in the first step shown in fig2 b , the imbedded particle is physically removed by milling using a focused ion beam ( fib ). see “ micro - machining using a focused ion beam ” r . j . young , vacuum 44 , 353 ( 1993 ), incorporated herein by reference . this step is not necessary if the defect is a pit or scratch . the fib has a gas source ( consisting of , for example , he , ne , ar , xe , f , cl , i , br ), or a liquid metal source ( consisting of , for example , ga ). using a fib operated near normal incidence , material can be removed with a depth resolution of 10 nm and a lateral resolution of 100 nm . typical operating parameters for a ga ion source are a beam voltage of 25 kev , a beam current of 40 pa , a beam diameter of 50 nm , and a milling rate of 10 μm 3 / na - min . an advantage of this approach is that the fib can simultaneously provide high - resolution images of the defect , which is useful for alignment and monitoring of the repair process . a potential problem of using the fib is that ga atoms are implanted into the coating to a depth of approximately 10 nm beneath the surface . this reduces the optical contrast of the mo and si layers directly underneath the amplitude defect , and requires that these layers be subsequently removed . a possible way to mitigate the implantation problem is to use a lower beam voltage at the cost of a larger beam diameter . at this stage there is a small hole 34 in the multilayer coating , as shown in fig2 b , having a depth sufficient to remove the imbedded particle . the remaining structure is still defective because the fib milling process produces collateral damage in the vicinity of the hole due to implantation and redeposition . furthermore , the hole itself will produce a phase perturbation in the reflected field . to complete the repair of the defect it is necessary to remove the remaining damaged part of the multilayer coating in the vicinity of the hole , and to smooth out the contour of the surface of the coating . specifically , the second step of the repair process replaces the hole and the surrounding damaged part of the coating with a large - diameter ( 10 μm - 1 mm - diameter ), shallow ( typically & lt ; 150 nm - depth ) crater 36 as shown in fig2 c . the crater is etched in the multilayer coating using a low - voltage (& lt ; 5000 v ) ion beam at a low angle of incidence (& lt ; 20 degrees from the coating surface ). this beam configuration is commonly used for the preparation of thin cross - sectional samples for transmission electron microscopy . see “ precision ion polishing system — a new instrument for tem specimen preparation of materials ” r . alani and p . r . swann , mat res . symp . proc . 254 , 43 ( 1992 ), incorporated herein by reference . it is well known that this technique can produce a shallow crater of controlled depth having a very smooth and gradual surface slope . the ion beam can be the same as that used for removing the particle ( for example , a ga - source fib ) or a second ion beam having a gas source ( consisting of , for example , he , ne , ar , xe , f , cl , i , br ). the beam can be relatively large ( up to 1 mm diameter ) and can be rotated with respect to the mask to improve the uniformity of the etching process . the conditions of low voltage and low angle of incidence for the ion beam are critical for avoiding damage to the underlying layers in the multilayer coating . one important requirement is that the temperature of the coating remains below approximately 200 ° c . throughout the repair process , since higher temperatures can activate structural relaxation at the mo - si interfaces . see “ stress , reflectance , and temporal stability of sputter deposited mo / si and mo / be multilayer films for extreme ultraviolet lithography ”, p . b . mirkarimi , opt eng . 38 , 1246 ( 1999 ) it has been shown that etching si using a ar ion beam of 4 kv and 1 ma at an grazing angle of 20 degrees increases the temperature of the sample to ˜ 85 ° c . see d . bahnck and r . hull , mat . res . soc . symp . proc . 199 , 253 ( 1990 ) ( title : “ experimental measurement of transmission electron microscope specimen temperature during ion milling ”). the temperature increase is expected to be similar for a mo - si multilayer coating , and even smaller for lower beam voltage and lower incidence angles . the other important advantage of using low voltage and low angle of incidence in the etching process is that it minimizes the damage to the layers exposed at the surface of the crater . there is always some mixing induced by the ion beam at the surface . however , studies of ar ion etching of si have shown that the thickness of this damaged surface region is in the range of 1 - 2 nm for a beam voltage of 2 kv and a grazing angle of 14 degrees . see t . schuhrke et al ., ultramicroscopy 41 , 429 ( 1992 ) ( title : “ investigation of surface amorphization of silicon wafers during ion - milling ”). in the case of the mo - si multilayer coating , the mixing induced by the ion beam is likely to result in a thin surface layer of mosi 2 . this will actually provide a benefit of protecting the pure mo and si layers from oxidation . alternatively , after the ion milling step a thin ( 1 - 2 nm ) layer of si can be deposited on top of the exposed multilayer coating in the repaired region , to limit the oxidation at the surface . in order to evaluate the efficacy of the repair , the effect of the residual crater on the lithographic image must be considered . the field reflected in the region of the crater will have a small modulation in phase and amplitude that will produce a small contrast in the bright field intensity at the wafer . the phase modulation is due to the slope of the surface inside the crater . the amplitude modulation arises from three effects . first , the reflectivity changes with the composition of the top layer and hence is modulated along rings within the surface of the crater , corresponding to the regions where the mo and si layers are alternately exposed . second , the reflectivity in the crater is reduced due to the absorption of the surface layer , which is assumed to be mosi 2 , produced by ion beam mixing . third , the reflectivity decreases with the number of bilayers that are remaining in the multilayer coating , which is a minimum in the bottom of the crater . since the size of the crater (& gt ; 10 μm radius ) is much larger than the resolution element , δ , at the mask ( δ ˜ 200 nm ), the residual effect of the repair on the imaging performance will be to cause a local variation in the critical dimension ( cd ). this can be seen in fig3 where the aerial image of a critical - dimension feature on an undamaged coating ( line 40 ) is compared to the same feature located in the repaired region ( line 42 ). using a simple threshold model for the resist , the cd is determined by the width of the aerial image at the threshold intensity . it is evident that the change in the bright field contrast associated with the repaired region produces an increase in the cd . an estimate of the increase in cd produced by a bright field contrast variation δc is , the total budget for the allowable cd variation in euvl is expected to be 5 %. this must be divided among many sources such as flare , pattern error , optical distortion and resist non - uniformity . hence the cd error budget available to mask defects is more likely to be in the range of ˜ 2 %. using eq . ( 1 ), this implies that the contrast variation in the bright field intensity produced by the repaired region of the multlayer coating should be less than 4 %. the different contributions to the bright field contrast variation must be considered . the contrast variation due to the changing of the composition of the top layer between mo and si is plotted in fig4 as a function of the thickness of the mosi 2 surface layer . the undamaged multilayer coating has a top layer of si ( actually sio 2 after oxidation when exposed to atmosphere ). the top layer in the repaired region will alternate between mo and si with increasing depth of the crater ( see fig2 c ). fig4 shows that the contrast variation is different for the mo ( 50 ) and si ( 52 ) top layers , but generally increases with increasing mosi 2 thickness . a similar behavior will occur if there is an oxidized protective layer of si deposited on the surface of the repaired region . another source of contrast variation within the repaired region is the decreased number of layer pairs in the multilayer coating . fig5 shows the contrast variation as a function of the number of layer pairs that are removed , assuming that the undamaged coating has 60 layer pairs . it can be seen that this is a fairly small effect ; the removal of 20 bilayers results in a contrast variation of less than 1 %. finally , the shallow crater in the surface of the repaired coating perturbs the phase of the reflected field , resulting in an additional variation of the contrast in the lithographic image . let us assume that the depth profile of the crater produced by the repair process is gaussian with a maximum depth of n bilayers and a radius w . then the resulting phase perturbation , φ ( r ), in the reflected field is given by , φ  ( r ) = 4  π   n  ( n - 1 ) n  exp  ( - r 2 / w 2 ) ( 1 ) where λ is the vacuum wavelength of the euv light and n is the average index of refraction of the multilayer coating ( n = 0 . 97 for mo / si ). the image intensity at a defocus value of δz is related to the second derivative of the phase according to [ j . m . cowley , “ diffraction physics , 2 nd ed .” ( north - holland , amsterdam , 1984 ) p . 61 ], i  ( r ) = 1 + δ   z  λ 2  π  ∇ 2  φ  ( r ) = 1 + λ 2 2  π  ( na ) 2  ∇ 2  φ  ( r ) = 1 + δ 2 2  π  ∇ 2  φ  ( r ) ( 2 ) here we have used for the defocus position a value of δz = λ /( na ) 2 which is twice the conventional depth of focus ( this is a very conservative case ), and we have defined the resolution element at the mask to be δ = λ /( na ). substituting into eq . ( 2 ) from eq . ( 1 ) we obtain , i  ( r ) = 1 - 4  n   δ 2  ( n - 1 ) n  w 2 - 2  r 2 w 4  exp  ( - r 2 / w 2 ) ( 3 ) the contrast variation in the image intensity is determined from eq . ( 3 ) to be , δ   c ≡ i max - i min i max + i min = 5 . 78  n  ( n - 1 ) n  δ 2 w 2 ( 4 ) now we can estimate the image contrast due to the phase error produced by the profile of the repaired region for realistic lithographic parameters . consider an operating wavelength of 13 nm and a numerical aperture on the image side of 0 . 25 , which corresponds to a resolution element on the mask of approximately 200 nm . the variation of the contrast with the maximum depth of the crater is shown in fig6 a for several different values of the radius w . it is evident that the contrast increases rapidly with increasing depth . however , when the radius is 5 μm the contrast remains less than 1 % for a depth as large as 30 bilayers . fig6 b shows the radius of the crater required to achieve a fixed value of contrast , as a function of the maximum depth . it is evident that a crater having a radius greater than 5 μm , or a diameter greater than 10 μm , will produce a contrast variation in the image intensity of less than 1 %. since the total allowable bright field contrast variation produced by the repaired defect is 4 %, then the contributions from each of the sources described above must be limited to around 1 %. this sets fairly narrow specifications for the structure of the repaired multilayer . the consideration of the modulation of the reflectivity due to the top layer ( fig4 ) requires that the thickness of the mosi 2 surface layer be ˜ 2 nm or less . a protective si layer deposited on the surface to limit oxidation can be approximately twice as thick , or up to 4 nm . the dependence of the contrast on the number of bilayers removed in the repair process restricts the crater to having a maximum depth of ˜ 20 bilayers ( fig5 ). a crater that is 20 bilayers deep must have a diameter greater than 10 μm to keep the phase contrast below the 1 % value ( fig6 b ). it is thus concluded that the repair method of removing an amplitude defect and replacing it with a shallow crater is viable in terms of its effect on the lithographic image . however , the resulting shallow crater is required to have a maximum depth of 20 bilayers and a minimum diameter of approximately 10 μm . this will maintain the local variation in the cd to be less than 2 %, well within the euvl error budget we note that there is no upper limit to the allowable diameter of the crater , and that in practice it could be more convenient to have the diameter of the crater be considerably larger than 10 μm , even as large as 1 mm . this would allow the use of a larger - diameter ion beam for the etching of the crater , i . e . the ion beam diameter could be as large as the crater diameter of 1 mm . the foregoing description of the invention has been presented for purposes of illustration and description and is not intended to be exhaustive or to limit the invention to the precise form disclosed . many modifications and variations are possible in light of the above teaching . the embodiments were chosen and described to best explain the principles of the invention and its practical application to thereby enable others skilled in the art to best use the invention in various embodiments and with various modifications suited to the particular use contemplated . the scope of the invention is to be defined by the following claims .