JP2006005272A - Correction matrix correction method in charged particle beam exposure apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for correcting a correction matrix in a charged-particle-beam exposure apparatus capable of easily measuring a practical value of an image vector in the case of correcting a determined correction matrix or determining the same again. <P>SOLUTION: When an manipulated variable vector <I> is expressed by the product of a correction matrix [C] and an image vector <E>, a suitable image vector <E> is determined in the case of polarizing the correction matrix [C], and a manipulated variable corresponding to the manipulated variable vector <I> determined by the determined image vector <E> is applied to the charged-particle-beam exposure apparatus. From relation between a practical image vector <F> obtained by the result and the manipulated variable vector <I>, a sensitivity matrix [S] for providing relation of <I>=[S]<F> is found out and a new correction matrix is found out as its reverse matrix. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to an image rotation apparatus, image magnification, focal position, orthogonality, anisotropic magnification, 0-90 degrees astigmatism, 45-135 degrees astigmatism, and image x direction in a charged particle beam exposure apparatus. At least one of the position and the y-direction position, a current flowing through the three focus coils, a current flowing through the coils of the two sets of stigmeters, or a voltage applied to the electrodes, and a coil of the one or more sets of deflectors An adjustment method in which at least one of a flowing current or a voltage applied to an electrode is changed, the rotation of the image, the magnification of the image, the focal position, the orthogonality, the anisotropic magnification, 0-90 degrees Astigmatism, 45-135 degree astigmatism, a vector (image vector) indicating each amount of change in the x-direction position and the y-direction position of the image, currents to be passed through the three focus coils, and the two sets of stigmators Electricity flowing through the coil Alternatively, a matrix (correction matrix) of 9 rows and 9 columns for obtaining a vector (an operation amount vector) indicating a voltage applied to the electrode and a current flowing through the coils of the one or more sets of deflectors or a change amount of the voltage applied to the electrode. When the state of the charged particle beam exposure apparatus is changed, the correction matrix is obtained in advance by determining the image vector to obtain the manipulated variable vector as a product of the image vector and the correction matrix. Is related to the method of correcting.

  The process of manufacturing a semiconductor device includes a process of exposing and transferring a pattern formed on a reticle (used to include a mask in the present specification and claims) to a sensitive substrate such as a wafer. In recent years, it has become difficult to resolve patterns refined by increasing the degree of integration of semiconductor devices using conventional exposure methods using ultraviolet light, and new exposures using charged particle beams and ultra-short ultraviolet rays (EUV). Methods are beginning to be used. Among them, an exposure apparatus using a charged particle beam has advantages such as good controllability by electric means, and is promising as a next-generation exposure means.

  In a charged particle beam exposure apparatus, a large area cannot be exposed and transferred at a time due to aberrations and distortions of a charged particle beam optical system. For this reason, for example, an area corresponding to one chip is divided into a plurality of areas called subfields, exposure transfer is performed for each subfield, and the patterns transferred by exposure are connected to obtain a pattern of one chip. The division exposure transfer system has been adopted.

  FIG. 1 shows an outline of a divided exposure transfer type charged particle beam exposure apparatus. In FIG. 1, reference numeral 100 denotes a reticle, 100a denotes a subfield on the reticle 100, 100b denotes a boundary region between the subfields 100a, 110 denotes a sensitive substrate such as a wafer coated with a resist, and 110a denotes an area for one chip of the sensitive substrate 110. , 110b is a transfer area of the sensitive substrate 110 corresponding to each subfield 100a, AX is an optical axis (system axis) of the charged particle beam optical system, EB is a charged particle beam, and CO is a crossover point of the charged particle optical system. is there.

  On the reticle 100, there are a large number of subfields 100a each having a pattern to be transferred to the sensitive substrate 110 on the membrane, separated by a boundary region 100b where no pattern exists. A grid-like column (crosspiece) is provided at a portion corresponding to the boundary region 100b to protect the membrane in terms of heat and strength.

  Each subfield 100a includes a partial pattern obtained by dividing a pattern to be transferred onto the area 110a for one chip of the sensitive substrate 110, and each divided partial pattern is transferred to the sensitive substrate 110.

  The appearance shape of the sensitive substrate 110 is as shown in FIG. 1B, and in FIG. 1A, a part of the sensitive substrate 110 (Va portion in FIG. 1B) is shown enlarged. .

  In FIG. 1, a z-axis is taken in parallel with the optical axis AX of the charged particle beam optical system, and an x-axis and a y-axis are taken in parallel with the arrangement direction of the subfields 100a. Then, as indicated by arrows Fm and Fw, the charged particle beam is scanned stepwise in the y-axis direction while continuously moving the reticle 100 and the sensitive substrate 110 in the opposite directions in the x-axis direction to form a row of subfields 100a. After the pattern transfer of the row is completed, the next subfield 100a row adjacent in the x-axis direction is scanned with a charged particle beam, and thereafter the transfer is performed for each subfield 100a (divided). The pattern for one chip is transferred by repeating (exposure transfer). The x-axis direction indicated by the arrows Fm and Fw is called the stage scanning direction.

  The scanning order of the subfield 100a and the transfer order to the sensitive substrate 110 at this time are as indicated by arrows Am and Aw, respectively. Note that the continuous movement direction of the reticle 100 and the sensitive substrate 110 is opposite because the x axis and the y axis are reversed between the reticle 100 and the sensitive substrate 110 by the pair of projection lenses.

  When performing transfer (divided transfer) in such a procedure, simply projecting the pattern of the subfield 100a in a row in the y-axis direction onto the sensitive substrate 110 with a pair of projection lenses as it is is a sensitive substrate corresponding to each subfield 100a. A gap corresponding to the boundary region 100b is generated between each of the 110 transferred regions 110b. As a countermeasure against this, the pattern transfer position is corrected by deflecting the charged particle beam EB that has passed through each subfield 100a in the y-axis direction by an amount corresponding to the width Ly of the boundary region 100b.

  Also in the x-axis direction, not only the scattering transmission reticle 100 and the sensitive substrate 110 are moved at a constant speed considering the pattern reduction ratio and the subfield interval Lx, but also the relative speed between the image of the subfield 100a and the sensitive substrate 110 is Exposure is performed while deflecting to zero, and the pattern transfer position is corrected so that there is no gap in the x-axis direction between the transferred regions 110b.

  As described above, in the divided exposure transfer method, a pattern corresponding to one chip on the reticle 100 is divided into a large number of subfields 100a, and lattice-like pillars are formed in the boundary region 100b formed between the subfields 100a. Since the (strut) is provided, deflection and thermal distortion of the reticle substrate due to charged particle beam irradiation can be suppressed, and accurate exposure transfer can be performed.

  In addition, since exposure is performed by such a method, compared to a conventional charged particle beam exposure apparatus, the subfield region is exposed all at once, and all the patterns to be exposed are formed on the reticle. Throughput can be improved.

  Note that the number of subfields that can be exposed by the above exposure method is about 20 in the y-axis direction. In the y-axis direction, about 10 subfields must be deflected in the positive and negative directions, respectively, whereas in the x-axis direction, one subfield is deflected in the positive and negative directions. Can be done. Therefore, in the present specification and claims, the y-axis direction is referred to as a “main deflection direction”.

  An example of the optical system of such a charged particle beam exposure apparatus is shown in FIG. FIG. 2 is a schematic diagram of an optical system of the charged particle beam exposure apparatus. In FIG. 2, 11 is a charged particle beam source, 12A to 12C are illumination lenses, 13 is a beam shaping aperture, 14 is an aperture stop, 15 is a reticle, 16A and 16B are projection lenses, 17 is a scattering aperture, and 18 is a wafer. It is.

  The charged particle beam emitted from the charged particle beam source 11 uniformly illuminates the aperture surface of the beam shaping aperture 13 by the illumination lens 12A, and images of the aperture surface of the beam shaping aperture 13 are obtained on the reticle 15 by the lenses 12B and 12C. To form. This image area is an illumination area. The pattern image formed on the reticle 15 is formed on the wafer 18 by the projection lenses 16A and 16B, and the resist on the wafer 18 is exposed. An aperture stop 14 is provided to limit the aperture angle of the illuminating charged particle beam, and a scattering aperture 17 is provided to cut the scattered radiation scattered by the reticle 15.

  In addition, focus coils (dynamic focus coils) 19A, 19B, and 19C are provided to quickly adjust the magnification, rotation, and focal position in small amounts, and can be used to adjust astigmatism, orthogonality, and anisotropic magnification. For this purpose, two stigmeters 20A and 20B are provided. In order to adjust the position of the pattern image, deflectors 21A to 21D are provided.

  In such a charged particle beam optical system, image rotation, image magnification, focal position, orthogonality, anisotropic magnification, 0-90 degree astigmatism, 45-135 degree astigmatism due to changes in some conditions. When at least one of the x-direction position and the y-direction position of the image fluctuates, the current flowing through the coils of the focus coils 19A, 19B, 19C, the stigmeters 20A, 20B, and the deflectors 21A to 21D or electrodes Compensation has been carried out by changing the voltage applied to.

  The method includes rotation of the image, image magnification, focal position, orthogonality, anisotropic magnification, 0-90 degree astigmatism, 45-135 degree astigmatism, image x-direction position, and y-direction position. From the vector (image vector) indicating the amount of change, the current to be passed through the three focus coils, the current to be passed through the coils of the two sets of stigmeters or the voltage applied to the electrodes, and the coils of the one or more sets of deflectors A 9-by-9 matrix (correction matrix) for obtaining a vector (operation amount vector) indicating a change amount of a current to be applied or a voltage applied to an electrode is obtained in advance, and the image vector is determined to determine the operation amount vector. Is obtained as a product of the image vector and the correction matrix.

That is, the rotation of the image is Rot, the magnification of the image is Mag, the focal position is Foc, the anisotropic magnification is AniMag, the orthogonality is Ortho, 0-90 degrees astigmatic blur is S1, and 45-135 degrees astigmatic blur is S2. The position of the image in the x direction is X, the position of the image in the y direction is Y, the current that flows through the first focus coil is I _FC1 , the current that flows through the second focus coil is I _FC2 , and the current that flows through the third focus coil I _FC3 , a current applied to the coil of the first set of _stigmeters, or a voltage applied to the electrode, I _{stig1 = 0} , I _{stig1 = 45} , applied to the current or electrode supplied to the coils of the second set of _stigmeters When the voltage is I _{stig2 = 0} , I _{stig2 = 45} , and the current flowing through one set of deflectors is I _DFx , I _DFy ,

A matrix [C] having C _{11 to} C ₉₉ as elements is given in advance so as to give the following relationship, and the rotation Rot of the image to be changed, the magnification Mag of the image, the focal position Foc, the anisotropic magnification AniMag, When the orthogonality Ortho, 0-90 degree astigmatic blur S1, 45-135 degree astigmatic blur S2, the x-direction position X of the image, and the y-direction position Y of the image are known, by substituting into the equation (3), Each operation amount is obtained. However, in equation (3), Δ represents the amount of change.

Such a matrix [C] is referred to as a “correction matrix” in the present specification and claims. In order to obtain the correction matrix, I _FC1 , I _FC2 , I _FC3 , I _{stig1 = 0} , I _{stig1 = 45} , I _{stig2 = 0} , I _{stig2 = 45} , I _DFx , I _DFy are changed, At that time, rotation Rot, image magnification Mag, focal position Foc, anisotropic magnification AniMag, orthogonality Ortho, 0-90 degrees astigmatism S1, 45-135 degrees astigmatism S2, image x-direction position X, The amount of change in the y-direction position Y of the image is measured, and the sensitivity matrix [S], which is the inverse matrix of the correction matrix [C], is obtained from these relationships using the least square method or the like. Then, the correction matrix [C] is determined by obtaining the inverse matrix of [S].

  However, once obtained, the correction matrix [C] may deviate from the original value when the exposure conditions change due to subsequent changes over time. In addition, when the lens barrel is disassembled and restarted due to overhaul or the like, the value may be considerably different from the original state.

In order to cope with this, the correction matrix [C] may be recreated by using the same method as when the correction matrix [C] is first obtained. However, in general, when first obtaining the sensitivity matrix [S], I _FC1 , I _FC2 , I _FC3 , I _{stig1 = 0} , I _{stig1 = 45} , I _{stig2 = 0} , I _{stig2 = 45} , I _DFx , I _DFy As a result, it is difficult to predict where the position of the image will be, and the values of the image position and other elements of the actual image vector will be changed. It takes considerable effort to measure.

  The present invention has been made in view of such circumstances, and in a charged particle beam exposure apparatus in which an actual value of an image vector can be easily measured when a predetermined correction matrix is corrected or determined again. It is an object of the present invention to provide a correction matrix correction method.

The first means for solving the above problem is that in a charged particle beam exposure apparatus, image rotation, image magnification, focal position, orthogonality, anisotropic magnification, 0-90 degree astigmatism, 45-135. Astigmatism, at least one of the x-direction position and the y-direction position of the image, a current flowing through the three focus coils, a current flowing through the coils of the two sets of stigmeters, or a voltage applied to the electrodes, An adjustment method for changing by changing at least one of a current flowing through a coil of the deflector or a voltage applied to an electrode, the rotation of the image, the magnification of the image, the focal position, the orthogonality, the unequal A current flowing through the three focus coils from a vector (image vector) indicating each amount of change in the direction magnification, 0-90 degrees astigmatism, 45-135 degrees astigmatism, x-direction position of the image, and y-direction position. The two sets of stigmes 9 rows and 9 columns to obtain a vector (operation amount vector) indicating the amount of change in the current applied to the coil of the data or the voltage applied to the electrode and the current applied to the coil of the one or more sets of deflectors or the voltage applied to the electrode. A matrix (correction matrix) is obtained in advance, and by determining the image vector, the state of the charged particle beam exposure apparatus is changed in obtaining the manipulated variable vector as a product of the image vector and the correction matrix. In some cases, the correction matrix is corrected by the correction matrix in the charged particle beam exposure apparatus (Claim 1).
(1) Among the image rotation, image magnification, focal position, orthogonality, anisotropic magnification, 0-90 degree astigmatism, 45-135 degree astigmatism, image x direction position, y direction position Step (2) for obtaining the manipulated variable vector by changing at least one and multiplying the image vector by the correction matrix (2) In the charged particle beam exposure apparatus, the three focus coils corresponding to the manipulated variable vector A step of applying a current flowing through the coil of the two sets of stigmators, a voltage applied to the electrodes or a voltage applied to the electrodes, and a change amount of the current flowing through the coils of the one or more deflectors or the voltage applied to the electrodes (3 ) With the amount of change in the step (2) given, actual image rotation, image magnification, focal position, orthogonality, anisotropic magnification, 0-90 degree astigmatism, 45-135 degree non-focus Point blur, x-direction position of image, y-direction position (4) In the image vector, the rotation of the image, the magnification of the image, the focal position, the orthogonality, the anisotropic magnification, the 0-90 degree astigmatism, and the 45-135 degree astigmatism. The combination of the image vectors is determined so that all of the blur, the x-direction position, and the y-direction position of the image are changed, the image vectors are changed, and the steps (2) and (3) are repeated a predetermined number of times. Returning step (5) Actual image rotation, image magnification, focal position, orthogonality, anisotropic magnification, 0-90 degree astigmatism, 45-135 degree measured in the steps (3) (6) A step of obtaining a sensitivity matrix that is an inverse matrix of the correction matrix from the relationship between astigmatism blur, each change amount of the x-direction position and the y-direction position of the image, and the combination of the manipulated variable vectors at that time Step for obtaining a new correction matrix from the sensitivity matrix obtained in step 5) In the means, when determining the manipulated variable vector, the image vector is determined in advance without using feeling or experience, and the manipulated variable vector is obtained by using this image vector and the correction matrix used so far. An operation amount corresponding to the obtained operation amount vector is given, and the actual value of each element of the image vector that appears as a result is measured. Since the correction matrix used so far is considered to be reliable to some extent, the position of the image formed as a result is the position of the x-direction position and y-direction position of the image in the image vector used to determine the manipulated variable vector. It should not deviate much from the position calculated from the amount of change. Therefore, since the position where the image is formed can be predicted in advance in the measurement of the actual image vector, the actual image vector can be easily measured.

  In the step (5), when the number of unknowns to be obtained is the same as the number of measurement points, the equation is solved. When the number of measurement points is larger than the number of unknowns to be obtained, a known fitting technique represented by the least square method is used. be able to.

The second means for solving the problem is the first means, wherein the rotation of the image is Rot, the magnification of the image is Mag, the focal position is Foc, the anisotropic magnification is AniMag, The orthogonality is Ortho, the 0-90 degree astigmatic blur is S1, the 45-135 degree astigmatic blur is S2, the x-direction position of the image is X, and the y-direction position of the image is Y. The current flowing through the focus coil is applied to I _FC1 , the current flowing through the second focus coil is I _FC2 , the current flowing through the third focus coil is applied to I _FC3 , and the current or electrode applied to the coil of the first set of stigmators I _{stig1 = 0} , I _{stig1 = 45} , current flowing through the coil of the second set of _stigmeters , or voltage applied to the electrodes I _{stig2 = 0} , I _{stig2 = 45} , current flowing through the one set of deflectors I _DFx, and _{I DFy} Come,

The sensitivity matrix represented by

And the step (5) is performed (claim 2). Note that Δ represents the amount of change.

  In a projection optical system of a general charged particle beam exposure apparatus, even if the stigmator is operated, the focal position, the rotation of the image, and the magnification hardly change. Further, even if the focus coil is operated, there is almost no change in the orthogonality, the anisotropic magnification, the 0-90 degree astigmatism, and the 45-135 degree astigmatism. Therefore, elements corresponding to these in the sensitivity matrix [S] can be regarded as 0.

  By doing so, the value of the unknown number of the sensitivity matrix decreases, and the sensitivity matrix can be obtained with a small number of measurements.

The third means for solving the problem is the second means, wherein elements S ₁₈ , S ₁₉ , S ₆₈ , S ₆₉ , S ₇₈ , and S ₇₉ of the sensitivity matrix are further set to 0. (Claim 3).

  Even if the deflector is operated, since the degree of change of the focal position, 0-90 degree astigmatism, and 45-135 degree astigmatism is small, these can also be regarded as approximately 0. In this way, the sensitivity matrix can be obtained with a small number of measurements.

The fourth means for solving the problem is the second means, and the sensitivity matrix elements S ₁₁ , S ₁₂ , S ₁₃ , S ₆₄ , S ₆₅ , S ₆₆ , S ₆₇ , S ₇₄ , S ₇₅ , S ₇₆ , and S ₇₇ use the values of the correction matrix before update as they are (claim 4).

  The amount of change in the focus position when the focus coil is operated, the amount of change in 0-90 degree astigmatism, and 45-135 degree astigmatism do not change even if the lens barrel is disassembled and reassembled. Conceivable. Therefore, in this means, the values of the original sensitivity matrix are used as they are. Thus, the sensitivity matrix can be obtained with a small number of measurements.

  A fifth means for solving the problem is any one of the first to fourth means, and the correction matrix and the sensitivity matrix correspond to each subfield arranged in the main deflection direction. In this case, they are respectively set (claim 5).

  As described in the background art section, the deflection amount with respect to the main deflection direction is large, but the deflection amount with respect to the direction perpendicular thereto is only one subfield in each of the positive and negative directions, and therefore, the direction perpendicular to the main deflection direction. May be treated as the same correction matrix depending on the subfield. For example, this makes it possible to halve the correction matrix to be obtained.

  A sixth means for solving the above-mentioned problem is that the correction matrix and the sensitivity matrix are respectively set corresponding to the respective subfields arranged in the main deflection direction. A correction method for a correction matrix in a charged particle beam exposure apparatus, which is one of the first to fifth means, is a matrix correction method, wherein both ends of a main deflection direction (maximum main deflection direction of a charged particle beam) This is performed for five or more subfields including the subfield at the deflection position), and for the remaining subfields, each result of the correction matrix is obtained by calculation using the result. Of correcting correction matrix in charged particle beam exposure apparatus. (Claim 6).

  In this means, since the correction matrix in the subfield that was not measured is obtained by calculation from the correction matrix of the measured subfield, the number of measurements can be reduced. The reason why the subfields at both ends of the main deflection direction (the maximum deflection position of the charged particle beam in the main deflection direction) is always measured is that the extrapolation calculation may not be accurate. is there. In addition, the actual measurement is performed on five or more subfields when each element of the sensitivity matrix is expressed as a function of the deflection position, and accuracy cannot be obtained unless it is approximated by a power series of at least a second order or higher. Because. Since three parameters are required to determine the secondary power series, the data of three subfields may be sufficient. However, in order to cancel the measurement error with redundancy, actual measurement is performed on at least five subfields. Like to do.

  A seventh means for solving the above-mentioned problem is the sixth means, wherein the calculation uses each element of the correction matrix and a deflection position of the charged particle beam corresponding to each subfield as a variable 3. Fitting to the power series up to the next (Claim 7).

  According to the results of experiments conducted by the inventor, in general, each element of the correction matrix can be expressed by a power series up to the third order with the deflection position of the charged particle beam as a variable.

  An eighth means for solving the problem is any one of the first to seventh means, and measures an X-direction position change amount and a Y-direction position change amount of an image in each subfield. In this case, in the image vector, one subfield in which both the X direction position change amount and the Y direction position change amount are set to zero, or the X direction position change amount and the Y direction position change amount are set to zero. When two subfields are set as reference subfields, and the actual X direction position change amount and Y direction position change amount in other subfields are measured, the X direction position and Y direction position of the image in the reference subfield are determined. Measurement is performed as a reference (claim 8).

  Of the image vectors, the X-direction position change amount and the Y-direction position change amount must be measured with reference to something, but when measuring the position change of the image, there is no reference position. Therefore, in this means, in the image vector, one subfield in which both the X direction position change amount and the Y direction position change amount are set to zero, or the X direction position change amount and the Y direction position change amount are each zero. Is set as a reference subfield. Then, with reference to the actual position of the reference subfield, the X direction position change amount and the Y direction position change amount in other subfields are measured.

  According to a ninth means for solving the above problem, a linear combination of the correction matrix obtained by any one of the first to eighth means and the original correction matrix is newly obtained. A correction matrix correction method in a charged particle beam exposure apparatus, wherein a correction matrix is used (claim 7).

  Apart from the case where the lens barrel is disassembled and overhauled, the change in the correction matrix is considered to occur moderately during normal aging, and the newly obtained correction matrix contains an error. It is also possible. Therefore, in this means, not only the newly obtained correction matrix but also the original correction matrix is taken into consideration, and a new correction matrix is determined by linearly combining them. A typical example calculates a new correction matrix by exponential smoothing calculation. As a result, it is possible to eliminate a sudden change in the correction matrix and make it less susceptible to noise.

  According to the present invention, there is provided a correction matrix correction method in a charged particle beam exposure apparatus that makes it easy to measure an actual value of an image vector when a determined correction matrix is corrected or determined again. Can do.

  Hereinafter, examples of embodiments of the present invention will be described. In the following description, the rotation of the image is Rot, the magnification of the image is Mag, the focal point is Foc, the anisotropic magnification is AniMag, the orthogonality is Ortho, 0-90 degrees astigmatic blur is S1, 45-135 degrees The point blur is S2, the x-direction position of the image is X, the y-direction position of the image is Y, and an image vector determined to be changed among these vectors (image vectors) is represented by <E>.

Also, the current flowing through the first focus coil is I _FC1 , the current flowing through the second focus coil is I _FC2 , the current flowing through the third focus coil is I _FC3 , and the current flowing through the coil of the first set of stigmeters Alternatively, the voltage applied to the electrodes is I _{stig1 = 0} , I _{stig1 = 45} , the current flowing through the coil of the second set of _stigmeters , or the voltage applied to the electrodes is I _{stig2 = 0} , I _{stig2 = 45} , one set of deflection I _DFx and I _DFy are currents flowing through the device, and an operation amount vector having these elements as <I>. An image vector observed when an operation amount corresponding to the operation vector <I> is given is represented by <F>.

  In addition, the correction matrix for combining these is represented by [C] as described above, and the sensitivity matrix is represented by [S]. Then, “′” (dash) is added to each of the correction matrix and sensitivity matrix before the update to distinguish them from those after the update.

First, it is checked whether the correction matrix [C ′] needs to be updated. At this point
<I> = [C ′] <E> (4)
Therefore, a predetermined image vector <E> is determined, and the manipulated variable vector <I> is obtained by substituting it into the equation (4). Then, a change corresponding to the determined manipulated variable vector <I> is given to each focus coil, stigmator, and deflector, and the actual image vector <F> obtained as a result is the predetermined image vector <E>. Find out how different it is. When this difference exceeds the allowable value, the correction matrix is updated.

  The simplest method for determining the predetermined image vector <E> is to select a vector in which only one element is zero and the other elements are zero. Then, for all elements, image vectors <E> that are not zero are sequentially determined, and for each, the difference between the set image vector <E> and the measured image vector <F> is obtained by the method described above. .

  When it is determined that the correction matrix [C] needs to be updated by the above method, a new image vector <E ″> is obtained by the following method.

First, N image vectors are determined. _Let these be <E _n > (n = 1 to N: N ≧ 9). Then, by substituting these into the equation (4), the corresponding manipulated variable vector <I _n > (n = 1 to N) is obtained, and these manipulated variables are given to each focus coil, stigmator, and deflector to actually An image vector <F _n > is obtained. From these, a new sensitivity matrix [S] is obtained.

If N = 9,
<F _n > = [S] <I _n > (n = 1 to 9) (5)
[S] can be obtained by solving the following equation. In this case, it is considered that [S] obtained by the measurement error becomes inaccurate.

  Therefore, normally, N> 9 and [S] is determined by the method of least squares. That is,

S _ji (element of [S]) is determined so as to minimize W determined by. _{Here, (F} j) _n, is _{(I j) n,} which is an element of each _{F n, I} n. As is well known, this is

Can be determined by solving If a new sensitivity matrix [S] is obtained in this way, a new correction matrix [C] can be obtained as its inverse matrix.

In the above description, calculation was performed on the assumption that equation (5) holds. However, in practice, equation (5) includes a measurement bias,
<F _n > = [S] <I _n > + <f> (7)
It may be more appropriate to think that Here, <f> is a bias vector (9 elements). In this case, instead of the equation (6),

S _ji and f _j may be determined by using.

  Actually, there is a relationship between the image vector and the manipulated variable vector that is determined by the physical properties of the focus coil, stigmator, and deflector. By using this relationship, a new sensitivity matrix can be obtained more easily. be able to. The method is shown below.

  That is, even if the stigmator is operated, the focal position, the rotation of the image, and the magnification hardly change. Further, even if the focus coil is operated, there is almost no change in the orthogonality, the anisotropic magnification, the 0-90 degree astigmatism, and the 45-135 degree astigmatism. Therefore, elements corresponding to these in the sensitivity matrix [S] can be regarded as 0. Similarly, even if the deflector is operated, since the degree of change of the focal position, 0-90 degree astigmatism, and 45-135 degree astigmatism is small, these can also be regarded as approximately 0.

  From the above relationship, the required sensitivity matrix [S] is

It can be expressed as. In the following description, considering the bias <f>, the least square method is used based on the equation (7). From the above assumptions, S ₁₁ , S ₁₂ , S ₁₃ , S ₆₄ , S ₆₅ , S ₆₆ , S ₆₇ , S ₇₄ , S ₇₅ , S ₇₆ , and S ₇₇ are determined and need not be obtained.

  For j = 2, 3,

Therefore, S _ji , S _j2 , S _j3 , S _j8 , S _j9 , and f _i are _obtained from these equations by the least square method.

  That is, for j = 2,3

The _S ji to minimize _{respectively,} to determine the _{S j2, S j3, S j8} , S j9, f i.
To do that,

As a result,

Is obtained.
here,

It is.

  For j = 4,5,

And S ₅₄ = S ₄₅ , S ₅₅ = −S ₄₄ , S ₅₆ = −S ₄₇ , S ₅₇ = S ₄₆ because of the symmetry with respect to the stigmator.
Using these relationships, the sum of squares

Each S _ji may be obtained so as to minimize.
To do that,

As a result,

Is obtained. here,

It is.

  For j = 8,9,

, The value of S _ji is determined by the least square method. Therefore, for each of j = 8, 9

Each S _ji may be obtained so as to minimize.
For each j = 8,9

As a result,

Is obtained.
here,

When the sensitivity matrix is obtained as described above, a correction matrix can be obtained as an inverse matrix thereof. In the above example, the fitting is performed using the least square method, but it goes without saying that the sensitivity matrix may be determined using another known fitting method.

In addition, in the second example in which all elements are not obtained by the least square method, the calculation is performed by applying the least square method for each row division. In this case, the sensitivity matrix is (2). as a kind of formula, and calculates the expression (6) as a constant rather than variable specific elements, by the least square method to 0 those obtained by partially differentiating the elements S _ij which not zero or constant, with unknown Each element S _ij may be obtained.

  By the way, strictly speaking, it is necessary to obtain the correction matrix for each subfield. Even if it is every subfield, the exposure is performed by changing the deflection amount into a figure of 8. Therefore, the deflection amount changes greatly corresponding to all subfields in the main deflection direction, but the main deflection direction. In the direction perpendicular to the direction, the amount of deflection differs only in two subfields, and the amount of deflection is small. Therefore, in a direction perpendicular to the main deflection direction, it is not a big problem to obtain a correction matrix with the deflection amount being zero and to use it in common for all subfields. In this way, the measurement can be performed for each subfield in the main deflection direction by changing the deflection amount in the main deflection direction.

  Usually, about 20 subfields are arranged in the main deflection direction, so about 20 subfields (with the deflection amount in a direction perpendicular to the main deflection direction being zero) are as described above. The correction matrix may be updated by the method.

  However, even in this case, a considerable number of measurement data must be collected for every 20 subfields, which requires a lot of labor. In order to deal with such a problem, the inventor examined the relationship between the elements of the correction matrix for each subfield, and these were approximated as the second or third power series of the deflection amount in the main deflection direction. I found it possible.

  Therefore, when approximating with a quadratic power series, measure three or more sub-fields to create a correction matrix, and approximate the quadratic power series from the data by solving an equation or fitting such as the least squares method Can be done. Similarly, when approximating with a third-order power series, measurement is performed on four or more subfields, and the fourth-order power series may be approximated by solving an equation from the data or by fitting such as a least square method. However, in order to mitigate measurement errors, it is preferable to create a correction matrix by measurement for at least five subfields, and to obtain a correction matrix for other subfields from the data by calculation.

  In any case, it is preferable to obtain a correction matrix by actual measurement for the subfields at both ends in the main deflection direction. The extrapolation calculation is for avoiding the possibility that the error may be larger than that of the interpolation calculation.

  Further, since there is nothing that can be used as an accurate absolute reference when measuring the position of an image, it is difficult to measure the position fluctuation of the image under each condition. Therefore, in the image vector, one subfield in which both the X direction position change amount and the Y direction position change amount are set to zero, or the X direction position change amount and the Y direction position change amount are set to zero. It is desirable to set the field as a reference subfield. If the X direction position change amount and the Y direction position change amount in the other subfields are measured with reference to the actual position of the reference subfield, the X direction position change amount in the other subfields, The amount of change in position in the Y direction can be accurately measured. In order to create the reference subfield, X = 0 and Y = 0 or X = Y = 0 in the image vector for determining the operation amount vector may be used.

  The new correction matrix obtained as described above may greatly deviate from the original correction matrix due to a change in the projection optical system when the lens barrel is disassembled and reassembled. Since it is considered, it is preferable to try it as it is.

On the other hand, the new correction matrix obtained to cope with the change with time rarely changes rapidly from the original correction matrix, and the measurement error may be relatively large. Therefore, in such a case, a correction matrix [C ″] that is actually used after exponential smoothing between the newly obtained correction matrix [C] and the original correction matrix [C ′]. It is preferable that
[C ″] = (1−α) [C ′] + α [C]
The correction matrix [C ″] that is actually used is obtained as follows. Α is an exponential smoothing coefficient. This reduces the influence of noise even when the newly obtained correction matrix [C] includes noise. Can do.

It is a figure which shows the outline | summary of the charged particle beam exposure apparatus of a division | segmentation exposure transfer system. It is a figure which shows an example of the optical system of a charged particle beam exposure apparatus.

Explanation of symbols

DESCRIPTION OF SYMBOLS 11 ... Charged particle beam source, 12A-12C ... Illumination lens, 13 ... Beam shaping aperture, 14 ... Aperture stop, 15 ... Reticle, 16A, 16B ... Projection lens, 17 ... Scattering aperture, 18 ... Wafer, 19A-19C ... Focus coil, 20A, 20B ... Stigmeter, 21A-21D ... Deflector, 100 ... Reticle, 100a ... Subfield, 100b ... Boundary region 110 ... Sensing substrate, AX ... Optical axis, EB ... Charged particle beam, CO ... Cross Over point

Claims (9)

In a charged particle beam exposure apparatus, image rotation, image magnification, focal position, orthogonality, anisotropic magnification, 0-90 degrees astigmatism, 45-135 degrees astigmatism, image x-direction position, y-direction At least one of the positions is applied to the current that flows through the three focus coils, the current that flows through the coils of the two sets of stigmeters or the voltage that is applied to the electrodes, and the current that flows through the coils of one or more sets of deflectors An adjustment method for changing at least one of the voltages to be applied, the rotation of the image, the magnification of the image, the focal position, the orthogonality, the anisotropic magnification, the 0-90 degree astigmatism, 45- From the 135 degree astigmatism, a vector (image vector) indicating the amount of change in each of the x-direction position and the y-direction position of the image, the current that flows to the three focus coils and the current that flows to the coils of the two sets of stigmeters Apply to electrode A matrix of 9 rows and 9 columns (correction matrix) for obtaining a vector (a manipulated variable vector) indicating a voltage and a change amount of a current applied to the coils of the one or more sets of deflectors or a voltage applied to the electrode is obtained in advance. By determining the image vector to obtain the manipulated variable vector as a product of the image vector and the correction matrix, the correction matrix is corrected when the state of the charged particle beam exposure apparatus changes. A method for correcting a correction matrix in a charged particle beam exposure apparatus, comprising the following steps.
(1) Among the image rotation, image magnification, focal position, orthogonality, anisotropic magnification, 0-90 degree astigmatism, 45-135 degree astigmatism, image x direction position, y direction position A step of obtaining the manipulated variable vector by changing at least one and applying the correction matrix to the image vector; and (2) a current passed through the three focus coils corresponding to the manipulated variable vector, and the two sets A step of giving a change amount of a current applied to a coil of a stigmator or a voltage applied to an electrode and a current applied to a coil of one or more sets of deflectors or a voltage applied to an electrode (3) to the charged particle beam exposure apparatus , With the amount of change in the step (2) given, actual image rotation, image magnification, focal position, orthogonality, anisotropic magnification, 0-90 degrees astigmatism, 45-135 degrees non-focus Point blur, x-direction position of image, y-direction position (4) In the image vector, the rotation of the image, the magnification of the image, the focal position, the orthogonality, the anisotropic magnification, the 0-90 degree astigmatism, and the 45-135 degree astigmatism. The combination of the image vectors is determined so that all of the blur, the x-direction position, and the y-direction position of the image are changed, the image vectors are changed, and the steps (2) and (3) are repeated a predetermined number of times. Returning step (5) Actual image rotation, image magnification, focal position, orthogonality, anisotropic magnification, 0-90 degree astigmatism, 45-135 degree measured in the steps (3) (6) A step of obtaining a sensitivity matrix that is an inverse matrix of the correction matrix from the relationship between astigmatism blur, each change amount of the x-direction position and the y-direction position of the image, and the combination of the manipulated variable vectors at that time Step for obtaining a new correction matrix from the sensitivity matrix obtained in step 5) The rotation of the image is Rot, the magnification of the image is Mag, the focal position is Foc, the anisotropic magnification is AniMag, the orthogonality is Ortho, the 0-90 degree astigmatic blur is S1, the 45-135 degree The astigmatic blur is S2, the x-direction position of the image is X, and the y-direction position of the image is Y. The current flowing through the first focus coil is I _FC1 , the current flowing through the second focus coil is I _FC2 , The current flowing through the focus coil of I ₃ is I _FC3 , the current flowing through the coil of the first set of _stigmeters or the voltage applied to the electrodes is I _{stig1 = 0} , I _{stig1 = 45} , and the coils of the second set of _stigmeters When the current to be applied or the voltage to be applied to the electrode is I _{stig2 = 0} , I _{stig2 = 45} , and the current to be supplied to one set of deflectors is I _DFx and I _DFy ,

The sensitivity matrix represented by

The method of correcting the correction matrix in the charged particle beam exposure apparatus according to claim 1, wherein the step (5) is performed. 3. The correction matrix correction method in the charged particle beam exposure apparatus according to claim 2, wherein elements S ₁₈ , S ₁₉ , S ₆₈ , S ₆₉ , S ₇₈ , and S ₇₉ of the sensitivity matrix are further set to 0. A correction matrix correction method in a charged particle beam exposure apparatus characterized by the above. A method for correcting a correction matrix in the charged particle beam exposure apparatus according to claim 2 or claim 3, wherein elements S ₁₁ , S ₁₂ , S ₁₃ , S ₆₄ , S ₆₅ , S ₆₆ , S _{67 of} the sensitivity matrix are provided. S ₇₄ , S ₇₅ , S ₇₆ , and S ₇₇ use correction matrix values before update as they are, and a correction matrix correction method in a charged particle beam exposure apparatus. 5. The correction matrix and the sensitivity matrix are respectively set corresponding to the respective subfields arranged in the main deflection direction. 6. Of correcting correction matrix in charged particle beam exposure apparatus. The correction matrix correction method in the charged particle beam exposure apparatus according to claim 1, wherein the correction matrix and the sensitivity matrix are respectively set corresponding to each subfield arranged in the main deflection direction. 5. The correction method of the correction matrix in the charged particle beam exposure apparatus according to any one of items 4 to 5 or more including subfields at both ends of the main deflection direction (maximum deflection positions in the main deflection direction of the charged particle beam) Correction matrix correction method in a charged particle beam exposure apparatus, wherein each element of the correction matrix is obtained by calculation using the result for the remaining subfields . 7. The method for correcting a correction matrix in a charged particle beam exposure apparatus according to claim 6, wherein the calculation is a cubic using each element of the correction matrix as a variable the deflection position of the charged particle beam corresponding to each subfield. And a correction matrix correction method in a charged particle beam exposure apparatus, wherein the correction matrix is fitted to a power series up to. One subfield in which both the X direction position change amount and the Y direction position change amount are set to zero in the image vector when measuring the X direction position change amount and the Y direction position change amount of each image in each subfield. Alternatively, two subfields in which the X direction position change amount and the Y direction position change amount are set to zero are set as reference subfields, and the actual X direction position change amount and Y direction position change amount in the other subfields are set. The charged particle beam exposure according to claim 1, wherein the measurement is performed with reference to an X-direction position and a Y-direction position of an image in a reference subfield. Correction method of correction matrix in apparatus. A new correction matrix obtained by linearly combining the correction matrix obtained by the correction matrix correcting method in the charged particle beam exposure apparatus according to any one of claims 1 to 8 and the original correction matrix. A correction matrix correction method in a charged particle beam exposure apparatus.

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